The manager of a garden shop mixes grass seed that is 40% rye grass with 100 pound of grass seed

System Linear Equations

1. The manager of a garden shop mixes grass seed that is 40% rye grass with 100 pound of grass seed that is 70% rye grass to make a mixture that is 50% rye grass. How much of the 40% mixture is used?

System Linear Equations

Set Theory. Shade the set. ( Hint: U union – all inclusive; ꓵ- Intersection- the common elements (area) A I complement of set A -“Not A” )

2A) A U B’

2B) A’ ∩ B

2C) B ‘

2D) A ꓵ U

2E) A ꓵ (B U C)

Probability

2. Find the Probability. (Hint: P = Favorable Outcomes / Total Outcomes ; 0 ≤ P ≤ 1 )

A) P ( A or B )

B) P (A and B)

C) P (B)

D) P (B I A)

E) Are events A and B independent?

3. Standard deck of 52 cards

4A) Find the probability to withdraw randomly a 7,8,9,or 10 card or a Diamond.

Hint: P(A or B) = P(A) + P(B) – P(A and B) Addition Rule

4B) Find the probability to withdraw first time a Red card and second time a Black face card without replacement.

Hint:  P(A and B) = P(A)xP(BIA)    Multiplication Rule

5. Find the Expected Value for the given game

(Hint: E = X1P1 + X2P2 + X3P3 + ….. + XnPn )

6. Combinations and Permutations ( Hint: order matters- n Pr ; order doesn’t matter -n C r )

6A) How many ways can choose 7 friends to be invited to the party out of 20 total friends ?

6B) How many different pictures can be made, choosing 5 people out of 30 and they will be sitting on one row?

6C) How many committees of 5 people can be formed from a pool of 32 people ?

6D) How many passwords with 5 different letters can be made from the letters A, B, C, D, E, F, G, H, I ?