document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210245>Question 1210245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the double integral by converting it into polar coordinates:  integral from 1 to 2 integral from 0 to sqrt (2x - x^2) (x^2y + y^3) dy dx\r<BR>\n" );
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document.write( "I can get the answer using rectangular coords as 47/60, but conversion into polar and evaluation gets me the wrong answer. I can't seem to get the correct limits or whatever. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852011 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I repeat this my post here for greater reliability.\r<BR>\n" );
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document.write( "In January, February, March and April of 2025, @CPhill (which is the synonym of the Google AI)<BR>\n" );
document.write( "posted 1941 solved problems to this forum.\r<BR>\n" );
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document.write( "He posted them at the rate of 25-30 solved problems per day.<BR>\n" );
document.write( "Some of them (many of them) were solved incorrectly.\r<BR>\n" );
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document.write( "During these months, I tried to check the incoming problems, but, surely, been a human, not a <BR>\n" );
document.write( "computer tool, I was not able to check all of them at the same rate.\r<BR>\n" );
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document.write( "Therefore, starting from the end of April 2025, and during May and June 2025, I checked <BR>\n" );
document.write( "the remaining problems- those of them where I was competent to check.\r<BR>\n" );
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document.write( "I did not check the advanced Statistics problems, since I am not an expert in this field.<BR>\n" );
document.write( "I also did not check advanced Finance problems, where I am not an expert.\r<BR>\n" );
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document.write( "But I checked a lot of other problems.<BR>\n" );
document.write( "So, this file below contains the list of problems that (in my opinion) are solved incorrectly by @CPhill.<BR>\n" );
document.write( "So far, this list contains 151 incorrectly solved problems.\r<BR>\n" );
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document.write( "For most of them, I placed my correct solutions.\r<BR>\n" );
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document.write( "Now some statistical counts.\r<BR>\n" );
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document.write( "As I said, the full number of solutions posted by @CPhill was 1941.\r<BR>\n" );
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document.write( "Of them, a huge portion were advanced statistics problems, which I did not check.<BR>\n" );
document.write( "Their number was 2/3 or 3/4 of all problems - I did not count them.\r<BR>\n" );
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document.write( "Also, I did not check advanced Finance problems.\r<BR>\n" );
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document.write( "I think (I estimate approximately) that I checked from 500 to 600 problems,<BR>\n" );
document.write( "As I said, the number of incorrect solutions is 151, so far.\r<BR>\n" );
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document.write( "This number 151 does not cover all erroneous solutions by @CPhill - the number <BR>\n" );
document.write( "of his erroneous solutions is more: I could miss some of them.\r<BR>\n" );
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document.write( "But this ratio \"wrong to checked\" = \"151 to 500 or to 600\" is HUGE.\r<BR>\n" );
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document.write( "It characterizes the level of this modern/contemporary version of this AI.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;********************************************\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Surely, it is unacceptable level for an AI.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;********************************************\r<BR>\n" );
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document.write( "I am not an enemy to AI. But I want we all have right/correct understanding of what is the AI now <BR>\n" );
document.write( "in solving school Math problems.\r<BR>\n" );
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document.write( "So, I hope that this my huge work on checking this AI is useful both for visitors of this site,<BR>\n" );
document.write( "as well as for the developers of this AI.\r<BR>\n" );
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document.write( "Probably, in the future I will return to this checking, and then this list of erroneously solved problems will become greater.\r<BR>\n" );
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document.write( "ikleyn<BR>\n" );
document.write( "June 29, 2025\r<BR>\n" );
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document.write( "  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The list of problems solved incorrectly by @CPhill<BR>\n" );
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document.write( "     \r<BR>\n" );
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document.write( "1208643<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1208643.html<BR>\n" );
document.write( "We call a number cozy if every digit in the number is either a $3$ or next to a $3.$ For example, the numbers $333,$ $83,$ $303,$ and $3773$ are all cozy, <BR>\n" );
document.write( "but the numbers $32423,$ $786,$ $340,$ and $3999$ are not cozy.<BR>\n" );
document.write( "How many positive $10$-digit numbers are cozy?\r<BR>\n" );
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document.write( "1209502<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209502.html<BR>\n" );
document.write( "Let be three positive numbers such that:<BR>\n" );
document.write( "x^2 + y^2 + z^2 = 2(xy + xz + yz).<BR>\n" );
document.write( "x + y + z + \frac{1}{xyz} > 4.\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209450<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209450.html<BR>\n" );
document.write( "A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB at D, such that |AD| = |CD| = |BC|. <BR>\n" );
document.write( "Find the measure of angle A in degrees.\r<BR>\n" );
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document.write( "\n" );
document.write( "1193410<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1193410.html<BR>\n" );
document.write( "Julita owes Jose the following am<BR>\n" );
document.write( "a. 55,000 at the end of 4 years,<BR>\n" );
document.write( "b. 48,000 at the end of 5 years, and<BR>\n" );
document.write( "c. 75,000 due in 3 years from today at 9% converted quarterly.<BR>\n" );
document.write( "What single payment at the end of 2 years will settle Julita’s<BR>\n" );
document.write( "obligations if money is worth 15% converted monthly?\r<BR>\n" );
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document.write( "1193440<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1193440.html<BR>\n" );
document.write( "A shipment of 10 items has two defective and eight non defective units. In the inspection of the shipment , a sample of units will be selected and tested. <BR>\n" );
document.write( "If a defective unit is found , the shipment of 10 units will be rejected. <BR>\n" );
document.write( "If a sample of four is selected , what is the probability that the shipment will be rejected?\r<BR>\n" );
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document.write( "1192630<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1192630.html<BR>\n" );
document.write( "the semiannual withdrawals possible over 4.5 years from an account earning 5.25% compounded semiannually <BR>\n" );
document.write( "and starting with $11,000. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "1192634<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192634.html<BR>\n" );
document.write( "In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance. <BR>\n" );
document.write( "IQ test scores are normally distributed with mean 100 and standard deviation 16<BR>\n" );
document.write( "a. What percentage of people would qualify for admittance to the school.<BR>\n" );
document.write( "b. If the public school wishes 95 percent of all children to qualify for admittance, <BR>\n" );
document.write( "   what minimum IQ test score should be required for admittance?\r<BR>\n" );
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document.write( "1209484<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1209484.html<BR>\n" );
document.write( "Trapezoid ABCD has diagonals that cross at E. The area of triangle EDC is n². <BR>\n" );
document.write( "If AB has length m and DC has length n, find the area of trapezoid ABCD in terms of m and n.<BR>\n" );
document.write( "Diagram: https://ibb.co/svwxc0w\r<BR>\n" );
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document.write( "1192431<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1192431.html<BR>\n" );
document.write( "you are given 20 true false questions and required to find probability of almost 4 are correct?\r<BR>\n" );
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document.write( "1192508                       (10)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192508.html<BR>\n" );
document.write( "A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood. <BR>\n" );
document.write( "The device is not totally reliable: 7 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser <BR>\n" );
document.write( "as being above the legal limit, while 10 % of drivers who are above the legal limit will give a reading below that level. <BR>\n" );
document.write( "Suppose that in fact 14 % of drivers are above the legal alcohol limit, and the police stop a driver at random. <BR>\n" );
document.write( "Give answers to the following to four decimal places.\r<BR>\n" );
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document.write( "Part a)<BR>\n" );
document.write( "What is the probability that the driver is incorrectly classified as being over the limit?\r<BR>\n" );
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document.write( "Part b)<BR>\n" );
document.write( "What is the probability that the driver is correctly classified as being over the limit?\r<BR>\n" );
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document.write( "Part c)<BR>\n" );
document.write( "Find the probability that the driver gives a breathalyser test reading that is over the limit.\r<BR>\n" );
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document.write( "Part d)<BR>\n" );
document.write( "Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.\r<BR>\n" );
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document.write( "1192522<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192522.html <BR>\n" );
document.write( "It is estimated that approximately 8.37% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes <BR>\n" );
document.write( "will correctly diagnose 98% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3% of all adults over 40 <BR>\n" );
document.write( "without diabetes as having the disease.<BR>\n" );
document.write( "a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as having diabetes <BR>\n" );
document.write( "(such diagnoses are called \"false positives\").\r<BR>\n" );
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document.write( "b) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes.\r<BR>\n" );
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document.write( "c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes <BR>\n" );
document.write( "(such diagnoses are called \"false negatives\").\r<BR>\n" );
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document.write( "(Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)\r<BR>\n" );
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document.write( "1209504<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209504.html<BR>\n" );
document.write( "Jamie spent 3/4 of her money on 3 books of the same price. Grace spent 5/9 of her money on 2 diaries. <BR>\n" );
document.write( "They were each left with an equal amount of money. One book cost $3.30 more than one diary. <BR>\n" );
document.write( "How much money did they have altogether.\r<BR>\n" );
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document.write( "1192298<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1192298.html<BR>\n" );
document.write( "Find the number of permutations of 10 numbers in a spinner.\r<BR>\n" );
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document.write( "1192052<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1192052.html<BR>\n" );
document.write( "Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. <BR>\n" );
document.write( "The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed <BR>\n" );
document.write( "is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school <BR>\n" );
document.write( "and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour.\r<BR>\n" );
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document.write( "a) On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, <BR>\n" );
document.write( "so Nikita and Peter walk the rest of the way home. How far from school is Peeta when the cyclists arrive home?\r<BR>\n" );
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document.write( "b) On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back <BR>\n" );
document.write( "towards school to collect Nikita. How far from school is Nikita when Reeta reaches her?\r<BR>\n" );
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document.write( "c) On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta hops off and walks the rest of the way, <BR>\n" );
document.write( "while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike?\r<BR>\n" );
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document.write( "d) On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home. Meanwhile he returns to pick up Reeta <BR>\n" );
document.write( "and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off and pick-up points?\r<BR>\n" );
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document.write( "    Part (d) is interpreted and solved INCORRECTLY by @CPhill.\r<BR>\n" );
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document.write( "1209514<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209514.html<BR>\n" );
document.write( "There were 220 chickens, ducks and goats on a farm. The ratio of chickens to ducks and goats is 3 to 2. The ratio of goats to ducks and chickens <BR>\n" );
document.write( "is 1 to 3. What is the ratio of chickens to ducks to goats. If a goat is sold at $98 each, Find the amount if all the goats are sold.\r<BR>\n" );
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document.write( "1209515<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209515.html<BR>\n" );
document.write( "There were some oranges in baskets A B and C. The ratio of A to B and C is 1 to 4. <BR>\n" );
document.write( "The ratio of C to A and B is 3 to 4. <BR>\n" );
document.write( "How many oranges were in C if there were 54 more oranges in B than in A.\r<BR>\n" );
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document.write( "1209520<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polygons/Polygons.faq.question.1209520.html<BR>\n" );
document.write( "Square SQUR has sides of length x. If triangle SQE is equilateral, find the area of triangle QAU.<BR>\n" );
document.write( "Link to diagram: https://ibb.co/C58rZ09R\r<BR>\n" );
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document.write( "1192249<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192249.html<BR>\n" );
document.write( "Hotel A and B offers 2 types of packages that include lodging only or lodging with<BR>\n" );
document.write( "breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only <BR>\n" );
document.write( "and 120 tourists choose Hotel B for lodging with breakfast. <BR>\n" );
document.write( "Altogether 110 tourists choose to stay in Hotel A. <BR>\n" );
document.write( "A tourist is selected randomly.<BR>\n" );
document.write( "(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?<BR>\n" );
document.write( "(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?<BR>\n" );
document.write( "(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?<BR>\n" );
document.write( "(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "1192250<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192250.html<BR>\n" );
document.write( "Hotel A and B offers 2 types of packages that include lodging only or lodging with<BR>\n" );
document.write( "breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only <BR>\n" );
document.write( "and 120 tourists choose Hotel B for lodging with breakfast. <BR>\n" );
document.write( "Altogether 110 tourists choose to stay in Hotel A. <BR>\n" );
document.write( "A tourist is selected randomly.<BR>\n" );
document.write( "(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?<BR>\n" );
document.write( "(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?<BR>\n" );
document.write( "(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?<BR>\n" );
document.write( "(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?\r<BR>\n" );
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document.write( "1209524        (20)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1209524.html<BR>\n" );
document.write( "Sector ABC is 1/12 of a circle with diameter 24k. Line segment AD is perpendicular to segment BC.<BR>\n" );
document.write( "Find the area of the shaded region.<BR>\n" );
document.write( "Link to diagram: https://ibb.co/5gNwX0K6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1191371<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1191371.html<BR>\n" );
document.write( "Suppose you want to have $600,000 for retirement in 30 years. Your account earns 10% interest.<BR>\n" );
document.write( "How much would you need to deposit in the account each month?\r<BR>\n" );
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document.write( "\n" );
document.write( "1190652<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190654.html<BR>\n" );
document.write( "What is the present value of an ordinary annuity having semi-annual payments<BR>\n" );
document.write( "of 8, 000 pesos for 12 years with an interest rate of 12% compounded annually?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209532<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1209532.html<BR>\n" );
document.write( "Point R is chosen on the circumference of a circle and arc PQ is drawn with R as its center. <BR>\n" );
document.write( "If P and Q are joined, the line segment formed is a diameter of the circle with length 2r cm. <BR>\n" );
document.write( "Find the area of the shaded region in terms of r, in square centimeters.<BR>\n" );
document.write( "Link to diagram: https://ibb.co/GQFdy2SV\r<BR>\n" );
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document.write( "\n" );
document.write( "1186907 <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1186907.html<BR>\n" );
document.write( "The world production of gold from 1970 to 1990 can be modelled by G = 5.2t 2 - 76t + 1492, where G is the<BR>\n" );
document.write( "number of tonnes of gold and t is the number of years since 1970, t = 1 for 1971 and so on.<BR>\n" );
document.write( "a. What was the most amount of gold mined in one year?<BR>\n" );
document.write( "b. How much gold was mined in 1978?\r<BR>\n" );
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document.write( "1186928<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1186928.html<BR>\n" );
document.write( "For each of the following statements, explain why it is true for all functions f and g or give <BR>\n" );
document.write( "an example of specific functions f and g showing that it is false.<BR>\n" );
document.write( "a. All elements in the domain of g must be in the domain of f o g (fog)<BR>\n" );
document.write( "b. All elements in the range of f must be in the range of f o g\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1187156<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1187156.html<BR>\n" );
document.write( "During the scholarship examination of a certain scholarship grant taken by 10,000 applicants,<BR>\n" );
document.write( "Donnabelle's score was 350 greater than the scores of 8995 applicants who took the examination.<BR>\n" );
document.write( "What is the percentile of Donnabelle's score?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209553<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209553.html<BR>\n" );
document.write( "If x + (24)^(⅓) = (16)^(⅓) + (36)^(⅓)<BR>\n" );
document.write( "find (10³/x⁶) - (x³/10³) - (30/x³)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186854<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1186854.html <BR>\n" );
document.write( "Two vertices of a regular quadrilateral are A(0,4) and B(0,24). Which of the following could be the other two vertices?<BR>\n" );
document.write( "a. C(4,4) and D(4,24)<BR>\n" );
document.write( "b. C(24,4) and D(24,24)<BR>\n" );
document.write( "c. C(8,24) and D(8,4)<BR>\n" );
document.write( "d. C(0,8) and D(0,28)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186205<BR>\n" );
document.write( "https://www.algebra.com/algebra/college/linear/Linear_Algebra.faq.question.1186205.html<BR>\n" );
document.write( "The Intellectual Company produces a chemical solution used for cleaning carpets. <BR>\n" );
document.write( "This chemical is made from a mixture of two other chemicals which contain cleaning agent X and cleaning agent Y. <BR>\n" );
document.write( "Their product must contain 175 units of agent X and 150 units of agent Y and weigh at least 100 pounds. <BR>\n" );
document.write( "Chemical A costs ₱ 8 per pound, while chemical B costs ₱ 6 per pound. <BR>\n" );
document.write( "Chemical A contains one unit of agent X and three units of agent Y. <BR>\n" );
document.write( "Chemical B contains seven units of agent X and one unit of agent Y.<BR>\n" );
document.write( "a. Set up the following:<BR>\n" );
document.write( "i. Variables<BR>\n" );
document.write( "ii. Constraints<BR>\n" );
document.write( "iii. Objective Function<BR>\n" );
document.write( "b. Find the minimum cost<BR>\n" );
document.write( "c. Determine the best combination of the ingredients to minimize the cost.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186248          (30)<BR>\n" );
document.write( "https://www.algebra.com/algebra/college/linear/Linear_Algebra.faq.question.1186248.html<BR>\n" );
document.write( "The Intellectual Company produces a chemical solution used for cleaning carpets. <BR>\n" );
document.write( "This chemical is made from a mixture of two other chemicals which contain cleaning agent X and cleaning agent Y. <BR>\n" );
document.write( "Their product must contain 175 units of agent X and 150 units of agent Y and weigh at least 100 pounds. <BR>\n" );
document.write( "Chemical A costs ₱ 8 per pound, while chemical B costs ₱ 6 per pound. <BR>\n" );
document.write( "Chemical A contains one unit of agent X and three units of agent Y. <BR>\n" );
document.write( "Chemical B contains seven units of agent X and one unit of agent Y.<BR>\n" );
document.write( "a. Set up the following:<BR>\n" );
document.write( "i. Variables<BR>\n" );
document.write( "ii. Constraints<BR>\n" );
document.write( "iii. Objective Function<BR>\n" );
document.write( "b. Find the minimum cost<BR>\n" );
document.write( "c. Determine the best combination of the ingredients to minimize the cost.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186455<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1186455.amp<BR>\n" );
document.write( "On her recent birthday, April 22, 2001, Nicole was given by her mother a certain sum of money as birthday present. <BR>\n" );
document.write( "She decided to invest the said amount on 20% exact simple interest. If the account will mature <BR>\n" );
document.write( "on Christmas day at an amount of P 10,000.00, How much did Nicole receive from her mother on her birthday\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186235<BR>\n" );
document.write( "beginning at the origin a spiral is constructed from three semmi-circles with centres at (1,0), (0,0) and (2,0) <BR>\n" );
document.write( "the area of the shaded region in u^2 is?<BR>\n" );
document.write( "https://drive.google.com/file/d/1OLUZW44XSyKqEXVuIhuwpkMDvT8E14xU/view?usp=sharing  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186272 <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1186272.html<BR>\n" );
document.write( "On a wall, 60 1/2 cm wide, Oscar is going to hang three pictures beside each other, each measuring 9 1/3 cm wide. <BR>\n" );
document.write( "He will leave 3 1/2 cm in between each pair of adjacent pictures. He plans to use two nails to hang each picture, <BR>\n" );
document.write( "and will centre these nails leaving 4 cm between each pair. How far, in cm, from the end of the wall(on either side) <BR>\n" );
document.write( "will the first nail be placed?   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209558   <<<---===  solution for (a) is incorrect.  solution for (c) is incorrect.<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209558.html<BR>\n" );
document.write( "a) If 7^sin²x - 7^cos²x = 8<BR>\n" );
document.write( "find the value of x.<BR>\n" );
document.write( "b) Let m be a given real number, Find all complex numbers x such that,<BR>\n" );
document.write( "([x/(x+1)]² + [x/(x-1)]² = m² + m<BR>\n" );
document.write( "c) ab = ½, bc = ⅓, ac = 1/6,<BR>\n" );
document.write( "find (1/a²) + (1/b²) + (1/c²)<BR>\n" );
document.write( "d) 2^x - 3^y = 5<BR>\n" );
document.write( "2^(x+2) + 3^(y+2) = 59.<BR>\n" );
document.write( "find xy<BR>\n" );
document.write( "e) find m,<BR>\n" );
document.write( "9^4^m = 4^9^m<BR>\n" );
document.write( "f) (7^log₈x)×(x^log₉x) = 3969,<BR>\n" );
document.write( "find x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186068<BR>\n" );
document.write( "Suppose events A and B are independent and\r<BR>\n" );
document.write( "\n" );
document.write( "P(A) = 1/4<BR>\n" );
document.write( "    <BR>\n" );
document.write( "P(B) = 1/5\r<BR>\n" );
document.write( "\n" );
document.write( "Find the probability. (Enter the probability as a fraction.)<BR>\n" );
document.write( "   _____<BR>\n" );
document.write( " P(A ∩ B)  the line is above a and b only\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1186121<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1186121.html<BR>\n" );
document.write( "Tickets for a raffle cost $12. There were 713 tickets sold. One ticket will be randomly selected as the winner, <BR>\n" );
document.write( "and that person wins $1800 and also the person is given back the cost of the ticket. <BR>\n" );
document.write( "For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1185780<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1185780.html<BR>\n" );
document.write( "The director of MIS Center At a large company wants to do stuff consulting station with two shifting teams: <BR>\n" );
document.write( "Team A will compromise of 3 senior programmers and 3 system analyst and <BR>\n" );
document.write( "team B will consist       2 senior programmers and 5 system analysts. <BR>\n" );
document.write( "the director wants to use no more than 42 individuals.<BR>\n" );
document.write( "There will be at least 48 hours to be filed during the week, with team A serving for 4 hours and the team B shift servings for 3 hours. <BR>\n" );
document.write( "The cost of team A is 3200 per hour and 2800 per hour for team B shift.<BR>\n" );
document.write( "Determine the number of shifts each team has to render in order to minimize the cost.<BR>\n" );
document.write( "•What is the Test ratio for table 2?<BR>\n" );
document.write( "•What is the pivotal/al column in Tableu 1?<BR>\n" );
document.write( "•What is the result in the last row of Tableu 4?<BR>\n" );
document.write( "•Show the proper representation of Tableu\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209595<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209595.html<BR>\n" );
document.write( "limit x (1 - 2 cos ((pi x)/(3 x - sqrt3))) as x \[LongRightArrow] + \[Infinity]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209654<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209654.html<BR>\n" );
document.write( "Find the unique pair of real numbers (x,y) satisfying<BR>\n" );
document.write( "(6x^2 - 18x + 17)  +  (3y^2 + 6y + 11)  =  28<BR>\n" );
document.write( "and  x + y = 20.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209644          (40)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209644.html<BR>\n" );
document.write( "Find all complex solutions to the equation z^8 + 144 = 25z^4 + 10z^6 + 10z^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209645<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209645.html<BR>\n" );
document.write( "Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209660      <<<---===  the problem is posed incorrectly, and the answer by @CPhill is incorrect<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1209660.html<BR>\n" );
document.write( "Find  the  conic  section  represented  by  the  equation\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 4x + y^2 = y^2 + 8x + 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209701<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209701.html<BR>\n" );
document.write( "Find  a  monic  quartic  polynomial  f(x)  with  rational  coefficients  whose  roots  include  x = 2 - i \sqrt[3]{3}$. <BR>\n" );
document.write( "Give  your  answer  in  expanded  form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209688                             <<<---===  Fake problem and wrong solution/answer by @CPhill<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209688.html<BR>\n" );
document.write( "The  polynomial<BR>\n" );
document.write( "f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66<BR>\n" );
document.write( "has  one  integer  root.  What is it?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1184157<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Distributive-associative-commutative-properties/Distributive-associative-commutative-properties.faq.question.1184157.html<BR>\n" );
document.write( "Construct  two  examples  of  bijective  function  from  ZxZ  to  Q  where  Z  is  set  of  all  integers  and  Q  is  set <BR>\n" );
document.write( "of rational numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1184450<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1184450.html<BR>\n" );
document.write( "A  certain  class  has  11  students,  2  of  whom  are  sisters.  The  class  needs  to  be  split  across  three  rooms <BR>\n" );
document.write( "for  a  socially  distanced  exam,  where  room  A  can  seat  2  students,  room  B  3 students,  and  room  C  6  students. <BR>\n" );
document.write( "How  many  ways  can  the  students  be  divided  across  the  rooms,  if  the  2  sisters  are  not  allowed  to  be  in <BR>\n" );
document.write( "the  same  room  (say,  for academic  integrity) ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1184115<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1184115.html<BR>\n" );
document.write( "Berlin and Cheryl had a total of 6750 stamps. At first, Andy have 50%<BR>\n" );
document.write( "of his stamps to Berlin. Berlin then gave 1/3 of her stamps to Cheryl.<BR>\n" );
document.write( "Finally, Cheryl gave 1/6 of her stamps to Andy. In the end, the ratio of the<BR>\n" );
document.write( "number of Andy’s stamps to the number of Berlin’s stamps became 4:5.<BR>\n" );
document.write( "Cheryl had twice the total number of stamps that Andy and Berlin had.<BR>\n" );
document.write( "How many stamps did Berlin and Cheryl have in total at first?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1174471<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1174471.html<BR>\n" );
document.write( "To save for​ retirement, Karla Harby put ​$500 each month into an ordinary annuity for 10 years. <BR>\n" );
document.write( "Interest was compounded monthly. At the end of the 10 ​years, the annuity was worth ​ $84,608. <BR>\n" );
document.write( "What annual interest rate did she​ receive?<BR>\n" );
document.write( "The interest rate she received was approximately ___%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1174826 <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1174826.html       <BR>\n" );
document.write( "find the equation of parabola which has contact of third order with the conic ax^2 +2hxy + by^2 +2gx +2fy +c =0 at origin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209808        (50)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209808.html<BR>\n" );
document.write( "Find  the  value  of  θ,<BR>\n" );
document.write( "sin(20°)*sin(θ) + sin(100°)*sin(20 - θ)° = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209677<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209677.html<BR>\n" );
document.write( "When g(x) is divided by x^2 - x - 6, the remainder is 2x + 7.  What is the value<BR>\n" );
document.write( "of g(8)?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209710<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1209710.html<BR>\n" );
document.write( "4^(1/√x)  +  16^(1/√x)  =  64^(1/√x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209712<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209712.html<BR>\n" );
document.write( "If  (x√x)^(1/x)  =  2,  find x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1181712<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1181712.html<BR>\n" );
document.write( "A rocket is being launched vertically over a point 𝐴 on the ground with<BR>\n" );
document.write( "a velocity of 550 𝑚𝑖Τℎ𝑟. Twenty five miles away from point 𝐴 on the<BR>\n" );
document.write( "ground,  there  is  a  photographer  video-taping  the  launch.  At what rate<BR>\n" );
document.write( "is the angle of elevation of the camera changing when the rocket<BR>\n" );
document.write( "achieves an altitude of 25 miles?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1181729<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181729.html<BR>\n" );
document.write( "The  diameter  of  a  sphere  coincides  with  the  axis  of  a  right  circular  cone,  and the surface of the cone intersects the surface of the sphere in in a great circle. Find<BR>\n" );
document.write( " (a) the vertical angle of the cone: <BR>\n" );
document.write( "(b) the volume of the cone; <BR>\n" );
document.write( "(c) the volume common to the two solids: <BR>\n" );
document.write( "(d) the volume of that portion of the cone which lies outside the sphere: <BR>\n" );
document.write( "(e) the volume of that portion of the sphere which lies outside the cone. Denote radius of sphere by R.<BR>\n" );
document.write( "Solve Problem if (a) R=2: (b) R=3.72.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1181730<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181730.html<BR>\n" );
document.write( "The center of each of three spheres of radius R lies in the surfaces of the other two. <BR>\n" );
document.write( "Pass a plane containing the centers of the spheres. <BR>\n" );
document.write( "Find the area common to the three great circles cut from the spheres by this plane.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1181731<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181731.html<BR>\n" );
document.write( "A sphere is inscribed in a right circular cone of altitude h and radius of base r. <BR>\n" );
document.write( "Write a formula in terms of r and h for the volume of the sphere.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1181618<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1181618.html<BR>\n" );
document.write( "Modern oil tankers weigh more than a 1/2 million tons and have lengths up to one - fourth mile. Such massive ships require a distance of 5.0 km about (3.0 mi) <BR>\n" );
document.write( "and a time of 20 minutes to come to a stop from top speed of 30 km/h.what is the magnitude of such ship's average acceleration in m/s squared in coming to a stop?<BR>\n" );
document.write( "B. What is the magnitude of the ship's average velocity in m/s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209741<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209741.html          <BR>\n" );
document.write( "If 1/9^(1/x) + 1/3^(1/x) = 30,<BR>\n" );
document.write( "find x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209729    (60)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209729.html<BR>\n" );
document.write( "Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209740<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209740.html<BR>\n" );
document.write( "Factor  x^2 - 2x - y^2 + 2yz + 5z^2  as  the product  of  two  polynomials  of  degree  1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209728<BR>\n" );
document.write( "Let  r,  s,  and  t  be  solutions  of  the  equation  3x^3 - 4x^2 - 2x + 12 = 0.<BR>\n" );
document.write( "Compute  (rs)/t^2  +  (rt)/s^2  +  (st)/r^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209735<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209735.html<BR>\n" );
document.write( "69% of all Americans are home owners. If 37 Americans are randomly selected, find the probability that<BR>\n" );
document.write( "a. Exactly 27 of them are are home owners.<BR>\n" );
document.write( "b. At most 27 of them are are home owners.<BR>\n" );
document.write( "c. At least 23 of them are home owners.<BR>\n" );
document.write( "d. Between 23 and 28 (including 23 and 28) of them are home owners.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209737<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209737.html<BR>\n" );
document.write( "The  dots  on  the  opposite  faces  of  a  die  have  a sum  of  7.  <BR>\n" );
document.write( "How many different sum of dots on three adjacent faces are there on a die?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209731<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209731.html<BR>\n" );
document.write( "Let r, s, and t be solutions of the equation x^3 + 2x^2 - 5x + 15 = 0. Compute<BR>\n" );
document.write( "1/(r - 2s - 2t) + 1/(s - 2r - 2t) + 1/(t - 2r - 2s)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1180634<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1180634.html<BR>\n" );
document.write( "This  pandemic,  Abheedette  learned  to  bake  while  on  home  quarantine. <BR>\n" );
document.write( "She  also  realized  that  she  will  be  able  to make  P60.00  profit  per  tray  of  banana muffins <BR>\n" );
document.write( "and P120.00 profit per tray of blueberry muffins. <BR>\n" );
document.write( "She needs 2 cups of milk and 3 cups of flour to bake a tray of banana muffins. <BR>\n" );
document.write( "And, baking a tray of blueberry muffins takes 4 cups of milk and 3 cups of flour. <BR>\n" );
document.write( "She has 16 cups of milk and 15 cups of flour. <BR>\n" );
document.write( "How many trays of each flavor must be baked to maximize the profit?\r<BR>\n" );
document.write( "\n" );
document.write( "a. Define the variable used: \r<BR>\n" );
document.write( "\n" );
document.write( "b. LP Model: \r<BR>\n" );
document.write( "\n" );
document.write( "c. Identify the feasible region: \r<BR>\n" );
document.write( "\n" );
document.write( "d. Corner Points and the objective functions:\r<BR>\n" );
document.write( "\n" );
document.write( "e. Optimal Solution (final answer):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209745<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209745.html<BR>\n" );
document.write( "in  the  blanks,  to  complete  the  factorization:\r<BR>\n" );
document.write( "\n" );
document.write( "(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1180382  <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1180382.html<BR>\n" );
document.write( "a particle  jumps  between  three  positions  A,  B,  and  C.  If it starts at A, it stays at A with probability 44%, <BR>\n" );
document.write( "and it goes to B with probability 18% and to C with probability 26%. If, however, it starts at C, it goes to A with probability 51% <BR>\n" );
document.write( "and to B with probability 16%.<BR>\n" );
document.write( "Find the transition matrix.<BR>\n" );
document.write( "If the particle stays at A, what is the probability that it stays at A after three jumps?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179711          <BR>\n" );
document.write( "Determine  the periodic  payments  on  the  given  loan  or  mortgage.<BR>\n" );
document.write( "$5,000,000  borrowed  at  7%  for 30 years,  with  quarterly  payments\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179768    (70)<BR>\n" );
document.write( "The problem on pendulum<BR>\n" );
document.write( "https://gyazo.com/78c37f667cf2af63efadea4314e5642c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179791<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1179791.html<BR>\n" );
document.write( "If  the  area  (in  square  units)  of  the  region  under  the  curve  of  the  function  f(x) = 3x − 1  on t he  interval  [a, 4], <BR>\n" );
document.write( "where  a < 4,  is  12  square units,  identify  all  the  possible  values  of  a.<BR>\n" );
document.write( "what  values  are  correct?<BR>\n" );
document.write( "a. -3<BR>\n" );
document.write( "b. 0<BR>\n" );
document.write( "c. -16/5<BR>\n" );
document.write( "d. 8/3<BR>\n" );
document.write( "e. -2<BR>\n" );
document.write( "f. 7/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179819<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1179819.html<BR>\n" );
document.write( "Find  the  present  values  of  the  following  annuities<BR>\n" );
document.write( "i.   RM6,000 every year for 8 years  at  12%  compounded  annually<BR>\n" );
document.write( "ii.  RM800   every month  for  2  years  5  months  at  5%  compounded  monthly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179653   - about a pendulum, horizontal displacement.<BR>\n" );
document.write( "https://gyazo.com/848645a235363970dae8196a58a2bbdc\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179602<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1179602.html<BR>\n" );
document.write( "If 35% of the people in a community use the emergency room at a hospital one year. <BR>\n" );
document.write( "Find these probabilities for a sample of 12 people <BR>\n" );
document.write( "A) exactly 4 used the emergency room <BR>\n" );
document.write( "B) At most 4 used the emergency room <BR>\n" );
document.write( "C) At least 10 used the emergency room\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209768                  <<<---===  incomplete solution: one solution is found; other solution is missed<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1209768.html<BR>\n" );
document.write( "If a = sin50(1 + 2cos170°),<BR>\n" );
document.write( "b = sin170°(1 + 2cos140°),<BR>\n" );
document.write( "c = sin140°(1 + 2cos50°),<BR>\n" );
document.write( "then (3 - 2A)ˣ = (x + 1)²,<BR>\n" );
document.write( "find x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209770                  <<<---===  Total, global and fatal deceiving of a reader<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209770.html<BR>\n" );
document.write( "Find  all  (real  or  nonreal)  x  satisfying<BR>\n" );
document.write( "(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1179081   <<<---===  The problem is non-sensical.  The solution by @CPhill is non-sensical, too.<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1179081.html<BR>\n" );
document.write( "Nick has  been  depositing  $190  in  a  savings  account  every  three  months  for  the  past  three  years.  This  account  paid  3 % convertible quarterly. <BR>\n" );
document.write( "Nick has just made the last deposit. Nick is buying a car for $ 14000. He is taking out a car loan. He will use the accumulated value of his savings account <BR>\n" );
document.write( "as the downpayment on the car. The loan is at 3 % convertible semiannually and has a term of 4 years. Find the size of Nick's monthly car loan payment.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209773<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.1209773.html<BR>\n" );
document.write( "If a_1, a_2, ..., a_19 satisfy\r<BR>\n" );
document.write( "\n" );
document.write( "a_1 + a_2 + a_3 + a_4 = 1,<BR>\n" );
document.write( "a_2 + a_3 + a_4 + a_5 = 2,<BR>\n" );
document.write( "a_3 + a_4 + a_5 + a_6 = 3,<BR>\n" );
document.write( "...<BR>\n" );
document.write( "a_{16} + a_{17} + a_{18} + a_{19} = 16,<BR>\n" );
document.write( "a_{17} + a_{18} + a_{19} + a_1 = 17,<BR>\n" );
document.write( "a_{18} + a_{19} + a_1 + a_2 = 18,<BR>\n" );
document.write( "a_{19} + a_1 + a_2 + a_3 = 19,\r<BR>\n" );
document.write( "\n" );
document.write( "what is the value of a_19?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1178715  <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1178715.html    <BR>\n" );
document.write( "Solve each problem.<BR>\n" );
document.write( "1. Your monthly electric bill has a mean of ₱120.00. what is the percentage that you will pay an amount between ₱1,380 and ₱1,740?<BR>\n" );
document.write( "2. Suppose the scores in the mathematics exam are normally distributed. If the exam has a mean score of 25 and a standard deviation of 5,what is the probability that if you take th\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1178377       (80)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1178377.html<BR>\n" );
document.write( "Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90, <BR>\n" );
document.write( "and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2. <BR>\n" );
document.write( "A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2. <BR>\n" );
document.write( "A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2. <BR>\n" );
document.write( "Formulate this as an LP problem to minimize the cost of the dog food. How many<BR>\n" );
document.write( "pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209775     <<<---=== AI produced the same wrong solution, kind of gibberish, and I reported to AI<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209775.html<BR>\n" );
document.write( "Let a, b, c, and d be distinct real numbers such that<BR>\n" );
document.write( "a = sqrt(4 + sqrt(5 + a)),<BR>\n" );
document.write( "b = sqrt(4 -  sqrt(7 + b)),<BR>\n" );
document.write( "c = sqrt(4 + sqrt(9 - c)),<BR>\n" );
document.write( "d = sqrt(4 -  sqrt(11 - d)).<BR>\n" );
document.write( "Compute abcd.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209776   <<<---===  the \"solution\" by @CPhill is unreadable gibberish<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209776.html<BR>\n" );
document.write( "Suppose the real numbers $a$, $b$, $x$, and $y$ satisfy the equations<BR>\n" );
document.write( "ax + by = 3,<BR>\n" );
document.write( "ax^2 + by^2 = 5,<BR>\n" );
document.write( "ax^3 + by^3 = 17,<BR>\n" );
document.write( "ax^4 + by^4 = 23.<BR>\n" );
document.write( "Evaluate ax^5 + by^5.\r<BR>\n" );
document.write( "\n" );
document.write( "See  the  solution  at  AoPS  under  this  link<BR>\n" );
document.write( "https://artofproblemsolving.com/wiki/index.php/1990_AIME_Problems/Problem_15?srsltid=AfmBOoq3eeok8NtsAuOBNtICcVv9fxgXqq0z4Tix5v0NoDfFL11W2Z72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209790<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209790.html<BR>\n" );
document.write( "If  x^x = 5,  find x^x^(x+1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1177476                   <<<---===  part (a) was solved INCORRECTLY by @CPhill<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1177476.html<BR>\n" );
document.write( "There are 150 people at an International Medical Conference. <BR>\n" );
document.write( "40 are Africans, 70 are women  and  110  are  doctors. <BR>\n" );
document.write( "12 of the women are Africans, 46 of the doctors are women and 31 of the Africans are doctors.<BR>\n" );
document.write( "If 5 of the African men are not doctors:<BR>\n" );
document.write( "(a) how many of the African women are doctors ?<BR>\n" );
document.write( "(b) how many of the men are neither African nor doctors?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1177187<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1177187.html<BR>\n" );
document.write( "Owen  is  jumping  on  a  trampoline.  When his feet hit the deck of the trampoline, the material depresses <BR>\n" );
document.write( "to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds.<BR>\n" );
document.write( " Determine the equation of a sinusoidal function that would model this situation, assuming <BR>\n" );
document.write( "Owen reaches his first maximum at 6 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1176885<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1176885.html<BR>\n" );
document.write( "If  a  simple,  connected,  graph  has  20  vertices,  what  is  the  maximum  number  of  edges  it  can  have?<BR>\n" );
document.write( "(Recall  that  a  simple  graph  does  not  have  loops  and  does  not  have  multiple / parallel  edges)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1176989<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1176989.html<BR>\n" );
document.write( "EVOL  is  a  cyclic  quadrilateral,  inscribed  in  a  circle  with  center  S.  Given  that  the  radius of this circle <BR>\n" );
document.write( "is  25 in.  and  angle  VEL  is  55 degrees,  explain  your  work  to  find  the following  measurements.<BR>\n" );
document.write( "a)  Length of Major Arc VL<BR>\n" );
document.write( "b)  Angle measure of Minor Arc VL<BR>\n" );
document.write( "c)  Angle VOL<BR>\n" );
document.write( "d)  Length of Chord VL\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1177001<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1177001.html<BR>\n" );
document.write( "EVOL  is  a  cyclic  quadrilateral,  inscribed  in  a  circle  with  center  S.  Given  that  the  radius of this circle <BR>\n" );
document.write( "is  25 in.  and  angle  VEL  is  55 degrees,  explain  your  work  to  find  the following  measurements.<BR>\n" );
document.write( "a)  Length of Major Arc VL<BR>\n" );
document.write( "b)  Angle measure of Minor Arc VL<BR>\n" );
document.write( "c)  Angle VOL<BR>\n" );
document.write( "d)  Length of Chord VL\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1176067                     <<<---===  Inaccurate/icorrect calculations  <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1176067.html    <BR>\n" );
document.write( "state  lotto  has  a  prize  that  pays  $1,700  each  week  for  40 years.<BR>\n" );
document.write( "Find  the  total  value  of  the  prize.<BR>\n" );
document.write( "If  the  state  can  earn  3%  interest  on  investments,  how  much  money  will  they  need  to  put <BR>\n" );
document.write( "into  an  account  now  to  cover  the weekly  prize  payments?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209804          (90)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209804.html<BR>\n" );
document.write( "If sinx + sin²x + sin³x = 1,<BR>\n" );
document.write( "find cos⁶x - 4cos⁴x + 8cos²x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1176479<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1176479.html<BR>\n" );
document.write( "Given seven equal circles on a hexagonal grid, how many permutations are possible where circles are always adjacent <BR>\n" );
document.write( "(repetitions such as inversions and reflections excluded)?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209808<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209808.html<BR>\n" );
document.write( "Find  the  value  of  θ,<BR>\n" );
document.write( "sin(20°)*sin(θ) + sin(100°*sin(20 - θ)° = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209794<BR>\n" );
document.write( "(x+4)^2/9+(y+3)^2 /4 =1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1177711<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1177711.html<BR>\n" );
document.write( "Roll a die once.  Then roll it as many times as the outcome from the first roll. <BR>\n" );
document.write( "Getting the special number \"3\" on any roll means a win. <BR>\n" );
document.write( "What is the expected number of wins from this experiment?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1177712<BR>\n" );
document.write( "A box has 3 red and 4 black balls. You randomly take one ball at a time without putting it back in. <BR>\n" );
document.write( "Stop as soon as all the black balls are drawn out of the box.  How many red balls do you expect to be left in the box? <BR>\n" );
document.write( "(Hint: find the expected value of the properly defined random variable)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209827<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209827.html<BR>\n" );
document.write( "Find a  closed  form  for  S_n = 1!*(1^2 + 1)  +  2!*(2^2 + 2)  +  . . .  + n!*(n^2 + n)<BR>\n" );
document.write( "for any integer n >= 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209826<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209826.html<BR>\n" );
document.write( "S_k = 1*(1^2)  +  2!*(2^2)*3  +  . . .  +  k*k!*(k + 1).<BR>\n" );
document.write( "Find  a  closed  form  for  S_k.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1173952<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1173952.html<BR>\n" );
document.write( "A spheroid  (or  oblate  spheroid)  is a surface obtained by rotating an ellipse around its minor axis the ball <BR>\n" );
document.write( "in figure 1.41 is in the shape of the lower half of a spheroid that is its horizontal cross-section as circles <BR>\n" );
document.write( "well its vertical cross-section that pass through the center a semi-ellipse s if this bowl is 10 inch wide <BR>\n" );
document.write( "at the opening and square root 10 in deep at the center how deep does a circular cover with diameter 9 in go into the bowl\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1174226    <<<---=== what is presented by @CPhill as \"the solution\", is a complete gibberish.<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Average/Average.faq.question.1174226.html          <BR>\n" );
document.write( "A ladder 4m long at a construction site is resting against a wall. The bottom of the ladder is slipping away from the wall. <BR>\n" );
document.write( "Find the estimate of the instantaneous rate of change of the Height H of the top of the ladder with respect to the Distance D <BR>\n" );
document.write( "of the bottom of the ladder from the wall when the bottom of the ladder is 2.5m away from the wall. <BR>\n" );
document.write( "Use h = 0.01 as the central interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209832      (100)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1209832.html<BR>\n" );
document.write( "A body of weight 500N rests on a plane inclined at 20o to the horizontal. The coefficient of friction<BR>\n" );
document.write( "is 0.4, determine a force F at an angle of 15o to the plane required to<BR>\n" );
document.write( "(a) Pull the body upwards<BR>\n" );
document.write( "(b) Push the body downwards<BR>\n" );
document.write( "(c) Pull the body downwards<BR>\n" );
document.write( "(d) Push the body upwards\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1173392<BR>\n" );
document.write( "In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, <BR>\n" );
document.write( "and the rest are optional. How many arrangements of the subjects are available for the students?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1172965<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1172965.html<BR>\n" );
document.write( "A certain household would like to buy a washing machine set payable for 6 months starting at the end of the month. <BR>\n" );
document.write( "How much is the cost of the washing machine if the monthly payment amounts to $3000 and interest is 9% compounded semi-annually?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1172947<BR>\n" );
document.write( "The Whittier Company needs to produce 40 units of Product A tomorrow. They can produce on either machine X or machine Y or both. <BR>\n" );
document.write( "Each unit of Product A when pro cessed on machine X takes 30 minutes of time, while a unit processed on machine Y takes 25 minutes. <BR>\n" );
document.write( "It costs the company $2 per minute and $3 per minute respectively to operate machines X and Y. <BR>\n" );
document.write( "Tomorrow, machine X has only 10 hours available to produce Product A, while machine Y can be operated as long as desired. <BR>\n" );
document.write( "Use the graphical method to deter mine how many hours to schedule on each machine to minimize production costs. <BR>\n" );
document.write( "Draw the isocost lines corresponding to production costs of $2,500, $2,700, $3,000, and $3,500. <BR>\n" );
document.write( "Which of the isocost lines result in a feasible but suboptimal solution: Which line is both feasible and optimal? Which is not feasible?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "117902<BR>\n" );
document.write( "In a class of 50 students 24 like football 21 basketball and cricket six like football and basketball 3 like basketball only, <BR>\n" );
document.write( "five like all three games, and 14 did not like any of the three games.<BR>\n" );
document.write( "1.illustrate this information of Venn diagram<BR>\n" );
document.write( "2. Find the number of students who like<BR>\n" );
document.write( "A. Football and cricket<BR>\n" );
document.write( "B. Exactly one of the game<BR>\n" );
document.write( "C. Exactly two of the game.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1172981<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1172981.html<BR>\n" );
document.write( "The Truth in Lending Law requires all lending institutions to fully disclose interest rates on all loans.<BR>\n" );
document.write( "$5000 is loaned for 36 months with monthly payments of $162.50. Determine annual interest rate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1171791<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1171791.html<BR>\n" );
document.write( "a predator requires 21 units of food A 12 units of food B, and 21 units of food C as its average daily consumption.<BR>\n" );
document.write( "these requirements are satisfied by feeling on two prey species.<BR>\n" );
document.write( "one prey of species A, provides 6,2 and 3 units of food of A,B, and C, respectively.<BR>\n" );
document.write( "to capture and digest a prey of species B provides 3,3 and 5 units of A, B and C, respectively.<BR>\n" );
document.write( "to capture and digest a prey of species A requires 7 units of energy, on the average.<BR>\n" );
document.write( "the corresponding energy.<BR>\n" );
document.write( "How many preys of each should the predator capture to meet its food requirement with minimum expenditure?<BR>\n" );
document.write( "find the objective function, constraints and max/min value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1171394<BR>\n" );
document.write( "​27 % adults favor the use of unmanned drones by police agencies.<BR>\n" );
document.write( "Twelve U.S. adults are randomly selected. Find the probability<BR>\n" );
document.write( "that the number of U.S. adults who favor the use of unmanned drones by police agencies is​<BR>\n" );
document.write( "(a) exactly​ three,<BR>\n" );
document.write( "(b) at least​ four,<BR>\n" );
document.write( "(c) less than eight.<BR>\n" );
document.write( "​(a) P(3)=\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209876 <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209876.html     <BR>\n" );
document.write( "Polynomials-and-rational-expressions/1209876: Find the largest value of x where the plots of<BR>\n" );
document.write( "f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209874   <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209874.html<BR>\n" );
document.write( "Let (x,y,z) be the real solution to the system of equations<BR>\n" );
document.write( "x + y = \sqrt{4z + 3}<BR>\n" );
document.write( "y + z = \sqrt{4x - 1}<BR>\n" );
document.write( "z + x = \sqrt{4y + 5}<BR>\n" );
document.write( "Find x + y + z.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1171432     (110)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1171432.html<BR>\n" );
document.write( "#1. Log2(3x-7)+log2(x+2)=log2(x+1)    <<<---===  the solution is incorrect.<BR>\n" );
document.write( "#2. Log2(3x+1)-log2(2-4x)>log2(5x-2) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209929<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1209929.amp<BR>\n" );
document.write( "The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip. <BR>\n" );
document.write( "If they deposit this money at the en each month into a savings account paying interest at the rate of 3%/year <BR>\n" );
document.write( "compounded monthly, how much money will be in their ‘travel fund at the end of the fourth year? <BR>\n" );
document.write( "(Round your answer to the nearest cent.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209924<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209924.html<BR>\n" );
document.write( "Let x_1, x_2, \dots, x_{100} be real numbers. If<BR>\n" );
document.write( "x_1 + 2x_2 + \dots + 100x_{100} = 1,<BR>\n" );
document.write( "then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209908<BR>\n" );
document.write( "Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2, <BR>\n" );
document.write( "then what is the maximum value of wxyz?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1170818<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1170818.html<BR>\n" );
document.write( "A company claims to have invented a device that can measure the momentum of objects inside it with extreme<BR>\n" );
document.write( "accuracy. The device fits within a matchbox, and the claimed precision with which it can measure momentum is<BR>\n" );
document.write( "δp = ±10^−26kg ms^−1<BR>\n" );
document.write( "Explain why the claimed performance cannot possibly be accurate, and estimate the smallest possible size of a<BR>\n" );
document.write( "device with such momentum precision, according to laws of quantum physics.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209937    <<<---===  the problem itself is SELF-CONTRADICTORY non-sensical gibberish<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209937.html<BR>\n" );
document.write( "Let f be a function such that<BR>\n" );
document.write( "f(xy) + x = xf(y) + f(x) + xy^2<BR>\n" );
document.write( "for all real numbers x and y. If f(-1) = 3, then compute f(100).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209938<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209938.html<BR>\n" );
document.write( "Let f be a function such that<BR>\n" );
document.write( "f(x) + f(2x + y) + 5xy = f(4x - y) - x^2 + 5xy - 8x + 17y + 1<BR>\n" );
document.write( "for all real numbers x and y. Find f(10).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209952<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209952.html<BR>\n" );
document.write( "The function f(n) is defined for all integers n, such that<BR>\n" );
document.write( "f(x) + f(y) = f(x + y) - 4xy - 1 + f(x^2) + f(y^2)<BR>\n" );
document.write( "for all integers x and y, and f(1) = 1. Find f(n).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209950  <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209950.html      <BR>\n" );
document.write( "The function f(n) takes the integers to the real numbers such that<BR>\n" );
document.write( "f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn<BR>\n" );
document.write( "for all integers m and n, and f(1) = 2. Find f(n).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209949      <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209949.html<BR>\n" );
document.write( "The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies<BR>\n" );
document.write( "f(x)*f(y) - f(xy) = -2x - 6y + 10<BR>\n" );
document.write( "for all x, y \in \mathbb{R}. Find f(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209964      (120)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1209964.html<BR>\n" );
document.write( "ACDF is a Parallelogram. DEF is a sector. ABC is a right triangle. Solve for the area of the composite figure.<BR>\n" );
document.write( "https://ibb.co/MyW8MZ2P\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209959<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209959.html<BR>\n" );
document.write( "A club buys tickets for 15 seats in a row for a local production and then sends the tickets randomly<BR>\n" );
document.write( "to the 15 people who ordered seats. Of these 15 people, 9 are actors and 6 are backstage workers.<BR>\n" );
document.write( "Find the probability that:<BR>\n" );
document.write( "(a) An actor and backstage worker will receive tickets sitting together.<BR>\n" );
document.write( "(b) The actors will be seated together, and the backstage workers will be seated together.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209960<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209960.html<BR>\n" );
document.write( "55% of all shark attacks are not fatal. Let r be the number of nonfatal attacks out of a random sample of five shark attacks. <BR>\n" );
document.write( "(a) What is the probability all five shark attacks are nonfatal? <BR>\n" );
document.write( "(b) What is the probability that three or more of the five shark attacks are nonfatal? <BR>\n" );
document.write( "(c) What is the expected number of nonfatal shark attacks out of the five? <BR>\n" );
document.write( "(d) What is the standard deviation of the r-probability distribution?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210228<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210228.html<BR>\n" );
document.write( "Find the number of subsets of<BR>\n" );
document.write( "S = \{1, 3, 8, 17, 30, 36, 47, 58\},<BR>\n" );
document.write( "so that the sum of the elements in the subset is a multiple of 5. <BR>\n" );
document.write( "(Note that for the empty subset, we take the sum of the elements as 0.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1169789<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1169789.html<BR>\n" );
document.write( "Given a right pyramid ABCDE, on a square base ABCD, with AB = 8 cm, and height EO = 5 cm,<BR>\n" );
document.write( "what are the values of the following:<BR>\n" );
document.write( "(a) angle EAB<BR>\n" );
document.write( "(b) angle β between a slant edge and the plane on the base.<BR>\n" );
document.write( "(c) angle θ between a slant face and the plane on the base.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210155<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1210155.html<BR>\n" );
document.write( "ABCE is a Parallelogram. ADEF is a Rhombus. Find the area of the composite figure.<BR>\n" );
document.write( "https://ibb.co/Jj2jKPD3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210151<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1210151.html<BR>\n" );
document.write( "In many ways can the letters of \"lyltalqdr\" be arranged such that no letter remains in its original position?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1168949<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1168949.html<BR>\n" );
document.write( "A quilt is made up of strips of cloth, starting with an inner square <BR>\n" );
document.write( "surrounded by rectangles to form successively larger squares. <BR>\n" );
document.write( "The inner square and all rectangles have a width of 1 foot. <BR>\n" );
document.write( "Write an expression using summation notation that gives the sum of<BR>\n" );
document.write( "the areas of all the strips of cloth used to make the quilt shown. <BR>\n" );
document.write( "Then evaluate the expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1168977<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1168977.html      <BR>\n" );
document.write( "Conjugate axis along the y-axis, ome vertex at (0,7), asymptotes are 6x-5y+30=0 and 6x+5y-30=0. <BR>\n" );
document.write( "Need help finding the Equation of this hyperbola. How?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1169051   <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1169051.html<BR>\n" );
document.write( "The sample of work produced by lathe is 10000.<BR>\n" );
document.write( "a. If the machine doubled this production every 20 minutes, how much will it produce<BR>\n" );
document.write( "in one hour?<BR>\n" );
document.write( "b. How long will it take the machine to produce 8 million?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210173      (130) <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1210173.html<BR>\n" );
document.write( "Let P be a point chosen uniformly at random inside triangle ABC. Extend ray BP to hit side AC at D. <BR>\n" );
document.write( "What is the probability that BD < 4 ?<BR>\n" );
document.write( "The sides of triangle ABC are 3, 5, and 7.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210172<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210172.html<BR>\n" );
document.write( "Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals <BR>\n" );
document.write( "intersect at an endpoint? Consider rotations and reflections distinct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210184<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210184.html<BR>\n" );
document.write( "I can only remember a seven-digit telephone number if the first three digits (the \"prefix\") are equal to the next <BR>\n" );
document.write( "three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.<BR>\n" );
document.write( "How many seven-digit telephone numbers can I remember?<BR>\n" );
document.write( "(For this problem, a telephone number cannot start with a 0.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210183<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210183.html<BR>\n" );
document.write( "In how many ways can we seat 3 pairs of siblings in a row of 10 chairs, so that nobody sits next to their sibling? <BR>\n" );
document.write( "(Two chairs will be left empty, of course.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1168409<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1168409.html<BR>\n" );
document.write( "73% of all Americans live in cities with population greater than 100,000 people. <BR>\n" );
document.write( "If 35 Americans are randomly selected, find the probability that<BR>\n" );
document.write( "a.  Exactly 26 of them live in cities with population greater than 100,000 people.<BR>\n" );
document.write( "b.  At most 26 of them live in cities with population greater than 100,000 people.<BR>\n" );
document.write( "c.  At least 25 of them live in cities with population greater than 100,000 people.<BR>\n" );
document.write( "d.  Between 21 and 25 (including 21 and 25) of them live in cities with population greater than 100,000 people.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210201<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1210201.html<BR>\n" );
document.write( "Let ABCD be a square with side length 1. A laser is located at vertex A, which fires a laser beam at point X on side BC, <BR>\n" );
document.write( "such that BX = 2/3. The beam reflects off the sides of the square, until it ends up at another vertex; at this point, <BR>\n" );
document.write( "the beam will stop. Find the length of the total path of the laser beam.  The diagram is linked below<BR>\n" );
document.write( "https://artofproblemsolving.com/texer/zqcbfanp\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210212<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210212.html<BR>\n" );
document.write( "How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, <BR>\n" );
document.write( "and the sum of the digits is 6?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210211<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210211.html<BR>\n" );
document.write( "How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, <BR>\n" );
document.write( "and the sum of the digits is 6?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210210 <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210210.html     <BR>\n" );
document.write( "How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210204      <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210204.html<BR>\n" );
document.write( "Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, <BR>\n" );
document.write( "no two Cs are next to each other, and no two Ds are next to each other.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209733      (140)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209733.html<BR>\n" );
document.write( "60% of all violent felons in the prison system are repeat offenders.<BR>\n" );
document.write( "If 45 violent felons are randomly selected, find the probability that<BR>\n" );
document.write( "a. Exactly 26 of them are repeat offenders.<BR>\n" );
document.write( "b. At most 29 of them are repeat offenders.<BR>\n" );
document.write( "c. At least 29 of them are repeat offenders.<BR>\n" );
document.write( "d. Between 25 and 33 (including 25 and 33) of them are repeat offenders.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1168408<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1168408.html<BR>\n" );
document.write( "64% of all violent felons in the prison system are repeat offenders. <BR>\n" );
document.write( "If 48 violent felons are randomly selected, find the probability that<BR>\n" );
document.write( "a. Exactly 28 of them are repeat offenders.<BR>\n" );
document.write( "b. At most 30 of them are repeat offenders.<BR>\n" );
document.write( "c. At least 32 of them are repeat offenders.<BR>\n" );
document.write( "d. Between 28 and 34 (including 28 and 34) of them are repeat offenders.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1168513<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1168513.html<BR>\n" );
document.write( "Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month<BR>\n" );
document.write( "for 3 1/2 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1210228      <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210228.html<BR>\n" );
document.write( "Find the number of subsets of<BR>\n" );
document.write( "S = \{1, 3, 8, 17, 30, 36, 47, 58\},<BR>\n" );
document.write( "so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209711<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1209711.html<BR>\n" );
document.write( "[x-(1/x)]^(1/x) + [1-(1/x)] ^(1/x) = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1209827<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209827.html<BR>\n" );
document.write( "Find a closed form for<BR>\n" );
document.write( "S_n = 1! \cdot (1^2 + 1) + 2! \cdot (2^2 + 2) + \dots + n! \cdot (n^2 + n).\]<BR>\n" );
document.write( "for any integer n \ge 1. Your response should have a factorial.\r<BR>\n" );
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document.write( "1209826<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209826.html<BR>\n" );
document.write( "For a positive integer k, let<BR>\n" );
document.write( "S_k = 1 \cdot 1! \cdot 2 + 2 \cdot 2! \cdot 3 + \dots + k \cdot k! \cdot (k + 1).<BR>\n" );
document.write( "Find a closed form for S_k.\r<BR>\n" );
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document.write( "1179819     <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1179819.html<BR>\n" );
document.write( "Find the present values of the following annuities<BR>\n" );
document.write( "i.   RM6,000 every year for 8 years at 12% compounded annually<BR>\n" );
document.write( "ii. RM800 every month for 2 years 5 months at 5% compounded monthly\r<BR>\n" );
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document.write( "1209870<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209870.html<BR>\n" );
document.write( "Fill in the blanks.\r<BR>\n" );
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document.write( "(a) If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.<BR>\n" );
document.write( "(b) If f(x) is an odd function and g(x) is an odd function and h(x) is an even function, then f(x)*g(x) + h(x) is an ___ function.<BR>\n" );
document.write( "(c) If f(x) is an even function and g(x) is an odd function and h(x) is an odd function, then f(x)*(g(x) + h(x)) is an ___ function.<BR>\n" );
document.write( "(d) If f(x) is an odd function and g(x) is an even function and h(x) is an odd function, then f(x)*g(x)*h(x) is an ___ function.\r<BR>\n" );
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document.write( "The answer to (d) in the post by @CPhill is incorrect.\r<BR>\n" );
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document.write( "1209715    <BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209715.html<BR>\n" );
document.write( " P(x) be a polynomial of the form<BR>\n" );
document.write( "P(x) = 2x^3 + ax^2 - 23x + c,<BR>\n" );
document.write( "such that 12 and 7 are roots of P(x). What is the third root?<BR>\n" );
document.write( "For the polynomial in part (a), compute the ordered pair (a,c).\r<BR>\n" );
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document.write( "1190651     (150)<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html<BR>\n" );
document.write( "What is the future value of an ordinary annuity having daily payments of 50 pesos for 30 days with an rate of 20% compounded daily?\r<BR>\n" );
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document.write( "1209897<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.1209897.html<BR>\n" );
document.write( "Let x and y be real numbers satisfying<BR>\n" );
document.write( "\frac{x^2y^2 - 1}{2y - 1} = 4x + y.<BR>\n" );
document.write( "Find the largest possible value of x.\r<BR>\n" );
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document.write( "\n" );
document.write( "ikleyn<BR>\n" );
document.write( "June 29, 2025\r<BR>\n" );
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document.write( " </SPAN>\n" );
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