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Recent problems solved by 'stanbon'

stanbon answered: 57146 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, >>Next

Rectangles/386955: 1) A rectangular storage unit has dimensions of : 1m , 2m, 3m. If each linear dimension is increased by the same amount. a) What increase would result in a new storage unit with a volume of 10 times the orginal? b) How many possible solutions are there to this problem? c) Sketch the graph of the information presented in this problem. Show how the zeros of the function relate to the answer. 1 solutions Answer 273497 by stanbon(57214)   on 2010-12-16 07:01:22 (Show Source): You can put this solution on YOUR website! duplicate

Geometry_Word_Problems/386954: 1) A rectangular storage unit has dimensions of : 1m by 2m by 3m. If each linear dimension is increased by the same amount. a) What increase would result in a new storage unit with a volume of 10 times the orginal? b) How many possible solutions are there to this problem? c) Sketch the graph of the information presented in this problem. Show how the zeros of the function relate to the answer. 1 solutions Answer 273496 by stanbon(57214)   on 2010-12-16 07:00:12 (Show Source): You can put this solution on YOUR website! 1) A rectangular storage unit has dimensions of : 1m by 2m by 3m. If each linear dimension is increased by the same amount. Old Volume 1*2*3 = 6 cubic meters New VOlume (x+1)(x+2)(x+3) cubic meters ----- a) What increase would result in a new storage unit with a volume of 10 times the orginal? Solve (x+1)(x+2)(x+3) = 10*6 I graphed the left side and the right side separately and found the x-value of the point of intersection. Ans: x = 2 ------------ b) How many possible solutions are there to this problem? Ans: One Real Number answer. ------------ c) Sketch the graph of the information presented in this problem. Show how the zeros of the function relate to the answer. Graph: (x+1)(x+2)(x+3)-60 = y x=2 is the only Real Number zero. ======= Cheers, Stan H. =======

Mixture_Word_Problems/386956: A PERSON DRIVES 800 MILES IN A DAY AND A HALF. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE TO DRIVE 2000 MILES. 1 solutions Answer 273495 by stanbon(57214)   on 2010-12-16 06:46:18 (Show Source): You can put this solution on YOUR website! A PERSON DRIVES 800 MILES IN A DAY AND A HALF. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE TO DRIVE 2000 MILES. ---- Use a proportion: days/distance = days/distance ------ Solve: x/2000 = 3.5/800 --- x = 2000(3.5)/800 x = 8.75 days ========================= Cheers, Stan H. ==============

Probability-and-statistics/386927: If a class has 34 students of which 12 are female and the rest are male. (a) We wish to form a committee of 6 people from the students. How many distinct committees can be formed? b) If there is a restriction that the committee has to be 3 male and 3 female. Now how many distinct committees can we form? Thank-you in advance. 1 solutions Answer 273494 by stanbon(57214)   on 2010-12-16 06:41:59 (Show Source): You can put this solution on YOUR website! If a class has 34 students of which 12 are female and the rest are male. (a) We wish to form a committee of 6 people from the students. How many distinct committees can be formed? Ans: 34C6 = 1,344,904 ================================== b) If there is a restriction that the committee has to be 3 male and 3 female. Now how many distinct committees can we form? # of ways to pick 3 male: 22C3 # of ways to pick 3 female: 12C3 ----- # of ways to pick 3male and 3femaile = 22C3*12C3 = 338,800 ================ Cheers, Stan H.

Rational-functions/386959: find the domain of the function 1 solutions Answer 273493 by stanbon(57214)   on 2010-12-16 06:28:58 (Show Source): You can put this solution on YOUR website! find the domain of the function Q(x)=(-x)(1-x)/(3x^2+2x-2) ---- Solve 3x^2+2x-2 = 0 x = [-2 +- sqrt(4-4*3*-2)]/6 --- x = [-2 +- sqrt(28)]/6 --- x = [-2 +- 2sqrt(7)]/6 --- x = (-1/3) + (1/3)sqrt(7) or x = (-1/3)-(1/3)sqrt(7) ---- Domain is All Real Numbers except those two values. =============== Cheers, Stan H.

Linear-equations/386966: The solution set for the system 6x + 9y = 15 is best described as follows: 4x + 6y = 10 a.undefined b.x=1. y=1 c. {(x,y)|y= (-2/3)x + (5/3)} d. inconsistent e. set of all points 1 solutions Answer 273492 by stanbon(57214)   on 2010-12-16 06:23:57 (Show Source): You can put this solution on YOUR website! The solution set for the system 6x + 9y = 15 4x + 6y = 10 is best described as follows: ----- slope of the 1st is -2/3 ; intercept = 5/3 slope of the 2nd is -2/3 ; intercept = 5/3 ----- Ans: The two equations are the same line. The answer is "c". ======================= Cheers, Stan H. ==================== a.undefined b.x=1. y=1 c. {(x,y)|y= (-2/3)x + (5/3)} d. inconsistent e. set of all points

logarithm/386968: log 81^x=1/4 1 solutions Answer 273491 by stanbon(57214)   on 2010-12-16 06:20:16 (Show Source): You can put this solution on YOUR website! log 81^x=1/4 ---- base = 10 exponent = 1/4 result = 81^x ---- Write in exponential form: 10^(1/4) = 81^x --- 81^x = 1.7783 --- Take the log of both sides to get: x*log(81) = log(1.7783) --- x = log(1.7783)/log(81) x = 0.1310 ================ Cheers, Stan H.

Quadratic_Equations/386970: The width of a rectangle is 3cm less than its length. The rectangle has area of 40cm^2. What is the length of the rectangle? Please help Im not very good at word problems!! 1 solutions Answer 273490 by stanbon(57214)   on 2010-12-16 06:14:42 (Show Source): You can put this solution on YOUR website! The width of a rectangle is 3cm less than its length. The rectangle has area of 40cm^2. What is the length of the rectangle? ------ Let length be "x": Then width is "x-3": --- Area = length * width 40 = x(x-3) x^2-3x-40 = 0 (x-8)(x+5) = 0 Positive solution: x = 8 cm (length) x-3 = 5 cm (width) ------------ Cheers, Stan H. =============

Rational-functions/386971: Hi, Can someone please help me with this. Thanks y = + square root (2x-3) Explain the why this is a function State the domain and range 1 solutions Answer 273489 by stanbon(57214)   on 2010-12-16 06:08:42 (Show Source): You can put this solution on YOUR website! y = + square root (2x-3) Explain the why this is a function State the domain and range ------------------------- That "plus" sign in front of the square root says you are only going to have one y-value for each value of sqrt(2x-3). That makes it a function. ------ Domain: 2x-3 must be non-negative. Solve 2x-3>=0 x >= 3/2 Domain: All Real Numbers >= 3/2 ----- Range: Since y is never negative, Range: All Real Numbers >= 0 ========== Cheers, Stan H.

logarithm/386972: The number of bacteria is growing exponentially. If the number of bacteria rises from 100 to 350 in 6.5hours, how many bacteria will there be after 14 hours? Please help!! 1 solutions Answer 273488 by stanbon(57214)   on 2010-12-16 06:01:32 (Show Source): You can put this solution on YOUR website! The number of bacteria is growing exponentially. If the number of bacteria rises from 100 to 350 in 6.5hours, how many bacteria will there be after 14 hours? ----- Exponential Form: y = ab^x 350 = 100*b^6.5 --- b^6.5 = 3.5 6.5log(b) = log(3.5) log(b) = [log3.5]/6.5 = 0.0837 --- b = 10^0.0837 b = 1.2126 ====== Equation: f(x) = 100*1.2126^x --how many bacteria will there be after 14 hours? f(14) = 100*1.2126^14 f(14) = 1485.34 Rounding down you get f(14) = 1485 ----------------- Cheers, Stan H.

Probability-and-statistics/386860: Choose a person at random and give him or her an iq test. the score y has the normal distribution with mean=100 and standard deviation=15. the probability that the person chosen has an iq score higher than 120 is what? 1 solutions Answer 273426 by stanbon(57214)   on 2010-12-15 22:09:48 (Show Source): You can put this solution on YOUR website! Choose a person at random and give him or her an iq test. the score y has the normal distribution with mean=100 and standard deviation=15. the probability that the person chosen has an iq score higher than 120 is what? -------------- z(120) = (120-100)/15 = 1.3333.. --- P(x > 120) = P(z > 1.3333..) = 0.0912 ========================================== Cheers, Stan H.

Polynomials-and-rational-expressions/386865: the answer to 98x-2x to the 5 power by factoring 1 solutions Answer 273422 by stanbon(57214)   on 2010-12-15 22:03:13 (Show Source): You can put this solution on YOUR website! the answer to 98x-2x to the 5 power by factoring -------------- 98x - 2x^5 ---- Factor: 2x(49 - x^4) --- 2x(7+x^2)(7+x)(7-x) ======================================== Cheers, Stan H.

Expressions-with-variables/386863: please help me to resoolve this equivalence 20 - 4/5x≥ 16 1 solutions Answer 273420 by stanbon(57214)   on 2010-12-15 21:59:09 (Show Source): You can put this solution on YOUR website! 20 - (4/5)x ≥ 16 --- 4 - (4/5)x >= 0 4 >= (4/5)x 20 >= 4x 5 >= x x <= 5 =========================== cheers, Stan H.

absolute-value/386867: /-3-/-7-7// 1 solutions Answer 273419 by stanbon(57214)   on 2010-12-15 21:53:06 (Show Source): You can put this solution on YOUR website! /-3-/-7-7// --------------- Work from the inside to the outside. = |-3-|-14|| --- = |-3-14| --- = |-17| --- = 17 ============ Cheers, Stan H.

Probability-and-statistics/386771: A European energy company is exploring the feasibility of a wind turbine at a specific location. It randomly sampled the peak wind speeds at this location over 27 days. Below are the peak wind speeds (in meters/sec) over the 27 sampled days. 1.1 1.4 1.6 1.6 2.7 3.7 3.9 4.1 4.9 5 6.5 6.7 7 7.3 8 8.2 8.5 8.5 8.6 8.7 9.1 9.5 10.4 10.7 12.5 14.2 14.9 From this data, find the sample mean, median, mode and midrange for peak wind speed. Round each to the nearest tenth if necessary. Include units with each answer Can some one please help me with this question please 1 solutions Answer 273413 by stanbon(57214)   on 2010-12-15 21:20:17 (Show Source): You can put this solution on YOUR website! 1.1 1.4 1.6 1.6 2.7 3.7 3.9 4.1 4.9 5 6.5 6.7 7 7.3 8 8.2 8.5 8.5 8.6 8.7 9.1 9.5 10.4 10.7 12.5 14.2 14.9 From this data, find the sample mean:::7.011 median:::7.3 mode::::: 1.6 midrange for peak wind speed. min = 1.1 ; max = 14.9 mid-range = (1.1+14.9)/2 = 8 ============ Cheers, Stan H.

Probability-and-statistics/386802: In the tests of a new pharmaceutical product, data were collected for use in the approval process required by the U.S. Food and Drug Administration (FDA). Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data are shown in the following table: Drug: No Help 22 Help 47 Placebo: No Help 31 Help 20 What is the probability that: a. the participants perceived that their “medication” helped if they received the drug? b. the participants perceived that their “medication” helped if they received the placebo? c. the participants perceived that their “medication” helped? 1 solutions Answer 273408 by stanbon(57214)   on 2010-12-15 21:03:59 (Show Source): You can put this solution on YOUR website! Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data are shown in the following table: Drug: No Help 22 Help 47 Placebo: No Help 31 Help 20 What is the probability that: a. the participants perceived that their “medication” helped if they received the drug? Ans: 47/69 ---------------------- b. the participants perceived that their “medication” helped if they received the placebo? Ans: 20/51 ---------------------- c. the participants perceived that their “medication” helped? Ans: 67/120 ================== Cheers, Stan H.

Probability-and-statistics/386819: For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made. The average age of graduating seniors is at least 18 years old 1 solutions Answer 273404 by stanbon(57214)   on 2010-12-15 20:47:44 (Show Source): You can put this solution on YOUR website! For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made. The average age of graduating seniors is at least 18 years old ----------------- Ho: u >= 18 (claim) Ha: u < 18 =================== Cheers, Stan H.

Probability-and-statistics/386700: A weighted coin is tossed four times. The probability for the number if heads observed is given below # heads Probability 0 .4096 1 .4096 2 .1536 3 .0256 4 .0016 What is the probability of getting at least ones head? 1 solutions Answer 273400 by stanbon(57214)   on 2010-12-15 20:38:26 (Show Source): You can put this solution on YOUR website! A weighted coin is tossed four times. The probability for the number if heads observed is given below # heads Probability 0 .4096 1 .4096 2 .1536 3 .0256 4 .0016 What is the probability of getting at least ones head? --- P(at least one head) = 1 - P(no head) = 1 - 0.4096 = 0.5904 ============ Cheers, Stan H.

Equations/386781: How do I figure out 3 X 7(to the 10th meter)? 1 solutions Answer 273382 by stanbon(57214)   on 2010-12-15 19:50:44 (Show Source): You can put this solution on YOUR website! How do I figure out 3 X 7(to the 10th meter)? --- 3*7^10 = 847,425,747 meters ============================ Cheers, Stan H.

absolute-value/386791: |x-1|=5 1 solutions Answer 273380 by stanbon(57214)   on 2010-12-15 19:47:52 (Show Source): You can put this solution on YOUR website! |x-1|=5 x-1 = 5 or x-1 = -5 x = 6 or x = -4 ======================== Cheers, Stan H.

logarithm/386787: how do you solve this? please give step by step instructions. logx(2x-3)=1 1 solutions Answer 273378 by stanbon(57214)   on 2010-12-15 19:46:32 (Show Source): You can put this solution on YOUR website! logx(2x-3)=1 --- base = x exponent = 1 result = 2x-3 ---- Write in exponential form: x^1 = (2x-3) x = 2x-3 x = 3 ----------------- Cheers, Stan H. ==============

Linear-systems/386782: I am not sure if I am posting this in the right place, but I do not know how to solve this...please help! Find the distance between the two points. Round an approximate result to the nearest hundredth. (-4, -1) and (-8, -4) 1 solutions Answer 273376 by stanbon(57214)   on 2010-12-15 19:44:16 (Show Source): You can put this solution on YOUR website! Find the distance between the two points. Round an approximate result to the nearest hundredth. (-4, -1) and (-8, -4) ----- dist = sqrt[(-8--4)^2 + (-4--1)^2] --- dist = sqrt[16 + 9] --- dist = 5 ============== Cheers, Stan H.

Linear-systems/386783: I guess this is similar to one I just asked, but I do not get how to approach this: Find the midpoint of the line segment having the given endpoints. 9) (8, -4) and (-7, 8) 1 solutions Answer 273375 by stanbon(57214)   on 2010-12-15 19:41:41 (Show Source): You can put this solution on YOUR website! Find the midpoint of the line segment having the given endpoints. (8, -4) and (-7, 8) --- If (x,y) is the midpoint: x = (-7+8)/2 = 1/2 y = (-4+8)/2 = 2 --- midpoint: (1/2 , 2) ====================== cheers, Stan H.

Polynomials-and-rational-expressions/386785: I have a word problem to solve but not sure if I did it right. I may have used the wrong formula. Please show me the correct formula steps to solving this question?......................I got the answer 4 x 9 but do not think it is correct. The area of a rectangle is 14 square meters. Find the length and width of the rectangle if its length is 5 meters greater than its width. Use an equation and the formula for the Area of a rectangle= (width)(length). 1 solutions Answer 273372 by stanbon(57214)   on 2010-12-15 19:38:30 (Show Source): You can put this solution on YOUR website! The area of a rectangle is 14 square meters. Find the length and width of the rectangle if its length is 5 meters greater than its width. Use an equation and the formula for the Area of a rectangle= (width)(length). ---- Let the width be "x" meters. Then the length is "x+5" meters. ---- Equation: A = w*L 14 = x(x+5) 14 = x^2+5x x^2+5x-14 = 0 Factor: (x+7)(x-2) = 0 x = -7 of x = 2 --- Only the positive solution is meaningful. width = 2 meters length = 7 meters =================== Cheers, Stan H.

Polynomials-and-rational-expressions/386776: Please help me with these problems. I need help with the steps to getting the answer.I am studying for a test tomorrow.Thank you for your help. Solve for X x- 7 )(5x + 2) = 0 X^2 + 3x – 28 = 0 1 solutions Answer 273367 by stanbon(57214)   on 2010-12-15 19:32:41 (Show Source): You can put this solution on YOUR website! Please help me with these problems. I need help with the steps to getting the answer.I am studying for a test tomorrow.Thank you for your help. Solve for X (x-7)(5x + 2) = 0 If that product is zero, one of those factors must be zero. Solve: x-7 = 0 or 5x+2 = 0 x = 7 or x = -2/5 ---------------------------- X^2 + 3x – 28 = 0 Factor to get: (x+7)(x-3) = 0 Solve: x+7 = 0 or x-3 = 0 x = -7 or x = 3 =========================== Cheers, Stan H.

Age_Word_Problems/386766: Grant is five times as old as Francis. One third of the sum of their ages is equal to 32. Find their ages. 1 solutions Answer 273360 by stanbon(57214)   on 2010-12-15 19:23:59 (Show Source): You can put this solution on YOUR website! Grant is five times as old as Francis. One third of the sum of their ages is equal to 32. Find their ages. ----------------------------------- Equations: g = 5f (1/3)(g+f) = 32 --- Rearrange: g=5f g+f = 96 ---- Substitute for "g" and and solve for "f": 5f + f = 96 6f = 96 f = 16 (Francis' age now) --- Since g = 5f, g = 5*16 = 80 (Grant's age now) ================================================ Cheers, Stan H.

Probability-and-statistics/386764: Find the probability of selecting 5 math books and 4 history books from a stack that contains 6 math books and 4 history books if the books are selected at random. 1 solutions Answer 273356 by stanbon(57214)   on 2010-12-15 19:16:29 (Show Source): You can put this solution on YOUR website! Find the probability of selecting 5 math books and 4 history books from a stack that contains 6 math books and 4 history books if the books are selected at random. ------------------ # of ways to succeed: # of ways to select 5 math: 6C5 = 6 # of ways to select 4 hist: 4C4 = 1 ---- # of ways to succeed: 6*1 = 6 ---------------- # of ways to select 9 books randomly: 10C9 = 10 ----- P(selecting 5 math and 4 hist) = 6/10 = 3/5 ============================================ Cheers, Stan H.

Age_Word_Problems/386758: Mona's age is 4 times Bailey's age. The sum of their ages is 15. Find the age of each. 1 solutions Answer 273353 by stanbon(57214)   on 2010-12-15 19:12:34 (Show Source): You can put this solution on YOUR website! Mona's age is 4 times Bailey's age. The sum of their ages is 15. Find the age of each. --------------------- Equations: m = 4b m+b = 15 ---- Substitute for "m" and solve for "b": 4b + b = 15 5b = 15 b = 3 (Bailey's age now) --- Since m = 3b, m = 3*3 = 9 (Mona's age now) =========================== Cheers, Stan H.

Triangles/386754: The side is 10 in. and the acute angle is 37 degrees. How to find the perimeter of the triangle? 1 solutions Answer 273349 by stanbon(57214)   on 2010-12-15 19:09:42 (Show Source): You can put this solution on YOUR website! Not enough information.

Linear-equations/386756: What is the start value for the table? x|y 0|3 1|9 2|15 1 solutions Answer 273348 by stanbon(57214)   on 2010-12-15 19:07:40 (Show Source): You can put this solution on YOUR website! What is the start value for the table? x|y 0|3 1|9 2|15 ---- Not sure what you mean by start value, but the equation the equation is y = 6x+3 ----- Cheers, Stan H.

Probability-and-statistics/386745: 34% of people in the US have type A+ blood. You randomly select 73 people in the US and ask them if their blood type is A+. A. Use the binomial formula to calculate the probability that between 9 and 12 people (inclusive will say they have A+ blood. B. Find the probability that at least 30 of these people will say they have A+ blood. 1 solutions Answer 273346 by stanbon(57214)   on 2010-12-15 19:04:46 (Show Source): You can put this solution on YOUR website! 34% of people in the US have type A+ blood. You randomly select 73 people in the US and ask them if their blood type is A+. --- Binomial Problem with n = 73 and p = 0.34 ----- A. Use the binomial formula to calculate the probability that between 9 and 12 people (inclusive will say they have A+ blood. P(9<= x <=12) = binomcdf(73,0.34,12)-binomcdf(73,0.34,8) = 0.0006644 ---------------------------------------------------------- B. Find the probability that at least 30 of these people will say they have A+ blood. P(30<= x <=73) = 1 - P(73,0.34,29) = 0.1245 ================================================ Cheers, Stan H.