Factor (x-8)^2 - (x+3)^2

A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While

Murljashka [212]

Answer:

The expected number of appearance defects in a new car = 0.64

standard deviation = 0.93(approximately)

Step-by-step explanation:

Given -

7% had exactly three, 11% exactly two, and 21% only one defect in cars.

Let X be no of defects in a car

P(X=3) = .07 , P(X=2) = .11 , P(X=3) = .21

P(X=0 ) = 1 - .07 - .11 - .21 = 0.61

The expected number of appearance defects in a new car =

E(X) = $\nu$ = $= \sum X P(X) =3\times 0.07 + 2\times0.11 + 3\times0.21 + 0\times0.61$ = 0.64

$\sigma^{2}$ = variation of E(X) = $\sum (X - \nu) ^{2}P(X)$ = $(3 - 0.64) ^{2}\times0.07 + (2 - 0.64) ^{2}\times0.11 + (1 - 0.64) ^{2}\times0.21 + (0 - 0.64) ^{2}\times0.61$

= $(2.36) ^{2}\times0.07 + (1.36) ^{2}\times0.11 + (.36) ^{2}\times0.21 + ( 0.64) ^{2}\times0.61$ = 0.8704

standard deviation = $\sqrt{\sigma^{2}}$ = $\sqrt{0.8704^{2}}$ = 0.93(approximately)

4 0

3 years ago

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some studen

ira [324]

Answer:

A. 0.1

B. 0.8

C. 0.5

Step-by-step explanation:

Given:

P(Science) = 0.3

P(Arts) = 0.6

P(none) = 0.2

From the above, it is understood that the events are independently events; meaning that the probability that a students gets a Bachelor of Science degree does not affect the probability of the same student getting a Bachelor of Arts degree.

A. The probability that a student gets a Bachelor of Science and Bachelor of Arts degree

Let P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degree

For independent events,

P(A) + P(B) - P(A and B) + P(none)= 1

If we translate the above formula to suit our needs, we have something like this

P(Science) + P(Arts) - P(Arts and Science) + P(none) = 1

Or

P(Arts) + P(Science) - P(Arts and Science) + P(none) = 1

From this, we have

0.3 + 0.6 - P(Arts and Science) + 0.2 = 1

1.1 - P(Arts and Science) = 1

-P(Arts and Science) = 1 - 1.1

-P(Arts and Science) = -0.1

P(Arts and Science) = 0.1

B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degree

For independent events

P(A or B) = P(A) + P(B) - P(A and B)

So, P(Arts or Science) = P(Arts) + P(Science) - P(Arts and Science)

P(Arts or Science) = 0.3 + 0.6 - 0.1

P(Arts or Science) = 0.8

C. The probability that a student gets only Bachelor of Arts

P(A only) = P(A) - P(A and B)

P(Arts) = P(Arts) - P(Arts and Science)

P(Arts) = 0.6 - 0.1

P(Arts) = 0.5

6 0

4 years ago

A smaller square is within a larger square as shown below. A point is chosen at random in the larger square. What percent of the

Bas_tet [7]

Answer: 84.5%

Step-by-step explanation:

15.2 × 15.2 = 231.04 cm² (area of the entire large square)

5.98 × 5.98 = 35.76 cm² (area of the small square)

large square - small square = area of the blue region

231.04 - 35.76 = 195.28 cm² (area of the blue region)

$\frac{area of the blue region}{large square}$ = percentage of time that the point will be in the blue region

$\frac{195.28}{231.04}$ = 0.845 --> 84.5%

4 0

3 years ago

How much should you put in an investment paying simple interest rate of 8% if you need 4000 in six months?

Nadusha1986 [10]

The amount you should put is 3846

<h3>How to determine the principal amount?</h3>

The given parameters are:

Amount, A = 4000

Rate, r = 8%

Time = 0.5 year i.e. 6 months

The amount on simple interest is calculated as:

A = P(1 + RT)

This gives

4000 = P * (1 + 8% * 0.5)

Evaluate the product

4000 = P * (1 + 0.04)

Evaluate the sum

4000 = P * (1.04)

Divide both sides by 1.04

P= 3846

Hence, the amount you should put is 3846