Factor this expression completely. 9x (squared) -16

A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential cust

AlexFokin [52]

Answer:

(a) The probability the salesperson will make exactly two sales in a day is 0.1488.

(b) The probability the salesperson will make at least two sales in a day is 0.1869.

(c) The percentage of days the salesperson does not makes a sale is 43.05%.

(d) The expected number of sales per day is 0.80.

Step-by-step explanation:

Let X = number of sales made by the salesperson.

The probability that a potential customer makes a purchase is 0.10.

The salesperson contacts n = 8 potential customers per day.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={8\choose x}0.10^{x}(1-0.10)^{8-x};\ x=0,1,2,3...$

(a)

Compute the probability the salesperson will make exactly two sales in a day as follows:

$P(X=2)={8\choose 2}0.10^{2}(1-0.10)^{8-2}\\=28\times 0.01\times 0.5314\\=0.1488$

Thus, the probability the salesperson will make exactly two sales in a day is 0.1488.

(b)

Compute the probability the salesperson will make at least two sales in a day as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-{8\choose 0}0.10^{0}(1-0.10)^{8-0}-{8\choose 1}0.10^{1}(1-0.10)^{8-1}\\=1-0.4305-0.3826\\=0.1869$

Thus, the probability the salesperson will make at least two sales in a day is 0.1869.

(c)

Compute the probability that a salesperson does not makes a sale is:

$P(X=0)={8\choose 0}0.10^{0}(1-0.10)^{8-0}\\=8\times 1\times 0.4305\\=0.4305$

The percentage of days the salesperson does not makes a sale is,

0.4305 × 100 = 43.05%

Thus, the percentage of days the salesperson does not makes a sale is 43.05%.

(d)

Compute the expected number of sales per day as follows:

$E(X)=np=8\times 0.10=0.80$

Thus, the expected number of sales per day is 0.80.

7 0

3 years ago

Draw a rhombus that is not a square. Label the lengths of its sides and its height so it represents a rhombus with an area of 20

Tcecarenko [31]

Answer:

/\

$\sqrt{20}$ / \ $\sqrt{20}$

/ \

\ /

$\sqrt{20}$ \ / $\sqrt{20}$

\/

Step-by-step explanation:

i hope this is right it took me 30 min for the ascii

6 0

3 years ago

Mike runs cross country. He runs 7 miles in 56

kondor19780726 [428]

It will take him 120 mins as he runs 8 minute miles

4 0

3 years ago

10 ways to divide 96 into equal groups

Andrew [12]

These are the ten ways to divide 96 into equal groups:

96 divided by 2 = 2 groups of 48

96 divided by 48 = 48 groups of 2

96 divided by 12 = 12 groups of 8

96 divided by 8 = 8 groups of 12

96 divided by 32 = 32 groups of 3

96 divided by 3 = 3 groups of 32

96 divided by 24 = 24 groups of 4

96 divided by 4 = 4 groups of 24

96 divided by 6 = 6 groups of 16

96 divided by 16 = 16 groups of 6

4 0

3 years ago

Which line on the graph represents the equation y=3x-2

Vika [28.1K]

Answer:

Line A.

Step-by-step explanation:

When you put x as zero into 3x-2, you get 3(0)-2. That equals -2. Therefore, y = -2. When x=0, that is the y-intercept, so the y-intercept is -2. Line A crosses the y-axis at -2, so line A has that y-intercept.

Slope is always y/x. On a graph, that is the number of squares UP over the number of squares ACROSS. Counting, we get, 3 squares up over 1 square across for line A. 3/1= 3. The slope is the number we multiply by x. In the equation, that is 3, because we see 3x, and no sign or space between 2 numbers automatically means we multiply. So line A also has the correct slope.

In linear equations (straight lines), the same slope and y-intercept are enough to tell you that the equation matches the line.

Therefore, the answer is A!

5 0

2 years ago

Factor this expression completely. 9x (squared) -16​

Factor this expression completely. 9x (squared) -16