help pleaseee just with the part circled ​

(a) Sample size: Increasing the sample size decreases the variance of the OLS estimator. (b) Variation in X: Greater variation in X leads to higher variance in the OLS estimator.

(a) Sample Size: Increasing the sample size tends to reduce the variance of the Ordinary Least Squares (OLS) estimator. As the sample size grows larger, the estimator becomes more precise and better captures the true underlying relationship between the variables. With more observations, the OLS estimator tends to average out random errors, leading to a decrease in variance. However, if there are influential outliers or systematic biases present in the data, increasing the sample size may not necessarily result in a significant reduction in the variance.

(b) Variation in X: The variance of the OLS estimator is influenced by the variation in the independent variable (X). When there is greater variation in X, the OLS estimator tends to have higher variance. This occurs because a wider range of X values can lead to a wider range of predicted Y values, resulting in larger deviations from the true regression line. In contrast, if there is less variation in X, the OLS estimator will have lower variance as the predicted Y values will be more tightly clustered around the regression line. Therefore, an increase in the variation of X tends to increase the variance of the OLS estimator.

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how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

\(\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53\)

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

The factors that determine the width of a confidence interval are: The chosen level of confidence, The population mean, The relative size of the sample mean, The size of the standard error.

The factors that determine the width of a confidence interval are:

The chosen level of confidence: The higher the level of confidence required, the wider the interval will be.

The size of the standard error: A larger standard error will result in a wider interval.

The size of the sample: A smaller sample size will result in a wider interval.

The population mean does not directly determine the width of a confidence interval, but it can affect the calculation of the standard error. The relative size of the sample mean is not a factor that determines the width of a confidence interval.

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The graph of the given equation is attached below.

The equation of a line in slope-intercept form is expressed as y = mx + b.

Given an xy plane, we are to plot the graph of the given equation

y = -2/3 x + 1

The given equation has a slope of -2/3 and a y-intercept of 1. This shows that the constructed line must cut the y-axis at the point (0, 1).

The graph of the equation is attached below.

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The correct answer is 32.

In an integer optimization problem with binary variables, each variable can take one of two possible values: 0 or 1. Therefore, for 5 binary variables, each variable can be assigned either 0 or 1, resulting in 2 possible choices for each variable. The maximum number of potential solutions in an integer optimization problem with 5 binary variables is 32 because each binary variable can take on 2 possible values (0 or 1)

In this case, we have 5 binary variables, so the maximum number of potential solutions is given by 2 * 2 * 2 * 2 * 2, which simplifies to 2^5. Calculating 2^5, we find that the maximum number of potential solutions is 32.

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Since the p-value (0.0588) is greater than the significance level (0.05), we do not reject the null hypothesis.

To test whether there is enough evidence to reject the claim that the average wind speed in a certain city is 8 miles per hour, we can perform a hypothesis test using the P-value method. Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The average wind speed is 8 miles per hour.

Alternative hypothesis (H1): The average wind speed is not equal to 8 miles per hour.

We can use a t-test since we have the sample mean, sample size, population standard deviation, and want to compare the sample mean to a given value.

Sample mean (\(\bar x\)) = 8.2 miles per hour

Sample size (n) = 32

Population standard deviation (σ) = 0.6 miles per hour

Significance level (α) = 0.05

We can calculate the t-value using the formula:

t = (\(\bar x\) - μ) / (σ / √n)

where μ is the population mean.

t = (8.2 - 8) / (0.6 / √32)

t ≈ 2.1602

Now, we need to calculate the degrees of freedom (df) for the t-distribution, which is n - 1:

df = 32 - 1 = 31

Using the t-distribution table or a calculator, we can find the p-value associated with the calculated t-value. In this case, the p-value is approximately 0.0588.

Given that the calculated p-value (0.0588) exceeds the chosen significance level of 0.05, there is insufficient evidence to reject the null hypothesis.

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Answer:

look at links below

Step-by-step explanation

Answer:

X=137

Step-by-step explanation:

(8-2)180=1080

use 1080-the angle and you get the answer

The equation representing this situation is 4a + 2.50s = 2820.

We have,

In this situation, we are trying to find the total cost of all adult and student tickets sold.

Let's assign variables to represent the number of adult tickets sold (a) and the number of student tickets sold (s).

The cost of one adult ticket is $4, so the total cost of all adult tickets sold is 4a.

Similarly, the cost of one student ticket is $2.50, so the total cost of all student tickets sold is 2.50s.

Since the school makes $2,820 in total from selling tickets, we can write the equation:

4a + 2.50s = 2820

This equation represents the relationship between the number of adult tickets sold, the number of student tickets sold, and the total revenue generated from ticket sales.

Thus,

The equation representing this situation is 4a + 2.50s = 2820.

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Answer: The compound interest on a savings account is calculated by multiplying the principal (initial amount deposited) by the interest rate, and then multiplying that result by the number of compounding periods.

In this case, the principal is $925, the interest rate is 5.5%, and the number of compounding periods is 2 (since the interest is compounded semiannually).

To calculate the compound interest, we can use the following formula:

Compound interest = principal * (1 + interest rate/number of compounding periods)^(number of compounding periods * number of years) - principal

Plugging in the values from the problem, we get:

Compound interest = $925 * (1 + 5.5%/2)^(2 * 1) - $925

= $925 * 1.0275^2 - $925

= $925 * 1.056 - $925

= $973.44 - $925

= $48.44

Therefore, the compound interest on Matthew's savings account is $48.44.

Answer:

10

Step-by-step explanation:

The measure of an angle∠I  is 10 degrees between the 450 cm and 640 cm sides.

The Law of Cosines (also called the Cosine Rule) is defined as it relates all three sides of a triangle with an angle of a triangle.

c² = a² + b² − 2ab cos(C)

The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. it relates the lengths of the sides of a triangle to the cosine of one of its angles.

In the given triangle ΔHIJ,

Sides:

h = 450 m

i = 210 m

j = 640 m

The angle of ∠I  is 10 degrees between the 450 cm and 640 cm sides.

According to the cosine rule,

j² = h² + i² − 2ab cos(I)

Substitute the values in the Cosine Rule,

450² = 210² + 640² - 2(210)(640)cos(I)

After solving we get the value of  angle ∠I :

∠I = 9.56038°

Rounded to the nearest degree.

∠I = 10°

Thus, the measure of an angle∠I  is 10 degrees.

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Answer:

Angle NOR is 127 degrees

Step-by-step explanation:

This is an example of the vertical angles theorem

Answer:

127

Step-by-step explanation:

This is ALSO called vertical angle. They are both congruent.

The topic that is typically discussed when referring to the need for relative figures as opposed to absolute figures is comparative analysis or relative measures.

Comparative analysis involves comparing data or figures in relation to other data or a reference point, rather than focusing solely on the absolute values. It helps provide context and a better understanding of the data by considering factors such as proportions, ratios, percentages, or changes over time. Relative figures are particularly important when dealing with data that varies significantly in scale or when comparing data across different contexts or populations. By using relative figures, researchers or analysts can gain insights into patterns, trends, and relationships that may not be evident when looking at absolute figures alone.

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The store that offers the best discount is store B

The graph that completes the question is added as an attachment

For store A, we have the following equation

y = 0.3x

On the graph of store B, we have the following points

(x, y) = (60, 24)

So, the equation is

y = 24/60x

Evaluate

y = 0.4x

The discounts for both stores are 0.3 and 0.4, respectively

0.4 is greater than 0.3

Hence, store B offers the best discount

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The rate at which water is being pumped into the tank is 37490.0 cm³/min.

Given: Water is leaking out of an inverted conical tank at a rate of 13100.0 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height 8.0 m, and the diameter at the top is 3.5 m. The water level is rising at a rate of 29.0 cm/min when the height of the water is 3.0 m.

The volume of the inverted cone tank = 1/3 πr²hThe diameter of the top of the conical tank = 3.5 m, therefore the radius, r = 1.75m, and the height, h = 8m. Therefore, the volume V of the tank is given by:V = 1/3 π (1.75²)(8) = 102.91 m³At time t, the height h of the water in the conical tank is 3 m, then the radius r of the surface of the water can be calculated using similar triangles.

Using the ratio of the similar triangles, we can write:r / (h - 3) = 1.75 / 8Therefore, r = 0.583 m and the volume of the water in the tank is given by:V = 1/3 π (0.583²)(3) = 0.377 m³.The water level is rising at a rate of 29.0 cm/min, therefore the volume V of the water is increasing at a rate of:dV/dt = πr² dh/dtWe know r = 0.583 m, h = 3m, and dh/dt = 29.0 cm/min, thusdV/dt = π (0.583)² (29/100) = 0.249 m³/minThe volume of water that is leaking out of the tank is 13100.0 cm³/min.

Therefore, the volume of water that is being pumped into the tank is given by:Pumping rate = Rate of increasing water volume + Rate of water leaking out of the tankPumping rate = (0.249 x 1000000) + 13100.0 = 37490.0 cm³/min. Therefore, the rate at which water is being pumped into the tank is 37490.0 cm³/min.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Cost of labor = $25 × Number of laborers

Total time required = 100 × 50 minutes

Cost of concrete = $120 × 100

Total cost = Cost of labor + Cost of concrete

To calculate the cost of pouring 100 cubic yards of concrete, we need to consider the cost of laborers and the cost of concrete per cubic yard. Given that each laborer costs $25, the labor cost for pouring 100 cubic yards would be $25 multiplied by the number of laborers.

Additionally, it is stated that each cubic yard of concrete requires 50 minutes of the crew's time. Assuming the crew works continuously, the total time required to pour 100 cubic yards would be 100 multiplied by 50 minutes.

To determine the total cost, we also need to consider the cost of concrete per cubic yard. Given that the cost of a concrete yard is $120, the total cost of pouring 100 cubic yards would be $120 multiplied by 100.

Therefore, the cost of pouring 100 cubic yards of concrete can be calculated by summing the labor cost and the cost of the concrete:

Cost of labor = $25 × Number of laborers

Total time required = 100 × 50 minutes

Cost of concrete = $120 × 100

Total cost = Cost of labor + Cost of concrete

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The value of p, the number of people who visited Venice in January 2019, the least popular month, is 585,168.

To find the value of p, we can set up an equation based on the given information. Let's denote p as the number of people who visited Venice in January 2019, the least popular month.

According to the information given, the most popular month, August, had 1,447,038 visitors. This number is stated to be 2 times the sum of 138,351 and p. We can write this equation as:

2 * (138,351 + p) = 1,447,038

To solve for p, we need to simplify and isolate it.

First, distribute the 2 on the left side of the equation:

276,702 + 2p = 1,447,038

Next, subtract 276,702 from both sides of the equation to isolate 2p:

2p = 1,447,038 - 276,702

2p = 1,170,336

Finally, divide both sides of the equation by 2 to solve for p:

p = 1,170,336 / 2

p = 585,168

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The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle.

The orthocenter is the intersection of the three altitudes of the triangle. It is a point on the plane of the triangle that is equidistant from the three sides of the triangle.

To find the orthocenter of a triangle, you can draw the altitudes of the triangle and find the point where they intersect. The orthocenter is the point of concurrency for the three altitudes.

An orthocenter of a triangle is a point where the three lines that are perpendicular to the sides of the triangle intersect. These lines are called altitudes of the triangle.

Alternatively, you can use the following formula to find the coordinates of the orthocenter:

Let's say that the vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3). The coordinates of the orthocenter (H) can be found using the following formula:

Hx = ( (y1 - y3) (x1^2 + y1^2 - x3^2 - y3^2) - (y1 - y2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (y1 - y3) - 2 * (y1 - y2))

Hy = ( (x1 - x3) (x1^2 + y1^2 - x3^2 - y3^2) - (x1 - x2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (x1 - x3) - 2 * (x1 - x2))

Therefore, The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle

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Answer:

1±√2=q

or

q=2.41, -0.41

Step-by-step explanation:

we are given the equation q²-2q-1=0, and we want to use the quadratic equation, which is (-b±√(b²-4ac))/2a

a is 1 (there is a 1 in front of q²)

b is -2

c is -1

substitute into the equation:

q=(2±√(4-4*1*-1))/2

solve for the discriminant:

√(4-4(1*-1))

√8

now the equation:

(2±√8)/2=q

simplify:

1±√2=q

or if your application asks for a decimal:

√2≈1.41

so:

1+1.41=2.41=q

or

1-1.41=-0.41=q

Hope this helps!

the potential at the center of the equilateral triangle is 3kq√3 / a.To find , we can use the formula for the electric potential due to a point charge:

V = kq / r

where k is the Coulomb constant, q is the charge, and r is the distance between the point charge and the center of the triangle.

Assuming the charges are all positive, the potential at the center due to each charge will be the same, so we can find the total potential by multiplying the potential due to one charge by three.

The distance from the center of the equilateral triangle to each charge is a/√3, since the height of the equilateral triangle is √3/2 times the side length.

Therefore, the potential at the center is:

V = 3(kq / (a/√3))

Simplifying:

V = 3kq√3 / a

Hence, the potential at the center of the equilateral triangle is 3kq√3 / a.

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Answer:

y=26

Step-by-step explanation:

2(3y+7+5)=196-16 do the () first and then subtract 16 from 16

6y+24=180 subtract 24 from both sides

6y=156  divide by 6

y=26

Answer:

26

Step-by-step explanation:

6y+14+10=180

6y=180-24

6y=156

y=26

2x-3=7

The answer would be 5.

Answer:

x=5

Step-by-step explanation:

2x−3=7

Add 3 to both sides.

2x=7+3

Add 7 and 3 to get 10.

2x=10

Divide both sides by 2.

x=10/2

Divide 10 by 2 to get 5.

x=5

Answer:

10% - 35

20% - 70

30% - 105

40% - 140

50% - 175

60% - 210

70% - 245

80% - 280

90% - 315

100% - 350

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

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y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

Given differential equation:  x²y'' - x(x + 2)y' + (x + 2)y = 0, x > 0;  

And, y₁ = x, y₂ = xeᵡ

In order to verify whether y₁ and y₂ are solutions of the given differential equation or not, we can substitute the value of y₁ and y₂ in the given differential equation and check if they satisfy the given equation or not. i.e.,

For y₁ = x  

Here,  y₁ = x

Therefore, y₁′ = 1, and y₁″ = 0

Putting the values in the differential equation, we getx²y₁″ - x(x + 2)y₁′ + (x + 2)y₁= x²(0) - x(x + 2)(1) + (x + 2)x

= -x³  + x³ + 2x = 2x

Therefore, LHS ≠ RHS  Therefore, y₁ = x is not the solution of the given differential equation. Now, to check whether y₁ and y₂ constitutes the fundamental set of solutions or not, we have to check whether they are linearly independent or not. i.e., We know that the Wronskian of the given differential equation is given by W[y₁, y₂] = \begin{vmatrix} x & xe^x \\ 1 & e^x + xe^x \end{vmatrix}  = xe²

Therefore, W[y₁, y₂] ≠ 0, ∀x > 0 Therefore, y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

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Answer:

40 more kids chose baseball over basketball.

Step-by-step explanation:

The best way to go about this is to use benchmark percentages.

For baseball, 25% of 800 people chose that, so we can do 800/4 to get 200, so 200 students chose baseball

For basketball, we could do 800/5 but that isn't mental math, so we can do 10% of 800 is 80 and 80*2=160. So 40 more kids chose baseball over basketball.