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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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 Graphs/721246: which graph represents the equation 3x-2y=-121 solutions Answer 442282 by stanbon(57361)   on 2013-03-03 11:20:29 (Show Source): You can put this solution on YOUR website!which graph represents the equation 3x-2y=-12 ----------- 2y = 3x+12 --- y = (3/2)x + 6 ------------------ -------------------- Cheers, Stan H. ------------
 Linear-equations/721248: 1. what is the y-intercept of the linear equation y= -3x? 2. what is the slope of the equation y= -4? 3. rearrange x + y= 4 into slope-intercept,and identify the slope and y-intercept? 4. given a slope of 5/3 and a y-intercept of 3, write the equation of the line in y= mx+b? 5. Name one point(other than the y-intercept) that is on the line with the given equation?1 solutions Answer 442281 by stanbon(57361)   on 2013-03-03 11:18:05 (Show Source): You can put this solution on YOUR website!1. what is the y-intercept of the linear equation y= -3x? Ans: (0,0) ------------------ 2. what is the slope of the equation y= -4? Ans: m = -4 ------------------ 3. rearrange x + y= 4 into slope-intercept,and identify the slope and y-intercept? Ans: y = -x+4 slope = -1 y-intercept: 4 -------------------------- 4. given a slope of 5/3 and a y-intercept of 3, write the equation of the line in y= mx+b? Ans: y = (5/3)x + 3 -------------------------- 5. Name one point(other than the y-intercept) that is on the line with the given equation? Ans: If x = 3, y = 5 + 3 = 8 Point: (3,8) =================== Cheers, Stan H. ===================
 Probability-and-statistics/721249: According to an Internet posting, 80% of adults enjoy drinking beer. A group of 7 adults is chosen randomly. The probability that no more than 3 of them enjoy drinking beer is: 1 solutions Answer 442280 by stanbon(57361)   on 2013-03-03 11:13:53 (Show Source): You can put this solution on YOUR website!According to an Internet posting, 80% of adults enjoy drinking beer. A group of 7 adults is chosen randomly. The probability that no more than 3 of them enjoy drinking beer is: -------------- Binomial Problem with n = 7 ; p(drink)= 0.8 ----- P(0<= x <=3) = binomcdf(7,0.8,3) = 0.0333 Cheers, Stan H.
 Trigonometry-basics/721127: How far will the bicycle move with each full rotation of the pedals. Assume the radius of the bicycle wheel is 13.1 inches, the radius of the crank sprocket is 5.54 inches, and the radius of the wheel sprocket is 1.93 inches.1 solutions Answer 442212 by stanbon(57361)   on 2013-03-02 23:09:31 (Show Source): You can put this solution on YOUR website!How far will the bicycle move with each full rotation of the pedals. Assume the radius of the bicycle wheel is 13.1 inches, the radius of the crank sprocket is 5.54 inches, and the radius of the wheel sprocket is 1.93 inches. ------ circumference of the pedal sprocket: pi*2*5.54 = 11.08pi inches circumference of the wheel sprocket: pi*2*1.93 = 3.86 pi inches corresponding revolutions of the wheel: 11.08pi/3.86pi = 5.54/1.93 = 2.87 revs ----- circumference of the bike wheel: pi*2*13.1 = 82.31 inches ---- distance traveled by wheel 2.87*82.31 = 236.23 inches = 19.68 ft. ================== Cheers, Stan H.
 Linear-equations/721124: Nielsen media research surveys tv watching habits and provides a list of the 20 most watched TV programs each week. each rating point in the survey represents 1102000 households. one week 60 minutes had rating of 11.0. how many households did this represent?1 solutions Answer 442211 by stanbon(57361)   on 2013-03-02 22:59:45 (Show Source): You can put this solution on YOUR website!Nielsen media research surveys tv watching habits and provides a list of the 20 most watched TV programs each week. each rating point in the survey represents 1102000 households. one week 60 minutes had rating of 11.0. how many households did this represent? ------ Ans: 11*1,102,000 = 12,122,000 households ================== Cheers, Stan H. ==================
 Age_Word_Problems/721114: a woman is twice as old as her daughter twenty years ago she was four times as old as her daughter how old are they now1 solutions Answer 442210 by stanbon(57361)   on 2013-03-02 22:56:54 (Show Source): You can put this solution on YOUR website!a woman is twice as old as her daughter twenty years ago she was four times as old as her daughter how old are they ----- Equations: m = 2d m-20 = 4(d-20) ---- Substitute for "m" and solve for "d": 2d-20 = 4d-80 2d = 60 daughter = 30 years (daughter's age now) ----------------------- Solve for "m": m = 2d = 60 years (mother's age now) ---------------- Cheers, Stan H. ====================
 Mixture_Word_Problems/721125: A 10% chlorine solution is to be mixed with a 25% chlorine solution to obtain 30 gallons of 20% solution. How many gallons of each must be used?1 solutions Answer 442208 by stanbon(57361)   on 2013-03-02 22:44:18 (Show Source): You can put this solution on YOUR website!A 10% chlorine solution is to be mixed with a 25% chlorine solution to obtain 30 gallons of 20% solution. How many gallons of each must be used? ---- Equation: chlor + chlor = chlor 0.10x + 0.25(30-x) = 0.20*30 ------ 10x + 25*30 - 25x = 20*30 ----- -15x = -5*30 x = 10 gallons (amt. of 10% solution needed) -------------- 30-x = 20 gallons (amt. of 25% solution needed) ============= Cheers, Stan H. ==================
 Rational-functions/721122: write as rates and unit rates 18 lines memorized in 45 mins 84 games packed in 6 boxes 1 solutions Answer 442205 by stanbon(57361)   on 2013-03-02 22:12:34 (Show Source): You can put this solution on YOUR website!write as rates and unit rates ----------------- 18 lines memorized in 45 mins rate = (18/45)(lines/min) = 0.4 lines per min ------------------------------------ 84 games packed in 6 boxes rate = (84/6)(games/box) = 14(games/box) ==================================== Cheers, Stan H. =====================
 Money_Word_Problems/721120: \$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is \$155. ----------------- The answer has to be one of the following but which? ----------------- \$1,000 \$3,000 \$4,0001 solutions Answer 442204 by stanbon(57361)   on 2013-03-02 22:09:14 (Show Source): You can put this solution on YOUR website!\$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is \$155. ----------------- Equations: x + y = 5000 3x + 3.5y = 15500 ------ 30x + 30y = 150000 30x + 35y = 155000 ----------------------- 5y = 5000 ---- y = \$1000.00 (amt invested at 3.5% --- x = \$4000.00 (amt. invested at 3% ===================================== Cheers, Stan H. ================= The answer has to be one of the following but which? ----------------- \$1,000 \$3,000 \$4,000
 Probability-and-statistics/721104: Lottery Ticket. In a bin are an equal number of balls marked with the digits 1-9. Three balls are to be selected from the bin, one after the other, at random with replacement to make the winning three-digit lottery number. Ms. Jones has a lottery ticket with a three digit number in the range 000 to 999. Determine the probability that Ms. Jones's number is the winning number.1 solutions Answer 442200 by stanbon(57361)   on 2013-03-02 22:01:44 (Show Source): You can put this solution on YOUR website!Lottery Ticket. In a bin are an equal number of balls marked with the digits 1-9. Three balls are to be selected from the bin, one after the other, at random with replacement to make the winning three-digit lottery number. Ms. Jones has a lottery ticket with a three digit number in the range 000 to 999. Determine the probability that Ms. Jones's number is the winning number. ------- # of possible 3-digit numbers: 1000 # of winners: 1 ------ P(get winning #) = 1/1000 = 0.001 ===================================== Cheers, Stan H. ================
 Probability-and-statistics/721116: Using the standard distribution tables, is the area under the standard normal curve corresponding to z is less than 1.1 0.8413? 1 solutions Answer 442199 by stanbon(57361)   on 2013-03-02 21:58:07 (Show Source): You can put this solution on YOUR website!Using the standard distribution tables, is "the area under the standard normal curve corresponding to z less than 1.1 is 0.8413" ? ----- Using a TI-84 I get normalcdf(-100,1,1) = 0.8643 ========================== Cheers, Stan H. ==========================
 Percentage-and-ratio-word-problems/721100: A company reduced the price of an article by 5%.by what per cent a retailer must increase the new price so as to sell the article at the old price ? 1 solutions Answer 442195 by stanbon(57361)   on 2013-03-02 21:13:12 (Show Source): You can put this solution on YOUR website!A company reduced the price of an article by 5%.by what per cent a retailer must increase the new price so as to sell the article at the old price ? ----- Let original price be "x": After reduction: 0.95x ------ Solve: k(0.95x) = x 0.95k = 1 k = 1/0.95 = 1.0526 ------- Ans: Increase price by 5.26% =============================== Cheers, Stan H. ========================
 Numeric_Fractions/721096: if 7+8=17 8+9=20 9+10=23 Find 13+14=x??1 solutions Answer 442193 by stanbon(57361)   on 2013-03-02 21:08:10 (Show Source): You can put this solution on YOUR website!answered
 Linear_Algebra/721087: A short test has 42 questions – some worth 2 marks, some 3 marks. It is out of 100 marks. Find how many questions of each type there are.1 solutions Answer 442190 by stanbon(57361)   on 2013-03-02 20:45:12 (Show Source): You can put this solution on YOUR website!A short test has 42 questions – some worth 2 marks, some 3 marks. It is out of 100 marks. Find how many questions of each type there are. ----- Questions Eq::: x + y = 42 Marks Eq:::::::2x +3y = 100 ----------------------- Modify: 2x + 2y = 84 2x + 3y = 100 ---- Subtract and solve for "y": y = 16 (# of 3 mark questions) ---- Solve for "x" using x + y = 42 x + 16 = 42 x = 26 (# of 2 mark questions) ==================== Cheers, Stan H. ==================== ----
 Rational-functions/721093: The ratio of the number of games Elly won to the number of games she lost is 7/3. she played a total of 40 games. How many games did she win?1 solutions Answer 442188 by stanbon(57361)   on 2013-03-02 20:37:48 (Show Source): You can put this solution on YOUR website! The ratio of the number of games Elly won to the number of games she lost is 7:3. she played a total of 40 games. How many games did she win? ----- 7x+3x = 40 10x = 40 x = 4 --------- 7x = 28 (# of games she won) =============================== Cheers, Stan H.
 Rational-functions/721092: how can i simplify this problem: x^2-y^2/x+y/x^4-y^41 solutions Answer 442187 by stanbon(57361)   on 2013-03-02 20:32:22 (Show Source): You can put this solution on YOUR website!simplify this problem: (x^2-y^2)/(x+y)/(x^4-y^4) ----- = (x-y)/(x^4-y^4) ----- = (x-y)/[(x^2+y^2)(x+y)(x-y)] ------- = 1/[(x^2+y^2)(x+y)] ==================== Cheers, Stan H. ====================
 sets-and-operations/721090: 24-6y /3y-121 solutions Answer 442186 by stanbon(57361)   on 2013-03-02 20:26:05 (Show Source): You can put this solution on YOUR website!24-6y /3y-12 ---- I'll assume you left out the parentheses. ---- (24-6y) / (3y-12) ------- = (6(4-y)) / (3(y-4)) ------ = (6/3)(4-y)/(y-4) ---- = 2 * (-1) ----- = -2 ============= Cheers, Stan H.
 Functions/721091: I am lost please help F(x)=x^2-12 G(x)=12-x Solve for (F-G)(10)=1 solutions Answer 442185 by stanbon(57361)   on 2013-03-02 20:21:26 (Show Source): You can put this solution on YOUR website!F(x)=x^2-12 G(x)=12-x Solve for (F-G)(10)= F(10) - G(10) ---- = (10^2-12) - (12-10) ------ = 88 - 2 ---- = 86 ====== Cheers, Stan H.
 Probability-and-statistics/721016: The probability that an appliance is in repair is 0.5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.1 solutions Answer 442180 by stanbon(57361)   on 2013-03-02 20:07:50 (Show Source): You can put this solution on YOUR website!The probability that an appliance is in repair is 0.5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial. ------ mean = np = 100*0.5 = 50 std = sqrt(npq) = sqrt(50*0.5) = 5 ------ P(59.5<= x <= 100.5) = ? ------- z(59.5) = (59.5-50)/5 = -0.1 ---- z(100.5) = (100.5-50)/5 = 50.5/5 = 10.1 ---------- = P(-0.1<= z <=10.1) = 0.5398 ===================================== Cheers, Stan H. =================
 Probability-and-statistics/721062: on a certain Saturday in July, the probability that the Wild Cats will win their baseball game is 0.4 and the probability that the Bulldogs will win their baseball game is 0.65. Assuming that they are not playing each other, what is the probability that the Wild Cats and the Bulldogs will both win their games on this given Saturday?1 solutions Answer 442178 by stanbon(57361)   on 2013-03-02 19:57:20 (Show Source): You can put this solution on YOUR website!on a certain Saturday in July, the probability that the Wild Cats will win their baseball game is 0.4 and the probability that the Bulldogs will win their baseball game is 0.65. Assuming that they are not playing each other, what is the probability that the Wild Cats and the Bulldogs will both win their games on this given Saturday? ----- P(both win) = 0.4*0.65 = 0.26 ---------------- Cheers, Stan H. ================
 Probability-and-statistics/721074: Find the critical value X²R corresponding to a sample size of 25 and a confidence level of 99% . 1 solutions Answer 442177 by stanbon(57361)   on 2013-03-02 19:52:39 (Show Source): You can put this solution on YOUR website!Find the critical value X²R corresponding to a sample size of 25 and a confidence level of 99% . ----- If you want a T-interval. invT(0.005,24) = +-2.797 ================================ Cheers, Stan H.
 Probability-and-statistics/721077: Use the given information to find the P-value. Also, use 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). Ho: p = 2/5 H1: p < 2/5; the test statistic is z = -1.68 1 solutions Answer 442175 by stanbon(57361)   on 2013-03-02 19:48:12 (Show Source): You can put this solution on YOUR website!Use the given information to find the P-value. Also, use 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). Ho: p = 2/5 H1: p < 2/5; the test statistic is z = -1.68 ---- p-value = P(z < -1.68) = 0.0465 ------ Since the p-value is less than 5%, reject Ho. ------------------- Cheers, Stan H.
 Linear-equations/721082: please help me Find the equation of the line: Parallel to y = 3x + 7;x- intercept is 21 solutions Answer 442174 by stanbon(57361)   on 2013-03-02 19:44:07 (Show Source): You can put this solution on YOUR website!Find the equation of the line: Parallel to y = 3x + 7; x- intercept is 2 ------ slope = 3 point: (2,0) -------- Form: y = mx + b Solve for "b": 0 = 3*2 + b b = -6 ----- Equation: y = 3x - 6 =============== Cheers, Stan H. ===============
 Linear_Equations_And_Systems_Word_Problems/721080: Zach has a total of 62 coins, all of which are either dimes or nickels. The total value of the coins is \$5.20. Find the number of each type of coin. x + y = 62 10x + 5y = 520 Don't know what else to do or if I am even going in the right direction. Little help!1 solutions Answer 442173 by stanbon(57361)   on 2013-03-02 19:41:14 (Show Source): You can put this solution on YOUR website!x + y = 62 10x + 5y = 520 ------------ 10x + 10y = 620 10x + 5y = 520 ---- Subtract and solve for "y": 5y = 100 y = 20 (# of nickels) ----- Solve for "x" using x + y = 62 x + 20 = 62 x = 42 (# of dimes) ===================== Cheers, Stan H. =================
 Linear-equations/721081: Please help me find the equation of the line 7/3(1/4-2/5) on line .Find the equation of the line1 solutions Answer 442172 by stanbon(57361)   on 2013-03-02 19:37:09 (Show Source): You can put this solution on YOUR website!find the equation of the line slope = 7/3 passing thru point (1/4,-2/5) ---- Form: y = mx + b Solve for "b": -2/5 = (7/3)(1/4) + b ---- -2/5 = 7/12 + b ----- Mutiply thru by 60 to get: -24 = 35 + 60b 60b = -59 b = -59/60 ----- Equation: y = (7/3)x -(59/60) ========================= Cheers, Stan H. ===========
 Linear_Equations_And_Systems_Word_Problems/721078: University Theater sold 445 tickets for a play. Tickets cost \$20 per adult and \$12 per senior citizen. If total receipts were \$6156, how many senior citizen tickets were sold? a=adults s=seniors a+s=445 20a+12s=6156 20a+12s=6165 a + s = 445 19a + 11s=5711 Don't know what else to do. Help?1 solutions Answer 442170 by stanbon(57361)   on 2013-03-02 19:32:50 (Show Source): You can put this solution on YOUR website!University Theater sold 445 tickets for a play. Tickets cost \$20 per adult and \$12 per senior citizen. If total receipts were \$6156, how many senior citizen tickets were sold? a=adults s=seniors a+s=445 20a+12s=6156 ------------------------- 20a+12s = 6156 12a+12s = 12*445 --- Subtract and solve for "a": 8a = 816 a = 102 (# of adult tickets sold) ---- Solve for "s": a + s = 445 102 + s = 445 s = 343 (# of student tickets sold) ================== Cheers, Stan H.
 Sequences-and-series/721075: 6.25 is 400% of what #?;1 solutions Answer 442169 by stanbon(57361)   on 2013-03-02 19:22:27 (Show Source): You can put this solution on YOUR website!6.25 is 400% of what Equation: 6.25 = (400/100)x 6.25 = 4x x = 1.5625 =============== Cheers, Stan H.
 Percentage-and-ratio-word-problems/721073: How much 60% disinfectant solution must be mixed with a 80% disinfectant solution to produce 25 gallons of a 72% disinfectant solution?1 solutions Answer 442168 by stanbon(57361)   on 2013-03-02 19:17:37 (Show Source): You can put this solution on YOUR website!How much 60% disinfectant solution must be mixed with a 80% disinfectant solution to produce 25 gallons of a 72% disinfectant solution? ------- Equation: active + active = active 0.60x + 0.80(25-x) = 0.72*25 ------ Multiply thru by 100 to get: 60x + 80*25 - 80x = 72*25 -20x = -8*25 x = 10 gallons (amt. of 60% solution needed) ====================================== Cheers, Stan H. ==============
 Permutations/721071: Student Painters, which specializes in painting the exterior of residential buildings, has eight people available to be organized into six-person and two-person teams. In how many ways can the company organize the available people into six- or two-person teams?1 solutions Answer 442166 by stanbon(57361)   on 2013-03-02 19:10:51 (Show Source): You can put this solution on YOUR website!Student Painters, which specializes in painting the exterior of residential buildings, has eight people available to be organized into six-person and two-person teams. In how many ways can the company organize the available people into six- or two-person teams? ------ Since there are 8 painters, every time a 6 member team is formed, a 2 member team is formed. So the number of 6 member teams quals the number of 2 member beams. Ans: 8c2 = (8*7)/(1*2) = 28 ============================= Cheers, Stan H.
 test/720833: explanation on how to solve the problem : -n = -50 and -2 = -w1 solutions Answer 441999 by stanbon(57361)   on 2013-03-01 20:55:33 (Show Source): You can put this solution on YOUR website!explanation on how to solve the problem : -n = -50 Multiply both sides by -1 to get: n = 50 ====================== -2 = -w Multiply both sides by -1 to get: w = 2 =============== Cheers, Stan H. =============
 Equations/720835: Solve and check the equation: 6y=9x3 Answer: 9=(3/2)x3 1 solutions Answer 441998 by stanbon(57361)   on 2013-03-01 20:53:27 (Show Source): You can put this solution on YOUR website!Solve and check the equation: 6y=9x^3 --- y = (9/6)x^3 y = (3/2)x^3 ====================== Answer: y = (3/2)x^3 ============== Cheers, Stan H. ==============