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# Recent problems solved by 'scott8148'

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 Quadratic_Equations/150639: How do you factor a^2 - 2ab - 15b^2 completly, whats the answer?1 solutions Answer 110588 by scott8148(6628)   on 2008-08-03 15:34:01 (Show Source): You can put this solution on YOUR website!factors of -15 that "combine" to -2 like 3 and -5 (a+3b)(a-5b)
 Quadratic_Equations/150645: How do you completly factor p^4 - 1, what is the answer?1 solutions Answer 110585 by scott8148(6628)   on 2008-08-03 15:28:38 (Show Source): You can put this solution on YOUR website!difference of squares __ (p^2+1)(p^2-1) difference of squares (again) __ (p^2+1)(p+1)(p-1)
 Quadratic_Equations/150646: How do you completly factor p^4 - 1, what is the answer?1 solutions Answer 110583 by scott8148(6628)   on 2008-08-03 15:27:54 (Show Source): You can put this solution on YOUR website!difference of squares __ (p^2+1)(p^2-1) difference of squares (again) __ (p^2+1)(p+1)(p-1)
 Quadratic_Equations/150644: How do you completly factor 4c^2 - 12c + 9, whats the answer?1 solutions Answer 110581 by scott8148(6628)   on 2008-08-03 15:25:07 (Show Source): You can put this solution on YOUR website!factors of 9 that can "combine" with factors of 4 to get -12 like -3 and 2 __ (2c-3)(2c-3)
 Mixture_Word_Problems/150420: This is a multiple choice proble that I am not getting any of the answers to. The average amount customers at a certain grocery store spend yearly is \$636.55. Assume the variable is normally distributed. If the standard deviation is \$89.46, find the probability that a randomly selected customer spends between \$550.67 and \$836.94. 0.144 = 14.4% 0.820 = 82.0% 0.156 = 15.6% 0.943 = 94.3% Please help, Ellen1 solutions Answer 110372 by scott8148(6628)   on 2008-07-31 22:43:59 (Show Source): You can put this solution on YOUR website!find the z values for the upper and bounds of the range and then find the portion of the distribution represented lower __ z=(550.67-636.55)/89.46 __ z=-.96 (approx) upper __ z=(836.94-636.55)/89.46 __ z=2.24 (approx) this range represents about 82% of the distribution
 Probability-and-statistics/150419: Find the area under the normal distribution curve to the right of z = –1.03. 0.151 –0.349 0.349 0.849 Please help. I can't figure which answer is right.1 solutions Answer 110371 by scott8148(6628)   on 2008-07-31 22:32:06 (Show Source): You can put this solution on YOUR website!since the z value is negative, it is to the left of the mean this means that everything to the right of the value is more than half of the area only one answer is more than .5
 Exponential-and-logarithmic-functions/150352: In order to plot the graphs of the following functions, what do I do first? I am so lost! f(x)=7^x f(x)=4^x-3 f(x)=(1/5)^x f(x)=log3x Thanks for your help!1 solutions Answer 110369 by scott8148(6628)   on 2008-07-31 22:25:21 (Show Source): You can put this solution on YOUR website!plotting the graphs is straight forward (a graphing calculator would be a big help) __ the f(x) values are on the vertical (y) axis and the x values are on the horizontal axis __ find the f(x) values by "plugging in" values for x 1. f(x)=7^x __ when x=0, f(x)=1 (this is the y-intercept) __ when x is 1, f(x)=7 __ as x becomes a large NEGATIVE value, f(x) approaches zero (horizontal asymptote) 2. f(x)=4^(x-3) __ when x=3, the exponent is 0 so f(x)=1 __ when x=0, f(x)=4^(-3) or 1/64 __ same general shape as #1 with different y-intercept 3. f(x)=(1/5)^x __ when x=0, f(x)=1 __ as x becomes a large POSITIVE value, f(x) approaches zero (horizontal asymptote) __ this graph is sort of a "mirror image" of #'s 1 and 2 4. logarithms are NOT defined for negative quantities, so this graph is only on the right-hand side of the vertical axis __ as x approaches zero (very small fractions), f(x) approaches negative infinity (vertical asymptote)
 Exponential-and-logarithmic-functions/150386: Oh dear God please help me!!! We are studying Graphs of Exponential and Logarithmic Functions and I am so lost I'm about to send out the hound dogs, but seriously if someone could please help just get me started I would greatly appreciate it. I am supposed to Plot the graphs of the following functions:I don't understand how 1. f(x) = 7x this x variable is actually an exponent so it is 7 to the x power 2. f(x) = 4x - 3 the x-3 here is also an exponent so it reads 4 to the x-3 power 3. f(x) = (1/5)x this is actually 1/5 to the x power again the x is an exponent 4. f(x) = log3x Thank you guys for always helping me out. I can't wait till I get this degree so I can help yall out with some \$\$\$. 1 solutions Answer 110311 by scott8148(6628)   on 2008-07-31 14:03:47 (Show Source): You can put this solution on YOUR website!\$\$\$, huh...WOW!! plotting the graphs is straight forward (a graphing calculator would be a big help) __ the f(x) values are on the vertical (y) axis and the x values are on the horizontal axis __ find the f(x) values by "plugging in" values for x 1. f(x)=7^x __ when x=0, f(x)=1 (this is the y-intercept) __ when x is 1, f(x)=7 __ as x becomes a large NEGATIVE value, f(x) approaches zero (horizontal asymptote) 2. f(x)=4^(x-3) __ when x=3, the exponent is 0 so f(x)=1 __ when x=0, f(x)=4^(-3) or 1/64 __ same general shape as #1 with different y-intercept 3. f(x)=(1/5)^x __ when x=0, f(x)=1 __ as x becomes a large POSITIVE value, f(x) approaches zero (horizontal asymptote) __ this graph is sort of a "mirror image" of #'s 1 and 2 4. logarithms are NOT defined for negative quantities, so this graph is only on the right-hand side of the vertical axis __ as x approaches zero (very small fractions), f(x) approaches negative infinity (vertical asymptote)
 Rational-functions/150309: The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet what force would be required to keep the same car from skidding on a curve of radius 570 feet at 50 mph? Round your answer to the nearest pound of force? I don't know what formula that would be to use... I don't know how to approach this task... 1 solutions Answer 110291 by scott8148(6628)   on 2008-07-30 21:34:34 (Show Source): You can put this solution on YOUR website!a formula is not needed __ this is a proportional problem __ k is the constant of proportionality 3600=[k*1800*20^2]/600 __ 3600=k*1200 __ dividing by 1200 __ 3=k f=[3*1800*50^2]/570 __ f=23684
 Rational-functions/150310: If an object is thrown upward with an initial velocity of 64 ft/sec, its height after t sec is given by h = 64t - 16t2. Find the number of seconds the object is in the air before it hits the ground. I figure that it would work with d=rt but I don't know how to convert it to this assignment. what throws me off is the h=64t-16t2...1 solutions Answer 110289 by scott8148(6628)   on 2008-07-30 21:24:27 (Show Source): You can put this solution on YOUR website!because of gravitational acceleration, r is constantly changing __ that makes d=rt not useful in this situation when it is on the ground, h=0 __ so we can substitute and solve 0=64t-16t^2 __ factoring __ 0=(16t)(4-t) 0=16t __ dividing by 16 __ 0=t __ this is the beginning of the "flight" 0=4-t __ adding t __ t=4 __ this is the "flight" time
 Miscellaneous_Word_Problems/150243: This question is from textbook Elementary and Intermediate Algebra Suppose Charlie O’Brian hits a baseball straight upward at 150ft/sec from a height of 5 feet. a) Use the formula to determine how long it takes the ball to return to Earth b) Use the graph on the next page to estimate the maximum height reached by the ball I have no idea how to set up the equation for the answer........1 solutions Answer 110260 by scott8148(6628)   on 2008-07-30 13:10:03 (Show Source): You can put this solution on YOUR website!a general trajectory related formula for baseballs, golf balls, artillery shells, etc. __ is h=-16t^2+(Vo)t+Ho __ h is the height at time (t), Vo is the initial upward (vertical) velocity __ and Ho is the initial height for part a), you need to find the time (t) when h=0 (return to Earth) 0=-16t^2+150t+5 __ use the quadratic formula to find t __ HINT __ the positive value is the one you want other HINT __ max height is approx 357'
 Percentage-and-ratio-word-problems/150272: An electrical resistor is rated at 4,550 Ohms with a tolerance of 8%. What are its tolerance limits? I tried .08*4550=364+4550=4914 Ohms. My teacher says its wrong. 1 solutions Answer 110256 by scott8148(6628)   on 2008-07-30 12:54:07 (Show Source): You can put this solution on YOUR website!you found the upper limit; what about the lower limit? there is a tolerance "band" __ lower to 4914
 Trigonometry-basics/150137: Will someone please help me! I do not understand how to get to the polar form! Write the following as a complex number in polar form: sqrt.3 + i Thank you for your time, Natalie1 solutions Answer 110208 by scott8148(6628)   on 2008-07-29 18:18:28 (Show Source): You can put this solution on YOUR website!with complex numbers, the real part is on the horizontal (x) axis __ and the imaginary part is on the vertical (y) axis so sqrt(3) on the x and 1 on the y forms two sides of a right triangle __ the 3rd side is the hypotenuse; which is the polar radius using Pythagoras, r^2=x^2+y^2 __ r^2=[sqrt(3)]^2+1^2 __ r^2=3+1 __ r=2 the tangent of the polar angle is [imaginary]/[real] or y/x __ tan(Θ)=1/sqrt(3) __ Θ=30º or π/6 radians
 Polynomials-and-rational-expressions/150140: I need help with this problem im not sure on how to solve this given its story problem setting, any help is appreciated. If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples?1 solutions Answer 110194 by scott8148(6628)   on 2008-07-29 15:05:40 (Show Source): You can put this solution on YOUR website!"If the total cost of x apples is b cents"; then each apple costs b/x so, y apples will cost y*(b/x) or yb/x
 Distributive-associative-commutative-properties/150092: Can you please factor out completely 2x^2+xy-6y^2?1 solutions Answer 110173 by scott8148(6628)   on 2008-07-28 22:11:54 (Show Source): You can put this solution on YOUR website!(2x-3y)(x+2y)
 Proportions/150083: Solve the prportion: 41.) x square+5x+6 over x square-2x-8 = x square -4x-5 over x square-8x+15 Please and thank you 1 solutions Answer 110172 by scott8148(6628)   on 2008-07-28 22:09:56 (Show Source): You can put this solution on YOUR website!factoring __ cancelling __ "cross" multiplying __ x^2-9=x^+5x+4 __ subtracting x^2+4 __ -13=5x __ dividing by -13 __ x=-5/13
 logarithm/150015: How long will it take for an investment to double in value if it is invested at 5% per annum compounded monthly?1 solutions Answer 110144 by scott8148(6628)   on 2008-07-28 16:32:23 (Show Source): You can put this solution on YOUR website!let t=time in months __ a=2p (doubling) __ r=.05 a=p(1+(r/12))^t __ dividing by p __ 2=(1+(.05/12)^t __ taking log __ log(2)=t*log(1+(.05/12) dividing by log(1+(.05/12) __ [log(2)]/[log(1+(.05/12)]=t t=166.7 (approx) __ should be 167 to get final compounding
 Exponents/150035: I am interested in finding a simple explanation as to why a number taken to a zero power is equal to 1. Thanks.1 solutions Answer 110136 by scott8148(6628)   on 2008-07-28 16:01:54 (Show Source): You can put this solution on YOUR website!demonstration is the most straight forward using rules for exponents, (x^a)/(x^b)=x^(a-b) __ (x^5)/(x^3)=x^2 __ (x*x*x*x*x)/(x*x*x)=x*x suppose a=b __ (x^a)/(x^b)=x^(a-b)=x^0 __ (x*x*x)/(x*x*x)=1=x^0
 Probability-and-statistics/149995: If anyone could help with this, that would be great.thanks Here is the problem: Mutual Funds The retirement plan for a company allows employees to invest in 10 different mutual funds. If Sam selected 4 of these funds at random, and 6 of the 10 grew by at least 10% over the last year, what is the probability that 3 of Sam's 4 funds grew by at least 10% last year? i have tried many things nothing works. Heidi 1 solutions Answer 110130 by scott8148(6628)   on 2008-07-28 15:46:44 (Show Source): You can put this solution on YOUR website!the number of ways to select 4 funds out of 10 is 10C4 or 210 the number of ways to select 3 funds out of 6 is 6C3 or 20 the number of ways to have 3 good funds with 1 poor fund is 20*6 or 120 so the probability of 3 out of 4 funds being good is 120/210 or 4/7
 Rational-functions/150024: I want to learn this (been 15+ yrs) so I am looking for the why or how answer. I already have the solution(solution manual). use the vertex abd intercepts to sketch the graph of each quadratic function. give equation of the parabola'a axis of symmetry. use the graph to determine the functions domain and ranges. f(x)=x^2+3x-101 solutions Answer 110127 by scott8148(6628)   on 2008-07-28 15:25:42 (Show Source): You can put this solution on YOUR website!15 years, huh...congratulations for an expression of the form ax^2+bx+c, the equation for the axis of symmetry is x=-b/(2a) since the vertex lies on the axis of symmetry, __ substituting this x value into the equation of the function will give the y value (and thus the coordinates) of the vertex the intercepts, where the graph crosses an axis, are found by substituting zero for x or y and solving for the other __ this is because when you are crossing an axis, the value of the other component is zero axis of symmetry __ x=-3/(2*1) __ x=-3/2 vertex __ y=(-3/2)^2+3(-3/2)-10 __ y=9/4-9/2-10 __ y=-49/4 __ so (-3/2,-49/4) is the location of the vertex intercepts __ substituting 0 for x __ y=0^2+3(0)-10 __ y=-10 __ this is the y intercept substituting 0 for y __ 0=x^2+3x-10 __ factoring __ 0=(x+5)(x-2) x+5=0 __ x=-5 x-2=0 __ x=2 these are the x intercepts (the axis of symmetry is midway between them)
 Radicals/149989: Hello there, I am currently working on an optional summer packet for school, and I came across this problem. I have the answer available to me, but I don't understand how to get the answer. If you could explain to me how to simplify this expression, I'd greatly appreciate it. (2)/(5 - ) Thank you!1 solutions Answer 110099 by scott8148(6628)   on 2008-07-28 11:46:51 (Show Source): You can put this solution on YOUR website!the radical in the denominator is a no-no __ so it is removed by multiplying the numerator and denominator by 5+sqrt(3), the conjugate of the denominator 2[5+sqrt(3)]/[(5-sqrt(3))*(5+sqrt(3))] __ [10+2sqrt(3)]/[5^2-(sqrt(3))^2] __ [10+2sqrt(3)]/(25-3) [5+sqrt(3)]/11
 Expressions-with-variables/149994: Hello, I'd really appreciate it if you could help me with this problem. It's for an optional summer math packet for school. Solve the quadratic by factoring. 2x^3 - 6x = 01 solutions Answer 110097 by scott8148(6628)   on 2008-07-28 11:32:22 (Show Source): You can put this solution on YOUR website!common factors first __ 2x(x^2-3)=0 factoring the remaining quadratic (difference of squares) __ 2x(x+sqrt(3))(x-sqrt(3))=0 2x=0 __ x=0 x+sqrt(3)=0 __ x=-sqrt(3) x-sqrt(3)=0 __ x=sqrt(3)
 Exponential-and-logarithmic-functions/149988: I have 2 questions: 1. What are the asymptotes of the functions f(x)=3^xn and g(x)= log52x ??? (Would this be a vertical asymptote? Would the denominator be 1?) 2. A cell divides into 2 identical copies every 4 minutes. How many cells will exist after 3 hours? Thanks sooooooooooooo much for your help! I have this week and next and this class will be over, I've never felt so dumb in all my life! I can't find anything in my text about this - I am doing this as an online class, so there is very little help!1 solutions Answer 110096 by scott8148(6628)   on 2008-07-28 11:26:33 (Show Source): You can put this solution on YOUR website!1. for f(x)=3^xn __ at x=0, f(x)=1 __ as x gets more negative, f(x) approaches zero (negative x-axis is horizontal asymptote) __ no asymptote for positive x for g(x)=log52x __ as x approaches zero, g(x) approaches -∞ (negative y-axis is vertical asymptote) __ logarithms are not defined for negative arguments (negative numbers don't have logs) __ no asymptote for positive x 2. there are 45 (180/4) 4 min periods in 3 hr __ the cells are doubling every 4 min __ the number of cells after 3 hrs would be 2^45 __ 35184372088832 (calculators are useful)
 Trigonometry-basics/149984: Please help! If we establish an identity: (tan A - cot A)/(tan A + cot A) would equal what? Thank you, Tami1 solutions Answer 110092 by scott8148(6628)   on 2008-07-28 10:57:05 (Show Source): You can put this solution on YOUR website!multiplying the numerator and denominator by sin(A)*cos(A) gives [sin^2(A)-cos^2(A)]/[sin^2(A)+cos^2(A)] since sin^2(A)+cos^2(A)=1, we are left with sin^2(A)-cos^2(A) or 1-2cos^2(A)
 Trigonometry-basics/149985: please help! Find the value of: tan^-1 (-sqrt. 3) Thank you, Tami1 solutions Answer 110089 by scott8148(6628)   on 2008-07-28 10:46:02 (Show Source): You can put this solution on YOUR website!the angle whose tangent is -sqrt(3) is part of a 30º-60º-90º triangle in the 2nd quadrant (tangent is negative) the reference angle in the 2nd quadrant is 60º, so the angle is 120º or 2pi/3 radians
 Rate-of-work-word-problems/149944: Working together, a painter and the painter's apprentice can paint a room in 4h. Working alone, the apprentice requires 7 more hours to paint the room that the painter requires working alone. How long does it take the painter, working alone, to paint the room? Please round your answer to one decimal place. 4/T + 4/T+7 = 1 T(T+7)(4/T + 4/T+7) = T(T+7)1 (T+7)4+4T = T(T+7) 4T +28 +4T = T^2 +T7 8T+28=T^2+T7 Am I doing this right? I keep coming up with the wrong answer, I think.1 solutions Answer 110048 by scott8148(6628)   on 2008-07-27 21:11:10 (Show Source): You can put this solution on YOUR website!subtracting 8T+28 __ 0=T^2-T-28 using quadratic formula __ T=[1±sqrt(1-(4*1*(-28)))]/2 __ T=[1±sqrt(113)]/2 T=5.82 (approx)
 Mixture_Word_Problems/149861: 18 out of 20 customers make a purchase. If three customers are selected randomly one at a time, what is the probability that all will make a purchase? Please help.1 solutions Answer 110044 by scott8148(6628)   on 2008-07-27 19:49:56 (Show Source): You can put this solution on YOUR website!there are 20C3 (1140) possible groups of 3 in 20 __ some of these groups contain non-purchasers there are 18C3 (816) possible groups of 3 in 18 __ none of these groups contain non-purchasers probability of all purchasers is 816/1140 or 0.716 (approx) if order of selection is thought to be important (permutation vs combination); the result will be the same
 Finance/149881: 18 out of 20 customers make a purchase. If three customers are selected randomly one at a time, what is the probability that all will make a purchase? Please help.1 solutions Answer 110043 by scott8148(6628)   on 2008-07-27 19:45:42 (Show Source): You can put this solution on YOUR website!there are 20C3 (1140) possible groups of 3 in 20 __ some of these groups contain non-purchasers there are 18C3 (816) possible groups of 3 in 18 __ none of these groups contain non-purchasers probability of all purchasers is 816/1140 or 0.716 (approx) if order of selection is thought to be important (permutation vs combination); the result will be the same
 Length-and-distance/149657: the altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8 inches and 18 inches. how long is the altitude??? thank you !1 solutions Answer 109981 by scott8148(6628)   on 2008-07-27 00:09:05 (Show Source): You can put this solution on YOUR website!the two smaller triangles created by the altitude are similar to the original triangle (and each other) using the similarity ratios, the altitude is the geometric mean of the two segments 8/a=a/18 __ "cross" multiplying __ a^2=144 __ taking square root __ a=12
 Graphs/149847: what is the slope of the line that passes through the following pairs... (-2/3, 6) (3, 9) I know the problem is M = 9-6/3-(-2/3) Im stuck after M = 3/3-(-2/3)....can someone help me find the slope1 solutions Answer 109979 by scott8148(6628)   on 2008-07-26 23:48:03 (Show Source): You can put this solution on YOUR website!good so far __ be careful with parentheses - to many is better than not enough M=3/[3-(-2/3)] __ M=3/(11/3) __ M=9/11
 Finance/149841: Dr. Sand borrowed some money for new furniture. She paid \$245. simple interest on a 3.5 year loan at 3.5%. Find the principle. Please help, Ellen1 solutions Answer 109978 by scott8148(6628)   on 2008-07-26 23:40:09 (Show Source): You can put this solution on YOUR website!for simple interest __ I=P*R*T dividing by R*T __ I/(R*T)=P __ 245/(.035*3.5)=P __ 2000=P