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Recent problems solved by 'stanbon'

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

 Equations/222465: a set of data is normally distrubuted with a mean of 16 and a standard deviation of 0.3.what percent of the data is between 15.2 and 16?1 solutions Answer 166564 by stanbon(57307)   on 2009-10-06 14:06:16 (Show Source): You can put this solution on YOUR website!a set of data is normally distrubuted with a mean of 16 and a standard deviation of 0.3.what percent of the data is between 15.2 and 16? ------------------------ Find the z-values of 15.2 and of 16. --- z(15.2) = (15.2-16) / 0.3 = -2.6667 z(16) = 0 ------------------- P(15.2 < x < 16) = P(-2.667 < z < 0) = 0.1051 ============================================= Cheers, Stan H.
 Complex_Numbers/222460: x/3-1/2=5/6 1 solutions Answer 166563 by stanbon(57307)   on 2009-10-06 14:02:24 (Show Source): You can put this solution on YOUR website!x/3-1/2=5/6 ------------------- Multiply thru by 6 to get: 2x - 3 = 5 2x = 8 x = 4 ============ Cheers, Stan H.
 Probability-and-statistics/222378: There are 7 black, 10 blue, 2 red, and 1 yellow marbles. What is the probability of selecting a black marble and then a blue marble if the marbles are replaced? What is the probability if the marbles are not replaced?1 solutions Answer 166562 by stanbon(57307)   on 2009-10-06 13:58:29 (Show Source): You can put this solution on YOUR website!There are 7 black, 10 blue, 2 red, and 1 yellow marbles. What is the probability of selecting a black marble and then a blue marble if the marbles are replaced? If replaced the events are independent. P(black then blue) = P(black)*P(blue) = (7/20)*(10/20) = 4/40 ------------------------------------------------------------- What is the probability if the marbles are not replaced? If not replaced the events are dependent. P(black then blue) = P(black)*P(blue|black) = (7/20)*(10/19) = 7/38 =============================================================== Cheers, Stan H.
 Proportions/222371: The ratio of men to women at a certain company is to . How many employees does the company have if there are male employees? 1 solutions Answer 166498 by stanbon(57307)   on 2009-10-06 08:41:38 (Show Source): You can put this solution on YOUR website!numbers are missing in your post. Cheers, Stan H.
 Money_Word_Problems/222373: Mrs. Lim invested two equal amounts of money, one at 4% and the other at 6%. Her yearly interest was P800. How much did she invest at each rate?1 solutions Answer 166497 by stanbon(57307)   on 2009-10-06 08:40:33 (Show Source): You can put this solution on YOUR website!Mrs. Lim invested two equal amounts of money, one at 4% and the other at 6%. Her yearly interest was P800. How much did she invest at each rate? ---------------------- Let amount invested at each rate be "x". Equation: interest + interest = interest 0.04x + 0.06x = 800 0.10x = 800 x = P8000 (amount she invested at each rate) ================================================ Cheers, Stan H.
 Mixture_Word_Problems/222374: How many gallons of milk containing 5% butterfat must be mixed with 90 gallons of 1% milk to get 2% milk?1 solutions Answer 166495 by stanbon(57307)   on 2009-10-06 08:37:10 (Show Source): You can put this solution on YOUR website!How many gallons of milk containing 5% butterfat must be mixed with 90 gallons of 1% milk to get 2% milk? ----------------------------- Equation: fat + fat = fat 0.05x + 0.01*90 = 0.02(x+90) Multiply thru by 100 to get: 5x + 1*90 = 2x + 2*90 3x = 90 x = 30 gallons (amount of 5% milk needed for the mixture) =========================== Cheers, Stan H.
 Human-and-algebraic-language/222375: A right triangle has one leg four times as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg. 1 solutions Answer 166494 by stanbon(57307)   on 2009-10-06 08:33:54 (Show Source): You can put this solution on YOUR website!A right triangle has one leg four times as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg. -------------------------------------- Let shortest leg be "x" 2nd leg = 4x hypotenuse = sqrt(x^2 + (4x)^2) = sqrt(17x^2) = x*sqrt(17) -------------------------------------------------------------- Perimeter = x + 4x + x*sqrt(17) P = (5+sqrt(17)x ==================================== Cheers, Stan H.
 Probability-and-statistics/222354: The historical mean for fish caught at a certain Florida lake is 10 pounds with a standard deviation of 1.2 pounds. A fishman goes on a Satuday and catches 12 fish whhich had a mean weight of 11 pounds. Has themean weight of fish at the Florida lake increased? Use a = .05 Please show calculation to problem.1 solutions Answer 166493 by stanbon(57307)   on 2009-10-06 08:27:17 (Show Source): You can put this solution on YOUR website!The historical mean for fish caught at a certain Florida lake is 10 pounds with a standard deviation of 1.2 pounds. A fishman goes on a Satuday and catches 12 fish whhich had a mean weight of 11 pounds. Has themean weight of fish at the Florida lake increased? Use a = .05 Please show calculation to problem. ----------------------------------------- Ho: u = 10 H1: u > 10 -------------- Critical value for 1-tail test with alpha = 5% and df = 10: t = 1.7959 ----------- test statistic: t(11)= (11-10)/[1.2/sqrt(11)] = 2.7639 p-value = P(t>2.7639 with df=11) = 0.0092 ----------------------------------------------- Conclusion: since the p-value is less than 5%, reject Ho. The mean wt. at the lake has increased. -------- Cheers, Stan H.
 Distributive-associative-commutative-properties/222370: Factor x squared - 4x + 4 1 solutions Answer 166491 by stanbon(57307)   on 2009-10-06 07:27:52 (Show Source): You can put this solution on YOUR website!Factor x squared - 4x + 4 --- x^2-4x+4 = (x-2)^2 ================= Cheers, Stan H.
 Angles/222369: angle A and B are supplementary. Find angle A and angle B given Angle A=3x+9 and Angle B=4x-18 1 solutions Answer 166490 by stanbon(57307)   on 2009-10-06 07:26:35 (Show Source): You can put this solution on YOUR website!angle A and B are supplementary. Find angle A and angle B given Angle A=3x+9 and Angle B=4x-18 -------------------------- If A and B are supp, A+B = 180 So, 3x+9 + 4x-18 = 180 7x -9 = 180 7x = 189 x = 27 ------------ A = 3x+9 = 3*27+9 = 90 B = 4x-18 = 4*27-18 = 90 ============================== Cheers, Stan H.
 Polynomials-and-rational-expressions/222357: This actually isn't for me, but for a friend of mine. She emailed me the problem, seeking help, and I have no idea how to do this. The problem is: 3y - 2 divided by 3y^3 + y^2 + 3y - 9 I would appreciate very much if you would answer this. It would teach me something, and hopefully it would help her better grasp the concept and execution of the solution. 1 solutions Answer 166489 by stanbon(57307)   on 2009-10-06 07:23:18 (Show Source): You can put this solution on YOUR website!The problem is: 3y - 2 divided by 3y^3 + y^2 + 3y - 9 ------------------------- The numerator is not a factor of the denominator so the fraction cannot be reduced. It is as it stands. ------------------------- Cheers, Stan H.
 Trigonometry-basics/222367: I just need an example on how to do one problem and then I will work on the other problems myself. Thank you in advance. Graph each function. Identify the domain and range. f(x)=[[x+1]] 1 solutions Answer 166488 by stanbon(57307)   on 2009-10-06 07:15:07 (Show Source): You can put this solution on YOUR website!Are you saying y = absolute (x+1) ? -------------------------- If you are: Let x=0, then y = |0+1| = 1 Let x=-1, then y = |-1+1| = 0 Let x = -2, then y = |-2+1| = |-1| = 1 --------------------------------------------- Plot those points and connect. =================================================== Cheers, Stan H.
 Linear-systems/222215: 1/2x+ (-1/2)y=1/2 (-1/3)x+(-3/4)y=2 I divided everything by 1/2 and you get x-y=1 for the first equation. the second equation i times everything by 12 and get (-4)x + (-9)y = 24 multiply the first equation by -9, so we get -9x +9y = -9. (-9)x + (9)y = -9 (-4)x + (-9)y = 24 I get (-15/13, -28/13) But it is wrong, what did i do wrong? Thanks for the help!1 solutions Answer 166467 by stanbon(57307)   on 2009-10-05 22:43:08 (Show Source): You can put this solution on YOUR website!1/2x+ (-1/2)y=1/2 (-1/3)x+(-3/4)y=2 ----------------------------- Multiply thru 1st by 2 Multiply thru 2nd by -12 ------------------------------- x - y = 1 4x +9y = -24 --- Multiply thru 1st by 4 ---------------------------- 4x - 4y = 4 4x + 9y = -24 ---------------- Subtract 1st from 2nd and solve for "y": 13y = -28 y = -28/13 ----- Substitute into x - y = 1 to solve for "x": x +(28/13) = 1 x = (13/13)-(28/13) x = -15/13 ================== Cheers, Stan H.
 real-numbers/222274: Suppose thatr an athlete free dives to an elevation of -42 meters in 60 seconds. Find the average rate of change in the divers elevation?1 solutions Answer 166461 by stanbon(57307)   on 2009-10-05 22:29:47 (Show Source): You can put this solution on YOUR website!Suppose thatr an athlete free dives to an elevation of -42 meters in 60 seconds. Find the average rate of change in the divers elevation? ----------------- Average rate = -42/60 = -7/10 meters per second ===================================================== Cheers, Stan H.
 Equations/222237: Find the coordinates of B. M is the midpoint of line AB. A(7,5), M(9,7)1 solutions Answer 166458 by stanbon(57307)   on 2009-10-05 22:24:55 (Show Source): You can put this solution on YOUR website!Find the coordinates of B. M is the midpoint of line AB. A(7,5), M(9,7) ------------------------- Let B have coordinates (x,y) --------------- If M is the midpoint (x+7)/2 = 9 ; x+7 = 18 ; x = 11 ---------------- If M is the midpoint (y+5)/2 = 7 ; y+5 = 14 ; y = 9 ------------------------- B has coordinates (11,9) =========================== Cheers, Stan H.
 Inverses/222269: 0.3(4+x)=4.5 could you show it step by step1 solutions Answer 166456 by stanbon(57307)   on 2009-10-05 22:18:52 (Show Source): You can put this solution on YOUR website!0.3(4+x)=4.5 --- Divide both sides by 0.3 to get: (4+x) = 15 Subtract 4 from both sides to get: x = 11 ============== Cheers, Stan H.
 Probability-and-statistics/222179: You have a traffic light of only a red and a green light. What is the probability that you will get 2 green lights out of 4 times the light changes? I figured that probability of one try is .5. It is either green or red the 1st time. Then I wrote out the possibilities of 2 light changes, and came up with rr, rg, gr, gg. (So 2 greens is 1/4, or .5 x .5 = .25.) After this, I am stuck. I don't think it's .5 x .5 x .5 x .5. That would be too small a probability. I think the events are independent and mutually exclusive, but then I don't know what to do. My dad and I tried to write out all the possibilities, and got 16 of them, with 6 times getting 2 greens, so that would be 6/16 or 3/8, but we're not sure. We did not count the cases where we got 3 or 4 greens... do you count those too? And I don't have a good formula to go by... if the problem were 9 tries or something, I'd never figure it out!1 solutions Answer 166452 by stanbon(57307)   on 2009-10-05 22:14:22 (Show Source): You can put this solution on YOUR website!You have a traffic light of only a red and a green light. What is the probability that you will get 2 green lights out of 4 times the light changes? I figured that probability of one try is .5. It is either green or red the 1st time. Then I wrote out the possibilities of 2 light changes, and came up with rr, rg, gr, gg. (So 2 greens is 1/4, or .5 x .5 = .25.) After this, I am stuck. I don't think it's .5 x .5 x .5 x .5. That would be too small a probability. I think the events are independent and mutually exclusive, but then I don't know what to do. My dad and I tried to write out all the possibilities, and got 16 of them, with 6 times getting 2 greens, so that would be 6/16 or 3/8, but we're not sure. We did not count the cases where we got 3 or 4 greens... do you count those too? And I don't have a good formula to go by... if the problem were 9 tries or something, I'd never figure it out! --------------------- I think you and your Dad did well. It's a binomial problem with n = 4, p = 1/2 , x = 2 --- P(x=2) = 4C2*(1/2)^2*(1/2)^2 --- P(x=2) = 6/16 = 3/8 -------------------------- It's the same as having exactly 2 girls born in a family of 4. The events (red and green) are independent because you don't know whether you will get a red or a green at each intersection. Similar to tossing a coin. =================================== Cheers, Stan H.
 Probability-and-statistics/222240: What is the probability that a randomly selected person in the town is a Republican or a Democrat? 1 solutions Answer 166439 by stanbon(57307)   on 2009-10-05 21:35:26 (Show Source): You can put this solution on YOUR website!You have to post more information than that. Cheers, Stan H.
 Equations/222208: A health food manager mixes 8 ounces of lentils that cost 70 cents per pound with white beans that cost \$1.10 per pound to make a soup mix.How many ounces of white beans should be used to produce a mixture that is worth 85 cents per pound?i need help setting up and equation for it1 solutions Answer 166433 by stanbon(57307)   on 2009-10-05 21:14:21 (Show Source): You can put this solution on YOUR website!A health food manager mixes 8 ounces of lentils that cost 70 cents per pound with white beans that cost \$1.10 per pound to make a soup mix.How many ounces of white beans should be used to produce a mixture that is worth 85 cents per pound?i need help setting up an equation for it. ---------------------------------- Equation: value + value = value 70(1/2) + 110x = 85(x+(1/2)) --- 35 + 110x = 85x + 42.5 25x = 7.5 x = 0.3 lbs. (amount of \$1.10 beans neede in the mixture) ============================================================ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/222205: determind the slope intercept form of (x/3) + (y/6)=-11 solutions Answer 166430 by stanbon(57307)   on 2009-10-05 20:59:32 (Show Source): You can put this solution on YOUR website!determine the slope intercept form of (x/3) + (y/6)=-1 ------------------------ Multiply thru by 6 to get: 2x + y = -6 Solve for "Y": y = -2x -6 That is the slope-intercept form. ===================================== Cheers, Stan H.
 Linear-systems/222199: -2 x - 2 y =5 8 x+ 8 y=-20 Having a hard time with these. thanks for all help!1 solutions Answer 166429 by stanbon(57307)   on 2009-10-05 20:53:24 (Show Source): You can put this solution on YOUR website! -2 x - 2 y =5 8 x+ 8 y=-20 --------------------- Multiply thru 1st by 4 to get: -8x -8y = 20 ------------------- Add that to the 2nd equation to get 0 + 0 = 0 ---------------- That means the two equations are really the same. Solve one of them for y and you get y = -x-(5/2) Solution: (x , -x-(5/2)) for x = any Real Number ================================= Cheers, Stan H.
 Probability-and-statistics/221887: It is asserted that 90 percent of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of six cars: At least four will have the transponder. (Round your answer to 4 decimal places.) Probability : 1 solutions Answer 166427 by stanbon(57307)   on 2009-10-05 20:44:11 (Show Source): You can put this solution on YOUR website!It is asserted that 90 percent of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of six cars: At least four will have the transponder. (Round your answer to 4 decimal places.) --------------------------- It's a binomial problem with n=6, p = 0.9, 4<=x<=6 --------------------------------------- P(4<=x<=6) = 1 - binomcdf(6,0.9,3) = 0.9842 ================================================ Cheers, Stan H.
 Mixture_Word_Problems/221852: A pharmacist is to prepare 15 liters of eye drops. eye drop solution must have a 4% active ingredient, but the pharmacist only has 10% solution and 2% solution in stock. How much of the 10% soulution should be used to fill the prescription?1 solutions Answer 166270 by stanbon(57307)   on 2009-10-05 12:22:23 (Show Source): You can put this solution on YOUR website!A pharmacist is to prepare 15 liters of eye drops. eye drop solution must have a 4% active ingredient, but the pharmacist only has 10% solution and 2% solution in stock. How much of the 10% soulution should be used to fill the prescription? ------------------------ Equation: active + active = active 0.10x + 0.02(15-x) = 0.04*15 Multiply thru by 100 to get: 10x + 2*15 - 2x = 4*15 10x = 2*15 x = 3 liters (amount of 10% solution needed in the mixture) ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/221864: please help me with these problems. I can't seem to understand. 45z^3 - 90z^2+ 40z and z^2 - 14z + 24 thank you!1 solutions Answer 166269 by stanbon(57307)   on 2009-10-05 12:11:28 (Show Source): You can put this solution on YOUR website!Are you being asked to factor or to solve? ---------------------- 45z^3 - 90z^2+ 40z Factor: = 5z(9z^2-18z+8) --- = 5z(3z-2)(3z-4) --- If you need to solve, set each factor equal to zero and solve to get: z = 0, z = 2/3, z = 4/3 ================================= and z^2 - 14z + 24 Factor: = z^2-12z-2z+24 --- = z(z-12)-2(z-12) --- = (z-12)(z-2) --- If you need to solve, set each factor equal to zero and solve to get: z = 12 or z = 2 ======================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/221863: The height of a projectile fired vertically nto the air (neglecting air resistance) at an initial velocity of 96 feet per second is a function of time, x, and is given by the equation f(x)=96-16x^2. Find the highest point reached by the projectile. 1 solutions Answer 166267 by stanbon(57307)   on 2009-10-05 12:01:13 (Show Source): You can put this solution on YOUR website!The height of a projectile fired vertically nto the air (neglecting air resistance) at an initial velocity of 96 feet per second is a function of time, x, and is given by the equation f(x)=96x-16x^2. Find the highest point reached by the projectile. ----------------------- That is a quadratic equation with a = -16 and b = 96 ----------------- The maximum height occurs when x = -b/(2a) = -96/(-32) = 3 seconds. ------------------- The height at that time is f(3) = 96*3-16(3)^2 = 144 ft. ============================ Cheers, Stan H.
 Numeric_Fractions/221860: z/5-1/2=z/61 solutions Answer 166266 by stanbon(57307)   on 2009-10-05 11:56:21 (Show Source): You can put this solution on YOUR website!z/5-1/2=z/6 Multiply thru by 30 to get rid of the fractions: 6z - 15 = 5z z = 15 =================== Cheers, Stan H.
 Probability-and-statistics/221751: an urn contains 4 red, 2 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?1 solutions Answer 166264 by stanbon(57307)   on 2009-10-05 11:53:36 (Show Source): You can put this solution on YOUR website! an urn contains 4 red, 2 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue? ------------------------------- P(no blue) + P(at least one blue) = 1 --------------------------------------------- So, P(at least one blue) = 1 - P(no blue) --- P(none blue) = 6C3/10C3 = 20/120 = 1/6 ---------------- Therefore: P(at least one blue) = 1-(1/6) = 5/6 ================================================== Cheers, Stan H.
 Age_Word_Problems/221827: jellyfish are about 19 water. if you have a 300 lb jellyfish( and yes, some do -- 20 grow to be that big!) what is the weight of the water it contains?(show your work, but you do not need a 5 step solution.)1 solutions Answer 166258 by stanbon(57307)   on 2009-10-05 10:33:54 (Show Source): You can put this solution on YOUR website!jellyfish are about 19 water. if you have a 300 lb jellyfish( and yes, some do -- 20 grow to be that big!) what is the weight of the water it contains?(show your work, but you do not need a 5 step solution.) ------------------------------------------------ x/300 = 19/20 x = (19/20)*300 --- x = 19*15 x = 285 lbs of water ============================ Cheers, Stan H.
 logarithm/221833: what is the logarithms of 0.00093581 solutions Answer 166257 by stanbon(57307)   on 2009-10-05 10:28:16 (Show Source): You can put this solution on YOUR website!what is the logarithms of 0.0009358 ---------------------------------------- You probably can find an on-line calculator that would give you that answer. Ans: -3.0288 ================= Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/221829: In direct variation, as one variable increases, does the constant increase,decrease, or remain the same?1 solutions Answer 166256 by stanbon(57307)   on 2009-10-05 10:24:45 (Show Source): You can put this solution on YOUR website!In direct variation, as one variable increases, does the constant increase,decrease, or remain the same? ------------------------------------------- If by constant you mean the "constant of variation", it's value changes as the x and/or y variables change. ------------- But once a certain x/y pair is determined the constant of variation is fixed for the situation being studied. That fact allows other x/y pairs to be determined. =============================================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/221832: Advance tickets to a show cost , and same-day tickets cost . The total number of tickets sold was for total receipts of . How many tickets of each type were sold? 1 solutions Answer 166255 by stanbon(57307)   on 2009-10-05 10:17:43 (Show Source): You can put this solution on YOUR website!The numbers do not appear in your post. Cheers, Stan H.