Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45. Write a linear function for the total cost C to operate the business and restore n cartridges during the first year, not including the hourly wage the owners wish to earn.

Use the number 3, 5, 6, 2, 54, and 5 in that order to write an expression that has a value of 100.

Archimedes takes a box of crackers to share at a picnic with Sen, Lady, and other friends. Archimedes did not have breakfast so he knows he will eat 3 crackers and the other critters will each eat one cracker.The equation y = x + 3 relates the amount crackers, y, Archimedes brings with the number of critters, x, who will eat the crackers. Interpret the meaning of the rate of change in this context.

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45.

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45. As the company becomes successful and is selling and restoring 25 cartridges each day of the 260 days it is open, the entrepreneurs decide to hire a part-time employee 4 h per day for each of the 260 days that the business is open and to pay the employee$8/h. How many additional cartridges must be restored and sold each year just to cover the cost of the new employee? You can neglect employee costs such as social security, worker’s compensation, and other benefits.

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45. Suppose the entrepreneurs are successful in their business and are restoring and selling 25 cartridges each day of the 260 days that they are open. What will be their hourly wage for the year if all the profit is shared equally?

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45. How many cartridges must the business restore and sell annually to break even, not including the hourly wage the owners wish to earn?

Suppose that the quantity supplied S and quantity demanded D of hot dogs at a baseball game are given by the following functions:

$$\begin{aligned} S(p) &=-2000+3000 p \\ D(p) &=10,000-1000 p \end{aligned}$$

where p is the price of a hot dog. Determine the prices for which quantity demanded is less than quantity supplied.

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $ 7000 per year and estimate that building maintenance, taxes, and insurance will cost $ 6500 per year. Each person wants to make $ 12 per hour in the first year and will work 10 hours per day for 260 days of the year. Assume that it costs $ 28 to restore a cartridge and that the restored cartridge can be sold for $ 45.

Suppose the company decides that it could increase its business by advertising. Answer Exercises 1, 2,3, and 5 if the owners decide to spend $ 400 per month on advertising.

1. Write a linear function for the total cost C to operate the business and restore n cartridges during the first year, not including the hourly wage the owners wish to earn.

2. Write a linear function for the total revenue R the business will earn during the first year by selling n cartridges.

3. How many cartridges must the business restore and sell annually to break even, not including the hourly wage the owners wish to earn?

4. How many cartridges must the business restore and sell annually for the owners to pay all expenses and earn the hourly wage they desire?

5. Suppose the entrepreneurs are successful in their business and are restoring and selling 25 cartridges each day of the 260 days they are open. What will be their hourly wage for the year if all the profit is shared equally?

Write a linear function for the total revenue R the business will earn during the fi rst

Prove that a polynomial function $f$ of odd degree has at least one real root. Hint. It may help to consider first the case of a cubic, i.e., $f(x)=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}$ where $a_{3} \neq 0$.

What are platelets, and how are they formed?

Maximize z=x+5y, subject to

$$\begin{array}{c}{x+y \leq 10} \\ {2 x+y \geq 10} \\ {x+2 y \geq 10} \\ {x \geq 0, y \geq 0}\end{array}$$

Given a right triangle with an acute angle

$$\theta$$

, if

$$\tan \theta = \cot \theta$$

, describe what this triangle would look like.