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Recent problems solved by 'stanbon'

stanbon answered: 57889 problems
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 Graphs/309227: find the equation of a line given x-intercept 4 and y intercept -61 solutions Answer 221140 by stanbon(57962)   on 2010-05-27 19:48:05 (Show Source): You can put this solution on YOUR website!find the equation of a line given x-intercept 4 and y intercept -6 --- Points: (4,0) ; (0,-6) ------------------------- slope = -6/-4 = 3/2 ---- intercept: -6 ---- Equation: y = (3/2)x-6 ================ Cheers, Stan H. ================
 Polynomials-and-rational-expressions/309235: Divide: (b^3 - 2b^2 - 33b - 7) / (b - 7)1 solutions Answer 221137 by stanbon(57962)   on 2010-05-27 19:42:51 (Show Source): You can put this solution on YOUR website!Divide: (b^3 - 2b^2 - 33b - 7) / (b - 7) Using synthetic division: 7)....1....-2....-33....-7 .......1....5.....2...|..7 Quotient: b^2 + 5b + 2 Remainder: 7 ================================== Cheers, Stan H. ==================================
 Radicals/309241: What are the laws of exponents?1 solutions Answer 221135 by stanbon(57962)   on 2010-05-27 19:38:32 (Show Source): You can put this solution on YOUR website!What are the laws of exponents? ----------------- a^x * a^y = a^(x+y) ---------------- a^x / a^y = a^(x-y) ---------------- (a^x)^y = a^(xy) ================= Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/309221: 2 positive numbers the sum of whose squares is 16 and whose product is as large as possible1 solutions Answer 221113 by stanbon(57962)   on 2010-05-27 18:55:17 (Show Source): You can put this solution on YOUR website!2 positive numbers the sum of whose squares is 16 and whose product is as large as possible --------------------- Equations: x^2 + y^2 = 16 Product = xy ------------------------ y = sqrt(16-x^2) -------- Product = x*sqrt(16-x^2) ---- Take the derivative dP/dx = x[(1/2)(16-x^2)^(-1/2)(-2x)] + [sqrt(16-x^2)] ---- dP/dx = [-x/sqrt(16-x^2)] + [sqrt(16-x^2)] ---- dP/dx = [-x + 16-x^2]/sqrt(16-x^2) ------ Solve -x+16-x^2 = 0 x^2+x-16 = 0 x = [-1+-sqrt(1+4*16)]/2 --- x = [-1+-sqrt(65)]/2 --- Positive solution: x = 3.53 ------------- Substitute into x^2 + y^2 = 16 y = sqrt(16-x^2) y = sqrt(16-12.4689) y = 1.8791 ============================== Cheers, Stan H.
 Rational-functions/309222: A rock falls from a clift that is 80 feet high. The function h=-16t^2+80 gives the height of the rock after t seconds. A. Graph the function B. What values make sense for the domain? C. What values make sense for the range? Please Help me Solve this1 solutions Answer 221110 by stanbon(57962)   on 2010-05-27 18:31:40 (Show Source): You can put this solution on YOUR website!A rock falls from a cliff that is 80 feet high. The function h = -16t^2+80 gives the height of the rock after t seconds. A. Graph the function -------------------------------------------------- B. What values make sense for the domain? -16t^2=-80 t^2 = 5 t = sqrt(5) Domain: 0<= t <= sqrt(5) -------------------------------------------------- C. What values make sense for the range? Range: 0<= h <= 80 ================================================== Cheers, Stan H. ==================================================
 Probability-and-statistics/309132: In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.) 1 solutions Answer 221106 by stanbon(57962)   on 2010-05-27 18:18:26 (Show Source): You can put this solution on YOUR website!In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. p-hat = 1143/86991 = 0.0131... E = 1.96*sqrt[0.0131*0.9869/86991] = 7.556x10^-4 C.I. (p-hat-E,p-hat+E) = (0.0131,0.0131) -------------------------- (b) Why is the normality assumption not a problem, despite the very small value of p? n is so large pn and qn both are greater than 5 --------------------- (Data are from Flying 120, no. 11 [November 1993], p. 31.) =============== Cheers, Stan H.
 Probability-and-statistics/309118: A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth. * 0.241 * 0.345 * 0.252 * 0.0341 solutions Answer 221105 by stanbon(57962)   on 2010-05-27 18:12:18 (Show Source): You can put this solution on YOUR website!A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth. Ans: 7/29 ----------------- Cheers, Stan H. ================= * 0.241 * 0.345 * 0.252 * 0.034
 Probability-and-statistics/309133: The letters G E O M E T R Y are written on a set of cards. You mix the cards thoroughly. Without looking, you draw one letter, replace it, then draw another. Find each probability. 1. P(E,T) 2. P(M,Y)1 solutions Answer 221104 by stanbon(57962)   on 2010-05-27 18:09:58 (Show Source): You can put this solution on YOUR website!The letters G E O M E T R Y are written on a set of cards. You mix the cards thoroughly. Without looking, you draw one letter, replace it, then draw another. Find each probability. 1. P(E,T) = (2/8)(1/8) = 1/32 ---------------------------------- 2. P(M,Y) = (1/8)(1/8) = 1/64 ---------------------------------- Cheers, Stan H.
 Probability-and-statistics/309134: Dave the jogger runs the same route every day (about 2.2 miles). On 18 consecutive days, he recorded the number of steps using a pedometer. The results were: 3,450 3,363 3,228 3,360 3,304 3,407 3,324 3,365 3,290 3,289 3,346 3,252 3,237 3,210 3,140 3,220 3,103 3,129 (a) Construct a 95 percent confidence interval for the true mean number of steps Dave takes on his run. (b) What sample size would be needed to obtain an error of ± 20 steps with 95 percent confidence? (c) Using Excel, plot a line chart of the data. What does the data suggest about the pattern over time? 1 solutions Answer 221102 by stanbon(57962)   on 2010-05-27 18:05:33 (Show Source): You can put this solution on YOUR website!Dave the jogger runs the same route every day (about 2.2 miles). On 18 consecutive days, he recorded the number of steps using a pedometer. The results were: 3,450 3,363 3,228 3,360 3,304 3,407 3,324 3,365 3,290 3,289 3,346 3,252 3,237 3,210 3,140 3,220 3,103 3,129 (a) Construct a 95 percent confidence interval for the true mean number of steps Dave takes on his run. 1st: find the mean of the sample = x-bar ; find the std = s --- 2nd: find standard error = E = 1.96*s/sqrt(18) --- 95% CI: x-bar - E < u < x-bar + E =============================================== (b) What sample size would be needed to obtain an error of ± 20 steps with 95 percent confidence? n = [1.96*s/20]^2 =============================================== (c) Using Excel, plot a line chart of the data. What does the data suggest about the pattern over time? --- I'll leave that plotting to you. =============================================== Cheers, Stan H. ===============================================
 Probability-and-statistics/309136: a market analyst is hired to provide information on the type of customers who shop at a particular store. a random survey is taken of 100 shoppers at this store. of these 100, 73 are women. the shoppers are grouped in three categories, under 30, 30 and up to 50 and 50 and over. the data is summerized in the table. let w be the event that a randomly selected shopper is a woman. let a be the event that a randomly selected shopper is under 30.1 solutions Answer 221094 by stanbon(57962)   on 2010-05-27 17:56:09 (Show Source): You can put this solution on YOUR website!The table was not included in the post. --- Cheers, Stan H.
 Probability-and-statistics/309143: 5. In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probability that: (A) exactly three will have this mild side effect (B) at least two will have this mild side effect.1 solutions Answer 221092 by stanbon(57962)   on 2010-05-27 17:53:56 (Show Source): You can put this solution on YOUR website!In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. ------------------- Binomial Problem with n = 12 ; p = 0.05 ----------------------------- Find the probability that: (A) exactly three will have this mild side effect P(x=3) = 0.05^3 = 0.125 -------------------------------------------------- (B) at least two will have this mild side effect. P(2<=x<=12) = 1 - P(0<= x <=1) = 0.1184 ==================================================== Cheers, Stan H.
 Probability-and-statistics/309161: Suppose you play a game where you flip a coin. If is heads, you lose \$1.00. If it is a tail, a die is rolled. If it is an even number, you win \$ 2.00. If it is an odd number, you lose \$3.00. Find the expected value1 solutions Answer 221085 by stanbon(57962)   on 2010-05-27 17:48:26 (Show Source): You can put this solution on YOUR website!Suppose you play a game where you flip a coin. If is heads, you lose \$1.00. If it is a tail, a die is rolled. If it is an even number, you win \$ 2.00. If it is an odd number, you lose \$3.00. Find the expected value ------ Random "gain" values: -1, 2, -3 Corresponding probabilites: 1/2 , (1/2)(1/2)= 1/4 , (1/2)(1/2) = 1/4 ----------------------------- E(X) = (1/2)(-2) + (1/4)(2) + (1/4)(-3) --- = [-2 + 2 -3]/4 --- = -3/4 --- = -\$.75 =========================== Cheers, Stan H. ===========================
 Miscellaneous_Word_Problems/309117: A school has 18 classes with 35 students in each class. In order to reduce class size to 30, how many new classes must be formed? 1 solutions Answer 221004 by stanbon(57962)   on 2010-05-27 11:10:57 (Show Source): You can put this solution on YOUR website!A school has 18 classes with 35 students in each class. In order to reduce class size to 30, how many new classes must be formed? ---------------- Total # of students = 18*35 = 630 ------------------------------------ # of classes needed if 30 in a class: 630/30 = 21 -------------------------------------- # of new classes needed: 3 ================================= Cheers, Stan H.
 Rational-functions/309115: Suppose that y varies jointly with w and x and inversely with z and y = 360 when w = 8, x = 25 and z = 5. Write the equation that models the relationship. Then find y when w = 4, x = 4 and z = 3. a. ; 48 b. ; 15 c. ; 80/30 d. ; 27/161 solutions Answer 221003 by stanbon(57962)   on 2010-05-27 11:07:10 (Show Source): You can put this solution on YOUR website!Suppose that y varies jointly with w and x and inversely with z. y = k(wx/z) ---------------------------- Solve for "k" using y = 360 when w = 8, x = 25 and z = 5. 360 = k(8*25/5) 360 = k(40) k = 9 ---------------------------- Write the equation that models the relationship. y = 9(wx/z) ----------------------------------------- Then find y when w = 4, x = 4 and z = 3. y = 9(4*4/3) y = 3*16 y = 48 ======================= Cheers, Stan H. ======================= a. ; 48 b. ; 15 c. ; 80/30 d. ; 27/16
 Probability-and-statistics/309114: The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? 3rd Period Class: Yes- 11 No- 6 6th Period Class: Yes- 12 No- 10 * 0.647 * 0.565 * 0.435 * 0.7651 solutions Answer 221001 by stanbon(57962)   on 2010-05-27 11:00:52 (Show Source): You can put this solution on YOUR website! The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class) = 12/22 = 0.546 ========================================= Cheers, Stan H. ================================================ Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? 3rd Period Class: Yes- 11 No- 6 6th Period Class: Yes- 12 No- 10 * 0.647 * 0.565 * 0.435 * 0.765
 Probability-and-statistics/309096: 5. In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. Find the probability that:1 solutions Answer 221000 by stanbon(57962)   on 2010-05-27 10:57:14 (Show Source): You can put this solution on YOUR website!The last part of your post is missing. Cheers, Stan H.
 percentage/309083: Need help: Find the measure of each exterior angle of a regular polygon with 30 sides. Please show the work. Thanks:1 solutions Answer 220999 by stanbon(57962)   on 2010-05-27 10:40:59 (Show Source): You can put this solution on YOUR website!Need help: Find the measure of each exterior angle of a regular polygon with 30 sides. Please show the work. ------------------------------------------- The sum all the exterior angles is 360 degrees. --- Size of each exterior angle = 360/30 = 12 degrees =================================================== Cheers, Stan H.
 Graphs/309091: Using the standard window settings, Emily graphed y=x^3+3x^2-x-3 on her graphing calculator. She then used her graph to correctly solve the inequality x^3+3x^3>- x+3. What is her solution.1 solutions Answer 220995 by stanbon(57962)   on 2010-05-27 10:11:52 (Show Source): You can put this solution on YOUR website! Using the standard window settings, Emily graphed y=x^3+3x^2-x-3 on her graphing calculator. She then used her graph to correctly solve the inequality x^3+3x^2 >- x+3. What is her solution. -------------------------------- Ans: x > 0.7693 ---------------------- ================================================== Cheers, Stan H. ===========
 Linear-equations/309092: Find an equation of the line containing the given pair of points (1/4, -1/2) and (3/4, 1)1 solutions Answer 220994 by stanbon(57962)   on 2010-05-27 10:05:59 (Show Source): You can put this solution on YOUR website!Find an equation of the line containing the given pair of points (1/4, -1/2) and (3/4, 1) ------------------------------ slope = (1--(1/2))/(3/4 - 1/4) = (3/2)/(1/2) = 3 --------------------- Form: y = mx + b You have m = 3, and y = 1 when x = 3/4; solve for "b": --- 1 = 3(3/4) + b b = (4/4)-(9/4) = -5/4 ------------------------ Equation: y = 3x - (5/4) ===================== Cheers, Stan H. =====================
 absolute-value/309041: At a bottling company, machine A fills a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between 11 1/8 and 12 1/8 If machine B accepts a bottle containing fluid ounces, which of the following describes all possible value of n ? (A) |n-12| = 1/8 (B) |n+12| = 1/8 (C) |n-12| < 1/8 (D) |n+12| < 1/8 (E) |n-12| > 1/8 1 solutions Answer 220992 by stanbon(57962)   on 2010-05-27 10:01:53 (Show Source): You can put this solution on YOUR website!At a bottling company, machine A fills a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between 11 1/8 and 12 1/8 If machine B accepts a bottle containing fluid ounces, which of the following describes all possible value of n ? ---------------- Comment: Based on the 5 answers you listed, your posted information is incorrect. The bottles should be filled between 11 7/8 and 12 1/8 fluid ounces. ---------------------------- 1st: Find the middle value between 11 7/8 and 12 1/8 Ans: 12 ---- 2nd: Find the distance from the middle to one of the end points Ans: 1/8 --- 3rd: Since you want the difference to be "less than" the solution is |n-12|< 1/8 ====================== Cheers, Stan H. ====================== (A) |n-12| = 1/8 (B) |n+12| = 1/8 (C) |n-12| < 1/8 (D) |n+12| < 1/8 (E) |n-12| > 1/8
 absolute-value/309084: determine the point(s) where y=abs(x-2) intersects y=5 algebraically show all work. thanks 1 solutions Answer 220990 by stanbon(57962)   on 2010-05-27 09:52:42 (Show Source): You can put this solution on YOUR website!determine the point(s) where y=abs(x-2) intersects y=5 algebraically show all work. --- |x-2| = 5 x-2 = 5 or x-2 = -5 x = 7 or x = -3 ----------------------- ============================================== Cheers, Stan H.
 logarithm/308969: Use the Change of Base formula to evaluate . Then convert to a logarithm in base 3. A) 2.161; B) 2.996; C) 1.301; D) 2.161; 1 solutions Answer 220969 by stanbon(57962)   on 2010-05-27 08:51:31 (Show Source): You can put this solution on YOUR website!Use the Change of Base formula to evaluate . = log(20)/log(4) = 2.1610 --------------------------------------- Then convert to a logarithm in base 3. 2.1610 = log3(x) x = 3^2.1610 x = 10.741 =========== Cheers, Stan H. =============================== A) 2.161; B) 2.996; C) 1.301; D) 2.161;
 logarithm/308970: Solve 2log4- log3 +2 logx-4=0 A) 12.3308 B) 43.3013 C) 86.6025 D) 18751 solutions Answer 220968 by stanbon(57962)   on 2010-05-27 08:34:10 (Show Source): You can put this solution on YOUR website!Solve 2log4- log3 +2 logx-4 = 0 --- log(16) - log(3) + log(x-4)^2 = 0 --- log[(16/3)(x-4)^2] = 0 ---- (16/3)(x-4)^2 = 10^0 --- (16/3)(x-4)^2 = 1 --- (x-4)^2 = 3/16 --- x-4 = +-sqrt(3)/4 --- x = 4 +- (1/4)sqrt(3) ================================ Cheers, Stan H. ================================ A) 12.3308 B) 43.3013 C) 86.6025 D) 1875
 logarithm/309072: log3(x-6)=31 solutions Answer 220967 by stanbon(57962)   on 2010-05-27 08:28:22 (Show Source): You can put this solution on YOUR website!log3(x-6)=3 --- base = 3 exponent = 3 result = x-6 ------------- x-6 = 3^3 x-6 = 27 x = 33 =============== Cheers, Stan H. ===============
 logarithm/308895: Solve the logarithmic equation for x . Please round the answer to four decimal places, if necessary. 2-ln(5-x)=01 solutions Answer 220903 by stanbon(57962)   on 2010-05-26 21:55:14 (Show Source): You can put this solution on YOUR website!Solve the logarithmic equation for x . Please round the answer to four decimal places, if necessary. 2-ln(5-x)=0 ---- ln(5-x) = 0 5-x = e^0 5-x = 1 x = 4 ================ Cheers, Stan H. ================
 logarithm/308963: Write the equation in logarithmic form. 1 solutions Answer 220901 by stanbon(57962)   on 2010-05-26 21:50:52 (Show Source): You can put this solution on YOUR website!6^4 = 1296 --- base = 6 exponent = 4 result = 1296 ---- Log Form: log6(1296) = 4 ========================== Cheers, Stan H. ==========================
 Subset/308958: How Do You Write 123.9621 And 22,309,870 In Words ?1 solutions Answer 220898 by stanbon(57962)   on 2010-05-26 21:45:29 (Show Source): You can put this solution on YOUR website!Write 123.9621 And 22,309,870 In Words ? ------ one-hundred twenty-three and nine thousand six hundred and twenty-one ten-thousanths ================================== twenty-two million, three hundred nine thousand, eight hundred and seventy. ========================================== Cheers, Stan H.
 Square-cubic-other-roots/308955: Please can you help me simplify this expression....I don't know what to do with the number outside the square root sign.... Thank you my name is Daniel and I'm in the 9th grade.... 10 square root of (5/36)1 solutions Answer 220897 by stanbon(57962)   on 2010-05-26 21:36:39 (Show Source): You can put this solution on YOUR website!10 square root of (5/36) ----------------------- = 10 --- = 10/6 --- = (10/6)sqrt(5) --- = (5/3)sqrt(5) ========================= Cheers, Stan H.
 Permutations/307812: Find the coefficient of b^5 in the expansion of (a-2b)^8 My answer = 1 Not sure if thats right. If you could show me the steps to solving this problem it would be much appreciated. Thank You. :)1 solutions Answer 220884 by stanbon(57962)   on 2010-05-26 21:05:12 (Show Source): You can put this solution on YOUR website!Find the coefficient of b^5 in the expansion of (a-2b)^8 ---------------- 8C3(a^3)(-2b)^5 --- = [(8*7*6)/(1*2*3)](a^3)(-32)b^5 --- = 56*(-32)a^3b^5 --- = -1792a^3b^5 ====================== Cheers, Stan H.
 Permutations/308851: An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice cream is always scooped before the toppings are added. In how many distinct ways can the serving be assembled? Also if the customer wants three different flovors of ice cream how many choices does he have?1 solutions Answer 220880 by stanbon(57962)   on 2010-05-26 20:56:33 (Show Source): You can put this solution on YOUR website!An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice cream is always scooped before the toppings are added. In how many distinct ways can the serving be assembled? --- ways to assemble the 3 scoops of ice cream: 5 ways to pick the 1st scoop 5 ways to pick the 2nd scoop 5 ways to pick the 3rd scoop Total ways: 5^3 = 125 ------------------------------ ways to assemple the 3 scoops of toppings: 3*3*3 = 27 ------------------------------- Total assemblies: 125*27 = 3375 ================================================== Also if the customer wants three different flavors of ice cream how many choices does he have? 5*4*3 = 60 choices ================================================== Cheers, Stan H.
 Permutations/308927: how many distinct arrangements can be made with the letter in the word TALLAHASSEE [A] 286 [B] 1,663,200 [c] 831,600 [d] 834,040 1 solutions Answer 220875 by stanbon(57962)   on 2010-05-26 20:45:34 (Show Source): You can put this solution on YOUR website!how many distinct arrangements can be made with the letter in the word TALLAHASSEE ------------------ # of arrangements = 11!/(3!*2!*2!*2!) = 831,600 =================== Cheers, Stan H. =================== [A] 286 [B] 1,663,200 [c] 831,600 [d] 834,040