Math Answers

Directions: Evaluate the following functions.

1. F(x) =x - x² find f(2)

2. g(a) = 3a - 2 find g(1)

3. g(x)=x²+7 find g(-2)

4.g(x)=3x-3 find g(-6)

5.h(x) = 4x-2 find h(3)

How many 10-bit strings contain 6 or more 1’s? Explain and show all the steps.

How many 9-bit strings (that is, bit strings of length 9) are there which:

(a) Start with the sub-string 101? Explain.

(b) Have weight 5 (i.e., contain exactly five 1’s) and start with the sub-string 101? Explain.

(c) Either start with 101 or end with 11 (or both)? Explain.

(d) Have weight 5 and either start with 101 or end with 11 (or both)?Explain

You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. Show all your steps with written explanation.

(a) You find yourself making rows containing an equal number of

pennies and nickels. For fun, you decide to lay out every possible

such row. How many coins will you need?

b) How many coins would you need to make all possible rows

of 6 coins (not necessarily with equal number of pennies and

nickels)?

The amount of sweetener used in a liter of milk tea is a normally distributed with a mean of 0.75 cup and a standard deviation of 0.6 cup. 

a. Suppose 10 liters of milk tea are randomly selected, what is the probability that it will have at least a cup of sweetener?

b.Suppose 20 liters of milk tea are randomly selected, what is the probability that it will have less than half a cup of sweetener?

c.15 liters of milk tea is randomly selected, what is the probability that it will have 0.50 to 1.25 cups of sweetener?

Given that there are 3 apples, 1 pear and 2 oranges in a box and one would get 1 fruit in that box what are the possible value of a random variable A given that A are the number of apple.

The following data show the probability distribution of the number of speakers sold daily in an appliance shop during the past several months, X={0, 1, 2, 3, 4, 5} P(X)={.07, .18, .27, .19, .08, .21}, what is the probability that exactly no speakers will be sold?

A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)

In a hospital,a statistician records the sex of newborn babies.let m be the random variable representing males among five newborn babies