Find the inverse of the following relation.

$$\{(4,-15),(-8,-18),(-2,-16.5),(3,-15.25)\}$$

State whether the following sentence is true or false. If false, replace the underlined term to make a true sentence.

A $\underline{\text{constraint}}$ is a condition that a solution must satisfy.

A local university is keeping track of the number of art students who use the pottery studio each day.

a. Write an equation of the regression line and find and interpret the correlation coefficient.

b. Graph the residual plot and determine if the regression line models the data well.

True or false (with counterexample if false): (a) If B is formed from A by exchanging two rows, then B is similar to A. (b) If a triangular matrix is similar to a diagonal matrix, it is already diagonal. (c) Any two of these statements imply the third: A is Hermitian, A is unitary, A² = I. (d) If A and B are diagonalizable, so is AB.

Find the sixth term of the geometric sequence whose first two terms are $4$ and $6$ .

Write the expression as the sine, cosine, or tangent of an angle.

$$\newline\cos\frac{\pi}{7}\cos\frac{\pi}{5}-\sin\frac{\pi}{7}\sin\frac{\pi}{5}$$

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of $\theta$ only. $\frac{1+\tan ^2 \theta}{1+\cot ^2 \theta}$

Write the expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of $\theta$ only.

$$\sin ^2(-\theta)+\tan ^2(-\theta)+\cos ^2(-\theta)$$

Under what conditions will the graph of

$$x = a ( y - k ) ^ { 2 } + h$$

have no y-intercepts?

Paco and Patricia are very different. As shown in the model, take the role of Paco to express your preferences. MODELO: Patricia: Me gusta esta chaqueta. Paco: Yo prefiero esa/aquella. Me gustan estos jabones. ______

Find the derivatives of the function. $r=\left(\frac{1+\sin \theta}{1-\cos \theta}\right)^{2}$

Find the sum of the infinite geometric series : $\displaystyle \sum_{n=1}^{\infty}0.04^{n}$, if possible.

How does a snake move?

Your class is going to explore the speed of nerve impulses in the body by performing an experiment that involves a human chain. In this experiment, a group of students forms a circle with each person gently holding the wrist of the person to his or her right. One student begins the chain, and another student ends the chain. Also, one student in the group must be the timekeeper. The group members must keep their eyes closed. When the experiment begins, the timekeeper says, "Go," and the first student carefully, but quickly squeezes the student's wrist to their right, then this next student squeezes a wrist, and so on. After the last student's wrist is squeezed, he or she says "Stop," and releases the next student's wrist. The amount of time from when the word go is spoken until the word stop is spoken (the amount of time it takes to complete the chain) is recorded by the timekeeper.

On the scatter plot, identify the point representing the least mean time. Then, identify the values of the point in the table. Explain how you identified the point and values.