Determine whether each statement makes sense or does not make sense, and explain your reasoning. Knowing that a parabola opening to the right has a vertex at (-1, 1) gives me enough information to determine its graph.

For the reaction to produce new particles, the two protons must approach each other to within a distance of about

$$8.0 \times 10 ^ { - 15 } \mathrm { m }$$

The moving proton must have a sufficient speed to overcome the repulsive Coulomb force. What must be the minimum initial kinetic energy (in MeV) of the proton?

The test statistic of z = 1.00 is obtained when testing the claim that p > 0.3. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

Complete the sentences using the review words. A(n) _____ contains at least one variable.

Evaluate the integral by completing the square and using trigonometric substitution.

$$\int \frac { d x } { \sqrt { x ^ { 2 } + 4 x + 13 } }$$

The U.S. Census at School website (www.amstat.org/censusatschool) has a random sampler that will select a random sample of students from the U.S. Census at School population. The random sampler was used to select a random sample of 20 seventh graders. The data on time to travel to school for these twenty students are shown here: Sample 1: Time to travel to school (in minutes)

$$\begin{matrix} \text{5} & \text{7} & \text{10} & \text{10} & \text{15} & \text{15} & \text{15} & \text{15} & \text{20} & \text{20}\\ \text{20} & \text{20} & \text{20} & \text{20} & \text{30} & \text{40} & \text{45} & \text{60} & \text{60} & \text{60}\\ \end{matrix}$$

The 20 times are arranged in order from shortest to longest. For Sample 1, calculate the following: a. the sample mean, b. the sample median.

An invertible linear transformation

$$\mathbb { R } ^ { n } \rightarrow \mathbb { R } ^ { n }$$

is given. Find a formula for the inverse linear transformation.

$$T _ { 1 } : \mathbb { R } ^ { 2 } \rightarrow \mathbb { R } ^ { 2 }$$

defined by

$$T _ { 1 } ( \mathbf { x } ) = A \mathbf { x },$$

where

$$A = \left[ \begin{array} { r r } { - 4 } & { - 1 } \\ { 2 } & { 2 } \end{array} \right].$$

Write the

$$\mathbf { a }.$$

converse,

$$\mathbf { b }.$$

inverse, and

$$\mathbf { c }.$$

contrapositive of the given statement. If we had a car, then we would be able to take the class.

You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

You are choosing between two health clubs. Club A offers membership for a fee of $40 plus a monthly fee of$25. Club B offers membership for a fee of $15 plus a monthly fee of$30. After how many months will the total cost at each health club be the same? What will be the total cost for each club?

Explain how behavior can play a role in the evolution of species?

Bernie invested a sum of money 5 years ago in a savings account, which has since paid interest at the rate of $8\% / \text{year}$ compounded quarterly. His investment is now worth $22,289.22. How much did he originally invest?

Show that the tangent lines to the graphs of the family of parabolas $f(x)=-\frac{1}{2} x^{2}+k$ are always perpendicular to tangent lines to the graphs of the family of natural logarithms $g(x)=\ln (b x)+c$ where $b, k$ and $c$ are constants.

Each rectangular place mat that your restaurant uses measures 20 inches long and 14 inches wide. What is the area of this place mat in square inches?