When is the population of all possible values of $s_{1}^{2}/s_{2}^{2}$ described by an $F$ distribution?

A man records his height every 5 years. Examine the table below. Does this table represent a continuous, discontinuous, and/or discrete function? Justify your answer.

$$\begin{array}{|l|c|c|c|c|} \hline \text { Age } & 5 & 10 & 15 & 20 \\ \hline \text { Height } & 36 \text { in. } & 48 \text { in. } & 60 \text { in. } & 72 \text { in. } \\ \hline \end{array}$$

For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form.\
$y$-intercept is 2 , and $(4,-1)$

Write an equation of each graph in the final position. The graph of $y = \left( \frac { 1 } { 2 } \right) ^ { x }$ is stretched vertically by a factor of 2 and then is shifted 5 units down.

Haz predicciones sobre qué habrán hecho tu familia y tú al final de una excursión a Segovia.
mi hermano / perderse tres veces

A college that had 40 students for each lecture course increased the number to 45 students. What is the percent increase in the number of students in a lecture course?

Solve the given initial-value problem.

$$y ^ { \prime \prime \prime } + 12 y ^ { \prime \prime } + 36 y ^ { \prime }=0, y(0)=0,y'(0)=1,y''(0)=-7$$

Marge has a flyer that is 10 inches wide and 12 inches long. She will increase the length and width of the flyer by the same percent to increase the size of the flyer.

a. Provide an equation that gives the new area A of the flyer in terms of x, where x is the percent increase in the length of the original flyer written as a decimal.

b. The area of the new flyer is 270 square inches. Use your equation from part a to determine the percent increase of the length of the flyer.

c. Discuss an alternate way of finding the percent increase of the length of the flyer, without using the equation from part a.

Compute the geometric mean of the following percent increases: 8, 12, 14, 26, and 5.

Find $f^{\prime \prime}(x)$ if $f(x)=\left|x^3\right|$. Does $f^{\prime \prime}(0)$ exist?

In this exercise, calculate f$^{\prime}$(x) in terms of P(x), Q(x), and R(x), assuming that P$^{\prime}$(x)=Q(x), Q$^{\prime}$(x)=-R(x), and R$^{\prime}$(x)=P(x).

f(x)=Q(x)P(x)

Find the power required for a $2000-\mathrm{kg}$ car to climb a $100-\mathrm{m}$-long uphill road with a slope of $30^{\circ}$ (from horizontal) in $10 \mathrm{~s}(a)$ at a constant velocity, $(b)$ from rest toa final velocity of $30 \mathrm{~m} / \mathrm{s}$, and (c) from $35 \mathrm{~m} / \mathrm{s}$ to a final velocity of $5 \mathrm{~m} / \mathrm{s}$. Disregard friction, air drag, and rolling resistance.

The "postage function" $p(x)$ can be described as follows:

$$p(x)= \begin{cases}41 & \text { if } 0<x \leq 1 \\ 58 & \text { if } 1<x \leq 2 \\ 75 & \text { if } 2<x \leq 3.5\end{cases}$$

where $x$ is the weight of a letter in ounces and $p(x)$ is the corresponding postage in cents. Sketch the graph of $p(x)$ for $0<x \leq 3$. For what values of $x$ is $p(x)$ discontinuous for $0<x \leq 3$ ?

When calculating the sample standard deviation for n items, we divide by _____.