BRAINLIEST PLUS 100 POINTS

An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the

lora16 [44]

Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

4000 if the device fails during the first year. The amount of the

benefit decreases by 1000 each successive year until it reaches 0.

If the device has not failed by the beginning of any given year, the

probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x 4000 3000 2000 1000 0

P(x) 0.4 0.6×0.4 0.6² × 0.4 0.6³ × 0.4 1 - 0.8704

(0.4) (0.24) (0.144) (0.0864) (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

= 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

= 1600 + 720 + 288 + 86.4 + 0

= 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

5 0

2 years ago

A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $8. Each additional inch cost

zaharov [31]

Answer:

8 + 1.50x + 0.75y = 19.25

Step-by-step explanation:

Let the number of additional inch = x

Let the number of toppings = y

From the question,

A 10-inch cheese pizza costs $8.

Each additional inch costs $1.50

Each additional topping costs $0.75.

The equation that represents Josh's pizza is when his total cost amounts to $19.25 is:

$8 + $1.50 × x + $0.75y = $19.25

8 + 1.50x + 0.75y = 19.25

7 0

2 years ago

Can someone explain to me in words how to do this problem 3x+122=22x-11

inn [45]

When you have this type of problem, you need to combine the like-terms and isolate the variable.

3x + 122 = 22x - 11

Add 11 to both sides to get rid of it

3x + 122 + 11 = 22x - 11 + 11 (-11 + 11=0)

3x + 133 = 22x

Then you would bring the 3x to the other side, so subtract 3x from both sides

3x + 133 = 22x

-3x -3x

133 = 22x - 3x

133 = 19x

Then divide both sides by 19 to isolate x

133/19 = 19x/19

133/19 = 7, so x = 7

Hope this helps!!

8 0

2 years ago

"A study conducted at a certain college shows that 56% of the school's graduates find a job in their chosen field within a year

KiRa [710]

Answer:

99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they find a job in their chosen field within one year of graduating, or they do not. The probability of a student finding a job in their chosen field within one year of graduating is independent of other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

56% of the school's graduates find a job in their chosen field within a year after graduation.

This means that $p = 0.56$

Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

This is $P(X \geq 1)$ when n = 6.

Either none find a job, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.56)^{0}.(0.44)^{6} = 0.0073$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0073 = 0.9927$

99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

8 0

3 years ago

Can a line segment have two midpoints ?

zzz [600]

Actually, no they cannot. The midpoint is the single point at the very center of the line segment. Since no segment can have multiple centers, they cannot have more than a single midpoint. Sorry :3

Hope this helped!! :D

5 0

3 years ago

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