Reagan's school is selling tickets to a spring musical. On the first day of ticket sales, the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in$67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each ticket?

Determine whether the given set of vectors forms a basis for the specified vector space.

$$\left\{\left[\begin{array}{c} 2 \\ -1 \\ 1 \end{array}\right],\left[\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right],\left[\begin{array}{l} 3 \\ 1 \\ 1 \end{array}\right]\right\}, \mathbb{R}^{4}$$

Discuss topics from the "Damped Oscillations" subsection. For each problem, classify the motion of the mass on a spring as either underdamped, critically damped, or overdamped. Assume $x = x(t)$, that is, x is a function of t. $x^{\prime \prime}+4 x^{\prime}+3 x=0$

Discuss the pros and cons of binomial probability tables.

Use the annihilator method to write the form of the particular solution but do not solve the differential equation. You will need to do Steps 1-5 of the summary. $y^{\prime \prime}+3 y^{\prime}=x^{2} e^{2 x}+\cos x$

By definition, a pericentric inversion includes the ________. a. centromere, b. chiasma, c. telomere, d. synapse.

Consider the particular solutions of their respective forced equations $P(D)(y)=F_{1}(x)$ and $P(D)(y)=F_{2}(x)$. Find a particular solution for the new forcing function in $P(D)(y)=F_{3}$. $y^{\prime \prime}+6 y^{\prime}+25 y=e^{-3 x} \sin 4 x$ with $y_{p}=\frac{-x}{8} e^{-3 x} \cos 4 x$ and $y^{\prime \prime}+6 y^{\prime}+25 y= e^{4 x}$ with $y_{p}=\frac{1}{65} e^{4 x} ; F_{2}(x)=8 e^{-3 x} \sin 4 x+5 e^{4 x}$

Define the function $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ by

$$f(x, y)=\left\{\begin{array}{ll} (x /|y|) \sqrt{x^{2}+y^{2}} & \text { if } y \neq 0 \\ 0 & \text { if } y=0 \end{array}\right.$$

a. Prove that the function $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ is not continuous at the point (0, 0). b. Prove that the function $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ has directional derivatives in all directions at the point (0, 0). c. Prove that if c is any number, then there is a vector $\mathbf{p}$ of norm 1 such that

$$\frac{\partial f}{\partial \mathbf{p}}(0,0)=c$$

d. Does (c) contradict Corollary 13.18?

Verify that the Pythagorean Theorem holds for the given orthogonal vectors.

$$\mathbf{u}_{1}=\left[\begin{array}{r} 2 \\ -3 \\ 1 \end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{l} 4 \\ 3 \\ 1 \end{array}\right]$$

Which of the following statements is true? a. Recombination of the body color and red/cinnabar eye alleles will occur more frequently than recombination of the alleles for wing length and aristae length. b. Recombination of the body color and aristae length alleles will occur more frequently than recombination of red/ brown eye alleles and the aristae length alleles. c. Recombination of the gray/black body color and long/short aristae alleles will not occur. d. Recombination of the red/brown eye and long/short aristae alleles will occur more frequently than recombination of the alleles for wing length and body color.

For a continuous probability distribution, $0 \leq x \leq 10.$ What is P(x = 7)?

X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability. $P(7<X<10)$

List and briefly describe the three processes that lead to variation in offspring with the same parents.

If the pH outside the cell decreases, would you expect the amount of amino acids transported into the cell to increase or decrease?