For a simple random sample of 15 items from a population that is approximately normally distributed, $\bar{x}=82.0$ and $s=20.5$. At the $0.05$ level of significance, test $H_0: \mu \geq 90.0$ versus $H_1: \mu<90.0$.

Use the fourth Taylor polynomial at x=0 to approximate the area under the graph of $f(x)=e^{-x^2 / 2}$ from $x=0$ to $x=0.5$.

Hint: $e^u=1+u+\frac{1}{2} u^2$.

Find (a) the fourth partial sum and (b) the sum of the infinite series. $\sum_{k=1}^{\infty} 7\left(\frac{1}{10}\right)^{k}$

What is the acceleration of two falling sky divers (total mass $=148 \mathrm{~kg}$ including parachute) when the upward force of air resistance is equal to one-fourth of their weight?

For the following exercise,

Find the indicated term of each binomial without fully expanding the binomial.

The fourth term of $\left(x^3-\frac{1}{2}\right)^{10}$

You know that a fourth-degree polynomial with real coefficients has -3, 1 + 2i, and 1 - 2i as zeros. Do you have sufficient information to write the polynomial? Why or why not?

These points are vertices of a rectangle: (3, -5), (7, -5), (7, 2). Plot these points and locate the fourth vertex. Then find the area and perimeter of the rectangle.

Words that may decribe others

What do you think the following people are going to do this weekend? Complete the sentences logically. Use your imagination.

Valérie va rester a la maison. Elle $\rule{4cm}{1pt}$

Find the nth term of the geometric sequence with given first term a and common ratio r. What is the fourth term?

$$a = \frac { 5 } { 2 } , \quad r = - \frac { 1 } { 2 }$$

Solve the system of equations by substitution. y = 2x + 6; y = 0

Solve.

Three vertices of a rectangle are $(-2,-3),(-7,-3)$, and $(-7,6)$.

a. Find the coordinates of the fourth vertex of the rectangle.

b. Find the perimeter of the rectangle.

c. Find the area of the rectangle.

Inventory data for Eggers Company are presented as follows.

$$\begin{array}{c} \underline{\textbf{Date}}&\underline{\textbf{Explanation}}&\underline{\textbf{Units}}&\underline{\textbf{Unit Cost}}&\underline{\textbf{Total Cost}}\\[5pt] \text{June 1\hspace{5pt}}&\text{Inventory}&\text{120}&\text{\$\hspace{1pt}5}&\text{\$\hspace{6pt}600}\\ \text{\hspace{13pt}12}&\text{Purchase\hspace{2pt}}&\text{370}&\text{\hspace{5pt}6}&\text{\hspace{5pt}2,220}\\ \text{\hspace{13pt}23}&\text{Purchase\hspace{2pt}}&\text{200}&\text{\hspace{5pt}7}&\text{\hspace{5pt}1,400}\\ \text{\hspace{13pt}30}&\text{Inventory}&\text{230}&\text{\hspace{5pt}}\\ \end{array}$$

Instructions

(b) How do the results differ from the previous exercise?

A company suffered a loss of $5.4 million in its first year. It lost another$3.1 million in the second year. It made a profit of $4.9 million in the third year.

a) Find the average profit or loss for the first three years.

b) After its fourth year of business, the company's combined profit for all four years was$0. Find the company's profit or loss during the fourth year.