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# Recent problems solved by 'stanbon'

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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Linear-equations/331046: Could you please Simplify (-5t^3r^3)^4 If you could answer asap that would be great! thankyou!1 solutions Answer 237328 by stanbon(57387)   on 2010-08-11 20:01:46 (Show Source): You can put this solution on YOUR website!Simplify (-5t^3r^3)^4 -------------------- = 625t^12r^9 ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/331047: Solve 9x^2-81=0 1 solutions Answer 237327 by stanbon(57387)   on 2010-08-11 19:59:55 (Show Source): You can put this solution on YOUR website! Solve 9x^2-81=0 ---------------- 9(x^2-9) = 0 Divide by 9 to get: (x^2-9) = 0 Factor: (x-3)(x+3) = 0 x = 3 or x = -3 ---------------- Cheers, Stan H.
 Probability-and-statistics/330976: 1. The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 50 cars is to be selected for a speed study. A) What is the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 50? B) What is the probability that a sample mean will be 69 miles per hour or more? C) What is the probability that the sample mean will be between 65 and 68 miles per hour? 1 solutions Answer 237325 by stanbon(57387)   on 2010-08-11 19:57:36 (Show Source): You can put this solution on YOUR website!The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 50 cars is to be selected for a speed study. ----------------------------- A) What is the shape, mean, and standard deviation of the sampling distribution Shape is normal; mean of the sample means = 67 mph ; std of the sample means = 6/(sqrt(50)) = (6/5)sqrt(2) ============================================== B) What is the probability that a sample mean will be 69 miles per hour or more? --- t(69) = (69-67)/[6/sqrt(50)] = 2.357 --- P(xbar >= 69) = P(t >= 2.357 when df = 49) = 0.0112 ============================================== C) What is the probability that the sample mean will be between 65 and 68 miles per hour? --- P(65 < xbar < 68) = P(-2.357 < t < 1.1785 when df = 49) = 0.8666 ==================== Cheers, Stan H. ====================
 Expressions-with-variables/330937: Judy and Mary started walking toward each other from two different locations. They started at the same time. Judsy walks 2 miles per hour and Mary walks 2.5 miles per hour. By the time Judy reached mid point, they were 3 miles apart. How far apart were they when they started? 1 solutions Answer 237263 by stanbon(57387)   on 2010-08-11 15:20:57 (Show Source): You can put this solution on YOUR website!Judy and Mary started walking toward each other from two different locations. They started at the same time. Judy walks 2 miles per hour and Mary walks 2.5 miles per hour. By the time Judy reached mid point, they were 3 miles apart. How far apart were they when they started? ------------------------------------------------ Judy DATA: rate = 2 mph ; time = x hrs ; distance = 2x miles -------------- Mary DATA: rate = 2.5 mph ; time = 2.5 hrs ; distance = 2.5x miles --------------- Equation: distance - distance = 3 miles 2.5x-2x = 3 miles 0.5x = 3 x = 6 hrs ================ Judy walked 2*6 = 12 miles Mary walked 2.5*6 = 15 miles ---- They started 2*12 = 24 miles apart. ====================================== Cheers, Stan
 Geometry_Word_Problems/330938: Jim has gotten scores of 88 and 69 on his first two test. What score must he get on his thrid test to keep on average of 85 or greater?1 solutions Answer 237260 by stanbon(57387)   on 2010-08-11 15:11:11 (Show Source): You can put this solution on YOUR website!Jim has gotten scores of 88 and 69 on his first two tests. What score must he get on his third test to keep an average of 85 or greater? ------------ Let the 3rd test score be "x": Equation: (88+69+x)/3 >= 85 157+x >= 260 x >= 103 ============= Note: He cannot reach an average of 85. ============= Cheers, Stan H. =============
 Linear-equations/330926: Could you please Graph 4x - 5y >_ 10 The sign if you can't tell is a less than or equal to than sign. please slove asap i have a text tomorrow thank you very much!!1 solutions Answer 237259 by stanbon(57387)   on 2010-08-11 15:08:00 (Show Source): You can put this solution on YOUR website!please Graph 4x - 5y >_ 10 ------------------ 1st: Solve for "y": 5y <= 4x-10 y <= (4/5)x-2 ------------------- 2nd: Graph the boundary of the inequality: ---------------------------- 3rd: Check a test point that is not on the boundary to see which side the solutions are on. --- Check (0,0) in y < (4/5)x-2 0 < -2 -------- That is false so the "<" solution is the half-plane that does not include (0,0) --------------- ================== Cheers, Stan H. ==================
 Linear-equations/330929: Could you please Simplify sqrt 45. i have to take a test tomorrow so if you could answer this asap that would be awesome! thanks!1 solutions Answer 237254 by stanbon(57387)   on 2010-08-11 14:59:48 (Show Source): You can put this solution on YOUR website!Simplify sqrt(45) = sqrt(9*5) = sqrt(9)*sqrt(5) = 3*sqrt(5) ============ Cheers, Stan H. ============
 Probability-and-statistics/330927: Help me solve this question please. A researcher wishes to estimate,with 90% confidence, the proportion of adults who have high speed internet access.Her estimate must be accurate within 3% of the true proportion.a)Find the minimun sample neede, using a prior study that found that 48% of the respondents said they have high speed internet access.n=? b)no preliminary estimate is available.Find the minimum sample size needed.n=?1 solutions Answer 237253 by stanbon(57387)   on 2010-08-11 14:57:40 (Show Source): You can put this solution on YOUR website!Help me solve this question please. A researcher wishes to estimate,with 90% confidence, the proportion of adults who have high speed internet access.Her estimate must be accurate within 3% of the true proportion. a)Find the minimum sample needed, using a prior study that found that 48% of the respondents said they have high speed internet access. n=[1.645/0.03]^(0.48)(0.52) = 750.47 n = 751 when rounded up =============================== b) No preliminary estimate is available.Find the minimum sample size needed. n = [1.645/0.03]^2(1/2)(1/2) = 751.67 n = 752 when rounded up ================ Cheers, Stan H. ---------------------
 Probability-and-statistics/330872: The critical value is A. Calculated from sample information. B. Cannot be negative. C. The point that divides the acceptance region from the rejection region. D. A value determined from the test statistic. 1 solutions Answer 237217 by stanbon(57387)   on 2010-08-11 11:13:15 (Show Source): You can put this solution on YOUR website!Ans: C Cheers, Stan H.
 Probability-and-statistics/330871: A p-value is A. The same as the population proportion. B. The same as the significance level. C. The fraction of the population that has a particular characteristic. D. The probability of finding a value of the test statistic this extreme when the null hypothesis is true. 1 solutions Answer 237216 by stanbon(57387)   on 2010-08-11 11:11:55 (Show Source): You can put this solution on YOUR website!Ans: D Cheers, Stan H.
 percentage/330891: 307 is what percentage of 467?1 solutions Answer 237215 by stanbon(57387)   on 2010-08-11 11:09:56 (Show Source): You can put this solution on YOUR website!307 is what percentage of 467? ---- Solve: x/100 = 307/467 x = 100(0.6574) ---- x = 65.74% =========== Cheers, Stan H.
 Probability-and-statistics/330873: In a one-tailed test A. The rejection region is in one of the tails. B. The rejection region is split between the tails. C. The p-value is always less than the significance level. D. The p-value is always more than the significance level. 1 solutions Answer 237213 by stanbon(57387)   on 2010-08-11 11:07:17 (Show Source): You can put this solution on YOUR website!Ans: A Cheers, Stan H.
 Linear-equations/330768: I'm having trouble with this problem. If anyone can help and explain how to get the answer that would be greatly appreciated. Have to take a test on thurs. "Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB?" Thanking you in advance. 1 solutions Answer 237122 by stanbon(57387)   on 2010-08-10 22:23:12 (Show Source): You can put this solution on YOUR website!Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB?" ----- Plot the point (-4,1) Draw the line x = 2 --------------------------- Notice that the line passes thru (2,1) That point is the midpoint of AB --- Let (x,y) be the coordinates of "B". -------------------------------------- Solve for x and for y: (x+(-4))/2 = 2 x-4 = 4 x = 8 --------- (y+1)/2 = 1 y+1 = 2 y = 1 ---------------------- The coordinates of "B" are(8,1) ====================================== Cheers, Stan H.
 Graphs/330761: I need to know the intercepts of the 2 equations as well as where the lines would intercept. The equations are x + y = 44 3(y) + x = 44 What I do know is that The 1st question says sales rep informs u that there are 2 floor plans available for a total of 44 houses. Use x for floor plan 1 and y for floor plan 2. The equation that illustrates this situation is? I came up with x + y = 44 The next part says that the rep then states there are 3 times as many homes available with floor plan 2. The equation that illustrates this situation is? (use the same variables) I came up with.... 3y + x = 44 Then it asks what the intercepts of equation 1 and 2 are as well as where the lines would intersect if solved by graphing. Can u help me with this? Thank you in advance!1 solutions Answer 237121 by stanbon(57387)   on 2010-08-10 22:14:48 (Show Source): You can put this solution on YOUR website!The equations are x + y = 44 3(y) + x = 44 -------- Solve the 2nd equation for "x": x = -3y+44 --- Substitute for "x" in x + y = 44 and solve for "y": --- -3y+y = 44 -2y = 44 y = -22 --------- Substitute into x = -3y+44 to solve for "x": x = -3(-22)+44 --- x = 66+44 = 100 ------------------ Solution: (100,-22) ===================== Cheers, Stan H. ----
 Length-and-distance/330759: If L is the midpoint of KM (it has - on top of the first KM) and KM = 5X-6 and LM = 2X+4, what is the value of x?1 solutions Answer 237119 by stanbon(57387)   on 2010-08-10 22:06:04 (Show Source): You can put this solution on YOUR website!If L is the midpoint of KM (it has - on top of the first KM) and KM = 5X-6 and LM = 2X+4, what is the value of x? -------------------- Equation: LM = (1/2)KM 2x+4 = (1/2)(5x-6) --- 4x+8 = 5x-6 x = 14 ================================= Cheers, Stan H. ============
 Linear-equations/330758: a^m*a^n=1 solutions Answer 237117 by stanbon(57387)   on 2010-08-10 21:58:43 (Show Source): You can put this solution on YOUR website!a^m*a^n ----- = a^(m+n) ============= Cheers, Stan H. =============
 Exponential-and-logarithmic-functions/330755: Given a starting population of 100 bacteria, the formula b = 100(2t ) can be used to find the number of bacteria, b, after t periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200?1 solutions Answer 237114 by stanbon(57387)   on 2010-08-10 21:54:22 (Show Source): You can put this solution on YOUR website!Given a starting population of 100 bacteria, the formula b = 100(2^t ) can be used to find the number of bacteria, b, after t periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200? ------------------------- Solve 51,200 = 100*2^(t/15) --- 2^(t/15) = 512 Take the log to get: (t/15)*log(2) = log(512) t/15 = 9 time = 15*9 = 2 hrs and 15 minutes =================================== Cheers, Stan H. ============
 Triangles/330754: (p/4)-(3p/8)=4 solve the equation.1 solutions Answer 237108 by stanbon(57387)   on 2010-08-10 21:44:14 (Show Source): You can put this solution on YOUR website! (p/4)-(3p/8)=4 ================== When you have an equation it is easy to get rid of the fractions. --------------- Multiply thru the equatiion by 8 to get: 2p - 3p = 32 -p = 32 p = -32 ================== Cheers, Stan H. ==================
 Money_Word_Problems/330729: How long would it take an investment of \$12,225 at 3 3/4% interest compounded quarterly to triple?1 solutions Answer 237095 by stanbon(57387)   on 2010-08-10 21:00:43 (Show Source): You can put this solution on YOUR website! How long would it take an investment of \$12,225 at 3 3/4% interest compounded quarterly to triple? ----- A(t)=Ao(1+(r/n))^(nt) ------ 3(12225)= 12225(1+(0.0375/4))^(4t) (1+0.0094)^(4t) = 3 Take the log of both sides and solve for "t": (4t) = log(3)/log(1.0094) --- 4t = 117.4221 --- t = 29.35 Rounding up you get: t = 30 years ===================================== Cheers, Stan H. ===========
 Polynomials-and-rational-expressions/330728: Identify the degree of each term of the polynomial and the degree of the polynomial. -5x^3+4x^2+6x+9 The degree of the first term is? the Degree of the second term is? The degree of the third term is? The degree of the forth term is? The degree of the polynomial is?1 solutions Answer 237093 by stanbon(57387)   on 2010-08-10 20:54:56 (Show Source): You can put this solution on YOUR website!Identify the degree of each term of the polynomial and the degree of the polynomial. -5x^3+4x^2+6x+9 The degree of the first term is?3 the Degree of the second term is?2 The degree of the third term is?1 The degree of the fourth term is?0 The degree of the polynomial is?3 ======================================= Cheers, Stan H. =========
 Equations/330726: how do i solve this problem 5a+4(3a-8)=4+13a1 solutions Answer 237092 by stanbon(57387)   on 2010-08-10 20:52:49 (Show Source): You can put this solution on YOUR website! how do i solve this problem 5a+4(3a-8)=4+13a -------------- 5a+12a-32 = 4+13a 4a = 36 a = 9 ======= Cheers, Stan H. =========
 Permutations/330718: Hanafuda is a japanese game that uses a deck of cards made up of 12 suits, with each suit having four cards. How many 7-card hands can be formed so that 3 are from one suit and 4 are from another?1 solutions Answer 237091 by stanbon(57387)   on 2010-08-10 20:50:47 (Show Source): You can put this solution on YOUR website!Hanafuda is a japanese game that uses a deck of cards made up of 12 suits, with each suit having four cards. How many 7-card hands can be formed so that 3 are from one suit and 4 are from another? ----------------- Pick a suit: 12 ways Pick 3 from that suit: 4C3 = 4 ways Pick a 2nd suit: 11 ways Pick 4 from that suit: 4C4 = 1 way ---------------------------------------- Total # of hands: 12*4*11*1 = 528 ========================================= Cheers, Stan H.
 Complex_Numbers/330420: Can I get more assistance with this problem, thanks! Find the quotient and remainder when x3 + 3x2  x  7 is divided by x  21 solutions Answer 236825 by stanbon(57387)   on 2010-08-09 22:24:05 (Show Source): You can put this solution on YOUR website!Find the quotient and remainder when x3 + 3x2  x  7 is divided by x  2 --- Using synthetic division: 2)....1....3....-1....-7 .......1....5....9...|..11 ================================== Quotient: x^2+5x+9 Remainder: 11 ===================== Cheers, Stan H.
 Numbers_Word_Problems/330416: Three unknown numbers are given. The second number is one more than the first. The third number is the sum of the first and second plus one. If the sum of the first and third is 21, what is the second number?1 solutions Answer 236824 by stanbon(57387)   on 2010-08-09 22:21:04 (Show Source): You can put this solution on YOUR website!Three unknown numbers are given::: x,y,z --------------------------------------------- The second number is one more than the first. y = x+1 --------------------------------------------- The third number is the sum of the first and second plus one. z = x+y+1 --------------------------------------------- If the sum of the first and third is 21 x+z = 21 --------------------- what is the second number? ================================ Rearrange the 3 equations: x + 0y + z = 21 x + y - z = -1 x + -y +0z = -1 ----------------------- I used a matrix method to get: x = 6 1/3 y = 7 1/3 z = 14 2/3 ================ Cheers, Stan H. ================
 Human-and-algebraic-language/330402: the number of chipmunks varied directly as the number of acorns in the forest. if it took 100 acorns to feed 5 chipmunks, how many acorns will it take to feed 30 chipmunks?1 solutions Answer 236823 by stanbon(57387)   on 2010-08-09 22:08:51 (Show Source): You can put this solution on YOUR website!the number of chipmunks varied directly as the number of acorns in the forest. if it took 100 acorns to feed 5 chipmunks, how many acorns will it take to feed 30 chipmunks? ---------------------- c = ka --- Solve for "k" using "100 acorns to feed 5 chipmunks". --- 5 = k*100 k = 0.05 ---- Equation: c = 0.05a ---- how many acorns will it take to feed 30 chipmunks? 30 = 0.05a # of acorns = 30/0.05 = 600 ================================ Cheers, Stan H.
 Angles/330418: two angles are supplementary. one angle is 3 degrees less than twice the other. find the measure of the 2 angles1 solutions Answer 236820 by stanbon(57387)   on 2010-08-09 22:04:00 (Show Source): You can put this solution on YOUR website!two angles are supplementary. one angle is 3 degrees less than twice the other. find the measure of the 2 angles --------------------- Equations: x + y = 180 x = 2y-3 -------------------- Substitute for "x" and solve for "y": 2y-3 + y = 180 3y = 183 y = 61 degrees ---- x = 2y-3 = 2*61-3 = 119 degrees ================================== Cheers, Stan H. ==========
 Probability-and-statistics/330394: Given the following information about a hypothesis test of the difference between two variances based on independent random samples, what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations. F = 2.0 F = 3.0 F = 1.667 F = 1.778 F = 2.778 1 solutions Answer 236819 by stanbon(57387)   on 2010-08-09 22:00:42 (Show Source): You can put this solution on YOUR website!Data is missing.
 Probability-and-statistics/330398: I am completely lost trying to figure out these tables! I would love some help trying to figure it out!! Thanks! The frequency distribution shown lists the number of hours per day a randomly selected sample of teenagers spent watching television. Hours per day # of teens = f Midpoint = x Fx Fx² 0 ≤ x < 1 18 1 ≤ x < 2 31 2 ≤ x < 3 24 3 ≤ x < 4 38 4 ≤ x < 5 27 5 ≤ x < 6 12 6 ≤ x < 7 15 a. Complete the table. b. Construct a histogram representing the data. c. Calculate the mean, median, and mode number of hours the teens watch television. d. Calculate the standard deviation. e. What percent of the data lies within one standard deviation of the mean? 1 solutions Answer 236817 by stanbon(57387)   on 2010-08-09 21:59:23 (Show Source): You can put this solution on YOUR website!I am completely lost trying to figure out these tables! I would love some help trying to figure it out!! Thanks! The frequency distribution shown lists the number of hours per day a randomly selected sample of teenagers spent watching television. Hours per day # of teens = f Midpoint = x Fx Fx² 0 ≤ x < 1 18 1 ≤ x < 2 31 2 ≤ x < 3 24 3 ≤ x < 4 38 4 ≤ x < 5 27 5 ≤ x < 6 12 6 ≤ x < 7 15 ---------------- Comment: When you have a frequency distribution of the kind you have lost the data because it has been sorted into bins. You must use the "mark" of each bin as the representative value for the bin. So for 0<= x <1 use (1+0)/2 = 0.5 with frequency 18 for 1<= x <2 use (2+1)/2 = 1.5 with frequency 31 Do that for each of the bins to complete the table. a. Complete the table. ---------------------------------------- b. Construct a histogram representing the data. You can do that that with the original data ---------------------------------------- c. Calculate the mean, median, and mode number of hours the teens watch television. The mode with be x = 3.5 with frequency 38. ---------------------------------------- d. Calculate the standard deviation. Hopefully you have tecnology to do this. ---------------------------------------- e. What percent of the data lies within one standard deviation of the mean? I'll leave that to you. ============================ Cheers, Stan H. ============================
 Probability-and-statistics/330396: When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable: Decreases Increases May decrease or increase depending on the number of rows and columns Will be unaffected 1 solutions Answer 236815 by stanbon(57387)   on 2010-08-09 21:49:56 (Show Source): You can put this solution on YOUR website!When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable: -------------------------- As the observed approaches the expected the Chi-Sq decreases. The probability of rejecting Ho decreases. The probability of independence increases. --------------------------------- Cheers, Stan H. ================== Decreases Increases May decrease or increase depending on the number of rows and columns Will be unaffected
 Probability-and-statistics/330411: P(x> or equal to 2) mu=3 and standard deviation =0.251 solutions Answer 236809 by stanbon(57387)   on 2010-08-09 21:40:47 (Show Source): You can put this solution on YOUR website!P(x> or equal to 2) mu=3 and standard deviation =0.25 ----- z(2) = (2-3)/0.25 = -1/0.25 = -4 ------------------- P(x >= 2) = P(z >= -4) = normalcdf(-4,1000) = 1.00 ==================================== Cheers, Stan H. ============
 Probability-and-statistics/330331: The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the sa 1 solutions Answer 236784 by stanbon(57387)   on 2010-08-09 20:15:58 (Show Source): You can put this solution on YOUR website!The statement of the problem is incomplete. You can find worked solutions by searching "Oh Baby" using the Google search on this site. Cheers, Stan H.