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Recent problems solved by 'robertb'

robertb answered: 4011 problems
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Problems-with-consecutive-odd-even-integers/405437: if x represents the first of two consecutive odd integers, express the sum of two integers in the term of x. 1 solutions Answer 286349 by robertb(4012)   on 2011-02-07 05:12:40 (Show Source): You can put this solution on YOUR website! x + x + 2 = 2x + 2

Equations/405365: the amount (A) on deposit in a bank account bearing simple interest is given by the formula A=P+PRT find A when P=$1200 R=0.08 T=3 1 solutions Answer 286348 by robertb(4012)   on 2011-02-07 05:11:53 (Show Source): You can put this solution on YOUR website! A = P(1+RT) = 1200(1 + 0.24) = 1200*1.24 = 1488 $

Trigonometry-basics/405373: Please help me with this math problem (thank you so much)? F(x)=1/x find different quotient, F(x+h)-f(x)/h of f: Also find the average rate of change of f of the interval [1,3] List the interval on which f is increasing or decreasing, if there is any 1 solutions Answer 286347 by robertb(4012)   on 2011-02-07 05:10:33 (Show Source): You can put this solution on YOUR website! . TO find the A.R.C. from 1 to 3, let x = 1, and h = 2 above, so that A.R.C. = -2/(1*3) = -2/3. The graph of F(x) = 1/x is a hyperbola with x-axis as horizontal asymptote and y-axis as vertical asymptote. It is decreasing over its domain.

Trigonometry-basics/405379: Given function f(x)=(x^2-8)/(x+3) is the point (-2, -4) on the graph of f? 1 solutions Answer 286346 by robertb(4012)   on 2011-02-07 05:02:26 (Show Source): You can put this solution on YOUR website! , so yes the point is on the graph of f.

Travel_Word_Problems/405402: Two cars leave Prima Community College traveling in opposite directions. One car travels at 60mph and the other at 64mph. In how many hours will they be 310 miles apart? 1 solutions Answer 286345 by robertb(4012)   on 2011-02-07 04:58:19 (Show Source): You can put this solution on YOUR website! If they take off at the same time, then 60t + 64t = 310 ==> 124t = 310 t = 2.5 hours.

Travel_Word_Problems/405439: Calculate the force F needed to keep a 525Kg wagon stationary on an uphill slope with an incline angle of 15 degrees. (friction is zero, and g = 9.81) I tried and found F=1332.98 Newtons. 1 solutions Answer 286344 by robertb(4012)   on 2011-02-07 04:56:15 (Show Source): You can put this solution on YOUR website! That is correct. You have to overcome a force equal to the component of the weight that is parallel to the incline, equal to m*g*sin15 = 1332.98 N.

Problems-with-consecutive-odd-even-integers/405412: The sum of three consecutive odd integers is 85 less than four times the first. What is the first integer? 1 solutions Answer 286343 by robertb(4012)   on 2011-02-07 04:50:52 (Show Source): You can put this solution on YOUR website! x + x+2 + x+4 = 4x -85 ==> 3x + 6 = 4x - 85 ==> 91 = x, the 1st odd integer.

Probability-and-statistics/405414: if IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person chosen at random will have an IQ score greater than 110? 1 solutions Answer 286342 by robertb(4012)   on 2011-02-07 04:48:42 (Show Source): You can put this solution on YOUR website! From the 68-95-99.7 rule for normal distributions, 110 is 2 sd's higher than the mean 100. Hence the probability the IQ is greater than 110 is .

Miscellaneous_Word_Problems/405417: Hi, I don't know if any of you answer statistics questions, but you really helped this struggling old lady get through algebra last year so I thought I would give you a try. (Yes, I'm struggling with Stats just as much.) My question reads: A fisherman arrives at his favorite fishing spot. From past experience he knows that the number of fish he catches per hour follows a Poisson distribution at .5/hr. What’s the probability that will catch at least 3 in four hrs. Here's my take: If he catches .5 in one hour, that makes the lambda .5/1? Multiplied by the time (4 hours) gives me 2. So I believe my 2 calculator numbers are 2 and 3. If I'm doing the keystrokes correctly, I come up with a .184 probability. Am I even in the ballpark? Thanks so much for ANY help you can give me! 1 solutions Answer 286341 by robertb(4012)   on 2011-02-07 04:43:02 (Show Source): You can put this solution on YOUR website! It depends on the parameter that you use. The probability mass function for the Poisson distribution is . The parameter is correct. The probability of catching 0, or 1, or 2 fish is . Hence the probability of catching at least 3 fish is , to 6 decimal places.

Average/405433: a student has two test scores. the difference between the scores is 12 and the mean or average of the scores is 80. what are the two test scores? 1 solutions Answer 286340 by robertb(4012)   on 2011-02-07 04:29:48 (Show Source): You can put this solution on YOUR website! L - S = 12, and L + S = 160. ==> 2L = 172 ==> L = 86, the higher-score test, and S = 160 - 86 = 74, the low-score test.

Probability-and-statistics/405436: Essay; show all work. A simple dartboard has three areas… the main board has a radius of 8 inches, there is a circle with a radius of 6 inches, and the bullseye has a radius of 4 inches. What is the probability of a random dart landing inside the bullseye? 1 solutions Answer 286339 by robertb(4012)   on 2011-02-07 04:26:13 (Show Source): You can put this solution on YOUR website!

Expressions-with-variables/404397: Let a and b be real numbers. A line passes through points (a,b) and (b,a). Consider another three points (a+1,b-1), (b+1,a-1), ((a+b)/2,(a+b)/2). Which of the following is true regardless of the choice of a and b? choose the answer and explain the reason to choose your response Exactly two of the points lie on the line All three of the points lie on the line Exactly one of the points lies on the line None of the points lie on the line 1 solutions Answer 285831 by robertb(4012)   on 2011-02-04 20:55:08 (Show Source): You can put this solution on YOUR website! All three of the points lie on the same line. The line through (a,b) and (b,a)has slope -1. The line through(a,b) and (a+1,b-1) has slope -1. The line through(a,b) and (b+1,a-1) has slope -1. The point ((a+b)/2,(a+b)/2) is the midpoint of the points (a,b) and (b,a).

Permutations/404417: How do you answer 26! It seems the bigger the number we get a scientific notation. What is an easy way to answer n! if n is a big number? 1 solutions Answer 285830 by robertb(4012)   on 2011-02-04 20:47:36 (Show Source): You can put this solution on YOUR website! Stirling's approximation gives n! ~. My calculator gives as , while 26! is .

logarithm/404465: Solve for x to the nearest thousandth: ln(5x+20)=2 1 solutions Answer 285827 by robertb(4012)   on 2011-02-04 20:37:41 (Show Source): You can put this solution on YOUR website! The equation is equivalent to ==>

Mixture_Word_Problems/404455: How much of an alloy that is 20% copper should be mixed with 300 oz of an alloy that is 80% copper to get an alloy that is 40% copper? 1 solutions Answer 285826 by robertb(4012)   on 2011-02-04 20:34:50 (Show Source): You can put this solution on YOUR website! 0.20x + 0.80*300 = 0.40*(x + 300) ==> 0.20x + 240 = 0.40x + 120 ==> 120 = 0.20x ==> x = 600 oz of the 20% copper alloy should be added.

Functions/404466: 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. P(x)= 1 solutions Answer 285824 by robertb(4012)   on 2011-02-04 20:30:17 (Show Source): You can put this solution on YOUR website! The hypotenuse is given by . Hence the perimeter is

Probability-and-statistics/404413: Determine the odds against the spinner landing on red. 3 red sections out of 8 total sections. this is where i ended up: P(not red)=5/8 P(red)=3/8 Where do I go next? 1 solutions Answer 285823 by robertb(4012)   on 2011-02-04 20:26:17 (Show Source): You can put this solution on YOUR website! Odds against = , or 5 to 3.

logarithm/404418: solve algebraically e^x = -x 1 solutions Answer 285821 by robertb(4012)   on 2011-02-04 20:20:14 (Show Source): You can put this solution on YOUR website! It's quite clear that no can satisfy the equation. (, but ). Considering the graphs of both and -x, there is only one solution (or intersection point), and it lies between -1 and -1/2. (This is because and . Now for small values of x. So to get an approximate value for the root, solve ==> , or . ==> . Eliminating the bottom value the answer is

logarithm/404461: Solve to the nearest hundredth: e^(x+2)=6 When I did the work, I got (x+2)ln e=6 x+2=6 x=4 **I think this is wrong though. Please help! Thanks! :) 1 solutions Answer 285812 by robertb(4012)   on 2011-02-04 20:03:17 (Show Source): You can put this solution on YOUR website! . ==> That's where the glitch is.

logarithm/404454: In the equation logx 3+logx 5=4 what is the value of x, to the nearest hundredth? 1 solutions Answer 285810 by robertb(4012)   on 2011-02-04 20:01:07 (Show Source): You can put this solution on YOUR website! logx 3+logx 5=4 ==> logx 15 = 4 ==> ==> , to the nearest hundredth. (Eliminate any negative real solutions, because x > 0 and not equal to 1.)

logarithm/404460: Solve the equation for all values of x. 9^(x^2+x)=3^4 1 solutions Answer 285807 by robertb(4012)   on 2011-02-04 19:56:10 (Show Source): You can put this solution on YOUR website! <==> <==> ==> ==> (x+2)(x-1) = 0 ==> x = -2, 1. Both values satisfy the original equation.

Linear_Equations_And_Systems_Word_Problems/404458: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? 1 solutions Answer 285805 by robertb(4012)   on 2011-02-04 19:53:24 (Show Source): You can put this solution on YOUR website! <==> ==> x = 2.4 hours, working together.

Exponential-and-logarithmic-functions/404182: "What are the real number solutions to g^3+3g^2-g-3=0" 1 solutions Answer 285682 by robertb(4012)   on 2011-02-04 06:50:52 (Show Source): You can put this solution on YOUR website! ==> g = -3, 1, -1.

Percentage-and-ratio-word-problems/404214: Last month, a factory produced 800 television sets. This month, the same factory produced 1,064 televisoion sets. The increase in production from last month to this month is? 1 solutions Answer 285681 by robertb(4012)   on 2011-02-04 06:46:25 (Show Source): You can put this solution on YOUR website! In quantity, the increase is 264. In percentage, the increase is % = 33%.

Finance/404183: find the accumulated amount at the end of eight months on a $2400 bank deposit paying simple interest at a rate of 8% a year 1 solutions Answer 285680 by robertb(4012)   on 2011-02-04 06:36:21 (Show Source): You can put this solution on YOUR website! Balance = B = P(1 + rt) = 2,400*(1 + 0.08*(2/3)) = 2400*(79/75) = $ 2528.

Surface-area/404191: PLS. HELP ME SOLVE THIS PROB. THANK YOU SO MUCH... FIND THE VOLUME AND TOTAL AREA OF THE LARGEST CUBE OF WOOD THAT CAN BE CUT FROM A LOG OF CIRCULAR CROSS SECTION WHOSE RADIUS IS 12.7 INCHES 1 solutions Answer 285679 by robertb(4012)   on 2011-02-04 06:32:46 (Show Source): You can put this solution on YOUR website! I will answer only the volume. ==> inches. ==> cu. in. This is assuming that the log is at least inches long.

Graphs/404188: find f (g(x)) and g (f(x)) and determine whether each pair of functions f and g are inverse of each other. F(x)=-x and g(x)=-x 1 solutions Answer 285678 by robertb(4012)   on 2011-02-04 06:24:39 (Show Source): You can put this solution on YOUR website! yes. f(g(x)) = f(-x) = -(-x) = x = g(-x) = g(f(x))

Surface-area/404190: SHOW THAT: A) TOTAL SURFACE OF A CUBE TWICE THE SQUARE OF ITS DIAGONAL. B) VOLUME OF A CUBE IS 1/9 TIMES SQUAROOT OF 3 TIMES THE CUBE OF ITS DIAGONAL. THANK YOU.... PLS. HELP ME... 1 solutions Answer 285677 by robertb(4012)   on 2011-02-04 06:22:53 (Show Source): You can put this solution on YOUR website! a) Let s = side of a cube. Then , or . ==> b)

Trigonometry-basics/404203: Find the area bounded by the curve r=2acos(θ) 1 solutions Answer 285676 by robertb(4012)   on 2011-02-04 06:05:48 (Show Source): You can put this solution on YOUR website! For polar coordinates, the area would be given by the integral = = = = NOTE: The polar equation is equivalent to the circle , after changing to rectangular coordinates. A direct calculation of the area of this circle using the formula would give the same answer .

Probability-and-statistics/404206: The probability that A occurs is 0.3, the probability that B does not occur is 0.6, and the probability that either A or B occurs is 0.5. Find: a) The probability that A does not occur. b) The probability that both A and B occur. c) The probability that A occurs and B does not occur. 1 solutions Answer 285673 by robertb(4012)   on 2011-02-04 05:34:32 (Show Source): You can put this solution on YOUR website! Given: P(A) = 0.3 P(B') = 0.6 ==> P(B) = 0.4 P(A U B) = 0.5 a) P(A') = 0.7 b) P(A AND B) = P(A) + P(B) - P(A U B) =0.3 + 0.4 - 0.5 = 0.2 c) P(A AND B') = P(A U B) - P(B) = 0.5 - 0.4 = 0.1

Probability-and-statistics/404204: Twenty percent of trees in a particular forest have a disease, 30% of the trees are too small to be used for lumber, and 40% are too small to be used for lumber or have a disease. What percent of the trees are too small to be used for lumber, given that they have a disease? 1 solutions Answer 285672 by robertb(4012)   on 2011-02-04 05:24:09 (Show Source): You can put this solution on YOUR website! P(diseased) = 0.20 P(too small) = 0.30 P(diseased U too small) = 0.40 ==> P(too small|diseased) = P(too small AND diseased)/P(diseased) =[P(too small) + P(diseased) - P(too small U diseased)]/P(diseased) =[0.30 + 0.20 - 0.40]/0.20 = 0.10/0.20 = 1/2, or 50% of the trees are too small to be used for lumber, given that they have a disease.