True or False: Given any real number r and any

$$3 \times 3$$

matrix A whose entries are all nonzero, it is always possible to change at most one entry of A to get a matrix B with det(B) = r.

Identify the vertex and the y -intercept of the graph of each function. $y=(x-125)^{2}+125$

Solve each matrix equation. If an equation cannot be solved, explain why.

$$\left[\begin{array}{cc}{0} & {-4} \\ {0} & {-1}\end{array}\right] X=\left[\begin{array}{l}{0} \\ {4}\end{array}\right]$$

The art teacher bought $19$ sketchbooks for $\$2.98$ per book. What equation can be used to find the total cost of the sketchbooks?

A. $c = 19 \cdot \$ 2.98$

B. $\frac { 19 } { \$ 2.98 } = c$

C. $\$ 2.98 \cdot c = 19$

D. $\frac { \$ 2.98 } { 19 } = c$

Fill in the blank with an appropriate word, phrase, or symbol(s). If a sample is drawn in such a way that each time an item is selected, each item in the population has an equal chance of being drawn, the sample is called a(n) _ sample

Sketch the graph of a function whose derivative is always positive.

Miguel is answering an e-mail from his friend Jorge. Answer Jorge's questions, saying that the people will have already done these things by the time indicated. Use the future perfect.

1. ¿Encontrarás un trabajo cuando te gradúes?
2. ¿Le comprarás un regalo a Maru cuando te paguen?
3. ¿Escribirá el Sr. Díaz una novela cuando se jubile?
4. ¿Harás los preparativos para ir a España cuando termine el año escolar (school year)?
5. ¿Llenará David la solicitud cuando llegue a la entrevista?
6. ¿Olvidaré a mi ex novia cuando me vaya de vacaciones?

Draw the Lewis structure for a molecule of each of these compounds and ions. a. $\mathrm{H}_{\mathrm{2}} \mathrm{S}$ b. ${BF_4} ^ -$ c. $\mathrm{SO}_{2}$ d. $\mathrm{SeCl}_{2}$

Evaluate the determinant of each matrix.

$$\left[\begin{array}{lll}{1} & {4} & {0} \\ {2} & {3} & {5} \\ {0} & {1} & {0}\end{array}\right]$$

Two sinusoidal waves of the same period, with amplitudes of 5.0 and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mm wave is 0. What is the phase constant of the 7.0 mm wave?

What are the two transition metals that are used in making jewelry and are the group 11 elements with the lowest atomic masses?

Select the best answer. A statistic is an unbiased estimator of a parameter when (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. (e) in many samples, the distribution of the statistic has a shape that is approximately Normal.

Consider the vector space

$$\mathbb { R } ^ { 2 }.$$

Define the mapping

$$\langle , \rangle \text { by } \langle \mathbf { v } , \mathbf { w } \rangle = 2 v _ { 1 } w _ { 1 } + v _ { 1 } w _ { 2 } + v _ { 2 } w _ { 1 } + 2 v _ { 2 } w _ { 2 } \quad \quad (5.1.14)$$

for all vectors

$$\mathbf { v } = \left( v _ { 1 } , v _ { 2 } \right) \text { and } \mathbf { w } = \left( w _ { 1 } , w _ { 2 } \right) \text { in } \mathbb { R } ^ { 2 }.$$

Verify that Equation (5.1.14) defines an inner product on

$$\mathbb { R } ^ { 2 }.$$

If the first two terms of a geometric sequence are negative, then so is the third. Justify your answer.