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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Triangles/716974: 1 angle is 60 another 20 whats the missing angle 1 solutions Answer 440045 by stanbon(57290)   on 2013-02-20 21:21:36 (Show Source): You can put this solution on YOUR website!1 angle is 60 another 20 whats the missing angle ------ Assuming you are referring to the angles of a triangle, the sum of the angles must be 180 degrees. ------- Equation: 60 + 20 + x = 180 x + 80 = 180 ----- x = 100 degrees (the 3rd angle) ============================= Cheers, Stan H. ===============
 test/716973: Find the GCF of the expression. Then factor the expression. 3x^2 + 15x + 121 solutions Answer 440037 by stanbon(57290)   on 2013-02-20 21:11:16 (Show Source): You can put this solution on YOUR website!factor the expression. 3x^2 + 15x + 12 ----------- GCF: 3 ---- Factor: = 3(x^2+5x+4) ---- = 3(x+4)(x+1) ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/716972: what is the solution to 2-11x2-8x+6x21 solutions Answer 440033 by stanbon(57290)   on 2013-02-20 21:06:21 (Show Source): You can put this solution on YOUR website!what is the solution to 2-11x2-8x+6x2 ----- = -5x^2 -8x + 2 ======================= Cheers, Stan H. =======================
 Linear-equations/716967: how to plot a graph when Y=(x-2)+3 WITH THE FOLLOWING DOMAIN 2,-2,0,4,6) 1 solutions Answer 440032 by stanbon(57290)   on 2013-02-20 21:03:33 (Show Source): You can put this solution on YOUR website!how to plot a graph when Y=(x-2)+3 WITH THE FOLLOWING DOMAIN 2,-2,0,4,6) ---- f(2) = (2-2)+3 = 3 f(-2) = (-2-2)+3 = -1 f(0) = (0-2)+3 = 1 f(4) = (4-2)+3 = 5 f(6) = (6-2)+3 = 7 --------- Plot those (x,y) points: (2,3);(-2,-1),(0,1),(4,5),(6,7) ===================== Cheers, Stan H. =========================
 Points-lines-and-rays/716817: Angles 1 and 2 are a linear pair, the measure of angle 1=x-39, and the measure of angle 2=x+61. Find the measure of each angle.1 solutions Answer 439993 by stanbon(57290)   on 2013-02-20 17:26:56 (Show Source): You can put this solution on YOUR website!Angles 1 and 2 are a linear pair, the measure of angle 1=x-39, and the measure of angle 2=x+61. Find the measure of each angle. ------ Equation: x-39 + x+61 = 180 2x + 22 = 180 x + 11 = 90 x = 79 --- Ans: x-39 = 40 degrees x+61 = 140 degrees ============================ Cheers, Stan H. ================
 Travel_Word_Problems/716776: It takes a small jet plane 4 hours less time than it takes a propeller-driven plane to travel from Glen Rock to Qakville. The jet averages 637 km/h while the propeller plane averages 273 km/h. How far is it from Glen Rock to Oakville?1 solutions Answer 439991 by stanbon(57290)   on 2013-02-20 17:23:49 (Show Source): You can put this solution on YOUR website! It takes a small jet plane 4 hours less time than it takes a propeller-driven plane to travel from Glen Rock to Qakville. The jet averages 637 km/h while the propeller plane averages 273 km/h. How far is it from Glen Rock to Oakville? --------- small jet DATA: time = x-4 hrs ; rate = 637 km/hr ; distance = 637*(x-4) km ========================= propeller plane DATA: time = x hrs ; rate = 273 km/hr ; distance = 273x km ------- Equation: 273x = 637x - 637*4 ------ -364 x = -2548 -------- x = 7 hrs ----- Ans: Distance = 273x = 1911 km =================================== Cheers, Stan H. ==================
 Money_Word_Problems/716773: Find the future value when investing \$4,000 at the annual interest rate of 3.5% for 7 years compounded quarterly.1 solutions Answer 439973 by stanbon(57290)   on 2013-02-20 15:55:48 (Show Source): You can put this solution on YOUR website!Find the future value when investing \$4,000 at the annual interest rate of 3.5% for 7 years compounded quarterly. ------------- A(t) = P(1+(r/n))^(nt) A(7) = 4000(1+(0.035/4))^(4*7) ------- A(7) = 4000*1.2763 = \$5105.04 ================================ Cheers, Stan H. ===================
 Rational-functions/716766: Rational Root to x^3 + 2x^2 - 8x - 16 = 01 solutions Answer 439972 by stanbon(57290)   on 2013-02-20 15:47:59 (Show Source): You can put this solution on YOUR website!Rational Root to x^3 + 2x^2 - 8x - 16 = 0 -------- Using synthetic division: -2)....1....2....-8....-16 .......1....0....-8...|..0 ----- Find roots of the the quotient: x^2 - 8 = 0 --- x = 2sqrt(2) or x = -2sqrt(2) or x = -2 ======================================== Cheers, Stan H. ========================
 Age_Word_Problems/716765: Mary's mother is 4 times the age of Mary. The difference of the ages are 28 how old are they?1 solutions Answer 439970 by stanbon(57290)   on 2013-02-20 15:39:32 (Show Source): You can put this solution on YOUR website!Mary's mother is 4 times the age of Mary. The difference of the ages are 28 how old are they? ------- m = 4M m - M = 28 --------- Substitute for "m" and solve for "M": 4M-M = 28 3M = 28 M = 9 1/3 years (Mary's age now) ---- Solve for "m": m = 4M m = 4(28/3) = 37 1/3 (mother's age now) -------------------------- Cheers, Stan H. ==========================
 Miscellaneous_Word_Problems/716615: Pumps A, B, C operates at their respective constant rates. Pumps A and B simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank? 1 solutions Answer 439968 by stanbon(57290)   on 2013-02-20 15:34:14 (Show Source): You can put this solution on YOUR website! Pumps A, B, C operates at their respective constant rates. Pumps A and B simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank? ----------
 Age_Word_Problems/716617: In four years, Steve's age will be two years less than twice Anne's age. Three years ago, Steve was three times as old as Anne was then. How old is each now?1 solutions Answer 439911 by stanbon(57290)   on 2013-02-20 07:36:44 (Show Source): You can put this solution on YOUR website!In four years, Steve's age will be two years less than twice Anne's age. Three years ago, Steve was three times as old as Anne was then. How old is each now? --------- Equations: s+4 = 2a-2 s-3 = 3(a-3) ------ Rearrange: s = 2a-6 s = 3a-6 -------- That is a contradiction. Ans: No solution ======================= Cheers, Stan H.
 Linear-systems/716477: write each equation in slope-intercept form: x/3+y/4=1 2x-3y=121 solutions Answer 439883 by stanbon(57290)   on 2013-02-19 21:38:22 (Show Source): You can put this solution on YOUR website!write each equation in slope-intercept form: x/3+y/4=1 Multiply thru by 12: 4x + 3y = 12 ---- solve for "y": y = (-4/3)x + 4 ------------------------ 2x-3y=12 --- 3y = 2x-12 y = (2/3)x - 4 ======================= Cheers, Stan H. =====================
 Trigonometry-basics/716473: If tanx= 5/3 and secx < 0, then what is the exact value of sinx? So far, I have: Opp: 5, Adj; 3, and Hyp: sqrt(34). Sin^2x= sinxcosx But after that I'm stuck! Please help! 1 solutions Answer 439882 by stanbon(57290)   on 2013-02-19 21:34:49 (Show Source): You can put this solution on YOUR website!If tanx= 5/3 and secx < 0, then what is the exact value of sinx? So far, I have: Opp: 5, Adj; 3, and Hyp: sqrt(34). Sin^2x= sinxcosx But after that I'm stuck! Please help! ----- Since tan is positive and sec is negative x in an angle in QIII ------------------------- tan = y/x = -5/-3, so y = -5, x = -3 --------------------------- Solve for "r": r = sqrt[5^2+3^2] = sqrt(34) ----- Ans: sin(x) = y/r = -5/sqrt(34) ================================= Cheers, Stan H. ===================
 Functions/716469: How do I write a domain that doesn't include -4 and is greater than or equal to -2?1 solutions Answer 439879 by stanbon(57290)   on 2013-02-19 21:30:04 (Show Source): You can put this solution on YOUR website! How do I write a domain that doesn't include -4 and is greater than or equal to -2? ---- Domain: (-oo,-4) U [-2,+oo) ============================= Cheers, Stan H. ==============
 test/716468: ok so in math we are learning how to solve equations with variables on both sides and i dont understand how to solve it example: 2x+16=-x-5 please help!1 solutions Answer 439876 by stanbon(57290)   on 2013-02-19 21:27:14 (Show Source): You can put this solution on YOUR website!2x+16=-x-5 ----- Add "x" to both sides: Subtract 16 from both sides: ---- 3x = -21 ---- Divide both sides by 3 to get: x = -7 ================ Cheers, Stan H. ================
 Miscellaneous_Word_Problems/716462: If a bank made an interest earning of \$1437.50 after one year on a loan with 5.75% simple interest, how much was the original loan?1 solutions Answer 439875 by stanbon(57290)   on 2013-02-19 21:25:21 (Show Source): You can put this solution on YOUR website!If a bank made an interest earning of \$1437.50 after one year on a loan with 5.75% simple interest, how much was the original loan? ---------------- I = Prt 1437.50 = P*0.0575*1 ----- P = \$25,000 =============== Cheers, Stan H.
 Linear-systems/716459: how do you slove ts question usingthe sub method 6x+14y=54 3x+5y=301 solutions Answer 439873 by stanbon(57290)   on 2013-02-19 21:19:19 (Show Source): You can put this solution on YOUR website!6x+14y=54 3x+5y=30 ---- Solve the bottom equation for "y": y = (30-3x)/5 -------------------- Substitute for "y" in the top equation and solve for "x": 6x + 14[(6-(3/5)x)] = 54 ------- 6x + 84 - (42/5)x = 54 6x - (42/5)x = -30 (30/5)x - (42/5)x = -30 (-12/5)x = -30 ------- -12x = -150 x = 12.5 ================= Cheers, Stan H. =================
 Expressions-with-variables/716458: 4x+9y=24 y=1/3x+21 solutions Answer 439871 by stanbon(57290)   on 2013-02-19 21:10:06 (Show Source): You can put this solution on YOUR website!4x+9y=24 y=1/3x+2 --------------- Rearrange: 4x + 9y = 24 x - 3y = -6 ================= Modify for elimination: 4x + 9y = 24 4x -12y =-24 -------------- Subtract and solve for "y": 21y = 48 y = 16/7 ----------------- Solve for "x": x = 3y - 6 x = 3(16/7) - 6 x = (48/7) - (42/7) x = 6/7 =============== Cheers, Stan H. ===============
 Probability-and-statistics/716435: 7. A SC Tourist Bureau survey showed that 75% of those who seek information about the state actually come to visit. The office received 12 requests for information. Find: a. The probability that more than five of the people will visit SC? ______ b. The probability that at least 3 of the people will not visit SC? ______ c. The probability that 4 to 8, inclusive, of the people will visit SC? _______ d. What is the expected number of visitors from this group? __________ e. Make the histogram of the binomial distribution for this situation. 1 solutions Answer 439867 by stanbon(57290)   on 2013-02-19 20:54:48 (Show Source): You can put this solution on YOUR website!A SC Tourist Bureau survey showed that 75% of those who seek information about the state actually come to visit. The office received 12 requests for information. --------- Binomial Problem with n = 12 ; p(visit) = 0.75 ; p(not visit) = 0.25 --------- Find: a. The probability that more than five of the people will visit SC? P(5<= x <= 12) = 1 - binomcdf(12,0.75,4) = 0.9972 --------------------------------------------------------------------- b. The probability that at least 3 of the people will not visit SC? P(3<= x <=12) = 1 - p(0<= x <=2) = 0.6093 --------------------------------------------------- c. The probability that 4 to 8, inclusive, of the people will visit SC? _______ d. What is the expected number of visitors from this group? Expected number = mean = np = 12*0.75 = 9 =============================================== e. Make the histogram of the binomial distribution for this situation. ================ Cheers, Stan H.
 Square-cubic-other-roots/716436: What is the solution for "2+√4y-3=11 Only 4y is under the radical. not -3 1 solutions Answer 439866 by stanbon(57290)   on 2013-02-19 20:30:50 (Show Source): You can put this solution on YOUR website!What is the solution for "2+√4y-3=11 Only 4y is under the radical. not -3 ----- 2 + sqrt(4y) - 3 = 11 ---- sqrt(4y) -1 = 11 --- sqrt(4y) = 12 ---- 4y = 144 y = 36 ===================== Cheers, Stan H. ==================
 Age_Word_Problems/716420: write the class mark of the class 29-341 solutions Answer 439865 by stanbon(57290)   on 2013-02-19 20:27:01 (Show Source): You can put this solution on YOUR website! write the class mark of the class 29-34 --------- The class mark is the middle value in the class. ---- class mark = (29+34)/2 = 63/2 = 31.5 =========================================== Cheers, Stan H. =============
 Travel_Word_Problems/716421: A six-passenger airplane has a gas tank that holds 240 gallons. When flying at maximum speed, the plane averages 6 1/4 miles per gallon. How far can the plane fly at maximum speed? 1 solutions Answer 439864 by stanbon(57290)   on 2013-02-19 20:15:16 (Show Source): You can put this solution on YOUR website!A six-passenger airplane has a gas tank that holds 240 gallons. When flying at maximum speed, the plane averages 6 1/4 miles per gallon. How far can the plane fly at maximum speed? ------ distance = 240*6.25 = 1500 miles ===================================== Cheers, Stan H. ==============
 Rational-functions/716422: Find all Zero's X^3+7X^2+7X-15=F(x)1 solutions Answer 439862 by stanbon(57290)   on 2013-02-19 20:12:07 (Show Source): You can put this solution on YOUR website!Find all Zero's X^3+7X^2+7X-15=F(x) ------- Since the coefficients add up to 0 x=1 is a root. Use synthetic division to find the remaining 2 roots: ------------- 1)....1....7....7....-15 ......1....8....15..|..0 ----- Solve the quotient for roots: x^2 + 8x + 15 = 0 (x+3)(x+5) = 0 ---- Roots: x = -3 ; x = -5 ; x = 1 ================================ Cheers, Stan H. ================================
 test/716418: I do not understand how exactly to solve this equation. |x-1|=|3x+2| those are absolute value signs around the x-1 and the 3x+2. My textbook says the answers are -3/2 and -1/4? Please explain 1 solutions Answer 439859 by stanbon(57290)   on 2013-02-19 20:01:49 (Show Source): You can put this solution on YOUR website!I do not understand how exactly to solve this equation. |x-1|=|3x+2| those are absolute value signs around the x-1 and the 3x+2. My textbook says the answers are -3/2 and -1/4? Please explain -------- Equations: x-1 = 3x+2 or x-1 = -(3x+2) 2x = -3 or x-1 = -3x-2 x = -3/2 or 4x = -1 x = -3/2 or x = -1/4 ============================== Cheers, Stan H. ====================
 Graphs/716413: What is 4x-2y=-6 when you graph it?1 solutions Answer 439858 by stanbon(57290)   on 2013-02-19 19:56:01 (Show Source): You can put this solution on YOUR website!What is 4x-2y=-6 when you graph it? ---- Solve for "y": 2y = 4x+6 ---- y = 2x + 3 --- If x = 0, y = 3 giving you point (0,3) If x = 2, y = 7 giving you point (2,7) ---- Plot the two points and draw a line thru them: ======================================== Cheers, Stan H. ===============
 Probability-and-statistics/715927: The help desk for a software company logs the lengths of times of each call that technicians have with customers. Historical records based on the past 3 years indicate that call length (L) is a normally distributed variable with an average (μ) of 9.00 minutes and a standard deviation (σ) of 0.95 min. For each of the problems below, find the appropriate probability. A) P(L ≤ 10.22) B) P(L > 10.74) C) P(7.67 ≤ L < 11.02) D) The call times that enclose the central 81% of the distribution are: Note: Round your answers to two decimal places for this problem. I really need step by step help. Im not coming up with the correct answers.. Low: to High: 1 solutions Answer 439751 by stanbon(57290)   on 2013-02-19 09:59:22 (Show Source): You can put this solution on YOUR website!call length (L) is a normally distributed variable with an average (μ) of 9.00 minutes and a standard deviation (σ) of 0.95 min. For each of the problems below, find the appropriate probability. A) P(L ≤ 10.22) z(10.22) = (10.22-9)/0.95 = 1.2842 Ans: P(L<= 10.22) = P(z<=1.2842) = normalcdf(-100,1.2842) = 0.9005 ------------------------------------ B) P(L > 10.74) Find the z-value of 10.74. Find the P(z is above that z-value) Ans: 0.0335 =================================== C) P(7.67 ≤ L < 11.02) Find the z-value of those numbers. Find the P(z is between those z-values) Ans: 0.9025 ==================== D) The call times that enclose the central 81% of the distribution are: Note: Round your answers to two decimal places for this problem. Draw the picture: You have a left tail of 0.5000- 0.4150 = 0.085 invNorm(0.085) = -1.3722 for the left tail and +1.3722 for the right tail: ---- Find the corresponding x-value using x = z*s+u x = -1.3722*0.95+9 = 7.70 x = +1.3622*0.95+9 = 10.30 =============================== Cheers, Stan H.
 Probability-and-statistics/715973: please help me solve this problem of probability and statistics on fundamental counting principle :In how many ways can 4 of 7 different kinds of bushes be planted along one side of a house? i'll be waiting for your help thanks!1 solutions Answer 439748 by stanbon(57290)   on 2013-02-19 09:44:16 (Show Source): You can put this solution on YOUR website!In how many ways can 4 of 7 different kinds of bushes be planted along one side of a house? i'll be waiting for your help thanks! -------- Ans: 7*6*5*4 = 840 ways ============================ Cheers, Stan H.
 Probability-and-statistics/715999: a shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchanse 5 of these sets and at least 2 of the defective sets?1 solutions Answer 439747 by stanbon(57290)   on 2013-02-19 09:41:55 (Show Source): You can put this solution on YOUR website!a shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchanse 5 of these sets and at least 2 of the defective sets? ------ Binomial Problem with n = 5 ; p(defective) = 1/4 ; p(not defective) = 3/4 ----------- P(2<= x <=5) = binomcdf(5,1/4,5)-binomcdf(5,1/4,1) = 0.3672 ========================== Cheers, Stan H. ==========================
 Probability-and-statistics/716114: Please help Sample with size n = 100 has mean = 30. Assuming the population standard deviation is 8, construct 95% confidence interval for population mean. Use formula , zα/2 = 1.96 1 solutions Answer 439745 by stanbon(57290)   on 2013-02-19 09:35:29 (Show Source): You can put this solution on YOUR website!Sample with size n = 100 has mean = 30. Assuming the population standard deviation is 8, construct 95% confidence interval for population mean. Use formula , zα/2 = 1.96 -------- x-bar = 30 --- E = z*s/sqrt(n) = 1.96*(8/sqrt(100)) = 1.568 -------------------------- 95% CI: 30-1.568 < u < 30+1.568 ================================== Cheers, Stan H. ============
 Permutations/716115: How many permutations can be formed from the 13 word COMBINATORICS? 1 solutions Answer 439744 by stanbon(57290)   on 2013-02-19 09:29:41 (Show Source): You can put this solution on YOUR website!How many permutations can be formed from the 13 word COMBINATORICS? ------ Ans: 13!/(2!*2!*2!) = 778,377,600 =============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/716012: Please help me solve this word problem 30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in the first bag, find the number of marbles in each bag. 1 solutions Answer 439690 by stanbon(57290)   on 2013-02-18 22:27:22 (Show Source): You can put this solution on YOUR website!30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag the third bag has twice as many as the first bag. If x is the number of marbles in the first bag, find the number of marbles in each bag. ----- 2nd bag has 3x ---- 3rd bag has 2x ==== Equation: x + 2x + 3x = 30 6x = 30 x = 5 (1st bag) 2x = 10 (3rd bag) 3x = 15 (2nd bag) ==================== Cheers, Stan H. ======================