## Will N.'s Resources The markup is 43% of the cost, which we get by multiplying    \$123*.46=\$56.58   The selling price is the number we just got plus the amount the store paid for the monitor:   \$123+\$56.58=\$179.58 The key is to note that 13-9=4 and 13+4+13=30.   At the beginning of the thirty minutes, start both hourglasses.   After nine minutes, the 9 minute hour glass will have emptied. Flip it over immediately.   In four more minutes, 13 minutes total will... The thing that makes this problem slightly tricky is that we aren't told how many E-Mails the the computers actually send. It turns out, though, that we don't need to know if we understand the units we use carefully.   We'll let x be the speed of the faster computer in E-Mails per minute... We'll let v be the speed of the car in mph, and t be the time it takes in hours to travel 780 miles.    The distance traveled is always v*t, so we have   780=v*t   If the speed had been 5 miles per hour faster, the time to travel this same 780 miles would... Are there some additional instructions to this problem? Picking 10 of these numbers that add to 37 is impossible.   To show this, let   a = the number of 7s chosen b = the number of 5s chosen c = the number of 3s chosen d = the number of 1s chosen.   Note... The most straightforward way to do this is to multiply each of the choices out and see which one matches the original polynomial:   (2x-1)(x+3)=2x(x+3)-1(x+3)=2x2+6x-x-3=2x2+5x-3, which does not match.   (2x+1)(x-3)=2x(x-3)+1(x-3)=2x2-6x+x-3=2x2-5x-3,... This is a difference of squares, since 16x2y2=(4xy)2   A difference of squares factors as a2-b2=(a+b)(a-b). In this problem, a=x+9y and b=4xy, so this comes out as   (x+9y+4xy)(x+9y-4xy)   I hope this helps. 1a   Start with (sinθ+cosθ)2. We need to get to 1+2sinθcosθ using valid operations. We'll start with the FOIL method.   (sinθ+cosθ)2=(sinθ+cosθ)(sinθ+cosθ)                   =sin2θ+2sinθcosθ+cos2θ   We... There are 16+6=22 total socks. The number of combinations of 2 of them is 22!/(20!*2!) Each combination is equally likely to be chosen. The number of combinations where both socks are white is 6!/(4!*2!)   The number of combinations where both... There are 16+6=22 total socks. The number of combinations of 2 of them is   22!/(20!*2!)   Each combination is equally likely to be chosen.   The number of combinations where both socks are white is   6!/(4!*2!)   The probability... Let's call the students A and B. There are four possible outcomes: 1. Both students are on time. 2. A is on time, B is late. 3. A is late, B is on time. 4. Both A and B are late.   The problem tells us that the probability of event 4 is .25   We know... You're actually done with the first part of the problem -- the matrix is in row echelon form and you have done it correctly. The next step is to recognize that this matrix corresponds to the system   x+5y=-6    16y=16   To find y, use the second equation:   16y=16 y=1   Back... These discrete probability problems are tricky, and it's very easy to get confused. That being said, I'm afraid I have to disagree with the previous answer.   Three more cards are going to be dealt, and the question is asking the for the probability that any two of them are a king.... That is the correct matrix. The next step is to eliminate from the first entry of the second row. This is done by adding -3 times the first row to the second row. The resulting matrix is:   1                3          ... Let's look at all of the questions:   First, the length of time in hours that the stray ran to catch up. We need to convert 5 minutes into hours:   5 min=(5 min)*((1 hr)/(60 min))   The minutes cancel and we have   (5/60) hr = (1/12) hr.   The... The first equation has no solution. To see this, first get the absolute value by itself by subtracting 4 and dividing by 2:   2|2x2+4x-6|=2-4=-2   |2x2+4x-6|=-1   This can never be satisfied since the absolute value of a number is always at least 0... If the price was originally x, then 20% of the original price is .2x. The pair of pants is 20% off its original price, so its current price is   x-.2x=.8x=16.   Now, just solve for x:   .1x=2 x=20   The original price is \$20. The key idea here is the cosine sum formula: cos(x+y)=cos(x)cos(y)-sin(x)sin(y). We are going to apply it to cos(x)=cos(2x-x)=cos(2x+(-x)). After we apply the formula, we get   cos(x) = cos(2x)cos(-x)-sin(2x)sin(-x).   Since cos is an even function, cos(-x)=cos(x) Since... The volume of a cylinder (which is the shape of a canister) is πr2h. We will say that r and h are the radius and height of Andrea's canister. The problem tells us then that   πr2h=200 cubic inches.   The radius of Guadalupe's canister is 2r and the height is 2h. The...