1. what is the slope of the line that passes through the points (-2, 5) and (1, 4)?

a. -3
b. -2
c. -1/3
d. 1/3

2. a line has a slope -5/3. through which two points could this line pass?

a. (12,13) (17, 10)
b. (16, 15) (13, 10)
c. (0, 7) (3, 10)
d. (11, 13) (8, 18)

3. the pair of points (6,y) and (10, -1) lie on a line with slope 1/4. what is the value of y?

a. -5
b. -2
c. 2
d. 5

4. what is the slope of a vertical line?

a. -1
b. 0
c. 1
d. undefined

5. the table below gives the best cost per person to rent a fishing charter boat. find the rate of change given that it is a constant. also explain what the rate of change means for this situation.

people l cost ($)
2 l 110
3 l 165
4 l 220
5 l 275

a. 1/55
b. 110/1
c. 1/275
d. 55/1

1. (-2,5)(1,4)
slope = (4 - 5) / (1 - (-2) = -1 / 3

2. (11,13)(8,18)

3. (6,y)(10,-1)
    slope = (-1 - y) / (10 - 6) = (-1- (-2) / 4 = 1/4
     y = -2

4. undefined

5. (2,110)(3,165)
     slope = (165 - 110) / (3 - 2) = 55/1 
     this basically means that to rent a charter boat, it will cost 55 per person

P(X=0) = 0.0224, P(X=1) = 0.2552, P(X=2) = 0.7224

Step-by-step explanation:

Let's define the following events

A: the first component meet specification

B: the second component meet specification

: the first component does not meet specification

: the second component does not meet specification

then

P(A) = 0.84, P() = 0.16, P(B) = 0.86 and P() = 0.14

we know that X = number of components that meet specifications, then, X can take the values 0, 1 or 2. Let's compute the probabilities P(X=0), P(X=1), P(X=2).

P(X=0) = P() = P()P() (because components are independent)

          = (0.16)(0.14)

          = 0.0224

P(X=1) = P[]

          = P() + P() (because and are mutually exclusive)

          = P(A)P() + P()P(B) (by independence)

          = (0.84)(0.14) + (0.16)(0.86) = 0.2552

P(X=2) = P(A∩B)=P(A)P(B) (by independence)

          = (0.84)(0.86)

        = 0.7224

         

and the probability mass function of X is given by

P(X=0) = 0.0224, P(X=1) = 0.2552, P(X=2) = 0.7224