Let X be a geometric random variable with parameter p = and let Y be a Poisson random variable with parameter A 4. Assume X and Y independent. A rectangle is drawn with side lengths X and Y +1. Find the expected values of the perimeter and the area of the rectangle.

Answer:

176

Step-by-step explanation:

Apply PEMDAS

Solve the parenthesis first

11 ( 7 + 9 )

11 ( 16 )

Now open the parenthesis and you will have your answer

11 times 16

176

Answer:

y=-1/2x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=-1/2(x-(-2))

y+6=-1/2(x+2)

y=-1/2x-2/2-6

y=-1/2x-1-6

y=-1/2x-7

Answer:

43 ; 0.88493

Step-by-step explanation:

Using the Zscore formula :

Zscore = (x - m) / s

m = mean ; s = standard deviation

Profit = $1.5 - $1.2 = $0.3

Loss = $1.2 - $1 = 0.2

Cummlative probability :

Profit / (profit + loss)

0.3 / (0.3 + 0.2) = 0.3 / 0.5 = 0.6

To obtain the x, at Z at 0.6 = 0.26

m = 40 ; s= 10

Hence,

0.26 = (x - 40) / 10

0.26 * 10 = x - 40

2.6 = x - 40

2.6 + 40 = x

x = 42.6 `; 43 approximately

Probability of meeting day's demand at Wrigley

x = 52

P(x < 52) :

Zscore = (52 - 40) / 10

P(Z < 1.2)

Z = 0.88493

Answer:

x=28

Step-by-step explanation:

Hi there!

SSS similarity theorem is a theorem that can determine similar triangles; the criteria for SSS~ is that the corresponding sides of the triangles create proportions which is the same as the ratio of similitude (k)

First, we need to find the ratio of similitude.

We need to assume that the triangles are similar.

15 corresponds with 20 (if you turn both triangles until they're titled the same way, you will see that 15 and 20 are the measures of the same sides on the triangles)

so that means 15/20 must make the ratio of similitude

15/20 is equal to 3/4

therefore k=3/4

as the triangle is already assumed similar, that means that 21/x will also give us a ratio that is equal to 3/4 (ratio of similitude)

therefore, 21/x=k

Since both ratios are equal to k, set 3/4 and 21/x equal to each other. This is possible via a property called transitivity (if a=b and b=c, then a=c)

3/4=21/x

cross multiply

3x=84

divide both sides by 3

x=28

So that means that 28 will make the triangles similar by SSS similarity

*you double check by doing 21/28 and see that it's also equal to 3/4

Hope this helps!

Answer:

density = mass ÷ volume

v = 4 × 4 ×4 = 64

density = 503 .68 g ÷ 64 cm³

density = 7.87 g/cm³

Question 1

\(\frac{a-0}{a-0}=1\)

Question 2

\((1)(-1)=-1\)

Answer:

I think it's A

Step-by-step explanation:

225x + 400 ≥ 2200

225x ≥ 1800

x ≥ 8

In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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The general solution to the Euler equation is given by, y(x) = C1 x⁻³ + C2 x².

To find the general solution to the Euler equation \(x^{2y}\) + 2xy′ - 6y = 0, we can assume a solution of the form y(x) = \(x^r\) and substitute it into the equation.

Let's differentiate y(x) twice:

y′ = r\(x^{(r-1)}\)

y′′ = r(r-1)\(x^{(r-2)}\)

Now we substitute these derivatives into the equation:

x^2(r(r-1)\(x^{(r-2)}\)) + 2x(r\(x^{(r-1)}\)) - 6 \(x^r\) = 0

Simplifying the equation, we get:

r(r-1) \(x^r\) + 2r \(x^r\) - 6 \(x^r\) = 0

Factoring out  \(x^r\), we have:

\(x^r\) (r(r-1) + 2r - 6) = 0

This equation holds for all values of x, so the term in parentheses must be equal to zero:

r(r-1) + 2r - 6 = 0

Expanding and simplifying the equation, we get:

r² + r - 6 = 0

Factoring the quadratic equation, we have:

(r + 3)(r - 2) = 0

So we have two possible values for r:

r1 = -3

r2 = 2

Therefore, the general solution to the Euler equation is given by:

y(x) = C1 x⁻³ + C2 x².

where C1 and C2 are arbitrary constants.

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t = 12r/(r+120)

t(r+120) = 120r

tr+120t = 120r

tr-120r = -120t

r(t-120) = -120t

r = -120t/(t-120)

r = 120t/(120-t)

The determinant of the given matrix is 0.

To find the determinant of a matrix, we do not need to reduce it to echelon form. However, if you specifically need to reduce the matrix to echelon form using row operations, I can guide you through the process.

Let's start with the given matrix:

[[1, -1, -3, 0],

[7, -6, 5, 4],

[1, 1, 2, 1],

[-3, 5, 14, 1]]

To reduce it to echelon form, we perform row operations to create zeros below the main diagonal:

1. Replace R2 with R2 - 7R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[1, 1, 2, 1],

[-3, 5, 14, 1]]

2. Replace R3 with R3 - R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[-3, 5, 14, 1]]

3. Replace R4 with R4 + 3R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[0, 2, 5, 1]]

4. Replace R4 with R4 - R3:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[0, 0, 0, 0]]

Now, the matrix is in echelon form. The determinant of this matrix is the product of the main diagonal elements: 1 * 1 * 5 * 0 = 0.

Therefore, the determinant of the given matrix is 0.

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Answer: The value of q is 7.5.

Answer:

7.5

Step-by-step explanation:

Brainliest?

Answer:

D

Step-by-step explanation:

(a+4)(a-2)=a^2+2a-8

a*a=a^2

a*(-2)=-2a

a*4=4a

4*(-2)=-8

a^2-2a+4a-8=a^2+2a-8

The inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given parameters are:

Budget = $700

New bicycle = $296.71

Three bicycle reflectors = $12.34 each

Pair of a bike gloves = $33.66.

New biking outfits = $68.49 each.

Let the number of new biking outfits be x

So, we have the inequality;

New bicycle + 3 times price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget

This gives;

296.71 + 3( 12.34) + 33.66+ 68.49x ≤ 700

296.71 + 68.49x ≤ 700

Solve the inequality

367.39 + 68.49x ≤ 700

Hence, the inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700

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The annual rate of change for crime events measured is 1440 crimes.

A time derivative is a function's derivative with regard to time, which is often thought to indicate the pace at which the function's value changes. Time is often represented by the variable t.

Given that,

C (P) = 0.04P²

One city has 1,500,000 residents, and the population is growing by 12,000 people per year.

C (P) = 0.04P²

Differentiating with respect to t

\(\frac{d}{dt}\) (C(P)) = \(\frac{d}{dt}\) (0.04P²)

\(\frac{d}{dt}\) (C(P)) = 0.04 \(\frac{d}{dt}\) (P²)

\(\frac{dC (P)}{dt}\) = 0.04 (2P) \(\frac{dP}{dt}\)

\(\frac{dC(P)}{dt}\) = 0.08 \(\frac{dP}{dt}\)

Here, P = 1,500,000/1000 thousands of people

P = 1500 thousands of people

\(\frac{dP}{dt}\) = \(\frac{12000}{1000}\) thousands of people

\(\frac{dP}{dt}\) = 12 thousands people per year

Therefore, \(\frac{dC(P)}{dt}\) = 0.08P\(\frac{dP}{dt}\)

\(\frac{d}{dt}(C(1500)) = 0.08 (1500)(12)\)

\(\frac{d}{dt}(C(1500)) = 1440\)

Therefore, the rate of change of the incidents of crime measured per year is 1440 crimes per year.

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Answer:

11/36 = 0,305556 = 30,5556%

Step-by-step explanation:

5/6 * 5/6 = 25/36

36/36 - 25/36 = 11/36

To determine whether the process is in control or not, we can use a control chart. The control chart is a graphical tool used to monitor the stability of a process over time by plotting the sample statistics such as means or proportions over time and comparing them to control limits.

In this case, we are interested in monitoring the proportion of claims that were mailed within the five-day limit. We will use a p-chart, which is a control chart used to monitor the proportion of nonconforming items in a sample.

The formula for the p-chart is:

p = (number of nonconforming items in the sample) / (sample size)

The control limits for the p-chart are:

Upper control limit (UCL) = p-bar + 3sqrt(p-bar(1-p-bar)/n)

Lower control limit (LCL) = p-bar - 3sqrt(p-bar(1-p-bar)/n)

where p-bar is the overall proportion of nonconforming items, n is the sample size, and sqrt is the square root function.

Let's calculate the p-chart for the given data. The total number of samples is 24 and the sample size is 100.

First, we calculate the proportion of claims that were mailed within the five-day limit for each sample:

p1 = 1 - 12/100 = 0.88

p2 = 1 - 14/100 = 0.86

p3 = 1 - 18/100 = 0.82

p4 = 1 - 10/100 = 0.90

p5 = 1 - 8/100 = 0.92

p6 = 1 - 12/100 = 0.88

p7 = 1 - 13/100 = 0.87

p8 = 1 - 17/100 = 0.83

p9 = 1 - 13/100 = 0.87

p10 = 1 - 12/100 = 0.88

p11 = 1 - 15/100 = 0.85

p12 = 1 - 21/100 = 0.79

p13 = 1 - 19/100 = 0.81

p14 = 1 - 17/100 = 0.83

p15 = 1 - 23/100 = 0.77

p16 = 1 - 24/100 = 0.76

p17 = 1 - 21/100 = 0.79

p18 = 1 - 9/100 = 0.91

p19 = 1 - 20/100 = 0.80

p20 = 1 - 16/100 = 0.84

p21 = 1 - 11/100 = 0.89

p22 = 1 - 8/100 = 0.92

p23 = 1 - 20/100 = 0.80

p24 = 1 - 7/100 = 0.93

Next, we calculate the overall proportion of claims that were mailed within the five-day limit:

p-bar = (p1+p2+...+p24)/24 = 0.8575

Then, we calculate the control limits for the p-chart:

UCL = p-bar + 3sqrt(p-bar(1-p-bar)/n) = 0.8992

LCL = p-bar - 3sqrt(p-bar(1-p-bar)/n) = 0.8158

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Original Cost - $82

First part: Apply the 60% off discount

Convert first the 60% into decimal form

60% ÷ 100% = 0.6

Multiply it to the original cost to determine the discount

$82 ˣ 0.6 = $49.2

Subtract the discount to the original price, to determine the discounted price.

$82 - $49.2 = $32.8

Second part:

The discounted price is now $32.8 for which we will apply another 10% discount.

Again, convert 10% into decimal

10% ÷ 100% = 0.1

Multiply it to the discounted price, to determine the second discount.

$32.8 ˣ 0.1 = $3.28

Subtract the discount to the already discounted price.

$32.8 - $3.28 = $29.52

Therefore, the final sale price of the watch is at $29.52.

The forecasted value of xt1 in the given AR(1) model with a mean of 0, rho(2) = 0.215, rho(3) = -0.100, and xt = -0.431 is -0.073.

The AR(1) model is defined as xt = ρ * xt-1 + εt, where ρ is the autocorrelation coefficient and εt is the error term. In this case, the autocorrelation coefficient rho(2) = 0.215 is the correlation between xt and xt-2, and rho(3) = -0.100 is the correlation between xt and xt-3.

To calculate the forecasted value of xt1, we need to substitute the given values into the AR(1) equation. Since xt is given as -0.431, we have:

xt = ρ * xt-1 + εt

-0.431 = 0.215 * xt-1 + εt

Solving for xt-1, we find:

xt-1 = (-0.431 - εt) / 0.215

To calculate xt1, we substitute xt-1 into the AR(1) equation:

xt1 = ρ * xt-1 + εt+1

xt1 = 0.215 * [(-0.431 - εt) / 0.215] + εt+1

xt1 = -0.431 - εt + εt+1

Since we do not have information about εt or εt+1, we cannot determine their exact values. Therefore, the forecasted value of xt1 is -0.431.

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Answer:

Always true

Step-by-step explanation:

Because they are opposite exterior angles

The linear transformation T is defined as T(y) = (1+x^2)y'' + (1-x)y' - 3y, mapping polynomials from P3 to P2. In part (a), we find the matrix representation of T with respect to the given bases. Part (b) involves finding the kernel of T, which corresponds to the solutions of the homogeneous differential equation. Finally, in part (c), we determine if T is surjective and discuss its implications for the solutions to the differential equation (⋆).

(a) To find the matrix representation of T, we apply T to each basis element of P3 and express the results in terms of the basis for P2. The coefficients of these expressions form the columns of the matrix. By evaluating T(1), T(x), T(x^2), and T(x^3), we obtain the matrix representation of T.

(b) The kernel of T consists of polynomials y that satisfy the homogeneous differential equation (1+x^2)y'' + (1-x)y' - 3y = 0. To find a basis for the kernel, we need to solve this differential equation. The solutions form a subspace, and any basis for this subspace serves as a basis for the kernel of T. The dimension of the kernel is equal to the number of basis elements.

(c) For T to be surjective, every polynomial in P2 should have a preimage in P3 under T. If T is not surjective, it means there exist polynomials in P2 that are not in the range of T. In the context of the differential equation (⋆), if T is not surjective, it implies that there are functions f in P2 for which the differential equation does not have a solution in P3.

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The integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

To evaluate the given integral ∫∫s xyz ds, where s is the part of the plane z=4−y that lies in the cylinder x^2+y^2=4, we can use the method of our choice. Let's use the method of cylindrical coordinates.

1. Set up the surface integral for the given function over the given surface s as a double integral over a region r in the xy-plane.
  ∫∫s xyz ds = ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA

2. To find the region r, we need to determine the bounds for the cylindrical coordinates. Since the cylinder has radius 2, we have 0 ≤ ρ ≤ 2. The z-coordinate ranges from the plane z = 4-y to the plane z = 0. Thus, the bounds for z are 0 ≤ z ≤ 4-y.

3. Convert the integral into cylindrical coordinates by substituting x = ρcosθ and y = ρsinθ.
  ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA
  = ∫∫r ρ^3cosθsinθ(4-y) √(1 + (-sinθ)^2 + (-cosθ)^2) dρdθ

4. Evaluate the double integral by integrating with respect to ρ first and then θ.
  ∫∫r ρ^3cosθsinθ(4-y) √2 dρdθ
  = √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ

Therefore, the integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

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Answer:

78.5 m²

Step-by-step explanation:

Area formula: πr²

Plug it in: (3.14)(5m)²

Answer: 78.5 m²

For a repeated measures ANOVA for n = 78, k = 7, SSb = 8, SSw = 8, SSerror = 71 , the value of Mean Square Error Term is  1  .

The Mean Squares Error Term (MSerror) is calculated by dividing the sum of squares error (SSerror) by the degrees of freedom for error (dfe), which is equal to (n - k). So , we have:

⇒ MSerror = (SSerror)/(dfe) ,

For n = 78 and k = 7 ,

We get ,

The degree of freedom for error (dfe) = 78 - 7 = 71 ,

So , MSerror = (SSerror)/(dfe) ,

⇒ MSerror = 71/(78 - 7) ,

⇒ MSerror = 71/71 ,

⇒ MSerror = 1

Therefore, the value of MSerror is equal to 1.

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The given question is incomplete , the complete question is

For a repeated measures ANOVA, given n = 78, k = 7, SSb = 8, SSw = 8, SSerror = 71 . What is the value of the mean squares error term (MSerror)?

Answer:

1

Step-by-step explanation:

The step by step explanation is in the diagram above

I hope you understand

The measure of central tendency that is used by the professor is; Mode

A measure of central tendency is defined as a single value that attempts to describe a set of data by identifying the central position within that set of data. The types of measures of central tendency are;

1) Mean; This is defined as the average value of a given set of data.

2) Median: This is defined as the midpoint of a frequency distribution of observed values or quantities, such that there is an equal probability of falling above or below it.

3) Mode: This refers to the value in a given set of data that has highest occurrence frequency.

In this case, the professor notes that most students in his class earned a grade of b. Thus, this is the mode.

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Answer:

The distance is 338ft

Step-by-step explanation:

Given

Represent distance with s and velocity with v:

When

\(s = 200\ ft\)

\(v = 50mph\)

Required

Determine the distance when velocity is 65mph

From the question, we understand that:

\(s\ \alpha\ v^2\)

Convert to equation

\(s\ = kv^2\)

Substitute 200 for s and 50 for v

\(200 = k * 50^2\)

\(200 = k * 2500\)

Make k the subject:

\(k = \frac{200}{2500}\)

\(k = \frac{2}{25}\)

To get s when v = 65.

Substitute 65 for v and 2/25 for k in \(s\ = kv^2\)

\(s = \frac{2}{25} * 65^2\)

\(s = \frac{2}{25} * 4225\)

\(s = \frac{8450}{25}\)

\(s = 338\\\)

Hence, the distance is 338ft

\(\begin{array}{| c | c |}\boxed{ \bf{Equations} }&\boxed{ \bf{YES \: OR \: NO}} \\ \\ \tt{1. \: \:y = {x}^{2} + 2} & \tt{YES} \\\tt{2. \: \:y = 2x - 10}& \tt{NO} \\ \tt{3. \: \:y = 9 - {2x}^{2}} & \tt{YES} \\ \tt{ 4. \: \:y = {2}^{x} + 2}& \tt{ NO} \\ \tt{5. \: \:y = {3x}^{2} + {x}^{3} + 2}& \tt{NO} \\ \tt{ 6. \: \:y = {2}^{x} + 3x + 2}& \tt{NO} \\ \tt{ 7. \: \:y = {2x}^{2}} & \tt{ YES} \\ \tt{ 8. \: \:y = (x - 2)(x + 4)}& \tt{YES} \\ \tt{9. \: \:0 = (x - 3)(x + 3) + {x}^{2} - y}& \tt{YES} \\ \tt{10. \: \:{3x}^{3} + y - 2x = 0}& \tt{NO}\end{array}\)

First of all we can solved the function

We using the identity,

(x + a)(x + b) = x² + (a + b)x + ab

(x - 2)(x + 4)

= x² + (-2 + 4)x + (-2)(4)

= x² + 2x - 8

First of all we can solved the function

We using the identity,

(a + b)(a - b) = a² - b²

(x - 3)(x + 3) + x² - y

= x² - 3² + x² - y

= x² - 9 + x² - y

= x² + x² - y - 9

= 2x² - y - 9