The pattern shown here is made from concentric circles cut into quarters. Find the total area of the shaded regions. I’ll give brainliest if you got the right answer :)

The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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Answer:

$10087.5

Step-by-step explanation:

take $7,500× 3.45% = $258.75 ×10= 2587.5+ the 7500= 10087.5

Answer:

Step-by-step explanation:

oops sorry i thought you where my friend oof

Answer:

i think the correct answer is letter D im not sure

Step-by-step explanation:

Answer:

The area of the sector is 9.43 ft^2

Step-by-step explanation:

Here, we want to find the area of the sector with a central angle of 30 degrees

To do this, we use the formula below;

Area of sector = theta/360 * pi * r^2

theta = central angle = 30 degrees

r = radius = 6 ft

Thus, we have it that;

Area of sector = 30/360 * pi * 6^2

= 30/10 * pi = 3 * 3.142 = 9.43 ft^2

Answer:

12.6 kilometers

Step-by-step explanation:

5.25/5 = x/12

cross multiply

5x = 63

divide both sides by 5

x = 12.6 kilometers

A Distance of 12.6 kilometers is traveled in a year. The distance traveled is the product of velocity and time.

Distance is a numerical representation of the distance between two objects or locations.

The distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.

The formula for the distance is;

\(\rm d = v \times t \\\\ v = \frac{d}{t}\)

The distance traveled in the 5-month period is 5.25 km equal to 1 by 12 of the total distance traveled.

\(\rm v=\frac{x}{12} \\\\ \frac{5.25}{5} =\frac{x}{12} \\\\ 5x=63 \\\\ x =12.6 \ km\)

Hence distance of 12.6 kilometers is traveled in a year.

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Answer:

18

Step-by-step explanation:

Just took the test

Answer:

The triangles are congruent by congruency theorem SAS.

Step-by-step explanation:

Side-Angle-Side, as it suggests, is when a triangle is congruent by the order of congruent side, congruent angle, and another congruent side. If named certain ways, they can be congruent. Since the question does not provide a specific way of naming the triangles, we can assume that any way is allowed. 2.5 and 2.5 are congruent, followed by angles D and G which have the congruent angle markers. The congruent angles are followed by 1.7 and 1.7, making the triangles congruent by Side-Angle-Side.

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

Step-by-step explanation:

we can replace 5 with \(\sqrt{5}^{2}\)

then.

\(\sqrt{5}^{n-1+2}=\sqrt{5}^{n+1}\)

Answer:

113.1

Step-by-step explanation:

To approximate the sum of the series [infinity] (−1)n 5n/(n!), we can use the alternating series test. To approximate the sum, we can calculate the partial sums and stop when the terms become insignificant.


1. The alternating series test states that if a series (-1)n an is such that the absolute value of the terms decrease and tend to zero as n approaches infinity, then the series converges.
2. In this series, the terms (-1)n 5n/(n!) decrease as n increases because the factorial term in the denominator grows faster than the exponential term in the numerator.
3. Therefore, we can conclude that the series converges.

The sum of the series [infinity] (-1)n 5n/(n!) converges.
To approximate the sum, we can calculate the partial sums and stop when the terms become insignificant.

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Answer:

sinθ=cscθ1 =csc2θ 1 =1+cot2θ 1 =1+tan2θ1 1 =tan2θ1+tan2θ 1 =1+tan2θ tanθ

cosθ=secθ1 =sec2θ 1 =1+tan2θ 1

cotθ=tanθ1

cscθ=csc2θ =1+cot2θ =1+tan2θ1 =tan2θtan2θ+1 =tanθ1+tan2θ

secθ=sec2θ

Answer:

t + c <= 17

Step-by-step explanation:

This inequality states that the total number of tables and chairs sold (t + c) must be less than or equal to 17, in order to satisfy the constraint that the store can ship at most 17 pieces of furniture per day.

Answer:

-1

Step-by-step explanation:

Answer:

less than < the first option

The features needed to describe a rotation are Center, Direction and Angle

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

The key features

From the key features, the terms that describe rotation are:

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The median is the middle number in the data.

Sort them out in order.

30, 33, 35, 38, 41, 43, 43, 50, 64

The middle number is 41 so the median is 41.

The null hypothesis in an independent-samples t-test refers to the assumption that there is no significant difference between the means of two independent populations. In this context, "independent-samples" denotes that the two samples come from different populations and are not related. "Population" refers to the larger group from which the samples are taken.

Given the group of answer choices, the correct option for the null hypothesis in an independent-samples t-test is:

c. The mean of sample 1 is equal to the mean of sample 2.

This statement asserts that there is no significant difference between the means of the two samples. The null hypothesis serves as a starting point in the analysis, and the purpose of the t-test is to determine whether there is enough evidence to reject the null hypothesis in favor of an alternative hypothesis, which states that the means of the two samples are significantly different. The other answer choices do not accurately represent the null hypothesis for an independent-samples t-test.

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Answer:

a.375

Step-by-step explanation:

The solution to the equation is x = (7/2)t, y = (5/2)t, z = t.

To solve the equation -6x + 4y - 9z = 0 for x, y, and z in terms of s and t, we can use the variable substitution x = s + t, y = s, and z = t.

Substituting these values into the equation, we get:

-6(s + t) + 4s - 9t = 0

Simplifying this equation, we get:

-2s - 5t = 0

Solving for s in terms of t, we get:

s = (5/2)t

Substituting this value of s into our original substitutions for x and y, we get:

x = s + t

  = (5/2)t + t

  = (7/2)t

Now

y = s

= (5/2)t

Now,

z = t

Therefore, the solution to the equation -6x + 4y - 9z = 0 in terms of s and t is:

x = (7/2)t

y = (5/2)t

z = t

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Answer:

20%

Explanation:

To know the percentage, we need to identify what percentage of $50 represents $10. So, we can calculate the percentage as:

Therefore, the answer is 20%

Answer:

19.4

Step-by-step explanation:

16^2+11^2=377

then square 377 which will equal to

19.416 which can be rounded up to 19.4

Answer:

\frac{d}{dx}\left(x^2+16x+63\right)=2x+16

Step-by-step explanation:

The equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is :

y = (7/3)x - (19/3).

To write the equation in slope-intercept form, we need to find the slope of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0.

First, we need to rearrange the equation 3x + 7y = 0 into slope-intercept form:

7y = -3x
y = (-3/7)x

The slope of this line is -3/7.

Since the line we are trying to find is perpendicular to this line, its slope will be the negative reciprocal of -3/7:

m = 7/3

Now we can use the point-slope formula to write the equation of the line that passes through (1,8) with slope 7/3:

y - 8 = (7/3)(x - 1)

Finally, we can rearrange this equation into slope-intercept form:

y = (7/3)x - (19/3)

So, the equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is y = (7/3)x - (19/3).

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Answer:

fourth option

Step-by-step explanation:

Given

\(\frac{2x-1}{y}\) = \(\frac{w+2}{2z}\) ( cross- multiply )

y(w + 2) = 2z(2x - 1) = 4xz - 2z ( divide both sides by y )

w + 2 = \(\frac{4xz-2z}{y}\) ( subtract 2 from both sides )

w = \(\frac{4xz-2z}{y}\) - 2

Answer:

i guess you have to find square root of every number

like of 15 is 3,87 therefore higher than it is 4 and less than it 3

Answer:

Step-By-Step Explanation: (Rounded to nearest hundred)

The velocity of the satellite is \(\sf 3.6 \times10^3 \ m / s\).

Given data:

The velocity of the satellite is,

\(\sf Velocity =\sqrt{\dfrac{GM}{R} }\)

\(=\sqrt{\dfrac{6.7\times10^{-11}\times4.4\times10^{24}}{2.3\times10^7} }\)

\(\sf = 3.6 \times10^3 \ m / s\).

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David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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Answer:

y = -3x + 7

Step-by-step explanation: