Forty observations were used to estimate $y=\beta_0+\beta_1 x_1+\beta_2 x_2+\varepsilon$. A portion of the regression results is shown in the accompanying table.

$$\begin{aligned} &\begin{array}{|l|l|l|l|l|} \hline & \text { Coefficients } & \text { Standard Error } & \text { tStat } & p \text {-value } \\ \hline \text { Intercept } & 13.83 & 2.42 & 5.71 & 1.56 \mathrm{E}-06 \\ \hline x_1 & -2.53 & 0.15 & -16.87 & 5.84 \mathrm{E}-19 \\ \hline x_2 & 0.29 & 0.06 & 4.83 & 2.38 \mathrm{E}-05 \\ \hline \end{array} \end{aligned}$$

b. What is the sample regression equation?

A scientist starts with a 1-gram sample of lead-211. The amount of the sample remaining after various times is shown in the table below.

$$\begin{array}{|l|c|c|c|c|} \hline \text { Times(min) } & 10 & 20 & 30 & 40 \\ \hline \text { Pb- 211 present (g) } & 0.83 & 0.68 & 0.56 & 0.46 \\ \hline \end{array}$$

. Write the regression equation in terms of base e.

Why, when solving rational inequalities, do we need to find values for which the function is undefined as well as zeros of the function?

Determine whether the statement is true or false. If $W=\operatorname{span}\left\{1, x^{2}\right\}$ is a subspace of $\mathcal{P}_{2}$ with inner product $\langle p, q\rangle=\int_{0}^{1} p(x) q(x) d x$ then a basis for $W^{\perp} \text { is }\{x\}$.

For the scatter plot shown, decide what type of function you might choose as a model for the data. Explain your choices.

Esta oración describe como es la vida de un estudiante. Completa la oración con el pretérito perfecto de indicativo de los verbos de la lista.

adelgazar - comer - llevar

aumentar - hacer - sufrir

Juan y Raúl ________ de peso porque no hacen ejercicio.

What types of organisms were first placed in the kingdom Protista?

Find the percentage. Round answer to the nearest hundredth. 5% of 516

What is the largest data type permitted by the FLD instruction, and how many bits does it contain?

Determine the linear regression equation for the given set.

$$\{(2,6),(3,6),(4,8),(6,11),(8,18)\}$$

Suppose that you expect to get a sample proportion around 0.5 so that the margin of error E is

$$E=2 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=2 \sqrt{\frac{0.5(1-0.5)}{n}} .$$

a. Simplify the expression on the right.

b. Make a graph of the function with sample size n, from 1 to 1,000, on the horizontal axis and margin of error on the vertical axis.

c. Describe how the margin of error changes as the sample size increases.

Assume a linear regression model with $\mu_y=51.6+3.1 x$ and standard deviation $\sigma=5.2$. (a) What is the slope of the population regression line? (b) Describe clearly what this slope says about the change in the mean of $y$ for a change in $x$. (c) What is the subpopulation mean when $x=10$ ? (d) Using the 68-95-99.7 rule, between what two values would approximately $95 \%$ of the observed responses, $y$ fall when $x=10$ ? (Hint: Refer to the two important parts of a linear regression on page 565 )

Perform the given operations and Write the answers in scientific notation, rounding to two decimal places. Then write the rounded answer in decimal notation as well.

$$\frac{4.2 \times 10^{-2}}{7 \times 10^{-3}}$$

Determine whether the quadratic function has a maximum or minimum value. Then find the value.

$$y = x ^ { 2 } - 4 x - 2$$