Answer the question below:

Answer:

\(\boxed{Area = 3.14 ft^2}\)

Step-by-step explanation:

Radius = r = 2 feet

Angle = θ = π/2 (In radians) = 1.57 radians

Area of Sector = \(\frac{1}{2} r^2 \theta\)

Area = \(\frac{1}{2} (4)(1.57)\)

Area = 2 * 1.57

Area = 3.14 ft²

Answer:

               \(\bold{2\pi\ ft^2\approx6,28\ ft^2}\)

Step-by-step explanation:

360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.

\(A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2\)

The assumption of a finite population is the answer to the question of which condition/assumption is not required for the one-sample t inference for the mean μ of a population.

The one-sample t inference for the mean μ of a population is based on several conditions and assumptions. Let's discuss each of them and identify which one is not a condition or assumption.

Random Sampling: One of the key assumptions is that the data used for the inference is obtained from a random sample. Random sampling ensures that the observations are independent and representative of the population.

Normality: The t inference assumes that the population follows a normal distribution. This assumption is necessary to apply the t-distribution for inference. However, for large sample sizes (typically above 30), the t-inference is robust to deviations from normality due to the Central Limit Theorem.

Independence: The observations in the sample should be independent of each other. This assumption ensures that each observation provides new information and is not influenced by other observations.

Finite Population: The t-inference assumes that the population from which the sample is drawn is finite. This assumption is relevant when the sample size is a large fraction of the population size. If the population is infinite or extremely large, this assumption is not necessary.

Homogeneity of Variance: The t-inference assumes that the variance of the population is the same across all levels of the independent variable. This assumption is known as homogeneity of variance. Violation of this assumption can lead to inaccurate results.

Based on these conditions and assumptions, it can be concluded that the assumption of a finite population is not a condition of the one-sample t inference for the mean μ. The assumption of a finite population is relevant only when the population size is small or the sample size is a large fraction of the population size. In most practical scenarios, where the population size is large or infinite, this assumption is not applicable.

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The trigonometric identity that is true is:

sin G = cos I. Option D

First, we need to know that;

One acute angle in a right triangle has a sine value equal to the cosine value of the other acute angle.

From the information given, we have;

In a right scalene triangle GHI, where both angle G and angle I are acute, the value of sin G is equivalent to cos I.

Several alternatives, including sin G = sin I, cos G = cos I, tan G = tan I, sin G = tan I, sin G being the inverse of cos I, and cos G being the inverse of cos I, are invalid for a right scalene triangle with a known right angle.

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Answer:

435cm³

is my answer correct?

im pretty sure it is...

what is the 4.7cm the radius or circumference

if its the circumferance the answer is 1.753

Step-by-step explanation:

Step-by-step explanation:

The Birch tree has a greater density.

Answer:

B.

Step-by-step explanation:

To calculate the marginal cost, find the change in total cost when one additional unit is produced.

Variable Fixed Total Average Variable Average Total Marginal Cost

Cost Cost Cost

0 $30 $30 - - -

2 $30 $34 $17 $17 $4

5 $30 $47 $9.4 $9.4 $13

6 $30 $56 $9.3 $9.3 $9

8 $30 $78 $9.75 $9.75 $22

10 $30 $100 $10 $10 $22

12 $30 $132 $11 $11 $32

Note: To calculate the average variable cost, divide the total variable cost by the quantity produced. To calculate the average total cost, add the total variable cost and the total fixed cost and divide by the quantity produced. To calculate the marginal cost, find the change in total cost when one additional unit is produced.

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Answer:

If the bisectors of two adjacent angles are perpendicular to each other, are the angles then supplementary angles?

Suppose two angles ABC and CBD are x and y.

x+y = 180 deg.

The bisector of angle ABC (BE) and the bisector of angle CBD (CF) will form angle EBF = (x/2)+(y/2) = 180/2 = 90 deg.

Conclusion: If the angle bisectors of two adjacent angles are perpendicular to eaxh other, the adjacent angles are supplementary angle

Adjacent angles are when the 2 angles have a common vertex and a common arm.

if the exterior sides of 2 adjacent angles are perpendicular, then the angles are complementary angles.

Then the sum of the 2 adjacent angles is a right angle - 90°.

When 2 angles add up to 90°, they are called a pair of complementary angles.

Step-by-step explanation:

Answer: Hello: ) ✨ If the bisectors of two adjacent angles are perpendicular to each other, are the angles then supplementary angles?

Suppose two angles ABC and CBD are x and y.

x+y = 180 deg.

The bisector of angle ABC (BE) and the bisector of angle CBD (CF) will form angle EBF = (x/2)+(y/2) = 180/2 = 90 deg.

Conclusion: If the angle bisectors of two adjacent angles are perpendicular to eaxh other, the adjacent angles are supplementary angle

Adjacent angles are when the 2 angles have a common vertex and a common arm.

if the exterior sides of 2 adjacent angles are perpendicular, then the angles are complementary angles.

Then the sum of the 2 adjacent angles is a right angle - 90°.

When 2 angles add up to 90°, they are called a pair of complementary angles.

Have an amazing Day/Night <3 .

Answer:

C)

Step-by-step explanation:

The sum of the 2 angles add up to 90 degrees.

Hope this helps! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

Answer:

3, 5, 7

Step-by-step explanation:

We can assign the first number as x. Since all the numbers are odd the next number will be x+2, and the last will be x+4.

3*(x+4) = 7(x)

3x+12 = 7x

12 = 4x

x = 3

x+2 = 5

x+4 = 7

The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Answer:

90°/• is the probability

The missing sides of the triangle are

The length of the sides is solved using sine rule.

This represented by the formula

Sine A / a = Sine B / b = Sine C / c

Solving for angle x

= 180 - 130 - 27 sum of angels in a triangle

= 23

applying the formula for the problem

Sine X / WY = Sine Y / WX

Sine 23 / 8 = Sine 27 / WX

cross multiplying

WX = 8 * Sine 27 / Sine 23

WX = 9.295

WX = 9.3 to the nearest tenth

Sine W / XY = Sine Y / WX

Sine 130 / XY = Sine 27 / 9.3

cross multiplying

XY = 9.3 * Sine 130 / Sine 27

XY = 15.692

WX = 15.7 to the nearest tenth

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Answer:

-18y-1

Step-by-step explanation:

algebra

The result of angles is 20 degree.

Now, According to the question:

What is an Angle Bisector?

An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.

From the question, we know that:

We will construct a bisector of ∠P

The angle is given as 40 degree

40 ÷ 2 = 20 degree [Angle bisector, division]

So, the result two angles is 20 degree.

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The complete question :

To see the attachment of figure.

Answer:

206.7 so yes they add up

Step-by-step explanation:

They add up because 103.8+100.+2.9

So therefore after adding them up yes they add up but past 100%

The expected value for a student to spend on lunch each day is $5.18, making the 3rd option a right choice.

In the question, we are given that the marketing club at the school is opening a student store for which they randomly surveyed 50 students about how much money they spend on lunch each day.

We are asked to find the expected value for a student to spend on lunch each day.

The expected value is the mean of the data where we can show the data as the following table:

x (in $) 10 8   6   5 4 3

f(x)       2  1 12 23 8 4.

The mean of the data can be calculated using the formula, μ = (∑ x f(x))/(∑ f(x)).

Thus, the expected value of the given data can be shown as:

μ = (10*2 + 8*1 + 6*12 + 5*23 + 4*8 + 3*4)/(2 + 1 + 12 + 23 + 8 + 4),

or, μ = (20 + 8 + 72 + 115 + 32 + 12)/(50),

or, μ = 259/50,

or, μ = 5.18.

Thus, the expected value for a student to spend on lunch each day is $5.18, making the 3rd option a right choice.

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For the complete question, refer to the attachment.

Answer:

$5.18

Step-by-step explanation:

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

980,000 hl

Step-by-step explanation:

There are 980,000 milliliters in 9.8 hectoliters.

Yes; since 35% is in the confidence interval they fail to reject the null hypothesis, concluding that there is not strong evidence of any change in financial aid requests. The correct answer is 5.

To test the hypothesis, we need to calculate the test statistic z and compare it with the critical value at the 0.10 level of significance. The test statistic is calculated as:

z = (p-bar - p) / √(p(1-p)/n)

where p-bar is the sample proportion, p is the hypothesized proportion, and n is the sample size.

In this case, p = 0.35, n is not given, but we can use the midpoint of the confidence interval as an estimate of p-bar. So, p-bar= (0.32 + 0.40) / 2 = 0.36.

Substituting these values, we get:

z = (0.36 - 0.35) / √(0.35(1-0.35)/n) = 0.15√(n)

Using a z-table or calculator, we find that the critical value for a one-tailed test at the 0.10 level of significance is 1.28.

Since the calculated z-value (0.15√(n)) is less than the critical value of 1.28, we fail to reject the null hypothesis. We can conclude that there is not strong evidence to suggest that the proportion of students requiring financial aid has changed from the historical value of 35%.

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Complete Question:

To plan the budget for next year, a college needs to estimate what impact the current economic downturn might have on student requests for financial aid. Historically this college has provided aid to 35% of its students. Officials look at a random sample of this year's applications to see what proportion indicate a need for financial aid. Based on these data they create a 90% confidence interval of (32%, 40%). Could this confidence interval be used to test the hypothesis H0: p = 0.35 versus Ha: p 0.35 at the a 0.10 level of significance?

1. Yes; since 35% is in the confidence interval they accept the null hypothesis, concluding that the percentage of students requiring financial aid will stay the same.

2. No, because financial aid anmounts may not be normally distributed.

3. No, because they only used a sample of the applicants instead of all of them.

4. Yes; since 35% is not at the center of the confidence interval they reject the null hypothesis concluding that the percentage of students requiring aid will change.

5. Yes; since 35% is in the confidence interval they fail to reject the null hypothesis, concluding that there is not strong evidence of any change in financial aid requests.

Answer:

c= hy−w /6y

Step-by-step explanation:This is what i got.

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

Chase earned 15 dollars roooooos

Step-by-step explanation:

Answer:

yo cant help u good do

Answer:

62°

Step-by-step explanation:

it basically falls under the formula of SOH CAH TOA

Answer: 14

Step-by-step explanation: An integer is any number that is not either a decimal or a fraction.

Hope this helps :)