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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Functions/734767: Use the functions to answer the question. f(x)=x^2+3; g(x)=x-7 Which is equal to (f + g)(x)?1 solutions Answer 449121 by stanbon(57219)   on 2013-04-07 13:01:09 (Show Source): You can put this solution on YOUR website!Just add f(x) and g(x) Cheers, Stan H. ============
 Evaluation_Word_Problems/734765: Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7 | ONLY AN ALGEBRAIC SOLUTION WILL BE ACCEPTED?|1 solutions Answer 449120 by stanbon(57219)   on 2013-04-07 12:58:22 (Show Source): You can put this solution on YOUR website!Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7 ------------------ 1st: 2x-3 2nd: 2x-1 3rd: 2x+1 ------- Equation: (2x-3)^2 = 2(2x+1)+7 ------ 4x^2 -12x + 9 = 4x+9 --- 4x^2 -16x = 0 Factor: 4x(x-4) = 0 x = 0 or x = 4 ---- If x = 0:: 1st: -3 2nd: -1 3rd: 1 ---- If x = 4 1st: 5 2nd: 7 3rd: 9 ----- Since you want positive odd only the x=4 set is acceptable. ===================== Cheers, Stan H. =====================
 Functions/734761: Use the function to answer the question. f(x) = 10x-5 What is the value of f –1(–4)?1 solutions Answer 449118 by stanbon(57219)   on 2013-04-07 12:53:40 (Show Source): You can put this solution on YOUR website!Use the function to answer the question. f(x) = 10x-5 What is the value of f –1(–4)? ---- Find the value of x which makes y = -4 ---- Solve 10x-5 = -4 10x = 1 x = 1/10 ----- Therefore f^(-1)(-4) = 1/10 --------------------------- Cheers, Stan H.
 Functions/734764: Use the functions to answer the question. f(x) = 2x+5;g(x)=3x^2 Which is equal to (f°g)(x)?1 solutions Answer 449117 by stanbon(57219)   on 2013-04-07 12:48:54 (Show Source): You can put this solution on YOUR website!Use the functions to answer the question. f(x) = 2x+5;g(x)=3x^2 Which is equal to (f°g)(x)? --------- fog(x) = f[g(x)] = f[3x^2] = 2(3x^2)+5 = 6x^2+5 ================= Cheers, Stan H.
 Mixture_Word_Problems/734624: in a chemical process, the temperature T is to be kept within 10 C of 100 C. Express this restriction as an absolute value inequality. 1 solutions Answer 449061 by stanbon(57219)   on 2013-04-06 23:33:41 (Show Source): You can put this solution on YOUR website!in a chemical process, the temperature T is to be kept within 10 C of 100 C. Express this restriction as an absolute value inequality. ------- |T-100| <= 10 ===================== Cheers, Stan H.
 Linear-equations/734625: Find a linear equation in the form y=mx+b that models the quantity y after x days. a. A quantity y is initially 750 and increases at a rate of 4 per day b. A quantity is initially 2300 and decreases at a rate of 50 per day c.A quantity y is initially 17, 875 and remains constant 1 solutions Answer 449060 by stanbon(57219)   on 2013-04-06 23:31:04 (Show Source): You can put this solution on YOUR website!Find a linear equation in the form y=mx+b that models the quantity y after x days. a. A quantity y is initially 750 and increases at a rate of 4 per day Y = 4x + 750 ------------------ b. A quantity is initially 2300 and decreases at a rate of 50 per day y = -50x + 2300 --------------------------- c.A quantity y is initially 17,875 and remains constant y = 17,875 ========================== Cheers, Stan H.
 Expressions-with-variables/734618: show me how to simplify this expression 2y 5 -------- + ----- y(2y - 1) 2y - 11 solutions Answer 449059 by stanbon(57219)   on 2013-04-06 23:23:33 (Show Source): You can put this solution on YOUR website!show me how to simplify this expression 2y 5 -------- + ----- y(2y - 1) 2y - 1 ------- least common denominator: y(2y-1) ----- Rewrite both fractions with the lcm as the denominator: ----- [2y/lcm] + [5y/lcm] ---- Combine the numerators over the lcm: = 7y/(y(2y-1)) ---- Cancel the common "y" factor: ---- = 7/(2y-1) =================== Cheers, Stan H. ===========================
 Numbers_Word_Problems/734620: translate five times a number is nine less than the triple the number1 solutions Answer 449057 by stanbon(57219)   on 2013-04-06 23:03:46 (Show Source): You can put this solution on YOUR website! translate five times a number is nine less than the triple the number ------- Equation: 5x = 3x-9 2x = -9 x = -9/2 ============== Cheers, Stan H. ===================
 Probability-and-statistics/734579: Please help with this question. Question: There are 8 light switches on the wall that connect to 8 different color lights inside the room. Each switch can either be in the on position or off position. a.) How many different lighting configurations are possible? b.) If you wanted to turn 3 of the lights on, how many choices of 3 lights could you make? c.) If you needed to pick one light to use for an event on Thursday and another light for an event on Tuesday, how many choices for the two lights could you make? 1 solutions Answer 449041 by stanbon(57219)   on 2013-04-06 20:59:08 (Show Source): You can put this solution on YOUR website!Question: There are 8 light switches on the wall that connect to 8 different color lights inside the room. Each switch can either be in the on position or off position. a.) How many different lighting configurations are possible? Ans: 2^8 = 256 ------------------------------ b.) If you wanted to turn 3 of the lights on, how many choices of 3 lights could you make? Ans: 8C3 = (8*7*6)/(1*2*3) = 56 ------------------------------ c.) If you needed to pick one light to use for an event on Thursday and another light for an event on Tuesday, how many choices for the two lights could you make? 8*2 = 56 if order makes a difference ---- 8C2 = 28 if order does not make a difference ================= Cheers, Stan H.
 Probability-and-statistics/734582: Please help. I'm not understanding this questions The scores on a national test were normally distributed with a mean of 83 and a standard deviation of 8 To the nearest percent, what percentage of test takers scored between 70 and 90 15% of test takers scored below what test score? (Round to nearest test score)1 solutions Answer 449039 by stanbon(57219)   on 2013-04-06 20:51:46 (Show Source): You can put this solution on YOUR website!The scores on a national test were normally distributed with a mean of 83 and a standard deviation of 8 To the nearest percent, what percentage of test takers scored between 70 and 90 z(70) = (70-83)/8 = -13/8 z(90) = (90-83)/8 = 7/8 ----- P(70< x <90) = P(-13/8 < z < 7/8) = normalcdf(-13/8,7/8) = 0.7571 = 75.71% ========================= 15% of test takers scored below what test score? (Round to nearest test score) Draw the picture: Find the z-score with a left tail of 15% invNorm(0.15) = -1.0364 ----- Find the corresponding score value: x = z*s + u x = -1.0364*8+83 = 74.71 ============================== Cheers, Stan H.
 Linear-equations/734578: What is the Equation of a line containing these points? (4,5) and (12,11)1 solutions Answer 449036 by stanbon(57219)   on 2013-04-06 20:33:06 (Show Source): You can put this solution on YOUR website!What is the Equation of a line containing these points? (4,5) and (12,11) ----------------- slope = (11-5)/(12-4) = 6/8 = 3/4 ------- Form: y = mx + b Solve for "b": 5 = (3/4)4 + b b = 2 ----- Equation: y = (3/4)x + 2 ======================= Cheers, Stan H. =======================
 Numeric_Fractions/734574: What is 2 3/8 divided by 1/41 solutions Answer 449035 by stanbon(57219)   on 2013-04-06 20:28:23 (Show Source): You can put this solution on YOUR website!What is 2 3/8 divided by 1/4 ------ = [(8*2+3)/8] / [1/4] -------- = (19/8) / (1/4) -------- Invert the denominator and multiply: ------ = (19/8) * (4/1) ----- = 19/2 ============= Cheers, Stan H. =============
 Quadratic_Equations/734575: need help with quadratic equation such as x^2 + 12x -64 = 0 x2 - 2x - 13 = 01 solutions Answer 449033 by stanbon(57219)   on 2013-04-06 20:22:13 (Show Source): You can put this solution on YOUR website!need help with quadratic equation such as x^2 + 12x -64 = 0 x2 - 2x - 13 = 0 ---- Use the quadratic formla: x = [-b +- sqrt(b^2-4ac)]/(2a) ======== Cheers, Stan H. ===========================
 Inequalities/734576: Select the values of x that are solutions to the inequality 0 > x^2 + 5x -21 solutions Answer 449032 by stanbon(57219)   on 2013-04-06 20:20:18 (Show Source): You can put this solution on YOUR website!Select the values of x that are solutions to the inequality 0 > x^2 + 5x -2 ---------- The parabola opens up. Find the x-intercepts: x = [-5 +- sqrt(25-4*-2)]/2 x = [-5+sqrt(33)]/2 or x = [-5-sqrt(33)]/2 ------- The solution set is the x-values between those two x-intercepts. ------- Cheers, Stan H. ==================
 Exponential-and-logarithmic-functions/734573: The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following. S = 10(1 – e^kx) When \$450 is spent on advertising 2600 units are sold. solve for k. Estimate the number of units that will be sold if advertising expenditures are raised to \$5501 solutions Answer 449031 by stanbon(57219)   on 2013-04-06 20:11:29 (Show Source): You can put this solution on YOUR website! The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following. S = 10(1 – e^(kx)) ----------------------------------- When \$450 is spent on advertising 2600 units are sold. solve for k. 450 = 10(1-e^(26k) ---- 45 = 1-e^(26k) e^(26k) = -44 --- Note: No power of e can result in a negative result. So, can't solve for "k". Cheers, Stan H. --------------------------------------------------------- Estimate the number of units that will be sold if advertising expenditures are raised to \$550
 Rational-functions/734401: Simplify the complex fraction. 1) 2x+12/3x-15/2x^2-6x-20/x^2-10x+25 thanks! 1 solutions Answer 448915 by stanbon(57219)   on 2013-04-06 10:59:03 (Show Source): You can put this solution on YOUR website!2x+12/3x-15/2x^2-6x-20/x^2-10x+25 Factor: [2(x+6)/3(x-5)]/[2(x-5)(x+2)/(x-5)^2] ------------------------ Invert the denominator and multiply: [2(x+6)/3(x-5)]*{(x-5)^2/[2(x-5)(x+2)]} ------- [2(x+6)/3] * {(x-5)^2/[2(x-5)^2*(x+2)]} --------- Cancel 2,(x-5)^2 to get: ------------------------------- [(x+6)/3]*{1/[(x+2)} ----- = (x+6)/[3(x+2)] ===================== Cheers, Stan H.
 Finance/734396: an investor invested a total of \$2300 in two mutual funds. one fund earned a 7% profit while the other earned a 2% profit. if the investors total profit was \$66, how much was invested in each mutual fund? 1 solutions Answer 448914 by stanbon(57219)   on 2013-04-06 10:48:58 (Show Source): You can put this solution on YOUR website!an investor invested a total of \$2300 in two mutual funds. one fund earned a 7% profit while the other earned a 2% profit. if the investors total profit was \$66, how much was invested in each mutual fund? -------- Quantity Equation: a + b = 2300 dollars Profit Equation: 7a +2b = 6600 -------- Multiply Quantity Eq through by 2: 2a + 2b = 2*2300 7a + 2b = 6600 ------------------- Subtract and solve for "a": 5a = 2000 a = \$500.00 (amt invested at 7% ---- b = 2300-500 = \$1800.00 (amt invested at 2%) ============================================== Cheers, Stan H.
 Numeric_Fractions/734397: can you please help me with this problem the expression 8m+5 represents the total cost in dollars, including shipping, for a certain number of music CD's, m. based on the expression .what is the total coast for 4 CDs1 solutions Answer 448913 by stanbon(57219)   on 2013-04-06 10:42:30 (Show Source): You can put this solution on YOUR website!the expression 8m+5 represents the total cost in dollars, including shipping, for a certain number of music CD's, m. based on the expression .what is the total coast for 4 CDs ------- Since 8m+5 is the cost of "m" CD, the cost of 4 CDs is 8*4+5 = 32+5 = \$37.00 ==================== Cheers, Stan H. ====================
 Surface-area/734377: Please help me solve this equation: it is very important I try it a lot of times and the answers are never the same and thank u for your time A rectangle is divided into nine squares regions, all are different in size. The area of square 3 is 64 cm2. And the area of square 5 is 81 cm2. What would be the area of the rectangle? 1 solutions Answer 448908 by stanbon(57219)   on 2013-04-06 09:33:28 (Show Source): You can put this solution on YOUR website!We would have to see the picture to help you with this problem. Cheers, Stan H. ==========
 Square-cubic-other-roots/734378: Find two roots of (x-30^2=25 without changing (x-3)^2 to a trinomial.1 solutions Answer 448907 by stanbon(57219)   on 2013-04-06 09:31:12 (Show Source): You can put this solution on YOUR website!Find two roots of (x-3)^2=25 without changing (x-3)^2 to a trinomial. ----- (x-3)^2 - 5^2 = 0 ---- The form is the "difference of squares". Factor: (x-3-5)(x-3+5) = 0 (x-8)(x+2) = 0 x = 8 or x = -2 ======================== Cheers, Stan H. ===================
 Money_Word_Problems/734385: A man invests a total of in two savings accounts. One account yields 9% simple interest and the other 10% simple interest. He earned a total of interest for the year. How much was invested in the 9% account?1 solutions Answer 448905 by stanbon(57219)   on 2013-04-06 09:27:49 (Show Source): You can put this solution on YOUR website!The interest quantity is missing from your post. Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/734381: 2p2 -15p + 25 = A man bought a shirt at a sale. He saves \$30 on the normal price when he paid \$120 for the shirt. What was the percentage discount on the shirt?1 solutions Answer 448904 by stanbon(57219)   on 2013-04-06 09:26:10 (Show Source): You can put this solution on YOUR website!2p2 -15p + 25 = 2p^2-10p-5p + 25 ------- = 2p(p-5)-5(p-5) = (p-5)(2p-5) =========================== A man bought a shirt at a sale. He saves \$30 on the normal price when he paid \$120 for the shirt. What was the percentage discount on the shirt? original price 120+30 = 150 Quantity discount: 30 Percent discount: 30/150 = 1/5 = 20% ======================================= Cheers, Stan H. =============
 Probability-and-statistics/734380: If you have a sample data set that is normally distributed with a mean of 41 and a standard deviation of 7.25. What is the median of this distribution?1 solutions Answer 448903 by stanbon(57219)   on 2013-04-06 09:21:53 (Show Source): You can put this solution on YOUR website!If you have a sample data set that is normally distributed with a mean of 41 and a standard deviation of 7.25. What is the median of this distribution? ---- If the data is normally distributed the mean is the median. ---- Cheers, Stan H.
 Probability-and-statistics/734382: A student scored 483 points on a quiz and the students standard or (z) score was -1. the standard deviation of quiz scores was 12. What was the mean of the quiz score?1 solutions Answer 448902 by stanbon(57219)   on 2013-04-06 09:19:16 (Show Source): You can put this solution on YOUR website!A student scored 483 points on a quiz and the students standard or (z) score was -1. the standard deviation of quiz scores was 12. What was the mean of the quiz score? ----- x = z*s + u --- u = x - z*s u = 483-(-1*12) u = 495 ============== Cheers, Stan H. --------------
 Rate-of-work-word-problems/734330: 2 pipes can fill up a water tank is 6hrs and 40min find the time each will take to fill the tank if one of the two pipes can fill it is 3hrs less than the other1 solutions Answer 448881 by stanbon(57219)   on 2013-04-05 23:06:21 (Show Source): You can put this solution on YOUR website!2 pipes can fill up a water tank is 6hrs and 40min find the time each will take to fill the tank if one of the two pipes can fill it is 3hrs less than the other ----- one pipe: time = x hrs/job ; rate = 1/x job/hr other pipe: time = x-3 hrs/job ; rate = 1/(x-3) job/hr ---- together: time = 6 2/3 hrs/job ; rate = 3/20 job/hr ----- Equation: rate + rate = together rate ---- 1/x + 1/(x-3) = 3/20 --- Multiply thru by 20x(x-3) to get: 20(x-3) + 20x = 3x(x-3) 40x - 60 = 3x^2-9x 3x^2-49x + 60 = 0 ----- (x-15)(3x-4) = 0 --- Usable solution: x = 15 hrs (time for the slower pipe) x-3 = 12 hrs (time for the faster pipe) ================ Cheers, Stan H. ================
 Probability-and-statistics/734286: Suppose that 50% of the women who gave birth at a certain hospital last year were over 30 years old, and that 45% were unmarried. If 55% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30?1 solutions Answer 448878 by stanbon(57219)   on 2013-04-05 22:45:04 (Show Source): You can put this solution on YOUR website!Suppose that 50% of the women who gave birth at a certain hospital last year were over 30 years old, and that 45% were unmarried. If 55% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30? -------------------------------- P(married AND >30) = P(married)+P(>30) - P(married OR >30) --- = 0.45 + 0.50 - 0.55 --- = 0.40 =================== Cheers, Stan H. =============
 Probability-and-statistics/734293: A season of football scores falls in a normal distribution with a mean of 35 and standard deviation of 6. What is the probability that a score was between 29 and 41?1 solutions Answer 448876 by stanbon(57219)   on 2013-04-05 22:38:17 (Show Source): You can put this solution on YOUR website!A season of football scores falls in a normal distribution with a mean of 35 and standard deviation of 6. What is the probability that a score was between 29 and 41? ----- z(41) = (41-35)/6 = 1 z(29) = (29-35)/6 = -1 ------------------------- P(29 < x < 41) = P(-1< z < 1) = normalcdf(-1,1) = 0.6827 ====================== Cheers, Stan H. ======================
 Probability-and-statistics/734326: A psychologist studied self esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5. What is the z-score that cuts off the bottom 10.03% of this distribution? What is the raw score that cuts off the bottom 10.03% of this distribution? Please help me with the steps on how to achieve these answers. Really lost and confused!1 solutions Answer 448873 by stanbon(57219)   on 2013-04-05 22:29:46 (Show Source): You can put this solution on YOUR website!A psychologist studied self esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5. What is the z-score that cuts off the bottom 10.03% of this distribution? Using a TI-84 calculator get invNorm(0.1003 = -1.2798 ------------------------------------------------------------- What is the raw score that cuts off the bottom 10.03% of this distribution? Use the form x = z*s + u to find the raw score x = -1.2798*5 + 50 = 43.6 -------- Cheers, Stan H.
 Miscellaneous_Word_Problems/734320: John is 23 years younger than his dad. His dad is x years old. Write a simplified expression, in terms of x, for the sum of the ages of both John and his dad.1 solutions Answer 448872 by stanbon(57219)   on 2013-04-05 22:23:48 (Show Source): You can put this solution on YOUR website!John is 23 years younger than his dad. His dad is d years old. Write a simplified expression, in terms of d, for the sum of the ages of both John and his dad. --------- Equations: j = d-23 Expression: j + d --- d-23 + d ---- 2d-23 ================ Cheers, Stan H.
 Linear-systems/734325: 8 + 4/x = 9 1/3 need help with some of the steps. Thank you for any help1 solutions Answer 448870 by stanbon(57219)   on 2013-04-05 22:19:15 (Show Source): You can put this solution on YOUR website!8 + 4/x = 9 1/3 ---- 8 + (4/x) = 28/3 -------- Multiply thru by 3x to get: 24x + 12 = 28x 4x = 12 x = 3 -------------- Cheers, Stan H. ==============
 Exponents-negative-and-fractional/734322: How to begin in a problem like this, 4x+3/15 - 2x-3/9 = 6x+4/6 - x . Thank you for any help!1 solutions Answer 448869 by stanbon(57219)   on 2013-04-05 22:12:03 (Show Source): You can put this solution on YOUR website!How to begin in a problem like this, ---------------------- 4x+3/15 - 2x-3/9 = 6x+4/6 - x Multiply thru by 90 to get: ----- 6*(4x+3) - 10(2x-3) = 15(6x+4) - 90x ----- 24x + 18 -20x + 30 = 90x + 60 - 90x ----- 4x + 48 = 60 4x = 12 x = 3 ================ Cheers, Stan H. ================