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 Trigonometry-basics/602443: Hi. How do I prove this equation to be an identity? (tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY Everytime I solve this I always end up with 1 - sinY cosY = sin Y + cos Y I really don't know what I should do here so I hope you can help me and show me how to do this. Thank you in advance!1 solutions Answer 380240 by jim_thompson5910(28595)   on 2012-04-23 14:44:58 (Show Source): You can put this solution on YOUR website!(tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY (tanY + 1)/secY = sinY + cosY tanY/secY + 1/secY = sinY + cosY (sinY/cosy)/(1/cosY) + 1/(1/cosY) = sinY + cosY (sinY/cosy)*(cosY/1) + cosY = sinY + cosY (sinYcosY)/cosY + cosY = sinY + cosY sinY + cosY = sinY + cosY So this verifies the identity.
 percentage/602441: If 40% of a given number is 8, then what is 15% of the given number? 1 solutions Answer 380236 by jim_thompson5910(28595)   on 2012-04-23 14:29:24 (Show Source): You can put this solution on YOUR website!Let x = the unknown number (ie the "given number") 40% of a given number is 8 40% of a given number is 8 0.4 * x = 8 0.4 x = 8 0.4x = 8 x = 8/0.4 x = 20 So the "given number" is 20 ------------------------------------------------------------------- Now take 15% of that given number: 20*0.15 = 3 So 15% of 20 is 3 ======================================================================= Answer: 15% of the given number is 3
 Trigonometry-basics/602403: How do you prove that this is an identity? sinX/cosX + cosX/sinX = secX cscX I've been thinking that in the end both sides should somehow end up with 1/(cosX)(sinX) but I really don't know how to do that since the left side has addition and not multiplication so maybe I'm wrong? IDK I'm so confused. Thank you to whoever answers this!1 solutions Answer 380235 by jim_thompson5910(28595)   on 2012-04-23 14:23:39 (Show Source): You can put this solution on YOUR website!(sin(x))/(cos(x))+(cos(x))/(sin(x)) = sec(x)csc(x) (sin(x)sin(x))/(sin(x)cos(x))+(cos(x))/(sin(x)) = sec(x)csc(x) (sin^2(x))/(sin(x)cos(x))+(cos(x))/(sin(x)) = sec(x)csc(x) (sin^2(x))/(sin(x)cos(x))+(cos(x)cos(x))/(sin(x)cos(x)) = sec(x)csc(x) (sin^2(x))/(sin(x)cos(x))+(cos^2(x))/(sin(x)cos(x)) = sec(x)csc(x) (sin^2(x)+cos^2(x))/(sin(x)cos(x)) = sec(x)csc(x) (1)/(sin(x)cos(x)) = sec(x)csc(x) (1/sin(x))*(1/cos(x))= sec(x)csc(x) csc(x)*sec(x)= sec(x)csc(x) sec(x)csc(x)= sec(x)csc(x) This verifies the identity.
 Money_Word_Problems/602369: How much do checking accounts cost each year?1 solutions Answer 380234 by jim_thompson5910(28595)   on 2012-04-23 14:19:45 (Show Source): You can put this solution on YOUR website!It varies widely as some banks and credit unions don't even charge at all for checking accounts (and advertise free checking accounts). So you'll have to check with your local bank or credit union.
 Probability-and-statistics/602387: What are the possible outcomes of menu choices if I have 5 appetizers, 5 entrees, 5 drinks and 5 desserts? Would it be 5x5x5x5? So my answer would be 625 possible outcomes?1 solutions Answer 380233 by jim_thompson5910(28595)   on 2012-04-23 14:18:04 (Show Source): You can put this solution on YOUR website!You are 100% correct. Nice work.
 Angles/602378: in a certain triangle, the measures of the interior angles can be represented as x, 2x, and x-20. what are the measures of all three interior angles1 solutions Answer 380231 by jim_thompson5910(28595)   on 2012-04-23 14:08:10 (Show Source): You can put this solution on YOUR website!Hint: the sum of all the angles in a triangle gives you 180 degrees. So we have the equation Solve this equation for x and use that solution to find your three angles.
 Money_Word_Problems/602368: If you had 1,000.00 in a savings account for one year, how much interest would you earn?1 solutions Answer 380230 by jim_thompson5910(28595)   on 2012-04-23 14:06:32 (Show Source): You can put this solution on YOUR website!It depends on the interest rate and how the interest is generated (either through simple interest, compound interest, or continuously compounded interest). So you're missing information.
 test/602432: |7-3|-|3-7|=?1 solutions Answer 380229 by jim_thompson5910(28595)   on 2012-04-23 14:04:51 (Show Source): You can put this solution on YOUR website!|7-3|-|3-7| |4|-|-4| 4-(4) 4-4 0 So |7-3|-|3-7| = 0
 Permutations/602377: How many different ways can you arrange the letters A,B,C, and D?1 solutions Answer 380228 by jim_thompson5910(28595)   on 2012-04-23 14:03:52 (Show Source): You can put this solution on YOUR website!There are four different letters, so there are 4! = 4*3*2*1 = 24 different ways.
 Probability-and-statistics/602407: A single card is drawn from a standard deck of cards. Find the probability of P(not a face card | 4).1 solutions Answer 380227 by jim_thompson5910(28595)   on 2012-04-23 14:03:08 (Show Source): You can put this solution on YOUR website!P(not a face card | 4) = "Probability of NOT drawing a face card given you've drawn a four" Since you know 100% that you've drawn a four card, and a four card is NOT a face card, this means that P(not a face card | 4) = 0 Since it's impossible to draw a face card given that you know this information.
 Polygons/602430: as the number of sides increases, the measure of each interior angle what?1 solutions Answer 380226 by jim_thompson5910(28595)   on 2012-04-23 14:00:35 (Show Source): You can put this solution on YOUR website!As the number of sides increase, the measure of each interior angle increases as well. The measure of each interior angle will slowly approach 180 degrees (but will never actually equal 180 degrees)
 Equations/602420: convert to scientific notation 18,3971 solutions Answer 380224 by jim_thompson5910(28595)   on 2012-04-23 13:58:09 (Show Source): You can put this solution on YOUR website!Start with 18397 and place the decimal point in between the first two digits to get 1.8397 Now move the decimal point 4 places to get it back to the original number of 18397 Since we counted out four places, this means that the answer is $\LARGE 18,397 = \color{red}1.8397 \times 10^{4}$
 Trigonometry-basics/602425: Verify that the equation is an identity: sin^4 - cos^4 = 2sin^2 - 1 Also please show the steps if you can. It will be a lot of help since I'm not at all good with Math. Thank you! :)1 solutions Answer 380223 by jim_thompson5910(28595)   on 2012-04-23 13:54:55 (Show Source): You can put this solution on YOUR website!sin^4 - cos^4 = 2sin^2 - 1 (sin^2)^2 - (cos^2)^2 = 2sin^2 - 1 (sin^2-cos^2)(sin^2+cos^2) = 2sin^2 - 1 (sin^2-cos^2)(1) = 2sin^2 - 1 sin^2-cos^2 = 2sin^2 - 1 sin^2 - (1 - sin^2) = 2sin^2 - 1 sin^2 - 1 + sin^2 = 2sin^2 - 1 2sin^2 - 1 = 2sin^2 - 1 So this verifies the identity.
 Quadratic_Equations/602215: Find the side of a square with an area of 90 ft^21 solutions Answer 380160 by jim_thompson5910(28595)   on 2012-04-22 23:18:29 (Show Source): You can put this solution on YOUR website!A = s^2 90 = s^2 s^2 = 90 s = sqrt(90) s = 3*sqrt(10) s = 9.48683298 So the side length is approximately 9.48683298 feet.
 Probability-and-statistics/602214: An English reading list ha 8 American novels and 6 English novels. A student must read 4 from the list and at least 2 must be American novels. In how many different ways can the four books be selected? {This answer is 836. I'm obviously not doing it with the correct functions. It seems logical the C(8,2) are part of this problem. My answer is 1050 when I tried C(8,4)*C(6,4) Any explanation for the correct way to do the work is greatly appreciated!1 solutions Answer 380159 by jim_thompson5910(28595)   on 2012-04-22 23:16:59 (Show Source): You can put this solution on YOUR website!There are C(8,2)*C(6,2) = 28*15 = 420 different ways to have exactly 2 American novels (and exactly two English novels) There are C(8,3)*C(6,1) = 56*6 = 336 different ways to have exactly 3 American novels (and exactly one English novel) and finally, There are C(8,4)*C(6,0) = 70*1 = 70 different ways to have exactly 4 American novels (and no English novels) Add these counts up to get 420+336+70 = 826 So there are 826 ways. Please make sure that the answer you typed is not a typo (since the numbers look very close)
 Probability-and-statistics/602213: A committee of 5 is selected from 5 men and 6 women. How many committees are possible if there must be at least 3 men of the committee? [181 is the correct answer, however, I'm not able to get that answer by multi. nCr of my groups of (5,5) and (6,3). Please explain how to get this answer. 1 solutions Answer 380158 by jim_thompson5910(28595)   on 2012-04-22 23:10:43 (Show Source): You can put this solution on YOUR website!There are (5 C 3)*(6 C 2) = 10*15 = 150 ways to have exactly 3 men on the committee. There are (5 C 4)*(6 C 1) = 5*6 = 30 ways to have exactly 4 men on the committee. and There is (5 C 5)*(6 C 0) = 1*1 = 1 way to have exactly 5 men on the committee. Add these results up: 150+30+1 = 181 So there are 181 ways to form the committee if there must be at least 3 men on the committee.
 Polynomials-and-rational-expressions/602132: Simplify the following quotient of complex numbers into the form a + bi. -9+2i/-8-(9i)= I have no idea where to start~ Please help! 1 solutions Answer 380157 by jim_thompson5910(28595)   on 2012-04-22 23:05:15 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by . Combine the fractions. FOIL the numerator. FOIL the denominator. Multiply. Replace with -1. Multiply Combine like terms. Break up the fraction. Reduce. So . So the expression is now in standard form where and
 Probability-and-statistics/602204: The Creamery serves dishes of frozen yogurt, and a customer may choose from 7 different toppings. How many ways can a customer choose a dish of yogurt with up to 3 different toppings, including the choice of no tipping? {I think this is a combination, or C(n,r), but does not provide the correct answer. That answer is: 64, however, I don't know how to correctly work it out. Help is appreciated! DC1 solutions Answer 380156 by jim_thompson5910(28595)   on 2012-04-22 22:48:29 (Show Source): You can put this solution on YOUR website!The key word "up to" means everything below that value and that value is included. So "up to 3 toppings" means you can choose 0, 1, 2, or 3 toppings. There are C(7,3) = 35 ways to choose 3 toppings There are C(7,2) = 21 ways to choose 2 toppings There are C(7,1) = 7 ways to choose 1 topping and finally, there is only one way to choose no toppings So overall, there are 35+21+7+1 = 64 different ways to choose up to 3 toppings. Note: C(n,r) = (n!)/(r!(n-r)!). So for example, C(7,3) = (7!)/(3!(7-3)!) = 35
 Linear-equations/602191: y=-1/5x-4 Find the slope of the line.1 solutions Answer 380152 by jim_thompson5910(28595)   on 2012-04-22 22:20:36 (Show Source): You can put this solution on YOUR website!The equation is y = mx+b form where the slope, m, is m = -1/5
 Probability-and-statistics/602166: Evaluate the factorial expression. 5!1 solutions Answer 380143 by jim_thompson5910(28595)   on 2012-04-22 21:34:14 (Show Source): You can put this solution on YOUR website!By definition, n! = n*(n-1)*(n-2)...3*2*1 So 5! = 5*4*3*2*1 = 120 Answer: 5! = 120
 Trigonometry-basics/602131: What is the cos and tan of 59.6 degrees rounded to 7 places?1 solutions Answer 380133 by jim_thompson5910(28595)   on 2012-04-22 20:21:05 (Show Source): You can put this solution on YOUR website!cos(59.6) = 0.5060338 tan(59.6) = 1.7044587
 Linear-equations/602130: Please show how to answer this (-x)^2 - 5x= and x= (-3) 1 solutions Answer 380132 by jim_thompson5910(28595)   on 2012-04-22 20:19:44 (Show Source): You can put this solution on YOUR website!(-x)^2 - 5x (-(-3))^2 - 5(-3) (3)^2 - 5(-3) 9 - 5(-3) 9 + 15 24 This means that (-x)^2 - 5x = 24 when x = -3
 Radicals/602126: Simplified form of square root of 125 minus square root of 801 solutions Answer 380131 by jim_thompson5910(28595)   on 2012-04-22 20:18:32 (Show Source): You can put this solution on YOUR website! So
 Exponential-and-logarithmic-functions/602121: The function of f(x)=log2x is decreasing? true or false? thinking its false.1 solutions Answer 380129 by jim_thompson5910(28595)   on 2012-04-22 20:14:16 (Show Source): You can put this solution on YOUR website!You are correct. Nice work. A graph will confirm this Graph of shown above in green
 Polygons/602117: If I know the polygon to get the number of diagonals I can use the formula n(n-3)/2 where n=the number of sides of the polygon. How can I find the polygon when I know the number of diagonals that can be drawn inside? ex. Which polygon has 20 diagonals that can be drawn inside? Is there a formula for this question?1 solutions Answer 380125 by jim_thompson5910(28595)   on 2012-04-22 20:08:15 (Show Source): You can put this solution on YOUR website!Let d = number of diagonals The formula to find the number of diagonals 'd' is Solve this for n to find the number of sides given the number of diagonals Now use the quadratic formula to solve for 'n' or So things are a bit uglier, but now you have a formula for 'n' given the number of diagonals 'd'.
 Exponential-and-logarithmic-functions/602115: The x-intercept of f(x)=log6x is1 solutions Answer 380124 by jim_thompson5910(28595)   on 2012-04-22 20:01:34 (Show Source): You can put this solution on YOUR website!Basic idea: Plug in f(x) = 0 and solve for x f(x) = log(6,x) 0 = log(6,x) 6^0 = x 1 = x x = 1 So the x-intercept is (1,0)
 Trigonometry-basics/602116: the expression csc x ÷ cot x is equivalent to? (a) sin x (b) cos x (c) sec x1 solutions Answer 380122 by jim_thompson5910(28595)   on 2012-04-22 20:00:37 (Show Source): You can put this solution on YOUR website!Hint: csc(x) = 1/sin(x) and cot(x) = cos(x)/sin(x)
 Exponential-and-logarithmic-functions/602112: which answer represents the domain of the logarithmic function given below? f(x)=log7x? A. x>=0 B. x<0 C. x>0 D. All real numbers 1 solutions Answer 380120 by jim_thompson5910(28595)   on 2012-04-22 19:50:16 (Show Source): You can put this solution on YOUR website!You cannot take the log of a negative number or zero. So this means that the domain is the set of all positive numbers. In algebraic form, the domain is choice C) x > 0
 Probability-and-statistics/602106: this is a class i have to take before statistics, help me solve this question if two cards are drawn with out replacement from a deck, find the probability that the second is a spade, given that the the first card was a spade.1 solutions Answer 380119 by jim_thompson5910(28595)   on 2012-04-22 19:46:26 (Show Source): You can put this solution on YOUR website!The first card is a spade. So there are 13-1 = 12 spades left. On the second draw, there are 52 - 1 = 51 cards left. So the probability of drawing a second spade given that the first is a spade is 12/51 = 4/17
 decimal-numbers/602101: What is 174.57 rounded to the nearest hundreds place ?1 solutions Answer 380118 by jim_thompson5910(28595)   on 2012-04-22 19:44:29 (Show Source): You can put this solution on YOUR website!Locate the hundreds place: 174.57 Locate the digit to the right of the hundreds place: 174.57 This value is less than 5, so we replace this digit and everything to the right of it with a '0'. We're basically rounding down. Giving us the final answer: 170
 Probability-and-statistics/602100: 76% of dog owners buy holiday presentes for their dogs. Suppose n=4 dog owners are randomly selected. Find the probability that three or more buy their dog holiday presents. Round to four decimal places1 solutions Answer 380116 by jim_thompson5910(28595)   on 2012-04-22 19:40:14 (Show Source): You can put this solution on YOUR website!First calculate the individual probabilities P(X = 3) and P(X = 4) P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x) P(X = 3) = (4 C 3)*(0.76)^(3)*(1-0.76)^(4-3) P(X = 3) = (4 C 3)*(0.76)^(3)*(0.24)^(4-3) P(X = 3) = (4)*(0.76)^(3)*(0.24)^1 P(X = 3) = (4)*(0.438976)*(0.24) P(X = 3) = 0.42141696 P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x) P(X = 4) = (4 C 4)*(0.76)^(4)*(1-0.76)^(4-4) P(X = 4) = (4 C 4)*(0.76)^(4)*(0.24)^(4-4) P(X = 4) = (1)*(0.76)^(4)*(0.24)^0 P(X = 4) = (1)*(0.33362176)*(1) P(X = 4) = 0.33362176 -------------------------------------------------------------------------- Then add them up to get your answer P(X >= 3) = P(X = 3) + P(X = 4) P(X >= 3) = 0.42141696 + 0.33362176 P(X >= 3) = 0.75503872 So the probability that three or more buy their dog holiday presents is 0.75503872