Amelia is shopping at an online store. Shipping for each order costs a flat fee of $6.75. Sales tax is 8%. a. Let x represent the cost of an order before shipping or sales tax. Write a function s(x) represents the cost of an order with shipping, and a function f(x) that represents the cost of an order with sales tax.

A law office orders business stationery. The cost is $21.95 per box. a. Write a function that represents the cost C(x) (in$) for x boxes of stationery. b. There is a 6%, sales tax on the cost of merchandise and $10.99 for shipping. Write a function that represents the total cost T(a) for a dollars spent in merchandise and shipping. c. Find$(T \circ C)(x)$. d. Find$(T \circ C)(4)$ and interpret its meaning in the context of this problem.

Jim tells you he paid a total of $23,078.90 for a car, and you would like to know the price of the car before sales tax so that you can compare the price of that model of carat various dealers. Find the price of the car before sales tax if Jim bought the car in each of the following states: a. Arizona, where the sales tax is 6.6%. b. New York, where the sales tax is 8.25%. c. A state where the sales tax is s%.

Let X have a Cauchy distribution. Find a. P(X > 1). b. P(X > 5). c. P(X > 10).

Calculate the limit for the given function and interval. Verify your answer by using geometry.

$$\lim _ { N \rightarrow \infty } R _ { N },$$

f(x) = 3x + 6, [1, 4]

Write a variable expression to represent the phrase. The quotient of a number and 4.

Write the standard decimal number for the following:

$$( 6 \times 10 ) + \left( 4 \times \frac { 1 } { 10 } \right) + \left( 3 \times \frac { 1 } { 100 } \right)$$

Multiply or divide.

$$\frac { 6 t ^ { 2 } - 30 t } { 2 t ^ { 2 } - 53 t - 55 } \cdot \frac { 6 t ^ { 2 } + 35 t + 11 } { 18 t ^ { 2 } }$$

Apply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. For each problem, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.

$$x _ { 1 } ^ { \prime } = 9 x _ { 1 } + 5 x _ { 2 } , \quad x _ { 2 } ^ { \prime } = - 6 x _ { 1 } - 2 x _ { 2 } ; x _ { 1 } ( 0 ) = 1 , x _ { 2 } ( 0 ) = 0$$

Dora has 8% of her earnings deducted from her paycheck for a college savings plan. She can choose to take the deduction either before taxes are withheld, which reduces her taxable income, or after taxes are withheld. Dora's tax rate is 17.5%. If her pay before taxes and deductions is $950, will she save more money if the deductions are taken before or after taxes are withheld? Explain.

if possible, find 4A, A = [2 -2 , 3 5], B = [-3 10 , 12 8]

The formula $D=5 e^{-0.4 h}$ can be used to find the number of milligrams D of a certain drug that is in a patient’s bloodstream h hours after the drug was administered. When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?

Determine whether the given consumption matrix is productive.

$$\left[ \begin{array} { c c c c } { 0.2 } & { 0.4 } & { 0.1 } & { 0.4 } \\ { 0.3 } & { 0.2 } & { 0.2 } & { 0.1 } \\ { 0 } & { 0.4 } & { 0.5 } & { 0.3 } \\ { 0.5 } & { 0 } & { 0.2 } & { 0.2 } \end{array} \right]$$