A patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol. Each ounce of meat provides 110 milligrams. Write an inequality that describes the patient's dietary restrictions for x eggs and y ounces of meat.

Fill in the blanks. A sequence is called an ________ sequence when the differences between consecutive terms are the same. This difference is called the ________ difference.

Find all real solutions of the equation.

$$\left( \frac { x + 1 } { x } \right) ^ { 2 } + 4 \left( \frac { x + 1 } { x } \right) + 3 = 0$$

Consider the region bounded by the graphs of

$$y = \sin ^ { - 1 } x , y = 0, \text { and } x = 1 / 2$$

a. Find the area of the region. b. Find the centroid of the region.

Use trig identities to simplify the expression.

$$sin2(π+θ)$$

When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37/38 probability of losing$5 and you have a 1/38 probability of making a net gain of $175. (The prize is$180, including your $5 bet, so the net gain is$175.) If you bet $5 that the outcome is an odd number, the probability of losing$5 is 20/38 and the probability of making a net gain of $5 is 18/38. (If you bet$5 on an odd number and win, you are given $10 that includes your bet, so the net gain is$5.) If you bet $5 on the number 7, what is your expected value?

Solve the equation. Check your solution. 12 + 6m = 2m

Solve each quadratic equation by graphing the related function. Round approximate solutions to the nearest tenth. x² - 121 = 0

Write the complex number in polar form with argument

$$\theta$$

between 0 and

$$2 \pi$$

. 3 + 2i

A hydraulic turbine operating at 180 rpm with a head of 100 ft develops 20,000 horsepower. Estimate the power if the same turbine were to operate under a head of 50 ft.

By installing some elaborate inspection equipment on its assembly line, the Robot Corp. can avoid hiring an extra worker who would have earned $36,000 a year in wages and an additional$9500 a year in employee benefits. The inspection equipment has a 6-year useful life and no salvage value. Use a nominal 18% interest rate in your calculations. How much can Robot afford to pay for the equipment if the wages and worker benefits were to have been paid (a) At the end of each year (b) Monthly Explain why the answer in (b) is larger.

Simplify using the Binomial Theorem.

$$\frac { ( x + h ) ^ { 3 } - x ^ { 3 } } { h }$$

Solve the equation. Check your solutions.

$$z + 12 = - 5$$

Let

$$Y _ { 1 } , Y _ { 2 } , \ldots , Y _ { n }$$

be a random sample of size n from a normal population with mean

$$\mu$$

and variance

$$\sigma ^ { 2 }$$

. Assuming that n = 2k for some integer k, one possible estimator for

$$\sigma ^ { 2 }$$

is given by

$$\hat { \sigma } ^ { 2 } = \frac { 1 } { 2 k } \sum _ { i = 1 } ^ { k } \left( Y _ { 2 i } - Y _ { 2 i - 1 } \right) ^ { 2 }$$

. Show that

$$\hat { \sigma } ^ { 2 }$$

is a consistent estimator for

$$\sigma ^ { 2 }$$

.