Noah and Kate are shopping for new guitar strings in a music store. Noah buys 2 packs of strings. Kate buys 2 packs of strings and a music book. The book costs $16. Their total cost is$72. How much is one pack of strings?

A hairdresser is deciding where to open her own studio. If the hairdresser chooses Location A, she will pay $1200 per month in rent and will charge$45 per haircut. Ifshe chooses Location B, she will pay $1800 permonth in rent and will charge$60 per haircut. How many haircuts would she have to give in one month to make the same profit at either location?

A hairdresser is deciding where to open her own studio. If the hairdresser chooses Location A, she will pay $1200 per month in rent and will charge$45 per haircut. If she chooses Location B, she will pay $1800 per month in rent and will charge$60 per haircut. How many haircuts would she have to give one month to make the same profit at either location?

We are given a color picture consisting of an m × n array A[1..m, 1..n] of pixels, where each pixel specifies a triple of red, green, and blue (RGB) intensities. Suppose that we wish to compress this picture slightly. Specifically, we wish to remove one pixel from each of the m rows, so that the whole picture becomes one pixel narrower. To avoid disturbing visual effects, however, we require that the pixels removed in two adjacent rows be in the same or adjacent columns; the pixels removed form a “seam” from the top row to the bottom row where successive pixels in the seam are adjacent vertically or diagonally. a. Show that the number of such possible seams grows at least exponentially in m, assuming that n > 1. b. Suppose now that along with each pixel A[i, j], we have calculated a real-valued disruption measure d[i, j], indicating how disruptive it would be to remove pixel A[i, j]. Intuitively, the lower a pixel’s disruption measure, the more similar the pixel is to its neighbors. Suppose further that we define the disruption measure of a seam to be the sum of the disruption measures of its pixels. Give an algorithm to find a seam with the lowest disruption measure. How efficient is your algorithm?

jake's solution to the equation -4(2x - 3) = 36 is shown. -4(2x - 3) = 36, -8x + 12 = 36, -8x + 12 - 12 = 36 - 12, -8x = 24, (-8x/-8) = (24/-8), x = -3 How is the solution to -4(2x - 3) > 36 similar to and different from the solution shown?

Graph the function. Is the function increasing or decreasing? Explain. y = 2/3 x + 1

Solve the equation. Check your solution. -15z = 0

If the wind becomes strong enough, it is “impossible” to paddle a canoe into the wind. Estimate the wind speed at which this will happen. List all assumptions and show all calculations.

Determine whether the given set is a generating set for $R^n$.

$$\begin{equation*}\begin{Bmatrix}\begin{bmatrix}-1\\2\\1\end{bmatrix},\begin{bmatrix}-1\\1\\3\end{bmatrix},\begin{bmatrix}1\\-3\\1\end{bmatrix}\end{Bmatrix}\end{equation*}$$

Find the slope and y-intercept of the graph of the equation Ax + By = C where

$$B \neq 0$$

. Use your results to find the slope and y-intercept of the graph of 3x + 2y = 18.

If the pattern continues, what is the 8th number in the sequence?

$$2 , 3, \frac{9}{2}, \frac{27}{4}, \frac{81}{8}, ...$$

F.

$$\frac{2187}{64}$$

G.

$$\frac{2245}{64}$$

H.

$$\frac{2281}{64}$$

J.

$$\frac{2445}{64}$$

By the method of least squares, fit the regression plane

$$y = β_1 + β_2x_1 + β_3x_2$$

to the following 12 observations of of

$$(x_1, x_2, y)$$

: (1, 1, 6), (0, 2, 3), (3, 0, 10), (–2, 0, –4), (–1, 2, 0), (0, 0, 1), (2, 1, 8), (–1, –1, –2), (0, –3, –3), (2, 1, 5), (1, 1, 1), (–1, 0, –2).

Determine the domain and the range of the function. $h(x)=-\frac{2}{5} x+4$

Assume that women's heights are normally distributed with a mean given by $\mu=63.6 \mathrm{in}$ and a standard deviation given by $\sigma=2.5 \mathrm{in}$. If 1 woman is randomly selected, find the probability that her height is between 63.5 in. and 64.5 in.