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Recent problems solved by 'stanbon'

stanbon answered: 57222 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

Inequalities/341343: how do you write 6.3 less than or equal to h less than or equal to 10.3 as an absolute value inequality 1 solutions Answer 244434 by stanbon(57290)   on 2010-09-10 09:49:58 (Show Source): You can put this solution on YOUR website! ): how do you write 6.3 less than or equal to h less than or equal to 10.3 as an absolute value inequality ---- 6.3 <= h <= 10.3 ----- Draw a number line. Plot the values 6.3 and 10.3 --- The point half-way between the two is 8.3 Note that each of the end points is at a distance of 2 from 8.3. ------ Ans: |h-8.3|<=2 ====================== Cheers, Stan H.

Travel_Word_Problems/341266: in order to qualify for a race emily needs to go at an average speed of 100 mi/h for two laps. but she only goes 75mi/h on the first lap. How fast does she need to go on the second lap to reach the average speed of 100 mi/h? 1 solutions Answer 244355 by stanbon(57290)   on 2010-09-09 22:18:44 (Show Source): You can put this solution on YOUR website! in order to qualify for a race emily needs to go at an average speed of 100 mi/h for two laps. but she only goes 75mi/h on the first lap. Let distance of a lap = x miles If rate = 75 mph, time = x/75 hrs ---------------------------------------- How fast does she need to go on the second lap to reach the average speed of 100 mi/h? Distance for 2 laps = 2x miles If rate = 100 mph, time = (2x)/100 = x/50 hrs --- Time for her 2nd lap would have to be time for 2 laps - time for 1st lap x/50-x/75 = (75x-50x)/(50*75) = 25x/(50*75) = x/150 hrs. ---- distance/time = rate x/(x/150) = 150 mph --- She would have to go 150 mph to average 100 mph for the 2 laps. ============================== Cheers, Stan H.

Angles/341260: Please help me solve this problem: In angle ABC, angle A and angle B measure exactly the same and C is half as large as angle A. Find the meaure of each angle. 1 solutions Answer 244346 by stanbon(57290)   on 2010-09-09 22:08:41 (Show Source): You can put this solution on YOUR website! Please help me solve this problem: In angle ABC, angle A and angle B measure exactly the same and C is half as large as angle A. Find the meaure of each angle. ----------------------------- A + B + C = 180 A = B C = (1/2)A ----------------- Substitute and solve for A: A + A + (1/2)A = 180 (2 1/2)A = 180 (5/2)A = 180 A = (2/5)180 A = 2*36 A = 72 degrees B = 72 degrees C = 36 degrees =================== Cheers, Stan H. ==========

Polynomials-and-rational-expressions/341252: Find the equation of the line for the demand equation. What format do I use to obtain the equation of price of p=$20, which would sell x=42 sneakers each week. If the price were lowered to p=$10, one could expect to sell x=52 of sneakers per week. How do I write an equation using 2 points in the form x,p.? 1 solutions Answer 244336 by stanbon(57290)   on 2010-09-09 22:02:19 (Show Source): You can put this solution on YOUR website! Find the equation of the line for the demand equation. What format do I use to obtain the equation of price of p=$20, which would sell x=42 sneakers each week. If the price were lowered to p=$10, one could expect to sell x=52 of sneakers per week. How do I write an equation using 2 points in the form x,p.? ---------- You have two points: (42,20) and (52,10) ---- slope = (10-20)/(52-42) = -10/10 = -1 ----- Use one of the points and the slope to get: 10 = -1(52)+b b = 62 --- Equation: price = -(number sold) + 62 p = -x + 62 ================================= Cheers, Stan H.

Inequalities/341255: How do you solve the problem, 9≥(x-4)/2>2 1 solutions Answer 244330 by stanbon(57290)   on 2010-09-09 21:52:49 (Show Source): You can put this solution on YOUR website! 9≥(x-4)/2>2 ----- Rearrange: 2 < (x-4)/2 < 9 Multiply thru by 2 to get: 4 < x-4 < 18 Add 4 along the line to get: 8 < x < 22 ================== Cheers, Stan H.

Polynomials-and-rational-expressions/341253: find the LCD and simplify (2/x^2-x-2)+ (10/x^2+2x-8) 1 solutions Answer 244329 by stanbon(57290)   on 2010-09-09 21:49:33 (Show Source): You can put this solution on YOUR website! find the LCD and simplify (2/x^2-x-2)+ (10/x^2+2x-8) ------ Factor: (2/[(x-2)(x+1)) + {10/[(x+4)(x-2)] ------- LCD: (x-2)(x+1)(x+4) ----------------------------------- Rewrite each term with the LCD as its denominator: [2(x+4)]/LCD + [10(x+1)]/LCD ----- Combine the numerators over the LCD: [2x+8+10x+10]/LCD ---- Simplify: (12x+18)/[(x-2)(x+1)(x+4)] --- [6(2x+3)]/[(x-2)(x+1)(x+4)] ================================ Cheers, Stan H.

Linear-equations/341221: Write an equation that is perpendicular to 2x+3y=6 with point (3,5). 1 solutions Answer 244318 by stanbon(57290)   on 2010-09-09 21:37:29 (Show Source): You can put this solution on YOUR website! Write an equation that is perpendicular to 2x+3y=6 with point (3,5). -------------------------- The given line: y = (-2/3)x+2 slope is -2/3 ------ A perpendicular line will have slope = 3/2 and pass thru (3,5) --- y = mx+b 5 = (3/2)3+b 5 = (9/2)+b (10/2) = (9/2) + b b = 1/2 --- Equation: y = (3/2)x + 1/2 ====================== Graph: ======================== Cheers, Stan H.

Graphs/341249: i need help with my math homework. i got stuck on this problem its inequality and graphing but i know how to do the graph. i only need to do is the problem.this one q - 1 1/3 > -2 1/2 1 solutions Answer 244314 by stanbon(57290)   on 2010-09-09 21:30:31 (Show Source): You can put this solution on YOUR website! q - 1 1/3 > -2 1/2 -------- q-4/3 > -5/2 --- q > (4/3)-(5/2) q > (8-15)/6 q > -7/6 ============== Cheers, Stan H.

Miscellaneous_Word_Problems/341239: In 2006 the population of the united states was 300.2 million. If the population continues to grow at an annual rate of 1.05% then the population in the year 202 will be 300.2(1.0105) to the power 14 million. A) Evaluate the expression to find the predicted population in 2020 to the nearest tenth of a million people. :-) Thanks 1 solutions Answer 244309 by stanbon(57290)   on 2010-09-09 21:26:15 (Show Source): You can put this solution on YOUR website! In 2006 the population of the united states was 300.2 million. If the population continues to grow at an annual rate of 1.05% then the population in the year 2020 will be [300.2(1.0105)^14] million. A) Evaluate the expression to find the predicted population in 2020 to the nearest tenth of a million people. :-) Thanks ----------------- Ans: 347.5 million ============== Cheers, stan H.

Rectangles/341234: what is the dimensions of a rectangle with a perimeter of 70ft and length to width ratio of 4 to 5? 1 solutions Answer 244304 by stanbon(57290)   on 2010-09-09 21:17:57 (Show Source): You can put this solution on YOUR website! what is the dimensions of a rectangle with a perimeter of 70ft and length to width ratio of 4 to 5? ---- 4:5 is the same as 4x:5x where length = 4x and width = 5x ------------------- Equation: P = 2(length + width) 70 = 2(4x+5x) 35 = 9x x = (35/9) --- length = 4x = 4(35/9) = 140/9 = 15.56 ft --- width = 5x = 5(35/9) = 175/9 = 19.44 ft. ============================================= Cheers, Stan H.

Travel_Word_Problems/341233: At 10 A.M. two cars leave the same location and travel in opposite directions. One car's speed is 50/mph, while the other's speed is 55/mph. At what time are the cars 273 miles apart? 1 solutions Answer 244301 by stanbon(57290)   on 2010-09-09 21:10:55 (Show Source): You can put this solution on YOUR website! two cars leave the same location and travel in opposite directions. One car's speed is 50/mph, while the other's speed is 55/mph. At what time are the cars 273 miles apart? --------------------- They are separating at a rate of 50+55 = 105 mph --------------------- time = distance/rate --- time = 273/105 = 2.6 hrs = 2 hr 36 minutes ======================== Cheers, Stan H.

Distributive-associative-commutative-properties/341231: solve 4(-12 -3x) = -24 please show the steps. so far i've got to 12x = 24 but i don't know where to go from here. 1 solutions Answer 244298 by stanbon(57290)   on 2010-09-09 21:07:33 (Show Source): You can put this solution on YOUR website! solve 4(-12 -3x) = -24 ---- Divide both sides by 4 to get: -12-3x = -6 --- Add 12 to both sides to get: -3x = 6 Divide both sides by -3 to get x = -2 ===================== Cheers, Stan H.

Rate-of-work-word-problems/341207: Parallel processing uses two or more computers, working together, to solve a single problem. Using parallel processing, two computers can solve a problem in 20 minutes. If, working alone, one computer can solve a problem in 9 minutes less than the time needed by the second computer, how long would it take the faster computer working alone to solve the problem? 1 solutions Answer 244286 by stanbon(57290)   on 2010-09-09 20:38:46 (Show Source): You can put this solution on YOUR website! Parallel processing uses two or more computers, working together, to solve a single problem. Using parallel processing, two computers can solve a problem in 20 minutes. If, working alone, one computer can solve a problem in 9 minutes less than the time needed by the second computer, how long would it take the faster computer working alone to solve the problem? ---------- together rate = 1/20 min/job one comp. rate = 1/(x-9) min/job 2nd comp. rate = 1/x min/job ------------------------------- Equation: rate + rate = together rate 1/x + 1/(x-9) = 1/20 --- 20(x-9) + 20x = x(x-9) 40x-9*20 = x^2-9x --- x^2-49x + 180 = 0 Factor: (x-45)(x-4) = 0 Realistic solution since 4-9 is negative: x = 45 minutes then x-9 = 36 minutes (faster computer time to do the job) ============= Cheers, Stan H.

Numeric_Fractions/341204: 1 1 1 - = - + - y 56.1 15.3 1 solutions Answer 244280 by stanbon(57290)   on 2010-09-09 20:28:52 (Show Source): You can put this solution on YOUR website! 1 1 1 - = - + - y 56.1 15.3 ----------------------------- (1/y) = (15.3+56.1)/(56.1*15.3) --- 1/y = 71.4/(858.330) y = (858.33/71.4) y = 12.0214 ================ Cheers, Stan H.

real-numbers/341192: can you please help me with this problem? fractions: 3 over 14 divided by 15 over 28 1 solutions Answer 244278 by stanbon(57290)   on 2010-09-09 20:23:55 (Show Source): You can put this solution on YOUR website! 3 over 14 divided by 15 over 28 ---------------- (3/14)/(15/28) --- Invert the denominator and multiply: --- (3/14)*(28/15) ---- Cancel any factor common to a numerator and a denominator to get: (1/1)*(2/5) === = 2/5 =============== Cheers, Stan H.

Functions/341202: What is the domain of f(x) = 10/x^2-2x ? 1 solutions Answer 244273 by stanbon(57290)   on 2010-09-09 20:19:27 (Show Source): You can put this solution on YOUR website! What is the domain of f(x) = 10/x^2-2x --- The denominator cannot be zero. Solve x^2-2x = 0 x(x-2) = 0 x = 0 or x = 2 ----- Domain is All Real Numbers except x = 0 and x = 2 ======================================================= Cheers, Stan H.

Angles/341194: Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 12. 1 solutions Answer 244272 by stanbon(57290)   on 2010-09-09 20:16:29 (Show Source): You can put this solution on YOUR website! Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 12. ----- Equations: x + y + z = 180 x = 2y z = 3y-12 --------------- Substitute and solve for "y"; 2y + y + 3y-12 = 180 6y = 192 y = 32 degrees --- x = 2y = 64 degrees z = 3y-12 = 96-12 = 84 degrees ---------------------------------- Cheers, Stan H.

Expressions-with-variables/341195: Can you help me solve this problem? -6-(3a-7)-2a=a-6 1 solutions Answer 244269 by stanbon(57290)   on 2010-09-09 20:11:36 (Show Source): You can put this solution on YOUR website! -6-(3a-7)-2a=a-6 --- -6-3a+7-2a = a-6 -5a + 1 = a-6 6a = 7 a = 7/6 ====================== Cheers, Stan H.

Linear-equations/341187: how do you find the slope of the straight line that passes through (−1, 14) and (3, 4) 1 solutions Answer 244268 by stanbon(57290)   on 2010-09-09 20:05:32 (Show Source): You can put this solution on YOUR website! find the slope of the straight line that passes through (−1, 14) and (3, 4) ---------------------- slope = change in y/change in x --- slope = (14-4)/(-1-3) = 10/-4 = -5/2 ======================================== cheers, Stan H.

Numbers_Word_Problems/341171: The product of some number plus 2 and 5 is 11 less than the number times 8. Find the number. 1 solutions Answer 244267 by stanbon(57290)   on 2010-09-09 20:00:57 (Show Source): You can put this solution on YOUR website! The product of some number plus 2 and 5 is 11 less than the number times 8. Find the number --------------------------- (x+2)5 = 8x-11 5x+10 = 8x-11 3x = 21 x = 7 ================= cheers, Stan H

Polynomials-and-rational-expressions/341184: How would you solve the equation L=2.43*W^0.3326 if w=3 1 solutions Answer 244266 by stanbon(57290)   on 2010-09-09 19:55:25 (Show Source): You can put this solution on YOUR website! How would you solve the equation L=2.43*W^0.3326 if w=3 --- Use a calculator to get: L = 2.43*3^0.3326 = 3.5018 ========================= Cheers, Stan H.

Percentage-and-ratio-word-problems/341181: You want to order a new computer. The manufacturer is offering a discount of 12% off the original price of the computer. With the discount, you pay $924. What is the original price? 1 solutions Answer 244265 by stanbon(57290)   on 2010-09-09 19:49:03 (Show Source): You can put this solution on YOUR website! You want to order a new computer. The manufacturer is offering a discount of 12% off the original price of the computer. With the discount, you pay $924. What is the original price? ------------------ Let the original price be "x". --- Equation: x - 0.12x = 924 dollars 0.88x = 924 x = 924/0.88 x = $1050 (original price) ====================== Cheers, Stan H.

logarithm/341176: x^log(x)= 10000/x What is the product of the solutions? I have simplified it to (log (x))^2 + log (x) = 4, but can't solve that equation. 1 solutions Answer 244264 by stanbon(57290)   on 2010-09-09 19:44:51 (Show Source): You can put this solution on YOUR website! x^log(x)= 10000/x ---- Multiply both sides by x to get: x*x^[log(x)] = 10000 --- Simplify: x^(1+log(x)] = 10000 --- I graphed the left side as Y1 and the right side as Y2. I found the intersection at x = 36.4379 ======================== Cheers, Stan H.

Trigonometry-basics/341177: i have an example problem that looks like this.. (X-12)^2=16 ^2..means to the second power. please help me understand this. 1 solutions Answer 244263 by stanbon(57290)   on 2010-09-09 19:35:56 (Show Source): You can put this solution on YOUR website! (X-12)^2=16 --- (x-12)^2-16 = 0 Factor: [(x-12)-4][(x-12)+4] = 0 --- Simplify: [x-16][x-8] = 0 --- Solve: x = 16 or x = 8 ======================= Cheers, Stan H.

Numbers_Word_Problems/341174: Solve equation 3(x-1)=12 1 solutions Answer 244262 by stanbon(57290)   on 2010-09-09 19:32:59 (Show Source): You can put this solution on YOUR website! Solve equation 3(x-1)=12 --- Divide both sides by 3 to get: x-1 = 4 --- Add 1 to both sides to get: x = 5 =========== Cheers, Stan H.

Functions/341175: Is (city,area code) a function? Is (person,birth date) a function? Is (first name, last name) a function? Is (student, school ID number) a function? 1 solutions Answer 244261 by stanbon(57290)   on 2010-09-09 19:30:18 (Show Source): You can put this solution on YOUR website! Is (city,area code) a function? No, because a city may have many area codes in it. ------ Is (person,birth date) a function? Yes, because each person has only one birth date -------------- Is (first name, last name) a function? No, because a given 1st name may have several last names associated. ------------------------ Is (student, school ID number) a function? Yes, because each student has only one school ID number. ==================== Cheers, Stan H.

Angles/341169: an angle is two and one half times the measure of its complement. Find the measure of the angle. which is a = 2.5*(90-a)? So how do I round to the nearest tenth? 1 solutions Answer 244260 by stanbon(57290)   on 2010-09-09 19:20:16 (Show Source): You can put this solution on YOUR website! an angle is two and one half times the measure of its complement. Find the measure of the angle. which is a = 2.5*(90-a)? So how do I round to the nearest tenth? --- Let the angle be "a". Its complement is "90-a" --- Equation: a = 2.5(90-a) 10a = 25(90-a) 10a = 2250 - 25a 35a = 2250 a = 2250/35 a = 64.3 degrees when rounded to the nearest tenth. ============== Cheers, Stan H.

decimal-numbers/341167: How would you write 10 to the 4th power in decimal form? 1 solutions Answer 244259 by stanbon(57290)   on 2010-09-09 19:16:08 (Show Source): You can put this solution on YOUR website! How would you write 10 to the 4th power in decimal form? --- 10^4 = 10,000 ================= Cheers, Stan H.

Graphs/341163: How do you solve for: x+12y=6 x-1/3y=4 1 solutions Answer 244258 by stanbon(57290)   on 2010-09-09 19:14:28 (Show Source): You can put this solution on YOUR website! solve for: x+12y=6 x-1/3y=4 --------------- Subtract the 2nd from the 1st equation to get: 12 1/3 y = 2 --- (37/3)y = 2 y = 2(3/37) y = 6/37 ============= Substitue for y in (x +12y = 6) and solve for "x": x + 12(6/37) = 6 --- x + 72/37 = 6 x = 150/37 ================= Cheers, Stan H. =============

Expressions-with-variables/341164: What does x equal ? x^2+3x=4 1 solutions Answer 244257 by stanbon(57290)   on 2010-09-09 19:07:51 (Show Source): You can put this solution on YOUR website! x^2+3x=4 ----- x^2+3x-4 = 0 Factor: (x+4)(x-1) = 0 x = -4 or x = 1 ======================= Cheers, Stan H.

test/341159: A sphere has a volume of 25m^3. What is the diameter in dm?? 1 solutions Answer 244256 by stanbon(57290)   on 2010-09-09 19:06:10 (Show Source): You can put this solution on YOUR website! A sphere has a volume of 25m^3. What is the diameter in dm?? ------------ V = (4/3)pi*r^3 ---- 25 = (4/3)pi*r^3 75/(4pi) = r^3 r^3 = 5.9683 r = 1.8139 2r = 3.6278 - diameter = 3.6278 meters --- diameter = 3.6278(meters)(10 decimeters/1 meter) = 36.278 decimeters ======================= Cheers, Stan H.