Ummi is setting up an aquarium in the shape shown here. She fills it

The manager of an industrial plant is planning to buy a new machine. For each day’s operation, the number of repairs X, that the

horsena [70]

Answer: Expected value of the daily cost of operating the machine is 235.264.

Step-by-step explanation:

Since we have given that

E[x]= 0.96 repairs per day

And Var[x] = 0.96 repairs per day.

$C=160+40x^2$

$E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264$

Hence, Expected value of the daily cost of operating the machine is 235.264.

5 0

2 years ago

On a coordinate plane, a triangle has points (negative 5, 1), (2, 1), (2, negative 1).

daser333 [38]

Answer:

Step-by-step explanation:

Given a triangle has points:

(-5,1),(2,1), (2,-1)

Let us label the points:

A(2,1),

B(-5,1) and

C(2,-1)

To find:

Distance between (−5, 1) and (2, −1) i.e. BC.

Horizontal leg AB and

Vertical leg, AC.

Solution:

Please refer to the attached diagram for the labeling of the points on xy coordinate plane.

We can simply use Distance formula here, to find the distance between two coordinates.

Distance formula :

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For BC:

$x_2 = 2\\x_1 = -5\\y_2 = -1\\y_1 = 1$

$BC = \sqrt{(2--5)^2+(-1-1)^2} = \sqrt{63}$

Horizontal leg, AC:

$x_2 = -5\\x_1 = 2\\y_2 = 1\\y_1 = 1$

$AC = \sqrt{(2-(-5))^2+(1-1)^2} = 7$

Vertical Leg, AB:

$x_2 = 2\\x_1 = 2\\y_2 = -1\\y_1 = 1$

$AB = \sqrt{(2-2)^2+(-1-1)^2} = 2$

5 0

2 years ago

Read 2 more answers

Nora's savings account has a balance of $3979. After 4 years, what will the amount of interest be at 12% compounded semiannually

alexgriva [62]

The correct answer is C.<span>$2362.92</span>

7 0

1 year ago

Read 2 more answers

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes ha

Bingel [31]

Answer:

Step-by-step explanation:

Hello!

Part A

First, determine your study variable:

X: Number of boxes with an extra donut in a sample of eight.

To see if the variable has a Binomial distribution you have to check if the binomial criteria are met:

1. The number of observation of the trial is fixed (In this case n = 8, the boxes each customer bought make the sample)

2. Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial (In this case, the amount of donuts in one box does not affect on the probability of the next box having an extra donut)

3. The probability of success in the same from one trial to another (In this case our "success" will be that the box has an extra donut, according to the owners claim that is 1/7; ρ=0,14)

So X≈ Bi (n;ρ)

Where n represents the sample (n=8) and ρ is the probability of success (ρ=0.14)

Part B

The mean of the binomial distribution is E(X)= nρ

E(X)= 8 * 0.14= 1.12

The mean of the distribution is also called the expected value. You'd expect that 1.12 boxes have an extra donut.

The variance of the binomial distribution is V(X)= nρ(1 - ρ)

V(X)= 8*0.14*(1 - 0.14)= 0.9632

Its square root is the standard deviation

√V(X)= 0.98

The standard deviation is a measure of dispersion, it indicates how much the values of the distribution of the central value are separated. In this case, 0.98 indicates that the distribution of the number of boxes with an extra donut is far from the expected value.

Part C

Two of the eight customers buy a box with an extra donut, symbolically:

P(X=2) = P(X≤2) - P(X≤1)= 0.91 - 0.68 = 0.22

There is a 22% chance that two customers bought a box with an extra donut.

Compute:

P(X≥2)= 1 - P(X<2)= 1 - P(X≤1)= 1 - 0.68= 0.32

There is a 32% chance that two or more customers bought a box with an extra donnut.

I hope it helps!

3 0

1 year ago

People are arriving at a party one at a time. While waiting for more people to arrive they entertain themselves by comparing the

Marina CMI [18]

Answer:

=(k−1)*P(X>k−1) or (k−1)365k(365k−1)(k−1)!

Step-by-step explanation:

First of all, we need to find PMF

Let X = k represent the case in which there is no birthday match within (k-1) people

However, there is a birthday match when kth person arrives

Hence, there is 365^k possibilities in birthday arrangements

Supposing (k-1) dates are placed on specific days in a year

Pick one of k-1 of them & make it the date of the kth person that arrives, then:

The CDF is P(X≤k)=(1−(365k)k)/!365k, so the can obtain the PMF by

P(X=k) =P (X≤k) − P(X≤k−1)=(1−(365k)k!/365^k)−(1−(365k−1)(k−1)!/365^(k−1))=

(k−1)/365^k * (365k−1) * (k−1)!

=(k−1)*(1−P(X≤k−1))

=(k−1)*P(X>k−1)

6 0

2 years ago