where Eſe|X] = 0. (a) What is Var(e|X)? (b) What is the asymptotic variance of your OLS estimator of ß? (c) How will you estimate this variance?

Answer:

10

Step-by-step explanation:

Given:

End points of a line segment are given as:

(2, 4) and (4, y)

Mid point of the line segment is: (3, 7).

To find:

Value of y = ?

Solution:

If end points of a line segment are \((x_1,y_1)\) and \((x_2,y_2)\), then mid point of the line (\(x, y\)) is given by The Mid Point Formula:

Mid point formula:

\(x = \dfrac{x_1+x_2}{2}\\y = \dfrac{y_1+y_2}{2}\)

Here,

\(x_1 = 2\\x_2 = 4\\y_1 = 4\\y_2 = y\\\)

\(x =3\\y=7\)

Putting all the value to find \(y\):

\(7 = \dfrac{4+y}{2}\\\Rightarrow 4+y=14\\\Rightarrow \bold{y =10}\)

So, the value of \(y\) is 10.

The quadratic equation is  3x² - 27.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given:

The roots are 3 and -3

We have

α= 3   and β=-3

So,

α+β = -b/a  and αβ = c/a

α+β = 0 =-b/a and  αβ= -9 = c/a

Comparing from above

a=1, b= 0 and c=-9

Also, the leading coefficient is 3.

Then the quadratic equation is,

= 3(ax² + bx + c)

= 3( x² +0x- 9)

Hence, the quadratic equation is 3x² - 27.

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Answer:

no this is wrong its souposed to be moved twice so it will look like this:

706.56

Step-by-step explanation:

Step-by-step explanation:

(3j - 5k^3) ( 3j + 5k^3)  =  9j^2 - 25k^6

Answer: 144pi in sq

Step-by-step explanation:

A=(Pi)(8)(10)+(pi)(8)=

Pi(80)+pi(64)

144pi in sq

Answer:

341.25

Step-by-step explanation:

You first split the figure into 2 pieces the triangular prism and the rectangular prism now that we know the dimensions of each figure we can create an expression, we will start with the triangular prism. the expression will be 3/2 x 5/2 x 10.5. Then we solve the rectangular prism. 5 x 5 x 10.5.

Now that we have acquired all the math that we need we can continue to simplify. 3 x 2 x 5/2 was derived from (3 x 5)/2 and we physically drew it out with properties of algebra (a later topic to study) anyways we get 15/2=7.5 and we multiply that by 10.5 giving us 78.75. the triangular prism is easier we just do 25 x 10.5 giving us 262.5. Now that we have succumbed both figures we can combine the to get the volume which is 341.25 (78.75 + 262.5).

Answer:

y = 4x + 57

Step-by-step explanation:

y = 4x + b

9 = 4(-12) + b

9 = -48 + b

57 = b

y = 4x + 57

Answer: -1

Step-by-step explanation:

    Slope can be found with change in y over change in x.

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

    This line has a slope of -1.

Answer:

Step-by-step explanation:

You have to identify two point that the line passes through.

I chose (-4,3) and (4,-3)

Find the slope of the points

slope=(y2-y21)/(x2-x1)

        =(-3-3)/(4--4)

        =-6/8

slope =-0.75

The inverse function for the function f(x) = (1 -2x) / 3x is 1/3x+2.

Inverse function:

Inverse function means a function that serves to “undo” another function.

For example,

if f(x) produces y, then putting y into the inverse of f produces the output x.

Given,

Here we have the function f(x) = (1 -2x) / 3x.

Now, we need to find the inverse function f⁻¹.

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables by interchange the value of x by y and the value of y as x.

Then we get,

x = (1 - 2y)/3y

Now, solve the equation

x = (1 - 2y)/2y

for y, then we get,

y = 1/(3x + 2)

Therefore, the inverse function is 1/3x+2.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

i think x=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

the last one

The resulting p-value would decrease in both scenarios if we sampled twice as many students but found the same sample proportion as before.

The p-value is the probability of observing a sample proportion as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true. When we increase the sample size, the standard error of the sample proportion decreases, which means that the sample proportion becomes more representative of the population proportion.

In other words, the larger the sample size, the more accurate the estimate of the population parameter (in this case, the proportion of students who support the change). As a result, the difference between the sample proportion and the hypothesized population proportion (under the null hypothesis) is likely to be smaller, leading to a smaller p-value.

To compute the p-value, we use the test statistic, which is a measure of how many standard errors the sample proportion is from the hypothesized population proportion under the null hypothesis. When we increase the sample size, the test statistic becomes larger, which means that the p-value becomes smaller. Therefore, the p-value would decrease if we sample twice as many students but find the same sample proportion as in exercise 6.

In summary, increasing the sample size while keeping the sample proportion constant would result in a smaller p-value, indicating stronger evidence against the null hypothesis.

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Answer:

y = 3/2x + 5

Step-by-step explanation:

2y - 3x - 10 = 0

2y = 3x + 10

y = 3/2x + 5

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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Angle ABC is greater than angle C, as required. Given triangle ABC with AC greater than AB, and BD drawn such that AD is congruent to AB, we need to prove that angle ABC is greater than angle C.

To begin with, we can draw a diagram to visualize the situation. In the diagram, we see that BD is an altitude of triangle ABC, as well as a median since it divides the base AC into two equal parts. We also see that triangles ABD and ABC are congruent by the side-side-side (SSS) criterion, which means that angle ABD is equal to angle ABC.

Now, we can use this information to prove our statement. Since triangle ABD and triangle ABC are congruent, their corresponding angles are also equal. Therefore, we know that angle ABD is equal to angle ABC.

Next, we observe that angle ABD is a right angle, since BD is an altitude of triangle ABC. This means that angle ABC is the sum of angles ABD and CBD.

Since AD is congruent to AB, we also know that angles ABD and ADB are congruent. Therefore, angle CBD is greater than angle ADB.

Putting all of this together, we can conclude that angle ABC is greater than angle C, as required.

In summary, we have shown that given triangle ABC with AC greater than AB and BD drawn such that AD is congruent to AB, angle ABC is greater than angle C. This is because angles ABD and CBD add up to angle ABC, and angle CBD is greater than angle ADB.

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Answer:

10 x 11 to the 10th power

Step-by-step explanation

The equation of the parabolic path of the water is y = (-3/256)x^2 + 6. This equation represents a downward-opening parabola with its vertex at (0, 6). The water reaches a maximum height of 6 feet and lands on the plants 16 feet away from the point of release.

To help Bee model the path of the water, we can consider a standard form equation for a parabola:

y = ax^2 + bx + c

To find the equation, we need to determine the values of a, b, and c based on the given information.

The highest point the water reached was 6 feet, which means the vertex of the parabola is at (0, 6). Therefore, the equation becomes:

y = ax^2 + 6

Next, we need to find the value of a. Since the nozzle of the hose and the top of the flowers were both 3 feet above the ground, the parabola passes through the point (16, 3). Substituting these values into the equation, we get:

3 = a(16)^2 + 6

Now we can solve for a:

3 = 256a + 6

256a = -3

a = -3/256

Finally, we have the equation of the parabolic path of the water:

y = (-3/256)x^2 + 6

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The limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

To test the convergence or divergence of the series Σ((-1)^(11n - 3))/(10n + 3) from n = 1 to infinity, we need to find the limit of the expression (11n - 3)/(10n + 3) as n approaches infinity.

To determine the highest power of n in the fraction, we can observe the exponents of n in the numerator and denominator. In this case, the highest power of n is n^1.

Let's calculate the limit:

lim(n→∞) [(11n - 3)/(10n + 3)]

To find the limit, we can divide the numerator and denominator by n:

lim(n→∞) [(11 - 3/n)/(10 + 3/n)]

As n approaches infinity, the terms with 3/n become negligible, and we are left with:

lim(n→∞) [11/10]

The limit evaluates to 11/10, which is a finite value.

Since the limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

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The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

A linear equation is one that can be written as display style a 1x 1+ldots +a nx n+b=0, where x 1, ldots, x n are the variables and display style b, a 1, ldots, a n are the coefficients, which are frequently real integers.

Let x and y be the quantity of kid and adult tickets sold, respectively. 1650 tickets were sold in total, as far as we know.

x + y = 1650

x = 1650 - y

At $12 for adults and $4 for children, the total revenue from tickets is $14200. There are

4x + 12y = 14200

substituting the value of x in the equation:

4(1650 - y) + 12y = 14200

6600 - 4y + 12y = 14200

6600 + 8y = 14200

8y = 14200 - 6600 = 7600

y = 7600 / 8

= 950 adult tickets

x = 1650 - 950

= 700 children tickets

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

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a. v = 4i - 2j + k and b = -2j + 5k

b. The angle between v and b is acute.

c. The direction angle of v is approximately 36 degrees.

d. The vector component of v along b is -26/29 j + 65/29 k.

e. The vector component of v orthogonal to b is 4i + (56/29) j - (36/29) k.

a. The given vectors are:

v = 4i - 2j + k

b = -2j + 5k

b. To determine the angle between v and b, we calculate the dot product of v and b:

v · b = (4)(0) + (-2)(-2) + (1)(5) = 4 + 4 + 5 = 13

Since the dot product is positive, the angle between v and b is acute.

c. To approximate the direction angle of v, we can calculate the direction cosine of v:

cos θ = v · i / |v| = (4)(1) / sqrt((4)^2 + (-2)^2 + (1)^2) = 4 / sqrt(21)

θ ≈ arccos(4 / sqrt(21))

Using a calculator, the approximate direction angle of v is about 36 degrees.

d. The vector component of v along b can be found using the projection formula:

v_parallel = (v · b / |b|^2) * b

First, calculate the magnitude of b:

|b| = sqrt((-2)^2 + 5^2) = sqrt(4 + 25) = sqrt(29)

Then calculate the vector component of v along b:

v_parallel = (v · b / |b|^2) * b

= (13 / 29) * (-2j + 5k)

= -26/29 j + 65/29 k

e. The vector component of v orthogonal to b can be obtained by subtracting the vector component of v along b from v:

v_orthogonal = v - v_parallel

= 4i - 2j + k - (-26/29 j + 65/29 k)

= 4i + (56/29) j - (36/29) k

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Answer:

a=w7-4b

Step-by-step explanation:

w=7a+4b

Multiply 7 to both sides to get a alone

w7=a+4b

Subtract 4b to both sides to get a alone

w7-4b=a

a=w7-4b

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The average speeds of the cars are 61 mph, 59 mph, 58 mph, and 57 mph. However, without additional context or information, it is not possible to directly determine the speed limit from these calculations.

To determine the speed limit, we can calculate the average speed of each car using the given distances and time taken. We'll divide the distance traveled by the time taken for each car:

Car 1: Average speed = 183 miles ÷ 3 hours = 61 mph

Car 2: Average speed = 236 miles ÷ 4 hours = 59 mph

Car 3: Average speed = 290 miles ÷ 5 hours = 58 mph

Car 4: Average speed = 342 miles ÷ 6 hours = 57 mph

Next, let's analyze the number of gallons and prices provided. We have the following data:

2 gallons for $6.60

3 gallons for $9.90

4 gallons for $13.20

1 gallon costs $3.30

1 gallon costs $4.60

1 gallon costs $5.60

1 gallon costs $6.50

Based on this information, we can observe that the price per gallon decreases as the number of gallons increases.

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Step-by-step explanation:

This is a family of curves represented by the equation:

y = a (x + 4) (x − 2)

Different values of the a coefficient result in different quadratic functions.

The vertex of the parabolas is halfway between the zeros, at x = -1.

y = a (-1 + 4) (-1 − 2)

y = -9a

So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.

A. y = ⅓ (x + 4) (x − 2)

B. y = (x + 4) (x − 2)

C. y = 2 (x + 4) (x − 2)

D. y = -⅓ (x + 4) (x − 2)

E. y = -2 (x + 4) (x − 2)

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

H = 120°

Step-by-step explanation:

The sum of the internal angles of a polygon with n sides is given by the formula:

S = (n-2)*180

So, for a pentagon, we have n = 5, then:

S = (5-2)*180 = 540°

So we have that:

M + A + T + H + S = 540° (eq1)

M = T = H (eq2)

A + S = 180° (eq3)

Using the second and third equation in the first one, we have:

H + H + H + 180 = 540

3H = 360

H = 120°

Answer:

If I am understanding this correctly you are asking that "A computer costs $400.000 (rounded) and is given a 15% discount if it is paid by cash?" then the sale price of the computer with the discount would be $60.00

Step-by-step explanation:

It can be easily calculated by dividing 15 by 100 and multiplying the answer with 1400 to get 60.

For the function f(x, y) = x+2y-5, the domain and range are:

The domain of f(x, y) is all real numbers, or (-∞, ∞).

Its range is also (-∞, ∞).

For the function f(x, y, z) = xsin(y + z), the domain and range are:

The domain is all real numbers, or (-∞, ∞) for each variable.

The domain is all real numbers, or (-∞, ∞) for each variable.

For the function f(x, y) = x+2y-5, the domain and range are:

Domain: The domain of a function is the set of all possible values that x and y can take without leading to any mathematical inconsistencies. Since there are no restrictions on the value of x and y in this case, the domain of f(x, y) is all real numbers, or (-∞, ∞).

Range: The range of a function is the set of all possible output values that the function can produce. In this case, we can see that the smallest possible value for f(x, y) is -∞ (when both x and y approach negative infinity). However, there is no upper bound on f(x, y), so its range is also (-∞, ∞).

For the function f(x, y, z) = xsin(y + z), the domain and range are:

Domain: The domain of this function is determined by any restrictions on x, y, and z that would lead to undefined or imaginary values. In this case, there are no explicit restrictions on any of the variables, so the domain is all real numbers, or (-∞, ∞) for each variable.

Range: To determine the range of the function, we need to consider the behavior of sin(y+z). Since sin can take any value between -1 and 1, we know that the range of xsin(y+z) will be between -x and x. That is, the domain is all real numbers, or (-∞, ∞) for each variable.

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Answer:

The variable is going to be divided

you solve by multiplying 9 to both sides to eliminate the fraction, then add 6 on both sides to get the variable by itself.

Step-by-step explanation: