A chocolatier claims that his candy averages at least 81 pieces per bag. Conrad randomly selects bags of the candies and counts the pieces. Assume that $\sigma=1.2.$

$$\text{Number of Pieces} \\ \begin{array}{|l|l|l|l|l|l|l|l|l|} \hline 81 & 80 & 82 & 82 & 83 & 82 & 84 & 81 & 81 \\ \hline 80 & 83 & 83 & 82 & 81 & 80 & 84 & 81 & 81 \\ \hline \end{array}$$

Write the null and alternative hypotheses, and state which hypothesis represents the claim.

At Chocolatier Incorporated, there are two factors that determine the cost of health care. If an employee makes less than $65,000 per year, he pays$52 per month for individual coverage and $98 per month for family coverage. If an employee makes at least$65,000 per year, individual coverage is $67 per month and family coverage is$122 per month. a. Graham makes $62,800 per year. He has individual health care. His yearly contribution is 10% of the total cost. How much does his employer contribute? b. Claudia 's annual salary is$75,400. She has family health care. Her employer contributes $1,052 per month towards her total coverage cost. What percent does Claudia contribute toward the total coverage? Round to the nearest tenth of a percent.

Dan's employee benefits include health-care coverage. His employer covers 78% of the cost, which is a contribution of $1,599.78 toward the total coverage amount. How much does Dan pay for his coverage?

Martha's employee benefits include family health-care coverage. She contributes 18% of the cost. Martha gels paid biweekly and $108.00 is taken out of each paycheck for family healthcare coverage. How much does her employer contribute annually for the family coverage?

When Alton started his current job, his employer told him that he had one day of paid vacation until he reaches his first year with the company. Then, at the end of the first year, he would receive three vacation days. After each year, his number of vacation days would triple up to 27 days of paid vacation. a. Let x represent the number of years worked and y represent the number of paid vacation days. Write an equation that models the relationship between these variables. b. How many vacation days will he have earned after two years? c. In what year will he have maxed out his vacation days?

When Tyler started at his current job, his employer gave him five days of paid vacation time with a promise of five additional paid vacation days for each two-year period he remains with the company to a maximum of five work weeks of paid vacation time. a. Let x represent the number of years he has worked for this employer and y represent the number of paid vacation days he has earned. Write an equation that models the relationship of these variables. b. It has been eight years since Tyler began working for this employer. How many paid vacation days has he earned? c. When will Tyler reach the maximum number of paid vacation days allowable?

Ina's employer offers a sliding paid vacation. When she started work, she was given two paid days of vacation. For each four-month period she stays at the job, her vacation is increased by one day. a. Let x represent the number of 4-month periods worked and y represent the total number of vacation days. Write an equation that models the relationship between these variables. b. How much vacation time will she have after working for this employer for 6.5 years?

Ali has worked at a fashion magazine for the last 5 years. Her current annual salary is $64,000. When she was hired, she was told that she had four days of paid vacation time. For each year that she worked at the magazine, she would gain another three days of paid vacation time to a maximum of 26 days. How many paid vacation days does she now get at the end of 5 years of employment?

In a 400-m race, runner A reaches her maximum velocity $V_4$ in 4 s with constant acceleration and maintains that velocity until she reaches the halfway point with a split time of 25 s. Runner B reaches her maximum velocity vB in 5 s with constant acceleration and maintains that velocity until she reaches the halfway point with a split time of 25.2 s. Both runners then run the second half of the race with the same constant deceleration of 0.1 $\mathrm{m} / \mathrm{s}^{2}$. Determine (a) the race times for both runners, (b) the position of the winner relative to the loser when the winner reaches the finish line.

Evaluate the function for the given value of x. g(t)

Use matrices A, B, and C to prove the given properties. Assume that the elements within A, B, and C are real nurnbers.

$$\scriptstyle \text{A=}\left[\begin{array}{ll}{a_{1}} & {a_{2}} \\ {a_{3}} & {a_{4}}\end{array}\right] \quad B=\left[\begin{array}{ll}{b_{1}} & {b_{2}} \\ {b_{3}} & {b_{4}}\end{array}\right] \quad C=\left[\begin{array}{ll}{c_{1}} & {c_{2}} \\ {c_{3}} & {c_{4}}\end{array}\right]$$

Distributive property of scalar multiplication t(A + B) = tA + tB

Use one of the three tests to prove the specified symmetry. $r=5 \cos 8 \theta,$ symmetric about the line $\theta=\frac{\pi}{2}$

Write an equation for and graph each parabola with focus F and the given characteristics. F(-1, 4); concave down; contains (7, -2)

Perform the partial fraction decomposition.

$$\frac{7 x^{3}+4 x^{2}+63 x+15}{x^{4}+11 x^{2}+18}$$