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# Recent problems solved by 'ewatrrr'

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 logarithm/440221: Solve for m. Round your answer to 4 decimal places if necessary. log5 m=1/3 log5 125 a.m = 2.6265 b.m = 5 c.m = 15 d.m = 41.66671 solutions Answer 304159 by ewatrrr(10682)   on 2011-04-25 13:11:27 (Show Source): You can put this solution on YOUR website! Hi log5 m=1/3 log5 125 5^0 = m/125^(1/3)= 1 = = m 5 = m
 Permutations/440145: In how many ways can a group of 7 students be selected from 8 students1 solutions Answer 304147 by ewatrrr(10682)   on 2011-04-25 11:55:03 (Show Source): You can put this solution on YOUR website! Hi In how many ways can a group of 7 students be selected from 8 students 8C7 = 8 ways
 Permutations/440198: a certain mathematics test consist of 10 questions. in how many ways can the test be answered if the possible answers are "true" and "false"" 1 solutions Answer 304146 by ewatrrr(10682)   on 2011-04-25 11:52:49 (Show Source): You can put this solution on YOUR website! Hi a certain mathematics test consist of 10 "true" and "false" questions 2^10 or 1024 is the number of ways the test can be answered
 Trigonometry-basics/440172: After an oven is turned on, its temperature T, is represented by the equation T = 420 - 350 (3.2)^-.1m , where m represents the number of minutes after the oven is turned on and T represents the temperature of the oven in degrees Fahrenheit. How many minutes does the oven take to reach a temperature of 320F? Round your answer to the nearest minute. 1 solutions Answer 304144 by ewatrrr(10682)   on 2011-04-25 11:49:17 (Show Source): You can put this solution on YOUR website! Hi T = 420 - 350 (3.2)^-.1m |where m represents the number of minutes after the oven is turned on and T represents the temperature of the oven in degrees Fahrenheit. T = 420 - 350 (3.2)^-.1m (T-420)/-350 = 3.2^.1m log[(T-420)/-350]/log(3.2) = -.1m T = 320 log[(-100)/-350]/log(3.2) = -.1m log .2857/log(3.2) = -.544/.5 = -.1m -1.08 = -.1m m = 10.8 min, time it takes to reach a temperature of 320F
 Mixture_Word_Problems/440157: Find the domain and the range of the given function. f(x) = -x^2 + 6x A. domain: {x|x≤ -3}; range: {y|y ≤ 9} B. domain: all real numbers; range: {y|y ≤ 9} C. domain: {x|x ≤ 3}; range: {y|y ≤ 9} D. domain: all real numbers;range: {y|y ≤ -9} 1 solutions Answer 304142 by ewatrrr(10682)   on 2011-04-25 11:32:56 (Show Source): You can put this solution on YOUR website! Hi Using the vertex form of a parabola, where(h,k) is the vertex f(x) = -x^2 + 6x |Completing Square to find the Vertex y = -[(x-3)^2 - 9] y = -(x-3)^2 + 9 |represents parabola opening downward, a<0 vertex Pt(3,9) f(3) = 9 is a maximum point Domain: and Range: {y|y ≤ 9}
 Graphs/440179: Could someone please help me solve the system by graphing then classify the system as consistent or inconsistent and dependent or independent? 8x-5y=20 5y-8x=-20 1 solutions Answer 304138 by ewatrrr(10682)   on 2011-04-25 11:20:10 (Show Source): You can put this solution on YOUR website! Hi solve the system by graphing 8x-5y=20 (0,-4) and (20/8,0) 5y-8x=-20 ( 0,-4) and (20/8,0) Graphing points and connecting with a line: These are the same lines, infinite solutions. System is Dependent. A consistent system has at least one solution. An inconsistent system has no solutions. An independent system has exactly one solution. A dependent system has infinitely many solutions.
 Mixture_Word_Problems/440161: A.Find the equation of the quadratic function in standard form vertex (0, 18) ; passing through (-3, 0) A. y = -2x2 + 18 B. y = -2x2 - 18 C. y = x2 + 18 D. y = 18x2 + 18 B. 6. Write the quadratic function in the vertex form. y = -3x^2 - 30x - 71 A. y = 3(x + 5) 2 + 4 B. y = -3(x - 5) 2 + 4 C. y = (x + 5) 2 + 4 D. y = -3(x + 5) 2 + 4 1 solutions Answer 304136 by ewatrrr(10682)   on 2011-04-25 11:13:02 (Show Source): You can put this solution on YOUR website! Hi Using the vertex form of a parabola, where(h,k) is the vertex vertex (0, 18) y = ax^2 + 18 |passing through (-3, 0) 0 = a*9 + 18 -18 = 9a -2 = a y = -2x^2 + 18 Write the quadratic function in the vertex form. y = -3x^2 - 30x - 71 |Completing the square to do so y = -3[x^2 +10x] - 71 y = -3[(x+5)^2 -25] - 71 y = -3(x+5)^2 + 75 - 71 y = -3(x+5)^2 + 4
 logarithm/440174: I need help to find the percentage of Carbon-14 in a sample using the equation: A= InP/-.000121 where P is the percentage of C-141 solutions Answer 304133 by ewatrrr(10682)   on 2011-04-25 10:56:12 (Show Source): You can put this solution on YOUR website! Hi If I am understanding Your Question properly A = lnP/-.000121 -.000121A = lnP e^( -.000121A) = P
 Functions/440171: If f(x) = 2x + 1 and g(x) = x/2 – 1/2 , then f(g(x)) =? the g(x) is x-1 divided by 21 solutions Answer 304130 by ewatrrr(10682)   on 2011-04-25 10:52:18 (Show Source): You can put this solution on YOUR website! Hi g(x) = and f(x) = 2x + 1 f(g(x)) = 2() + 1 |substituting g(x) for x f(g(x)) = x - 1 + 1 f(g(x)) = x
 test/440166: i need to solve this equation for homework: square root 3x+4 +3/2=3 i know that i have to bring over 3/2 but then im not sure of what to do after that. if you could help that would be great1 solutions Answer 304129 by ewatrrr(10682)   on 2011-04-25 10:47:04 (Show Source): You can put this solution on YOUR website! Hi If I am understanding Your Question properly: | 3 - 3/2 = 3/2 3x+ 4 = 9/4 3x = 9/4 - 16/4 3x = -7/4 x = -7/12 CHECKING our Answer***
 Miscellaneous_Word_Problems/440156: . The function f(x) = 0.0037x^2 – 0.41x +36.23 models the average age at which Kentucky men were first married x years after 1900. In which year was this average age at a minimum? What was the average age at first marriage for that year? A. 1955, 47.6 years old B. 1936, 47.6 years old C. 1955, 24.9 years old D. 1951, 36 years old 1 solutions Answer 304128 by ewatrrr(10682)   on 2011-04-25 10:41:36 (Show Source): You can put this solution on YOUR website! Hi, Note use of ^ (uppercase 6) Using the vertex form of a parabola, where(h,k) is the vertex f(x) = 0.0037x^2 – 0.41x +36.23 |graphically a parabola opening upward a>0 models the average age at which Kentucky men were first married x years 'after 1900' f(x) = 0.0037x^2 – 0.41x +36.23 |Completing square to find the vertex (min point) f(x) = .0037[(x - 55.4)^2 - 3069.7589] + 36.23 f(x) = .0037(x - 55.4)^2 - 11.36 + 36.23 f(x) = .0037(x - )^2 + The year, average age at a minimum: 1900+55 = 1955 The average age at first marriage: 24.9
 Miscellaneous_Word_Problems/440163: The number of fruit flies F(x) in a farming area depends on the spring rainfall x: F(x) = 15x – x^2. What rainfall produces the maximum number of fruit flies? A. 225 in. B. 0 in. C. 7.5 in. D. 15 in. 1 solutions Answer 304127 by ewatrrr(10682)   on 2011-04-25 10:28:17 (Show Source): You can put this solution on YOUR website! Hi The number of fruit flies F(x) in a farming area depends on the spring rainfall x: f(x) = -x^2+15x |graphically a parabola opening downward a< 0 Using the vertex form of a parabola, where(h,k) is the vertex f(x) = -(x -7.5)^2 + 56.25 | completing the square to find the vertex Vertex is Pt(7.5, 56.25) 7.5" rainfall produces the maximum number of fruit flies
 Linear_Equations_And_Systems_Word_Problems/440160: In 1920 the record for a certain race was 45.1 sec. In, 1980, it was 4303 sec. Let R(t)= the record in the race and let t= the number of years since 1920. Question Find a linear function that fits this data R(t)=?1 solutions Answer 304126 by ewatrrr(10682)   on 2011-04-25 10:20:56 (Show Source): You can put this solution on YOUR website! Hi In 1920 the record for a certain race was 45.1 sec In, 1980, it was 4303 sec. (1980,4303) (1920, 45.1) m = 4257.9 / 60 = 70.965 R(t) = 70.965t + 45.1 where t= the number of years since 1920.
 logarithm/440159: ok using the formula A=P(1+r/n)^nt how do I solve this word problem? jacobs sixth bday he got a $3,000 cd it earns 5% interest,compounded quarterly. If the CD matures on his 16th bday what amount will be available then?1 solutions Answer 304124 by ewatrrr(10682) on 2011-04-25 10:12:59 (Show Source): You can put this solution on YOUR website! Hi jacobs sixth bday he got a$3,000 cd it earns 5% interest,compounded quarterly. If the CD matures on his 16th bday what amount will be available then A=P(1+r/n)^nt A=$3000(1+.05/4)^4*10 A=$3000(1.0125)^40 = $4930.86  Probability-and-statistics/439886: A light bulb has an average life of 500 hours with a std. deviation of 100 hours. This can be approx. by a normal distr. curve. An amusement park buys and installs 10,000 of such bulbs. Find the total number than can be expected to last for: a) Less than 500 hours b)more than 440 hours1 solutions Answer 304121 by ewatrrr(10682) on 2011-04-25 10:07:13 (Show Source): You can put this solution on YOUR website! Hi A light bulb has an average life of 500 hours with a SD = 100 hours. amusement park buys and installs 10,000 of such bulbs. Number lasting <500hr: 50% of them OR 5,000 Number lasting more than 440 hours = .7557*10,000 = 7,557 *Note: z = (440-500)/100 = -.6 P(z > -.6) = 1 - NORMSDIST(-.6)= 1 - .2743 = .7557 OR 75.57%  Probability-and-statistics/440003: Good Time Movie Theaters has studied the spending habits of customers at their concession counters to find the data normally distributed with a mean of$13.40 and a standard deviation of $2.10. A theater manager wants to know the probability of a customer spending more than$17.50 at the concession stand.1 solutions Answer 304119 by ewatrrr(10682)   on 2011-04-25 09:58:15 (Show Source): You can put this solution on YOUR website! Hi *Note: z = (17.50-13.40)/2.10 = 1.9524 P(z > 1.9524) = 1 - NORMSDIST(1.9524)= 1 - .9746 = .0254
 Probability-and-statistics/440002: If the completion time for a task is normally distributed with a mean of 15 seconds and a standard deviation of 2.5 seconds, what is the probability of getting a time less than 9.7 seconds?1 solutions Answer 304117 by ewatrrr(10682)   on 2011-04-25 09:51:27 (Show Source): You can put this solution on YOUR website! Hi *Note: z = (9.7-15)/2.5 = -2.12 P(z < -2.12) = NORMSDIST(-2.12)= .017
 Probability-and-statistics/440004: The scores on a National High School English Test are normally distributed with an average sore of 83 and a standard deviation of 6. What is the probability that someone will score between 80.24 and 96.26?1 solutions Answer 304114 by ewatrrr(10682)   on 2011-04-25 09:44:55 (Show Source): You can put this solution on YOUR website! Hi *Note: z = (80.24-83)/6 = -.46 and z =(96.26-83)/6 = 2.21 P(.46 < z < 2.21) = NORMSDIST(2.21)-NORMSDIST(-0.46) = .9864 - .3228 = .6637
 Probability-and-statistics/440136: I randomly take three lightbulbs from a box containing 80 lightbulbs of which 5 are defective. What is the probability that none of the three lightbulbs I take are defective? What is the probability that at least one of the lightbulbs I take is defective?1 solutions Answer 304110 by ewatrrr(10682)   on 2011-04-25 09:32:53 (Show Source): You can put this solution on YOUR website! Hi Note: The probability of x successes in n trials is: P = nCx* where p and q are the probabilities of success and failure respectively. In this case p(defective) = 5/80 =.0625 and q = .9375 nCx = randomly take three light bulbs from the box P(none are defective) = (.9375)^3 = .824 P(at least one is defective) = 1 - P(none are defective) = 1 -.824 = .176
 Probability-and-statistics/440129: Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 7 8 3 18 Female 10 14 11 35 Total 17 22 14 53 If one student is chosen at random, Find the probability that the student was NOT a male that got a "B" Enter your answer as a fraction. 1 solutions Answer 304108 by ewatrrr(10682)   on 2011-04-25 09:24:40 (Show Source): You can put this solution on YOUR website! Hi A B C Total Male 7 3 18 Female 10 14 11 35 Total 17 22 14 P( student was NOT a male that got a "B") = 1 -(male with a "B") = 1 - 8/53 = 45/53
 test/440123: hi i need help with the following problem: the cubed root of 2x+7=5 (the five is not under the radical). i have it for homwork and i dont know what to do. i tried looking at my notes but thats not really helping me. if you could show me how to figure out this problem that would be great! thank you1 solutions Answer 304106 by ewatrrr(10682)   on 2011-04-25 09:02:30 (Show Source): You can put this solution on YOUR website! Hi 2x+ 7 = 125 |Cubing both sides of the EQ 2x = 118 x = 59
 Coordinate-system/440112: Could someone please show me how to plot (0, -3) on the coordinate axes?1 solutions Answer 304105 by ewatrrr(10682)   on 2011-04-25 08:59:20 (Show Source): You can put this solution on YOUR website! Hi Re: Plot ordered pair Pt(0,-3) on the coordinate axis Note: (0,-3) the 1st value (0) represents the x-value and (-3) the y-value
 Volume/440116: The perimeter of a rectangle is 54 inches, and its area is 176 sqaure inches. Find the length and width of the rectangle. 1 solutions Answer 304104 by ewatrrr(10682)   on 2011-04-25 08:54:10 (Show Source): You can put this solution on YOUR website! Hi The perimeter of a rectangle is 54 inches: 2L + 2W = 54 OR L + W = 27 AND L = 27-W Let x AND (27-x) represent the width and length respectively Question states***area is 176 square inches Area(rectangle) = L*W (27-x)x = 176 x^2 - 27x + 176 = 0 x = 22/2 = 11, the width. Length 16 or x = 32/2 = 16, the width. Length 11
 Linear-systems/440105: Malome is presently half his brother's age. Five years ago his age and his brother's age added up to 26. What is Malome's present age.?1 solutions Answer 304102 by ewatrrr(10682)   on 2011-04-25 08:22:49 (Show Source): You can put this solution on YOUR website! Hi Malome is presently half his brother's age Let x and 2x represent Malome and his brother's ages NOW Question states***5 years ago... (x-5) + (2x - 5) = 26 3x = 36 x = 12, Malome's age NOW. His brother is 24. (2*12) CHECKING our Answer***5 years ago... 7 + 19 = 26
 Numbers_Word_Problems/440108: Find two numbers such that thier sum is 8 and their product is 91 solutions Answer 304099 by ewatrrr(10682)   on 2011-04-25 08:18:42 (Show Source): You can put this solution on YOUR website! Hi Find two numbers such that their sum is 8 Let x and (8-x) represent the numbers Question states***their product is 9 x(8-x) = 9 8x-x^2=9 x^2 - 8x + 9 = 0 factoring (x-9)(x+1) = 0 (x-9)= 0 x = 9 and (8-x) = -1 (x+1) = 0 x = -1 and (8-(-1) = 9 In either event, The numbers are 9 and -1
 Percentage-and-ratio-word-problems/440110: Tom has taken 5 of the 8 equally weighted tests in his US History class. He has an average score of 78.0 points. How many points does he need to earn on the 6th test to bring his average score to 80 points?1 solutions Answer 304097 by ewatrrr(10682)   on 2011-04-25 08:13:24 (Show Source): You can put this solution on YOUR website! Hi Tom has taken 5 of the 8 equally weighted tests in his US History class. He has an average score of 78.0 points. Total point thru 5 tests = 5*78 = 390 How many points does he need to earn on the 6th test to bring his average score to 80 points? Let x represent his points on his 6th test (390 + x)/6 = 80 390 + x = 480 x = 90 points
 Linear_Equations_And_Systems_Word_Problems/440037: The sum of three numbers is 4. The first, minus the second, plus 4 times the third, is 11. The third plus 3 times the first, plus the second, is -6. What are the numbers?1 solutions Answer 304095 by ewatrrr(10682)   on 2011-04-25 08:08:52 (Show Source): You can put this solution on YOUR website! Hi Let x, y, z represent the numbers: The sum of three numbers is 4: x + y + x = 4 The first, minus the second, plus 4 times the third, is 11: x - y +4z = 11 The third plus 3 times the first, plus the second, is -6: 3x + y + z = -6 Solving for x by substitution x + y + z = 4 OR (y + z) = (4 - x) x - y +4z = 11 3x + y + z = -6 AND 3x + (4-x) = -6 x = -5 Solving for z by Eliminating y x + y + z = 4 x - y +4z = 11 2x + 5z = 15 2*-5 + 5z = 15 z = 5 and y = 4 (x+y+z = -5 + 5 + z = 4) the Numbers are -5,4,5
 Equations/438971: The area A of a triangle with base b and height h is given by A = 1/2bh. Find the area when b=22m (meters) and h=24m. 1 solutions Answer 303437 by ewatrrr(10682)   on 2011-04-21 17:10:54 (Show Source): You can put this solution on YOUR website! Hi A(triangle) = 1/2bh Find the area when b=22m (meters) and h=24m. substituting the b and h values A(triangle) = (1/2)22m*24m = 264 m^2
 logarithm/438962: Determine the time necessary for $1000 to double if it is invested at interest rate r=10% compounded continously.1 solutions Answer 303436 by ewatrrr(10682) on 2011-04-21 17:07:34 (Show Source): You can put this solution on YOUR website! Hi Determine the time necessary for$1000 to double if it is invested at interest rate r=10% compounded continously. 2000 = \$1000e^(.10*t) Compounding continously ln (2000/1000) = .10t 6.9315 yrs = t
 logarithm/438530: log 1/49 = -21 solutions Answer 303435 by ewatrrr(10682)   on 2011-04-21 17:01:27 (Show Source): You can put this solution on YOUR website! Hi x^2 = 1/49 x = 1/7 |Negative solution is Extraneous
 logarithm/438969: 2^6=64 what is the logarithmic form 1 solutions Answer 303434 by ewatrrr(10682)   on 2011-04-21 16:57:51 (Show Source): You can put this solution on YOUR website! Hi