Let Y be an exponentially distributed random variable with mean β. Define a random variable X in the following way: X = k if k − 1 ≤ Y < k for k = 1, 2, . . . .
a Find P( X = k) for each k = 1, 2, . . . .

Answer:

[tex]\begin{array}{cc}{Cars} & {Months} & {28} & {3} & {29} & {3} & {30} & {1} & {31} & {2} \ \end{array}[/tex]

Step-by-step explanation:

Given

Data:

[tex]29\ 30\ 29[/tex]

[tex]29\ 31\ 28[/tex]

[tex]28\ 31\ 28[/tex]

Required

Construct a frequency table

From the given data, we have:

28 occurs 3 times

29 occurs 3 times

30 occurs 1 time

31 occur 2 times

Hence, the frequency table is:

[tex]\begin{array}{cc}{Cars} & {Months} & {28} & {3} & {29} & {3} & {30} & {1} & {31} & {2} \ \end{array}[/tex]

Answer:

Hope it helps! follow me!  brainliest! Peace out!

Step-by-step explanation:

Cars:      months:

28           3

29           3

30           1

31            2

Answer:

3x+y=13

+2x-y=12

SOlve it like what you would normally do

3x+2x=5x

y+(-y)=0

13+12=25

Basically

5x+0=25

Bring down all appropiate signs

Now solve that

5x=25

x=5

Now to find “y”

Plug in The “x”

3*5=15

15+y=13 now solve that and you’d get -2

If you plug it into the other one, it would be the same thing

2*5=10

10-y=12

-y=2

y= -2

x=5

y= -2

Answer:

20

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

7x10 is 70 plus 7 is 77

Answer:

3(y +8) (d+e) /4

Step-by-step explanation:

I gotta get to class too soon so my explanation here is just to get this sent. hopefully it does. I tried my best. could be wrong

Answer:

4.046 m

Step-by-step explanation:

Yes, the given matrix A is diagonalizable.

Let the matrix A be given by A = [−2 2 1 0 0 2].

To determine if this matrix is diagonalizable, we need to check whether A has enough linearly independent eigenvectors. If there are enough such eigenvectors, then A will be diagonalizable. Otherwise, A will not be diagonalizable.

To find the eigenvalues and eigenvectors of the matrix A, we solve the equation Ax = λx, where λ is a scalar (eigenvalue) and x is the corresponding eigenvector. This gives: (A - λI)x = 0, where I is the identity matrix.To solve for the eigenvalues, we need to find λ such that det(A - λI) = 0. This gives us the characteristic equation:

(−2 − λ)(2 − λ)(1 − λ) − 4(2 − λ) = 0, which simplifies to λ^3 − λ^2 − 10λ − 12 = 0.

To find the eigenvectors, we solve for x in the equation (A - λI)x = 0, using each eigenvalue λ obtained from the characteristic equation.To solve for λ, we need to solve the characteristic equation. Factoring it gives (λ - 4)(λ + 1)^2 = 0, which has eigenvalues λ1 = 4 and λ2 = −1 (multiplicity 2).

Since we have two distinct eigenvalues (λ1 = 4 and λ2 = −1), we know that A is diagonalizable if and only if it has two linearly independent eigenvectors corresponding to each eigenvalue.To find the eigenvectors corresponding to λ1 = 4, we need to solve the system (A - 4I)x = 0.

This gives the matrix equation:

[−6 2 1 0 0 −2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]

Solving this system gives x1 = -x3/6 - x6/2, x2 = x2, and x4 = x4. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them.

Doing so gives:

x1 = -1/6

x3 - x6/2x2 = x2x4 = x4x5 = 0

So, the eigenvectors corresponding to λ1 = 4 are of the form [x1 x2 x3 x4 x5 x6] = [−1/6t  −2s  t  0  0  −2t], where t and s are arbitrary constants.To find the eigenvectors corresponding to λ2 = −1, we need to solve the system (A + I)x = 0.

This gives the matrix equation: [−1 2 1 0 0 2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]

Solving this system gives x1 = -x3 + 2x6, x2 = x2, and x4 = -2x6. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them. Doing so gives: x1 = 2t - s, x2 = x2, x4 = -2t ,x5 = 0

So, the eigenvectors corresponding to λ2 = −1 are of the form [x1 x2 x3 x4 x5 x6] = [2t − s  0  t  −2t  0], where t and s are arbitrary constants.Since we have four linearly independent eigenvectors (two corresponding to each eigenvalue), we can diagonalize the matrix A by forming the matrix P whose columns are these eigenvectors.

The matrix P is given by P = [−1/6 −2 2 0 0 2][0 1 0 0 0 0][1 −2 0 0 0 0][0 0 0 1 0 0][0 0 1 0 0 0][−2 0 0 0 0 1]

Hence A is diagonalizable.

Answer: Yes, the given matrix A is diagonalizable.

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Answer:

Steps:

V = H × (h×bl)/2

V = 6 × (4.2×2.8)/2

V = 6 × 11.76/2

V = 6 × 5.88

V = 35.28 m³

Answer: What percentage is 15 out of 75?

20

Percentage Calculator: 15 is what percent of 75? = 20.

Answer:

5%

Step-by-step explanation:

the 95% confidence interval for the true proportion of all adults in the town who do not have health insurance is approximately (0.2686, 0.4586).

To find a confidence interval for the true proportion of adults in the town who do not have health insurance, we can use the following formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, we need to calculate the sample proportion:

Sample Proportion ([tex]\hat{p}[/tex]) = Number of adults without health insurance / Total number of adults

Total number of adults = 99 (given)

Number of adults with health insurance = 99 - 63 = 36

Sample Proportion ([tex]\hat{p}[/tex]) = 36 / 99 ≈ 0.3636

Next, we need to calculate the margin of error. Since the sample size is large and we are working with proportions, we can use the formula for the margin of error in a proportion:

Margin of Error = Z * √[([tex]\hat{p}[/tex] * (1 - [tex]\hat{p}[/tex])) / n]

Where:

Z is the Z-score corresponding to the desired level of confidence (95% confidence corresponds to a Z-score of approximately 1.96)

[tex]\hat{p}[/tex] is the sample proportion

n is the sample size

Margin of Error = 1.96 * √[(0.3636 * (1 - 0.3636)) / 99]

Calculating the margin of error:

Margin of Error ≈ 1.96 * √(0.2332 / 99)

             ≈ 1.96 * √(0.002352525)

Margin of Error ≈ 1.96 * 0.048503

Margin of Error ≈ 0.095

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.3636 ± 0.095

Confidence Interval ≈ (0.2686, 0.4586)

Therefore, the 95% confidence interval for the true proportion of all adults in the town who do not have health insurance is approximately (0.2686, 0.4586).

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Step-by-step explanation:

6×10

=60

niceeeeeeeeeeee

Answer:

9 hours.

Step-by-step explanation:

$357 / 17 = $21. ($21 per hour.)

$189/$21 = 9. BOOM

Answer: a

Step-by-step explanation: A plane is a 2d surface so if it ever intersects a 3d object the cross-section will be a 2d figure, in this case, a rectangle.

Answer:

sorry

Step-by-step explanation:

i can't understand your question

there is no clarity

The client index of the company in 2020 compared to 2019 is 2.14.

To calculate the client index of the company in 2020 compared to 2019 we can use the formula below;

Client Index = (Number of clients in current year / Number of stores in current year) / (Number of clients in previous year / Number of stores in previous year)

The client index of the company in 2020 compared to 2019 is: 2.14 (rounded to 2 decimal places).

Clients in 2019 = 9539Clients in 2020 = 12504Premium Clients of the Year 2020 = 1230Stores in 2019 = 17Stores in 2020 = 12

To calculate the client index of the company in 2020 compared to 2019 we can use the formula below;

Client Index = (Number of clients in current year / Number of stores in current year) / (Number of clients in previous year / Number of stores in previous year)We can substitute the values into the formula and simplify it as follows;

Client Index = (12504 / 12) / (9539 / 17) = (1042 / 1) / (561 / 1) = 1042 / 561 = 1.85714285714 ≈ 2.14

Therefore, the client index of the company in 2020 compared to 2019 is 2.14 (rounded to 2 decimal places).

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The variance is calculated as the average of the squared deviations from the average return. The standard deviation is the square root of the variance. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.

First, calculate the average returns by summing up the returns for each year and dividing by the total number of years. For X, the average return is

(21% - 16% + 9% + 18% + 4%) / 5 = 7.2%.

For Y, the average return is

(24% - 3% + 26% - 13% + 30%) / 5 = 12.8%.

Next, calculate the variances. For X, subtract the average return from each year's return, square the result, and calculate the average of these squared deviations. The variance for X is

(6.2^2 + (-23.2)^2 + 1.8^2 + 10.8^2 + (-3.2)^2) / 5 = 130.24%.

Similarly, for Y, the variance is

(11.2^2 + (-15.8)^2 + 13.2^2 + (-25.8)^2 + 17.2^2) / 5 = 388.48%.

Finally, calculate the standard deviations by taking the square root of the variances. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.

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Answer: M=1/3

Step-by-step explanation: We know how to find the slope by using the formula: y2-y1/x2-x1

Then we get 3-1/3--3=2/6=

1/3

that's the correct answer!

Answer:

324

Step-by-step explanation:

1 yards = 36 inches

36 x 9 = 324

Answer:

(x+1)(x+9)

Step-by-step explanation:

Hope this helps!

Phone calls and days of the week are independent. There is insufficient evidence to conclude otherwise.

In the analysis of phone call frequencies for each day of the week, we need to determine if phone calls are equally likely to occur on any day. Using a significance level of 0.10, we can perform a chi-square goodness-of-fit test.

The null hypothesis (H₀) states that the distribution of phone calls is uniform over the days of the week, while the alternative hypothesis (H₁) suggests that the distribution is not uniform.

To calculate the expected frequencies, we divide the total number of phone calls (581) by the number of days (7), resulting in an expected frequency of 83 for each day.

The degrees of freedom for this test are (number of categories - 1), which in this case is 7 - 1 = 6.

Using the chi-square test statistic and the calculated expected frequencies, we can find the p-value associated with the test statistic. If the p-value is less than the significance level of 0.10, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.

Based on the analysis, the p-value is not provided, so we cannot draw a specific conclusion.

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Answer:

Option 3 is not true for f(x) and g(x).

The incorrect statement will be;

⇒ f (x) × g(x) = 4x⁵ + 8x⁴ - 13x³ - 17x² + 3x + 9

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The function are,

⇒ f(x) = 2x² + x - 3

And , g(x) = 2x³ + 3x² - 2x - 3

Now,

Since, The function are,

⇒ f(x) = 2x² + x - 3

And , g(x) = 2x³ + 3x² - 2x - 3

Hence, We get;

⇒ f (x) + g(x) = 2x² + x - 3 + 2x³ + 3x² - 2x - 3

                   = 2x³ + 5x² - x - 6

⇒ g (x) - f (x) = (2x³ + 3x² - 2x - 3) - (2x² + x - 3)

                   = 2x³ + 3x² - 2x - 3 - 2x² - x + 3

                   = 2x³ + x² - 3x

⇒ f (x) × g(x) = (2x² + x - 3) (2x³ + 3x² - 2x - 3)

                 = 4x⁵ + 6x⁴ - 4x³ - 6x² + 2x⁴ + 3x³ - 2x² - 3x - 6x³ - 9x² + 6x +9

                = 4x⁵ + 8x⁴ - 7x³ - 17x² + 3x + 9

Thus, The incorrect statement is,

⇒ f (x) × g(x) = 4x⁵ + 8x⁴ - 13x³ - 17x² + 3x + 9

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Answer:

2 2/5

Step-by-step explanation:

2.4 = 2 4/10 = 2 2/5 (all you had to do is divide by 2)

The answer would be 2 2/5 (could also be 1.2 as a decimal)

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

Step-by-step explanation:

The

2

is in the ones place, and the

4

is in the tenths place.

2.4

means two and four tenths. So in fraction form it is 2 4/10

Answer link

Answer:

a. 8 years

b. $49.20

Step-by-step explanation:

The computation is shown below:

a. The mark age is

Given that

232 is 8 times of the sum of mark and his sister ages

And, his sister is 21

So,

Let us assume the mark age be x

now

8(x + 21) = 232

x + 21 = 29

x = 29 -21

x = 8

b. The original price of the socks is

As each pair get $3 off

And she bought 6 pairs for $31.20

= $31.20 + 6 × $3

= $31.20 + 18

= $49.20

Answer:

581

mark me as brainliest plz

Step-by-step explanation:

f(x) = x^2 represents a quadratic function, where the input value (x) is squared and the resulting output value is equal to the square of x.

g(x) = (x+3)^2 - 1 represents another quadratic function, where the input value (x) is first added to 3, then squared, and the resulting output value is equal to the square of (x+3) minus 1.

To evaluate these functions for a specific value of x, we simply substitute that value into the function in place of x. For example, if we want to find f(4), we would replace x with 4 to get:

f(4) = 4^2 = 16

Similarly, if we want to find g(-2), we would replace x with -2 to get:

g(-2) = (-2+3)^2 - 1 = 1^2 - 1 = 0

We can also graph these functions on a coordinate plane by plotting points for various values of x and their corresponding values of f(x) or g(x). The graph of f(x) = x^2 is a parabola that opens upwards, while the graph of g(x) = (x+3)^2 - 1 is also a parabola, but it has been shifted 3 units to the left and 1 unit downwards compared to the graph of f(x).

Answer:

I think the answer is 49in^2

Answer:

Option A

Step-by-step explanation:

You're welcome.