Prove that the given function is a linear transformation. $T: V \rightarrow W$ with $T(\mathbf{v})=\mathbf{0}_{W}$ for all v.

In adults, over 90% of all cancers are either adenomas (adenocarcinomas) or carcinomas. In fact, cancers of the skin, lung, colon, breast, and prostate are all in these categories. Which one of the four basic tissue types gives rise to most cancers? Why do you think this is so?

Describe the transformation from the graph of $f(x)=\sqrt x$ to the graph of $h(x)=2\sqrt{x-1}+4$.

The graph of $h$ is a translation ______ unit(s) _______, then ______by a factor of ______, and last a translation ______ unit(s) ______ of the graph of $f$.

• up

• down

• left

• right

• vertical stretch

• vertical shrink

• horizontal stretch

• horizontal shrink

• 1/2

• 1

• 4

• 2

Find the determinant of the matrix.

$$\left[\begin{array}{ll} 2 & 1 \\ 3 & 4 \end{array}\right]$$

Find the set of solutions for the given linear system. Note that some systems have only one equation.

$$\begin{array}{r} 3 x_{1}-2 x_{2}+x_{3}=4 \\ -6 x_{3}=-12 \end{array}$$

The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to solve each exercise. The data set has mean 15 and standard deviation 2. Approximately what percentage of the observations lie between 13 and 17?

Construct the integers $\mathbb{Z}$ from the natural numbers $\mathbb{N}$ in a method similar to that used in the Exercise by defining an appropriate equivalence relation on $\mathbb{N} \times \mathbb{N}$.

Write the following systems using vectors and matrices.

$$\left\{\begin{array}{l} 2 x+5 y-z=2 \\ -x+2 y=-1 \\ x+4 z=0 \end{array}\right.$$

Osmosis always involves (a) a selectively permeable membrane, (b) a difference in solvent concentration, (c) diffusion, (d) active transport, (e) a, b, and c.

Explain how biodiversity loss can impact crop diversity.

Candidates A and B are running for office and 55% of the electorate favor candidate B. What is the probability that in a sample of size 100 at least one-half of those sampled will favor candidate A?

Suppose $X \sim N(4,2).$ What value of x is two standard deviations to the right of the mean?

A confidence interval for a population mean has a margin of error of 10.7. a. Obtain the length of the confidence interval. b. If the mean of the sample is 75.2, determine the confidence interval. c. Express the confidence interval in the form “point estimate $\pm$ margin of error."

If the level of significance is 0.05 and the p-value is 0.04, what conclusion can you draw?