1. How many integers between 0 and 999 contain a single digit that is a 7?
2. The probability of scoring 90 or above is .35 in a group of 11 students, find the probability that 10 or 11 score a 90 or above?
3. Staples now sells their own notebooks. Making notebook has a fixed factory cost of$6,000 and a per unit cost of $0.58 per notebook. Staples sells these notebooks for $3.99 each.
a. As a function of the number of notebooks staples sells (n), write an equation for Staples’ profit P(n).
b. How many notebooks does Staples need to sell in order to make $7,500 in profit?
c. Write Staples’ cost function for notebooks where C(n) is cost in terms of the number of notebooks Staples produces. What is the fixed cost and the variable cost?
d. In 2013, Staples decided to sell these notebooks for $2.50 instead of $3.99. The company returned zero profit. How many notebooks were sold? What was Staples revenue for notebooks in 2013?
4. Sarah goes to Staples and buys 8 notebooks, on sale for 15% off. The notebooks are subject to a 7.5% New Jersey sales tax. The final price of the notebook is 2.98. What was the original price?
5. Staples also sells pens. Pens ordinarily cost $1.55 each. This month, they are on sale in Vermont for 18% off, but are subject to an 8% sales tax. What is the final price of the pens?
6. The final price of an item is F. The initial price is P. If the item is on sale for 22% off but subject to a 19% tax, find the value of P in terms of F.
7. Alan has 11 friends and is selecting 5 to come on a trip with him. How many ways can this be done?
8. 12 students run for Environmental Club Leadership Council which includes a President, Vice President, and Secretary. How many distinct Councils can be formed?
9. In a group of 8 girls and 4 boys, how many ways are there to select 2 boys and 2 girls?
10. A bag contains 12 marbles-3 green, 4 red, and 5 yellow.
a. 3 marbles are randomly selected. Find the probability that 2 marbles are green and 1 is red.
b. 3 marbles are again randomly selected. Find the probability that 3 are blue.
11. abc is a randomly selected 3 digit integer from 100 to 999. Find the probability that abc contains exactly 1 digit that is an 8.