We are interested on the following linear model: Y
i
​
=α+βX
i
​
+ϵ
i
​
,i=1,2,…,N (a) Write down the OLS objective function. What does the OLS estimator minimize? (b) Using any relevant formula, what do we mean when we say that a is an unbiased estimator of α ? (c) What do we mean when we say that the OLS estimator is BLUE? (d) What do we imply when we say that shocks (ϵ
i
​
) are heteroskedastic? What does it imply for OLS standard errors?

Answer:

x is 6

Step-by-step explanation:

x is 1/4 of y. so divide 24 by 4 and get 6

The magnitude and direction of its momentum are approximately 139.89 kilogram-meters per second and2.05744º.

We have the information from the question is:

A 2.90 kg particle has a velocity of (2.99i − 3.95 j)

We have to find the magnitude and direction of its momentum.

Now, According to the question:

We know that the formula of momentum is:

p = m . v (1)

Where:

p - Vector momentum, measured in kilogram-meters per second.

m - Mass of the particle, measured in kilograms.

v - Vector velocity, measured in meters per second.

And, m = 2.90 kg and v = (2.99i − 3.95 j) m/sec

Then, the momentum is:

p = (2.90)(2.99i − 3.95 j) kg.m/sec

p = (8.671i - 11.455 j) kg.m/sec

The x and y components of the momentum are 8.671 kg.m/sec and -11.455 kg.m/sec, respectively.

The magnitude and direction of momentum are represented by the following expressions:

\(||p||=\sqrt{p^2_x+p^2_y} \\\\\theta=tan^-^1(\frac{p_y}{p_x} )\)

Where:

||p|| = Magnitude of momentum, measured in kilogram-meters per second.

\(\theta\) = Direction of momentum, measured in sexagesimal degrees.

And we know that \(p_x =\)8.671 and \(p_y\) = -11.455

then the magnitude and direction of momentum are, respectively:

\(||p||=\sqrt{(8.671(\frac{kg.m}{sec} ))^2+(-11.455(\frac{kg.m}{sec } ))^2}\)

||p|| = 139.89 kg.m /sec

\(\theta=tan^-^1(\frac{-11.455}{8.671} )\)

\(\theta\) ≈ 2.05744°

The magnitude and direction of its momentum are approximately 139.89 kilogram-meters per second and2.05744º.

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Given question is not in proper form. Then the proper form of the  question is :

A 2.90 kg particle has a velocity of (2.99i − 3.95 j) m/sec. Find the magnitude and direction of its momentum.

The calculated value of the surface area​ is 184 sq inches

From the question, we have the following parameters that can be used in our computation:

11.5 in by 16 in

The surface area​ of the shape is then calculated as

Area = product of dimensions

In other words

Area = Length * Width

Substitute the known values in the above equation, so, we have the following representation

Area = 11.5 * 16

Evaluate

Area = 184 sq inches

Hence, the surface area​ is 184 sq inches

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\(y = {x}^{2} + 4x + 3\)

Answer:

An apportionment is the allocation of a loss between all of the insurance companies that insure a piece of property. This allocation is used to determine a percentage of liability for each insurer.

I'm new here! Sorry if this didn't help

Answer:

  you will save $3.69

Step-by-step explanation:

You save 20% of the marked price on each of the three books. Your savings are ...

Then the total savings is ...

  $1.70 +0.59 +1.40 = $3.69 . . . total savings

__

It can be easier to do the addition first:

  ($8.50 +2.95 +7.00) × 0.20 = $18.45 × 0.20 = $3.69 . . . total savings

Let's graph the equation

Notice that this equation corresponds to a line.

1. First, let's clear y, so we can get the equation of the line in the slope-intercept form:

This way, he equation of the line in the slope-intercept form is

2. Now, we have to expose two points contained in the line. To do so, we give x any value we want and we calculate the corresponding y value.

Let's do this with x = 0 and x = 1

3. Put those points in the cartesian plane:

4. Draw a straight line that passes through both points. This will be the graph of the line

The volume of the cone in this problem is given as follows:

V = 48π units³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

From the image given in this problem, the parameters are given as follows:

r = 6 mm, h = 4 mm.

Hence the volume is given as follows:

V = π x 6² x 4/3

V = 48π units³.

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Rounding to two decimal places, the obtained chi-square statistic is 6.67.

We can use the chi-square goodness-of-fit test to determine if there is a significant difference in the preference for class format. We need to calculate the expected frequencies under the assumption that all groups have an equal preference. The total sample size is 90, so each group would be expected to have 30 students.

Observed frequencies:

Online: 50

In-person: 18

Hybrid: 22

Expected frequencies:

Online: 30

In-person: 30

Hybrid: 30

We can use the chi-square formula to calculate the test statistic:

χ^2 = Σ [(O - E)^2 / E]

where Σ is the sum of all the cells, O is the observed frequency, E is the expected frequency.

Plugging in the values:

χ^2 = [(50 - 30)^2 / 30] + [(18 - 30)^2 / 30] + [(22 - 30)^2 / 30]

χ^2 = 6.67

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You can look the image.

It is very clear.

Answer:

\(\sin (Z)=\sf\dfrac{9}{15}\)        \(\cos (Z)=\sf\dfrac{12}{15}\)        \(\tan(Z)=\sf \dfrac{9}{12}\)

Step-by-step explanation:

To create trigonometric ratios for angle Z in the given right triangle XYZ, we can use the trigonometric ratios.

\(\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the right triangle XYZ:

Substitute these values into the three ratios to create the trigonometric ratios for angle Z:

\(\sin (Z)=\sf \dfrac{O}{H}=\dfrac{9}{15}\)

\(\cos (Z)=\sf \dfrac{A}{H}=\dfrac{12}{15}\)

\(\tan(Z)=\sf \dfrac{O}{A}=\dfrac{9}{12}\)

Answer:

2.45

Step-by-step explanation:

Answer:97 °

Step-by-step explanation:

83° & b° are a supplementary angle, meaning that they equal 180°. So:

83 + b = 180

b = 97°

Here's link to the answer:

tinyurl.com/wpazsebu

Answer:

it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.

Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.

Step-by-step explanation:

a is wrong because it only describes positive correlation, not negative correlation.

c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.

d and f are wrong because they assume causation from correlation, which is a logical fallacy.

e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.

If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.

If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.

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There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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The variance is the average squared deviation of each value from the mean. It calculates how far each value in a group is from the mean, and then it squares the result of each of those calculations. Finally, it averages the sum of the squares to produce a figure that represents how varied the data is from the mean.

The variance formula is as follows:

Var(X) = (Σ (Xi - μ)^2) / (n - 1)

Where, X is a random variable representing the group data, μ is the mean of the group data, Xi is each value in the group data, Σ is the sum of all Xi values, and n is the number of values in the group data.

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According to given information, the probability that a contract will last between 15 and 35 weeks is `0.905`.

To compute the probability that a contract will last between 15 and 35 weeks, we must utilize the standard deviation for the normal distribution.

To solve for the probability of a normal distribution, we use the formula `z = (x - μ) / σ`, where `x` is the value we are looking for, `μ` is the mean, and `σ` is the standard deviation.

We can compute the standard deviation using the variance, which is the square of the standard deviation, which is `σ^2`.

To begin, we first find the standard deviation.  `σ = sqrt(36) = 6`.

Next, we will calculate the `z-scores` for 15 and 35.

\(`z1 = (15 - 25) / 6 = -10 / 6 = -1.67`\)

and \(`z2 = (35 - 25) / 6 = 10 / 6 = 1.67`\).

Now we can use the `Z-table` to find the probabilities that correspond to `z1` and `z2`. We can see that the probability of `z1` is `0.0475` and the probability of `z2` is `0.9525`.

Finally, to obtain the probability that a contract will last between 15 and 35 weeks, we must subtract the probabilities corresponding to `z1` from `z2`.

\(`P(15 ≤ X ≤ 35) = P(Z ≤ 1.67) − P(Z ≤ −1.67) = 0.9525 − 0.0475 = 0.905`\).

Therefore, the probability that a contract will last between 15 and 35 weeks is `0.905`.

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Answer: The correct answer is point and line. Explanation: These are two of the fundamental undefined terms in geometry. A line segment is a part of a line that has two defined points at each end; therefore "line" and "point" are used in the definition.

Step-by-step explanation:

The undefined terms which are needed to define a line segment are Point and line.

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Answer:

5,010

Step-by-step explanation:

Can I have Brainliest? TYSMMMMMMMMM if it is divisible by 10 it is divisible by 5. divisible by 10 is usually even

4.25 is DECIMAL FORM

17/4 is exact form

4 1/4 is mixed form

HOPE THIS HELPS :)

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer:

56 cola flavored gumboils

Step-by-step explanation:

Bob's 40 count of gumballs has 16 cola gumballs

Therefore the probability of a gumball being cola based on the sample size of Bob's purchase = 16/40 = 2/5

There are 140 gumballs left in the machine so we can expect that, on an average, 2/5 of them should be cola gumballs

So number of cola gumballs left is expected to be  2/5 x 140 = 56

This is only a prediction based on Bob's sample of 40 cola gumballs

Answer:

Short answer: 3.14 Long answer: First 1000 decimal places

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

Step-by-step explanation:

Answer:

The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159.

Therefore, the dimensions of triangle ABC and the angles opposite to these sides are:

a ≈ 6.85 units

b = 13 units

c ≈ 9.39 units

A ≈ 40 degrees

B = 97 degrees

C = 43 degrees

A triangle is a geometrical shape that has three sides and three angles. It is formed by connecting three non-collinear points in a plane with straight line segments. The three sides may have different lengths, and the three angles may have different measures. The sum of the angles in a triangle is always 180 degrees. Triangles are used in many fields of mathematics, as well as in science, engineering, and everyday life. They can be classified by their side lengths and angle measures, and there are various formulas and theorems that apply to triangles.

Here,

We can use the Law of Sines to find the missing measures of the triangle.

Recall that the Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

Given that b=13 units, and angle B=97 degrees, we can set up the proportion:

13/sin(97) = c/sin(43)

Solving for c, we get:

c = (13*sin(43))/sin(97) ≈ 9.39

Now, to find the remaining angle and side, we can use the fact that the angles of a triangle sum up to 180 degrees. We know that angle C is 43 degrees, so we can find angle A as:

A = 180 - 97 - 43 = 40 degrees

And we can find side a using the Law of Sines:

a/sin(40) = 13/sin(97)

Solving for a, we get:

a = (13*sin(40))/sin(97) ≈ 6.85

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Answer:

option b (4,-4)

Step-by-step explanation:

this is because this is a less than or greater than inequality and there is no equal so we can’t have anything touching the line and that eliminates d. But all the others are outside the shaded blue so, option b is the only one in there

The height of the tree is 26.52 feet

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The total height of the Tree = 6+x

using trigonometry;

tan 43 = x/22

x = tan43 ×22

x = 20.52 feet

the height of the tree = 6+x

= 6+20.52

= 26.52 feet

therefore the height of the tree is 26.52 feet

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The proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.

A proportion is the answer the poll question is asking as it is expressing the percentage of people who answered the question. It is asking what fraction or percentage of people report worrying a great deal about federal spending and the budget deficit. Proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.

Mean is not the appropriate answer because it involves calculating the average of a set of numbers, such as a list of individual responses, not percentages. Calculating the mean is not possible in this situation because the poll question does not provide individual responses but rather presents the data in a summed format (i.e., 64%), which cannot be averaged.

Therefore, the proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.

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Answer:

D. 74⁻⁶ (74^-6)

Step-by-step explanation:

Looking at the expression, I remember the following: 1 over an exponent (as a fraction) is the same thing as a negative exponent. None of these answers involve an exponent except for D (although A does involve a negative number). So D, which is 74⁻⁶, is the answer here.

The events A and B are not independent. The occurrence of event B affects the probability of event A.

To determine whether events A and B are independent,

we need to check if the probability of event A occurring is affected by the occurrence of event B, and vice versa.

Probability of event A: Since we are flipping two coins,

the probability of getting heads on each flip is 1/2.

Therefore, the probability of getting two consecutive heads is

\((1/2) \times (1/2) = 1/4\)

Probability of event B: The first or last flip yielding tails means there are two possibilities:

either the first flip is tails and the second flip is any outcome,

or the first flip is any outcome and the second flip is tails.

Each of these individual possibilities has a probability of

\((1/2) \times (1/2) = 1/4\)

Hence, theprobability of event B is 1/4 + 1/4 = 1/2.

Since the probability of event A is 1/4 and the probability of event B is 1/2, and 1/4 ≠ 1/2,

we can conclude that events A and B are not independent.

The occurrence of event B (first or last flip yielding tails) affects the probability of event A (two consecutive flips yielding heads).

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