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 Proportions/567525: 66 is 40% of what number? 1 solutions Answer 366590 by stanbon(57967)   on 2012-02-03 21:16:22 (Show Source): You can put this solution on YOUR website!66 is 40% of what number --- 66 = 0.40x x = 66/0.4 x = 165 ============ Cheers, Stan H. ===========
 Inequalities/567508: Q: If x is a positive integer such that 350<7x^2<450, find x.1 solutions Answer 366588 by stanbon(57967)   on 2012-02-03 21:08:42 (Show Source): You can put this solution on YOUR website!x in an integer such that 200<3x^3<400, find x. ----- Divide thru by "3" to get: (200/3) < x^3 < (400/3) ---- Take the cube root along the line: --- cbrt[200/3] < x < cbrt[400/3] 4.0548 < x < 5.1087 --- Answer: 5 ================================== cheers, Stan H.
 Linear-equations/567511: i have to graph the solution set y is less than 1/3 x -3. i know how to get y=0,-3 and m=1/3 i know how to graph those points but am stock after that, please help1 solutions Answer 366587 by stanbon(57967)   on 2012-02-03 21:03:58 (Show Source): You can put this solution on YOUR website!graph the solution set y is less than 1/3 x -3. y < (1/3)x -3 ---- Graph the boudary as a dashed line thru (0,-3), (3,-2) ---- Shade the half-plane BELOW the boundary because you want y to be LESS THAN (1/3)x-3 ======================================== Cheers, Stan H.
 Probability-and-statistics/567524: In the formula for the Confidence Interval for the Mean, if the Confidence Coefficient, z(α/2) = 2.58, what is the Confidence Level? 1 solutions Answer 366586 by stanbon(57967)   on 2012-02-03 20:59:26 (Show Source): You can put this solution on YOUR website!In the formula for the Confidence Interval for the Mean, if the Confidence Coefficient, z(α/2) = 2.58, what is the Confidence Level? ---- Draw a normal curve where the horizontal axis is the z-values. Plot z = 2.58 Find the area to the right of 2.58 normalcdf(2.58,100) = 0.0049 ---- Then alpha = 2(0.0049) = 0.0099 ---- So, 1% is in the two tails. So the confidence level is 99% ================================== Cheers, Stan H.
 Travel_Word_Problems/567516: a kayaker can paddle 12 mi in 2 h moving with the river current. paddling at the same pace, the trip back against the current takes 4 h. assume that the river current is constant. find what the kayaker's speed would be in still water.1 solutions Answer 366584 by stanbon(57967)   on 2012-02-03 20:54:29 (Show Source): You can put this solution on YOUR website!a kayaker can paddle 12 mi in 2 h moving with the river current. paddling at the same pace, the trip back against the current takes 4 h. assume that the river current is constant. find what the kayaker's speed would be in still water. --------- Downstream DATA: distance = 12 miles ; time = 2 hours ; rate = 12/2 = 6 mph ---------------- Upstream DATA: distance = 12 miles ; time = 4 hrs ; rate = 12/4 = 3 mph ---- Equations: Downstream: b + c = 6 Upstream::: b - c = 3 ------ Add to get: 2b = 9 b = 4.5 mph (speed of the boat in still water. ----- Solve for "c": b + c = 6 4.5 + c = 6 c = 1.5 mph (speed of the current) ======================================= Cheers, Stan H. ===================
 Polynomials-and-rational-expressions/567522: Factor, state prime if so 8xy^4+27x^4y1 solutions Answer 366581 by stanbon(57967)   on 2012-02-03 20:50:47 (Show Source): You can put this solution on YOUR website!Factor, state prime if so 8xy^4+27x^4y ---- = xy[8y^3 + 27x^3] ---- You have the sum of squares: ------ = xy(2y+3x)((2y)^2-(2y)(3x)+(3x)^2] ------ = xy(4y^2-6xy+9x^2) ====================== Cheers, Stan H. ======================
 Polynomials-and-rational-expressions/567520: factor completely, indicate if prime 3x^3+14x^2-5x1 solutions Answer 366580 by stanbon(57967)   on 2012-02-03 20:47:47 (Show Source): You can put this solution on YOUR website!factor completely, indicate if prime 3x^3+14x^2-5x ---- = x(3x^2+14x-5) -- = x[3x^2 + 15x-x -5] --- = x[3x(x+5)-(x+5)] ---- = x(x+5)(3x-1) =================== Cheers, Stan H. ================
 Mixture_Word_Problems/567512: A jeweler has 5 rings, each weighing 16 g, made of an alloy of 15% silver and 85% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add?1 solutions Answer 366579 by stanbon(57967)   on 2012-02-03 20:45:43 (Show Source): You can put this solution on YOUR website!A jeweler has 5 rings, each weighing 16 g, made of an alloy of 15% silver and 85% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add? ------ Equation: silver + silver = silver 0.15*5*16 + 1*x = 0.20(80+x) ---- Multiply thru by 100 to get: 15*80 + 100x = 20*80 + 20x 80x = 5*80 x = 5 grams of silver (amt. of silver to be added) ========================================================= Cheers, Stan H. ============
 Money_Word_Problems/567483: How much will be in someone's account at the end of 3 years if they deposit \$700 and the simple interest is 5% per year? 1 solutions Answer 366541 by stanbon(57967)   on 2012-02-03 18:15:51 (Show Source): You can put this solution on YOUR website!How much will be in someone's account at the end of 3 years if they deposit \$700 and the simple interest is 5% per year? --------------- A(t) = P(1 + rt) ----- A(3) = 700(1 + 0.05*3) = 700*1.15 = 805 =========================================== Cheers, Stan H. ==========
 Permutations/567482: An identification code is to consist of three letters followed by six digits. How many different codes are possible if repetition is permitted?1 solutions Answer 366540 by stanbon(57967)   on 2012-02-03 18:11:21 (Show Source): You can put this solution on YOUR website!An identification code is to consist of three letters followed by six digits. How many different codes are possible if repetition is permitted? ---- Ans: 26^3*10^6 = 17576000000 ================= Cheers, Stan H.
 Permutations/567481: Hello Tutors. Can I get some help with this homework problem please. Given that P(A) = 0.6 and P(B) = 0.3, and P(A and B) = 0.18, determine P(B|A1 solutions Answer 366539 by stanbon(57967)   on 2012-02-03 18:07:14 (Show Source): You can put this solution on YOUR website!Given that P(A) = 0.6 and P(B) = 0.3, and P(A and B) = 0.18, determine P(B|A) ----------------- P(B | A) = P(B and A)/P(A) = 0.18/0.6 = 0.3 =================== Cheers, Stan H. ================
 Linear_Equations_And_Systems_Word_Problems/567468: The local train is 25 miles down the track from the Central Station when the express leaves he station.The local train travels at a rate of 50 mi/hr and the express train travels at a rate of 80 mi/hr.Let n represent the number of hours since the express train left Central Station. a.Write an expression that represents the express train's distance from Central Station in n hours. b.When will the express train catch up with the local train?1 solutions Answer 366538 by stanbon(57967)   on 2012-02-03 18:02:09 (Show Source): You can put this solution on YOUR website!The local train is 25 miles down the track from the Central Station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express train travels at a rate of 80 mi/hr. Let n represent the number of hours since the express train left Central Station. a.Write an expression that represents the express train's distance from Central Station in n hours. distance = 80n miles -------------------------------------- b.When will the express train catch up with the local train? Local train DAta: distance = (80n - 25) miles ; rate = 50 mph ; time = (80n-25)/50 hr ----- Express train DATA: distance = 80n ; rate = 80 mph ; time = n hr. ======= Equation: time = time n = (80n-25)/50 50n = 80n-25 30n = 25 n = 5/6 hrs n = 50 minutes =================== Cheers, Stan H.
 Expressions-with-variables/567358: w=s/f solve for f can you show the steps? Thanks! 1 solutions Answer 366513 by stanbon(57967)   on 2012-02-03 12:07:37 (Show Source): You can put this solution on YOUR website!w=s/f solve for f can you show the steps? Thanks! --- Multiply both sides by f to get: fw = s Divide both sides by w to get: f = s/w ----- OR w = s/f Invert both sides to get: f/s = 1/w Multiply both sides by s to get: f = s/w ============================== Cheers, Stan H. ================
 Probability-and-statistics/567359: Two students, Jim and Joan are registered for the same class and attend independently to each other, Jim 91,9% of the time and Joan 84.3% of the time. What is the probability that on any given day a) at least on of them will be in class? b) neither will be in class?1 solutions Answer 366512 by stanbon(57967)   on 2012-02-03 12:04:43 (Show Source): You can put this solution on YOUR website!Two students, Jim and Joan are registered for the same class and attend independently to each other, Jim 91,9% of the time and Joan 84.3% of the time. What is the probability that on any given day a) at least on of them will be in class? P(at least one) = 1 - P(neither in class) = 1 - 0.081*0.157 = 0.9873 -------------------------------------- b) neither will be in class? P(neither) = 0.081*0.157 = 0.0127 ======================================= cheers, Stan H. ==============
 Probability-and-statistics/567302: 120 students were selected among all those at college number 1. 30 of them are sophomores. Find the margin of error1 solutions Answer 366510 by stanbon(57967)   on 2012-02-03 11:52:33 (Show Source): You can put this solution on YOUR website!120 students were selected among all those at college number 1. 30 of them are sophomores. Find the margin of error ----- Comment: I guess you are say that 0.30 of them are sophomores. --- Assuming you want 95% confidence you get: ME: z*sqrt[pq/n] = 1.96*sqrt[0.3*0.7/120] = 0.0820 ============================================================ cheers, Stan H.
 Probability-and-statistics/567330: Find the z-score for the value 50, when the mean is 77 and the standard deviation is 8.1 solutions Answer 366508 by stanbon(57967)   on 2012-02-03 11:48:05 (Show Source): You can put this solution on YOUR website!Find the z-score for the value 50, when the mean is 77 and the standard deviation is 8. ---- z(50) = (50-77)/8 = -27/8 = -3.3750 ====================================== Cheers, Stan H. ============
 Polynomials-and-rational-expressions/567198: Factor and explain: 1/4x^2 - 9. I have (1/36x^2-1)(9) as the answer which I got from using Mathway.com, but this doesn't make sense to me and I am unable to factor this on my own.1 solutions Answer 366456 by stanbon(57967)   on 2012-02-02 22:48:34 (Show Source): You can put this solution on YOUR website!Factor and explain: 1/4x^2 - 9. --- The form is a "difference of squares". It factors as follows: [(1/2)x-3] =========================== cheers, Stan H. ============
 logarithm/567199: how do you solve 3.5^x=47.9 without using a calculator? I get really confused when it comes to the decimals..1 solutions Answer 366454 by stanbon(57967)   on 2012-02-02 22:46:32 (Show Source): You can put this solution on YOUR website!3.5^x=47.9 ---- You have no choice but to take the log of both sides: x(log(3.5)) = log(47.9) ---- x = log(47.9)/(log(3.5)) ---- x = 3.0885 ------ Unless you use a slide rule of log tables you cannot get this answer without a calculator. ---- Cheers, Stan H. =============
 Linear-systems/567190: Scenario: Gas Mileage of Cars A BMW 128ci mile per gallon is 18. The Mercedes-Benz C300 mile per gallon is 19. It cost \$20.83 for the BMW to travel 100 miles. It cost \$19.73 for the Mercedes-Benz to travel 100 miles. The price for a gallon of gas is \$3.75. How many gallons does it take to travel 100 miles for each vehicle? Also, what are the equations? (solve by elimination, and show your work)1 solutions Answer 366453 by stanbon(57967)   on 2012-02-02 22:43:15 (Show Source): You can put this solution on YOUR website!Scenario: Gas Mileage of Cars A BMW 128ci mile per gallon is 18. --- 100 miles/18 mpgallon = 5.5555 gallons -------------------- The Mercedes-Benz C300 mile per gallon is 19. 100 miles/19 mpgallon = 5.2632 gallons --------------------------- Cheers, Stan H. ---- You don't need the cost per gallon information. It cost \$20.83 for the BMW to travel 100 miles. It cost \$19.73 for the Mercedes-Benz to travel 100 miles. The price for a gallon of gas is \$3.75. How many gallons does it take to travel 100 miles for each vehicle?
 Probability-and-statistics/567195: On a math test, 5 out of 20 students got an "A". If 2 out of the 20 students are chosen at random, what is the probability that all 3 got an "A" on the test?1 solutions Answer 366450 by stanbon(57967)   on 2012-02-02 22:37:17 (Show Source): You can put this solution on YOUR website!On a math test, 5 out of 20 students got an "A". If 2 out of the 20 students are chosen at random, what is the probability that all 3 got an "A" on the test? ---- Binomial Problem with n = 3 and p(got A) = 1/4 --- P(3 of 3 got A) = (1/4)^3 = 1/64 ===================================== Cheers, Stan H. ===============
 Human-and-algebraic-language/567192: One more question from this crazy "practice test" for a job. again its been 17 years since HS algebra...Kids you will have to use algebra again...mark my words. :) Question: Three individuals form a partnership and agree to divide the profits eqally. x invest 9000, Y invest 7000, and z invest 4000. If the profits are 4800 how much less does x receive than if the profits were divided in proportion to the amount invested? (let me first say that x isn't the smartes investor...) What I have so far is x+y+z=20000 9000/20000 = x/4800 so proportionaly x's investmet would yeild \$2160. The second part would be figuring out what equal % so 1/3 = x/4800 that would be 1600 and then you just subtract 1600 from 2160 and that is \$560. Did I do that correctly? any suggestions of more problems like these and the other one I did that I could practice on would be greatly appreciated.1 solutions Answer 366449 by stanbon(57967)   on 2012-02-02 22:35:10 (Show Source): You can put this solution on YOUR website!Question: Three individuals form a partnership and agree to divide the profits eqally. x invest 9000, Y invest 7000, and z invest 4000. If the profits are 4800 how much less does x receive than if the profits were divided in proportion to the amount invested? ---- They invested in a ratio of 9:7:4 --- Equation: 9x + 7x + 4x = 4800 20x = 4800 x = 240 ---- Proportional Distribution: 9x would get 9*240 7x would get 7*240 4x would get 4*240 --- Equal distribution: 1600 1600 1600 --------------- You can figure out the difference for each of the individuals. ================================= Cheers, Stan H.
 Average/567193: find the average of 7, 11, 14, 28, and 711 solutions Answer 366447 by stanbon(57967)   on 2012-02-02 22:28:06 (Show Source): You can put this solution on YOUR website!Add those numbers and divide the sum by 5 to get the average. Cheers, Stan H.
 Miscellaneous_Word_Problems/567191: Things did not go quite as planned. You invested \$10,250.00, part of it in stock that paid 12.5% annual interest. However, the rest of the money suffered a 6.7% loss. If the total annual income from both investments was \$346.00, how much was invested at each rate?1 solutions Answer 366446 by stanbon(57967)   on 2012-02-02 22:26:57 (Show Source): You can put this solution on YOUR website!You invested \$10,250.00, part of it in stock that paid 12.5% annual interest. However, the rest of the money suffered a 6.7% loss. If the total annual income from both investments was \$346.00, how much was invested at each rate? ---- Quantity Eq::: x + y = 10,250 Interest Eq::0.125x - 0.067y = 346 ----------------------------------- Multiply thru the Interest equation by 1000 Multiply thru the Quantity Eq. by 125 -------------------------- 125x + 125y = 125*10,250 125x - 67y = 346000 --------------------------------------- Subtract and solve for "y": 192y = \$935,250 y = \$4871.09 (amt. invested at 6.7% Solve for "x": x + y = 10,250 x + 4671.09 = 10,250 x = \$5378.91 (amt. invested at 12.5% ========================================= Cheers, Stan H. ==============
 Human-and-algebraic-language/567189: Ok its been 17 years since I took algebra and I have a test for a job interview and this was one of the questions. I got the correct answer but it took me a long time with pen to paper. I know there is a better way to write it. In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the larger type, a printed page contains 1800 word. Using smaller type, a page contains 2400 words. The article is alloted 21 full pages in a magazine. How many pages must be in smaller type? I know I need to use x+y=21 and 1800x +2400y = 48000 but I am not sure how to relate the two.1 solutions Answer 366445 by stanbon(57967)   on 2012-02-02 22:19:56 (Show Source): You can put this solution on YOUR website!In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the larger type, a printed page contains 1800 word. Using smaller type, a page contains 2400 words. The article is alloted 21 full pages in a magazine. How many pages must be in smaller type? I know I need to use x+y=21 and 1800x +2400y = 48000 but I am not sure how to relate the two. ---- Page Equation: x + y = 21 Words Equatiion: 1800x + 2400y = 48000 ------------------- Multiply thru the "Page" Eq. by 1800 to get: 1800x + 1800y = 21*1800 1800x + 2400y = 48000 ---- Subtract and solve for "y": 600y = 10200 y = 17 (# of pages with 1800 words) ---- Solve for "x": x + y = 21 x + 17 = 21 x = 4 (# of pages with 2400 words) ======================================= cheers, Stan H. ================
 Linear-equations/567187: find the slope of the line through each pair of points, if possible, and based on the slope, indicate whether the line through the points risess from left to right, falls from left to right, is horizonal, or is vertical (-4,1)and(-3,4)and (1.5,2.6)and(0.5,(3.6)1 solutions Answer 366444 by stanbon(57967)   on 2012-02-02 22:13:34 (Show Source): You can put this solution on YOUR website!find the slope of the line through each pair of points, if possible, and based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizonal, or is vertical (-4,1)and(-3,4) slope = (4-1)/(-3--4) = 3/1 = 3 ;;therefore rises ------------------------ (1.5,2.6)and(0.5,(3.6) slope = (3.6-2.6)/(0.5-1.5) = 1/-1 = -1 ;; therefore falls -------------------------- Cheers, Stan H. ===============
 Trigonometry-basics/567026: an arc is 0.04 meters long and is intercepted by a central angle of circumfrence/8 radians. what is the diameter of the circle?1 solutions Answer 366416 by stanbon(57967)   on 2012-02-02 19:10:01 (Show Source): You can put this solution on YOUR website!an arc is 0.04 meters long and is intercepted by a central angle of circumfrence/8 radians. what is the diameter of the circle? ----- Formula: theta(in radians) = (arc length)/(radius) ------ radius = (arc length)/theta --- radius = (0.04 meters)/(2pi/8) --- = 0.04/(pi/4) --- = 0.04*4/pi === = 0.16/pi =============== Therefore diameter = 2(0.16/pi) = 0.32/pi meters ======================================================= Cheers, Stan H.
 Linear-systems/567023: I'm having trouble with a math problem about systems of linear equations. FInd out the values of x and y and please show your work. 7x+3y=1 4x-y=6 I thank you for the help.1 solutions Answer 366415 by stanbon(57967)   on 2012-02-02 19:05:41 (Show Source): You can put this solution on YOUR website!7x+3y=1 4x-y=6 ---- Multiply thru the bottom equation by 3: ------- 7x + 3y = 1 12x -3y = 18 --------------------- Add and solve for "x": 19x = 19 x = 1 ---- Solve for "y": 4x-y = 6 4 - y = 6 y = -2 ================== Cheers, Stan H. ===================
 Money_Word_Problems/567015: I have trouble answering this simple interest question. A loan company advertises that you only pay 8 cents per day for each \$100 borrowed. If a person borrows \$500 for 90 days, what amount must the person repay and what annual simple interest rate is the loan company actually charging?(use a 360-day year)1 solutions Answer 366413 by stanbon(57967)   on 2012-02-02 19:03:09 (Show Source): You can put this solution on YOUR website!A loan company advertises that you only pay 8 cents per day for each \$100 borrowed. If a person borrows \$500 for 90 days, what amount must the person repay and what annual simple interest rate is the loan company actually charging?(use a 360-day year) ------ 8 cents per day implies 8*360 = \$28.80 per year Actual simple interest rate = 28.80/100 = 28.8% ----------------------------- If borrow 500 for 90 days you pay 5*(8 cents)*90 = \$36.00 ============================================================ Using the formula I = Prt you get: I = 500*0.288(90/360) I = 500*0.288(1/4) I = 500*0.072 I = \$36.00 Cheers, Stan H.
 Numbers_Word_Problems/567014: One number is one less than twice the other number. The sum of thetwo numbers is 35. Find the two numbers?1 solutions Answer 366410 by stanbon(57967)   on 2012-02-02 18:57:13 (Show Source): You can put this solution on YOUR website!One number is one less than twice the other number. The sum of the two numbers is 35. Find the two numbers? ---- Equations: x = 2y-1 x + y = 35 ----------- Substitute for "x" and solve for "y": 2y-1 + y = 35 3y = 36 y = 12 ----- Solve for "x": x = 2y-1 x = 24-1 x = 23 ================= Cheers, Stan H. =================
 Miscellaneous_Word_Problems/566995: John, Paul, George, and Stuart were four school friends. After one particularly hard day's night, they went to see a movie together. After the first time, they began going regularly but on different schedules. (They even went on weekends.) John went every fourth day, Paul went every fifth day, George went every seventh day, and Stuart went every ninth day. How many days was it before all four went to the movies together again?1 solutions Answer 366409 by stanbon(57967)   on 2012-02-02 18:53:47 (Show Source): You can put this solution on YOUR website!John, Paul, George, and Stuart were four school friends. After one particularly hard day's night, they went to see a movie together. After the first time, they began going regularly but on different schedules. (They even went on weekends.) -------------------------------------------- John went every fourth day, Paul went every fifth day, George went every seventh day, and Stuart went every ninth day. How many days was it before all four went to the movies together again? -------------------- Least common multiple: 4*5*7*9 = 1260 days ======================================== Cheers, Stan H. =============
 Triangles/566996: If a triangle has a 3 inch side on each side is is a triangle?1 solutions Answer 366406 by stanbon(57967)   on 2012-02-02 18:35:03 (Show Source): You can put this solution on YOUR website!If a triangle has a 3 inch side on each side is is a triangle? ----- Please read your post again.