Consider the linear regression model Y
i
​
=β
0
​
+β
1
​
X
1i
​
+β
2
​
X
2i
​
+u
i
​
. a) Suppose you multiply all the X
2
​
values by 2 . What will be the effect of this rescaling, if any, on the estimates of the parameters and their standard errors? b) Now instead of (a), suppose you multiply all the Y values by 2. What will be the effect of this, if any, on the estimated parameters and their standard errors?

Answer:

Step-by-step explanation: what’s the equation?

Given the provided information, if a woman over 35 tests positive for ovarian cancer, the probability that she actually has cancer is approximately 1.96%.

To determine the probability that a woman over 35 actually has ovarian cancer given a positive test result, we can create a contingency table and use conditional probability. Let's consider a hypothetical sample of 100,000 women:

Out of 100,000 women, 1 in every 2,500 (or 40 out of 100,000) actually has ovarian cancer. Since the test has a 0% rate of false negatives, all the women with ovarian cancer will test positive.

The test also has a 5% rate of false positives. This means that out of the remaining 99,960 women who do not have ovarian cancer, approximately 5% (or 4,998) will test positive incorrectly.

Therefore, out of a total of 5,038 positive test results (40 true positives + 4,998 false positives), only 40 are true positives for ovarian cancer. The probability that a woman who tests positive actually has ovarian cancer can be calculated as the ratio of true positives to the total positive tests:

Probability = (True Positives) / (Total Positive Tests) = 40 / 5,038 ≈ 0.00795 ≈ 0.795%

Thus, the probability that a woman over 35 actually has ovarian cancer given a positive test result is approximately 1.96%. This calculation highlights the importance of considering both the prevalence of the disease and the accuracy of the test in interpreting the results correctly.

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Answer: 3.78m

Step-by-step explanation: I hope that helps

Answer:

the 3 and 6 are constants.

the x is a variable

hope it helped:)))))))))))))))))

false I believe

hope this helps.

Answer:

y = -4x + 5

Step-by-step explanation:

hope this helps

Answer:

C

Step-by-step explanation:

The answer is C because you plugin using the area formula.

Answer:

100:20 or 100/20 or 100 to 20

Answer:

\(15^{3}\)

Step-by-step explanation:

\(15 * 15 *15 \\15^{3}\)

The task is to find f '(0.4) for the function f(x) = ∫[0 to x] arcsin(t) dt. The possible answers are: 0.081, 0.412, 0.389, and 1.091. The closest value to 0.4115 is 0.412. Thus, the answer is 0.412.

To find f '(0.4), we need to differentiate the function f(x) with respect to x. Applying the Fundamental Theorem of Calculus, we have f '(x) = arcsin(x). Therefore, to find f '(0.4), we substitute x = 0.4 into the derivative expression: f '(0.4) = arcsin(0.4). Evaluating this trigonometric function, we find that arcsin(0.4) is approximately 0.4115. Among the given options, the closest value to 0.4115 is 0.412. Thus, the answer is 0.412.

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Using the combination formula, the probabilities are given as follows:

a) P(4 seniors) = 0.0008.

b) P(1 of each) = 0.0999.

c) P(2 sophomore, 2 freshmen) = 0.0225.

d) P (at least one senior) = 0.5866.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the formula presented below, involving factorials.

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

In this problem, 4 captains are taken from a set of 13 + 13 + 10 + 16 = 52, hence the number of outcomes is:

\(C_{52,4} = \frac{52!}{4!48!} = 270725\)

The number of outcomes with four seniors is given as follows:

\(C_{10,4} = \frac{10!}{4!6!} = 210\)

Hence the probability is:

p = 210/270725 = 0.0008.

With no seniors, the number of outcomes is:

\(C_{42,4} = \frac{42!}{4!38!} = 111930\)

Hence with at least one senior, the number of outcomes is:

270725 - 111930 = 158795.

Hence the probability is:

p = 158795/270725 = 0.5866.

With one of each, the number of outcomes is:

13 x 13 x 10 x 16 = 27040

Then the probability is:

27040/270725 = 0.0999.

With two sophomores and two freshmen, the number of outcomes is:

\(C_{13,2} \times C_{13,2} = \frac{13!}{2!11!} \times \frac{13!}{2!11!} = 6084\)

Then the probability is:

6084/270725 = 0.0225.

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The acceleration of a particle is given by the derivative of its velocity vector with respect to time. The acceleration vector of the particle at time t = 2 is (12, 7).

So, to find the acceleration of the particle at time t = 2, we need to find the derivative of its velocity vector with respect to time and then evaluate it at t = 2.

The velocity vector is\(v(t) = (3t^2, 7t)\), so its derivative with respect to time is:

\(dv(t)/dt = (d/dt)(3t^2, 7t) = (6t, 7)\)

Evaluating this at t = 2, we have:

dv(t)/dt = (6 * 2, 7) = (12, 7)

So, the acceleration vector of the particle at time t = 2 is (12, 7).

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1. At time t > 0, a particle moving in the xy-plane has velocity vector given by v(t) = (3t2,7t). What is the acceleration vector of the particle at time t = 2?

Answer:

3/1 or 3

Step-by-step explanation:

It rises up three and to the side one

Answer: The slope is 3.

Mrs. Richardson makes a profit of $21.33 from each flower arrangement for the wedding.

To calculate the profit, we subtract the cost from the selling price. Mrs. Richardson's cost for arranging the bouquet is $13.67, and she charges the bride $35 for the arrangement.

Profit = Selling Price - Cost

Profit = $35 - $13.67

Profit = $21.33

Therefore, Mrs. Richardson makes a profit of $21.33 from each flower arrangement for the wedding.

In this scenario, the profit is calculated by subtracting the cost of arranging the bouquet from the selling price. The cost incurred by Mrs. Richardson is $13.67, which includes the expenses for materials, labor, and any other associated costs. On the other hand, the selling price is $35, which is what the bride pays for the arrangement.

By subtracting the cost from the selling price, we find that the profit per arrangement is $21.33. This means that Mrs. Richardson earns $21.33 for each bouquet she arranges for a wedding, after covering her costs.

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The  quotient of the expression \((-12x^3 + 21x^2 - 6x) / (-3x)\) is \(4x^2 - 7x + 2.\)

To find the quotient of the given expression, we divide the numerator by the denominator.

Expression:\((-12x^3 + 21x^2 - 6x) / (-3x)\)

Factoring  out the common term 'x' from the numerator:

\(x * (-12x^2 + 21x - 6) / (-3x)\)

Simplify the expression by canceling out the common terms 'x':

\((-12x^2 + 21x - 6) / (-3)\)

Dividing  each term in the numerator by -3:

\((-12x^2 / -3) + (21x / -3) + (-6 / -3)\)

Simplifying y each term:

\(4x^2 - 7x + 2\)

Therefore, the quotient of the expression \((-12x^3 + 21x^2 - 6x) / (-3x)\) is \(4x^2 - 7x + 2.\)

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The surface area of the figure which comprises two rectangular prisms is: 328 in.²

Surface area = 2(wl+hl+hw)

Decompose the given figure into two.

Surface area of the figure = surface area of the top rectangular prism + surface area of the bottom rectangular prism - 2(area of base of the top rectangular prism)

Surface area of top rectangular prism:

l = 6 in.

w = 4 in.

h = 5 in.

Surface area = 2(wl+hl+hw) = 2(4×6 + 5×6 + 5×4) = 148 in.²

Surface area of bottom rectangular prism:

l = 6 in.

w = 9 in.

h = 4 in.

Surface area = 2(wl+hl+hw) = 2(9×6 + 4×6 + 4×9) = 228 in.²

Area of base of the top rectangular prism:

Area = (l)(w) = (6)(4) = 24 in.²

Surface area of the figure = 148  + 228 - 2(24)

Surface area of the figure = 328 in.²

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25 minutes long

Hope this helps!

Ok so we know that the movie starts at 7:15 PM. The duration of the movie is 1.5 hours long. She begins eating her snack after the movie which, sense 7:15 plus 1.5 hours is 8:45, is 8:45. She finishes her snack at 9:10. What is the difference between 9:10 and 8:45?

For me, the easiest thing to do we would be to add a half hour (30 minutes) to the 8:45. This gets 9:15. Since 9:15 is past 9:10, I subtract the difference to get 5 minutes. I then take the 30 minutes I added to the 8:45 and subtract the 5 minutes that it went over to get 25 minutes. This is the easiest way to get the answer in my opinion. Sorry if this could not be of help to you!

Diagram to better understand maybe? (I did the best I could with this lol)

                                              x (the 25 minutes you found once you solved it)

                                                                                      ^

7:15 PM ----------------------------- 1.5 hours later----------------------------------- 9:10 PM

^                                                          ^                                                            ^

Time the movie started          Movie length             When she finished eating

Answer:

All

Explanation:

When an equation is in the form of y=kx, it displays direct variation, meaning that the y-intercept is 0. For example, take an equation in slope-intercept form, it has an equation of y=mx+b. Since there is no "b", in the form y=kx, that means that the line must pass through the origin, or (0,0)

Answer:

one

Step-by-step explanation:

Plug in (0,0) for the solution.

0(y)=k x 0(x)

simplify

0=0

that is true so that would be the answer.

Answer:

θ ≈ 50.1°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cosθ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{61}{95}\) , then

θ = \(cos^{-1}\) ( \(\frac{61}{95}\) ) ≈ 50.1° ( to the nearest tenth )

Answer:

32

Step-by-step explanation:

b^2c^1

Let b=-4 and c= 2

(-4)^2 ( 2)^1

16 * 2

32

Answer:

The correct answer is

-32

Step-by-step explanation:

All you need to do is plug in -4 and 2 into the equation to get:

4^2 times 2^1

This equals ...

-32

Hope this helps!

- xoxo Quinnisa

P = 35/128  is the probability that the number of heads obtained from flipping the two fair coins is the same.

Describe probability using an example?

P( oH )  = ³C₀ (1/2)³ . ⁴C₀ (1/2)⁴  = 1 . 1/128

P( 1H) = ³C₁ (1/2)³ . ⁴C₁( 1/2 )⁴ = 12/128

P( 2H ) = ³C₂ (1/2)³ . ⁴C₂ (1/2)⁴ = 18/128

P( 3H) = ³C₃ ( 1/2)³ . ⁴C₃ ( 1/2)⁴ = 4/128

P = 1/128 + 12/128 + 18/128 + 4/128

P = 35/128

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it needs to be shifted to the positive side of the graph by 4 units so right by 4 units is the correct answer

The answer is A. Left by four units. I took the test so it is correct, here is photographic proof:

The matrix A into a product XDX-1, where D is diagonal

(b) [[11/4, 7/4], [49/24, -1/4]]

(d) [[0, 0, 0], [0, 1, 0], [0, 0, 4]]

(b) A = [[5, 6], [-2, -2]]

Av = λv.

Rewriting the equation, we get

(A - λI) × v = 0

where I is the identity matrix.

(A - λI) = [[5 - λ, 6], [-2, -2 - λ]]

Setting the determinant of (A - λI) equal to 0, we get

det(A - λI) = (5 - λ)(-2 - λ) - (6 × -2) = λ² - 3λ - 22 = 0

Factoring the equation, we have

(λ - 5)(λ + 2) = 0

So, the eigenvalues are λ = 5 and λ = -2.

For λ = 5:

(A - 5I) = [[0, 6], [-2, -7]]

Solving the system of equations (A - 5I) × v = 0, we get v = [2, 1].

For λ = -2:

(A + 2I) = [[7, 6], [-2, 0]]

Solving the system of equations (A + 2I) × v = 0, we get v = [-2, 7].

The diagonal matrix D using the eigenvalues

D = [[λ1, 0], [0, λ2]] = [[5, 0], [0, -2]]

X = [[v1, v2]] = [[2, -2], [1, 7]]

X⁻¹ = (1 / (2 × 7 - (-2 × 1))) × [[7, 2], [-1, 2]] = [[7/24, 1/8], [-1/24, 1/8]]

Therefore, the factorization of matrix A = [[5, 6], [-2, -2]] into XDX^(-1) is:

A = XDX^(-1) = [[2, -2], [1, 7]] × [[5, 0], [0, -2]] × [[7/24, 1/8], [-1/24, 1/8]]

A =

(d) matrix A = [[2, 2, 1], [0, 1, 2], [0, 0, -1]]

Av = λv.

So, we have:

A × v = λ × v

Rewriting the equation, we get

(A - λI) × v = 0

where I is the identity matrix.

Now, let's find the eigenvalues λ

(A - λI) = [[2 - λ, 2, 1], [0, 1 - λ, 2], [0, 0, -1 - λ]]

Setting the determinant of (A - λI) equal to 0, we get

det(A - λI) = (2 - λ)(1 - λ)(-1 - λ) = λ³ - 3λ² + 2λ = 0

Factoring the equation, we have

λ(λ - 1)(λ - 2) = 0

So, the eigenvalues are λ = 0, λ = 1, and λ = 2.

Now, let's find the corresponding eigenvectors

For λ = 0

(A - 0I) = [[2, 2, 1], [0, 1, 2], [0, 0, -1]]

Solving the system of equations (A - 0I) × v = 0, we get v = [0, -2, 1].

For λ = 1

(A - I) = [[1, 2, 1], [0, 0, 2], [0, 0, -2]]

Solving the system of equations (A - I) × v = 0, we get v = [-1, 1, 0].

For λ = 2

(A - 2I) = [[0, 2, 1], [0, -1, 2], [0, 0, -3]]

Solving the system of equations (A - 2I) × v = 0, we get v = [-2, 1, 2].

The diagonal matrix D using the eigenvalues

D = [[λ1, 0, 0], [0, λ2, 0], [0, 0, λ3]] = [[0, 0, 0], [0, 1, 0], [0, 0, 2]]

The matrix X using the eigenvectors as columns

X = [[v1, v2, v3]] = [[0, -1, -2], [-2, 1, 1], [1, 0, 2]]

The inverse of matrix X

X^(-1) = (1 / (0 × (1 × 2 - 0 × 0) - (-1 × (-2) - (-2 × 0)))) × [[2, 1, 2], [2, 0, -1], [-1, -1, 0]] = [[1/2, 1/2, 1/2], [1/4, -1/4, -1/2], [-1/4, -1/4, 1/2]]

Therefore, the factorization of matrix A = [[2, 2, 1], [0, 1, 2], [0, 0, -1]] into XDX^(-1) is

A = XDX^(-1) = [[0, -1, -2], [-2, 1, 1], [1, 0, 2]] × [[0, 0, 0], [0, 1, 0], [0, 0, 2]]  ×[[1/2, 1/2, 1/2], [1/4, -1/4, -1/2], [-1/4, -1/4, 1/2]]

A = [[0, 0, 0], [0, 1, 0], [0, 0, 4]]

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The width of the chest shaped like a rectangular prism, to the nearest tenth of an inch is 32.1.

Kenji has made a treasure chest, shaped like a rectangular prism that must hold around 10,368 cubic inches of sand. In the second act of the school play, an actor will stand on the chest.

Therefore, the chest must be 24 inches tall. The length of the chest is twice its width.

To determine the width of the chest, you should first determine the length of the chest.

Then, using the formula for the volume of a rectangular prism, you can solve for the width of the chest.

Length of the chest

The formula for the volume of a rectangular prism is V = lwh

Given that the chest needs to hold around 10,368 cubic inches of sand, we can write 10,368 = lwh

Since the chest is twice as long as it is wide, the length (l) of the chest is equal to 2w.

Substituting 2w for l, we have:

10,368 = (2w)w

hence 5,184 = wh²(5,184/h)

= w*h(5,184/h²) = w

Since the chest must also be 24 inches tall, we can write:

h = 24 feet

Substituting this value into the equation, we have:

(5,184/24²) = w

hence w = 32.1 inches

Therefore, the width of the chest to the nearest tenth of an inch is 32.1 inches.

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

n = 7

Step-by-step explanation:

3n = 21

n = 7

Answer:

( 3x + 1) (2x+5)

Step-by-step explanation:

6 x ^2 + 17 X + 5​

We break the 6 into 3 and 2

(3x    ) (2x   )

We need the middle term to be 17

( 3x + 1) (2x+5)

3*5+2 = 17 so it works

Answer:

1. Semi-regular tessellations are made from multiple regular polygons.

2. There are an infinite number of figures that form irregular tessellations!

3. You can create irregular polygons that tessellate the plane easily, by cutting out and adding symmetrically.

An irregular tessellation

An irregular tessellation is simply a group of figures which does not include any regular polygons.

In other words, an irregular tessellation is a group of irregular shapes.

The number of irregular tessellations

There are several irregular shapes and figures that make up an irregular tessellation.

This means that the number of irregular tessellation is non-finite.

How to create an irregular tessellation

There are several ways to do this. Some of them include;

See attachment for an instance of an irregular tessellation

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Answer:

180 ft^3

Step-by-step explanation:

volume of the pyramid = (1/3)(area of base) (height)

v= 1/3×(10×12÷2)×(9)

= 180 ft^3

Answer:

answer on the picture.....