Study the graph below and answer the question.



U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics.

What is the purpose of the graph?

to show that Conservative Christian enrollment increased
to show that Catholic enrollment decreased
to show that overall enrollment increased
to show the changes in private school enrollment

Answer:

\( \sqrt{58} \)

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 3² + 7² = 9 + 49 = 58 ( take square root of both sides )

x = \(\sqrt{58}\) → B

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer:

A. -68

B. 37

C. -61

D. 171

Step-by-step explanation:

Rule for A, B, D: 2 negatives is the same as addition

(how I did C: add them together then add the negative)

A. -68

B. 37

C. -61

D. 171

Step-by-step explanation:

Rule for A, B, D: 2 negatives is the same as addition

(how I did C: add them together then add the negative)

So the coefficient of determination is 0.476 or 47.6%. This means that 47.6% of the total variation in the dependent variable can be explained by the independent variable(s) in the regression model.

The coefficient of determination (R-squared) is the proportion of the total variance in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the sum of squares due to regression (SSR) to the total sum of squares (SST).

R-squared = SSR / SST

In this case, SSR = 11.06 and SST = 23.22. Therefore,

R-squared = SSR / SST = 11.06 / 23.22 = 0.476

The remaining 52.4% is due to other factors not included in the model.

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Answer:

Man o dont know the answer but just give me brainalis

Step-by-step explanation:

wen you see my answer clike the hart buton and the buton that says make Brinalist

Answer:

B. \(k(x)=(-x+3)^{1/2}\)

Step-by-step explanation:

When we're talking about a restricted domain, we're looking for a function that's undefined for certain values of x. A classic example is the function f(x) = 1/x. Division by 0 is undefined, so this restricts our domain to all real numbers except 0.

A key feature of our problem is in the exponents - are there any exponents that would limit the possible values of x? Let's strip away the rest of the details and just look at those powers for each option:

For A, let's look at the function \(f(x) = x^{1/5}\). Remember that fractional exponents are the same as roots, so we could also say \(f(x)=\sqrt[5]{x}\). Any odd root like this can take any value for x, positive and negative. This has to do with the fact that any odd power of a negative is always negative. So no restrictions on A.

For B, just looking at the exponent, let's see if there are restrictions on the function \(k(x) = x^{1/2}\). Again, we can rewrite the right side as a root: \(k(x) = \sqrt{x}\).

Unline f(x), k(x) is restricted. The square root of a negative number has no real solutions, so k(x) comes with the restriction that x ≥ 0. We could look at C and D, but we've already found our solution at this point, so I'll stop here!

Answer:

5) 22.95

6) 21.93

Step-by-step explanation:

Area of Triangle = BxH/2

= CxH/2

The 1-week growth factor for the mass of the bacteria is 3.29.

The 1-day growth factor for the mass of the bacteria is 1.185.

The percentage increase in the mass of bacteria is 18.5%.

The 1-day growth percent for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 27.7%.

The 1-week growth factor for the mass of the bacteria is 1 + (229%*1).

The 1-week growth factor for the mass of the bacteria is 3.29.

The 1-day growth factor for the mass of the bacteria is (3.29)^(1/7).

The 1-day growth factor for the mass of the bacteria is 1.185.

The percentage increase in the mass of bacteria is 18.5%.

The new 1-week growth factor for the mass of the bacteria is 1 + (453%*1).

The new 1-week growth factor for the mass of the bacteria is 5.53.

The 1-day growth factor for the mass of the bacteria if the mass of the bacteria increased by 453% per week is (5.53)^(1/7).

The 1-day growth factor for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 1.277.

The 1-day growth percent for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 27.7%.

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Answer:

The answer would be 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

8 times 4 = 32

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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The mean absolute deviation of the data set is 6.5.

The mean absolute deviation of a data set is the average distance between each data point and the mean. It is a measure of the variability of a data set.

To calculate the mean absolute deviation, you must first find the mean of the data set.

In this case, the mean of the data set is (20 + 10 + 20 + 20 + 4 + 16 + 6 + 4) / 8 = 12.5.

Then, find the absolute deviation of each data point from the mean.

The absolute deviations of each data point from the mean are:

|20 - 12.5| = 7.5

|10 - 12.5| = 2.5

|20 - 12.5| = 7.5

|20 - 12.5| = 7.5

|4 - 12.5| = 8.5

|16 - 12.5| = 3.5

|6 - 12.5| = 6.5

|4 - 12.5| = 8.5

Finally, take the average of these absolute deviations to find the mean absolute deviation.

(7.5 + 2.5 + 7.5 + 7.5 + 8.5 + 3.5 + 6.5 + 8.5) / 8 = 6.5

Therefore, the mean absolute deviation of the data set is 6.5.

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Answer:

8218.406
Go through the process yourself to make sure my answer is correct

Step-by-step explanation:

The best way to solve these problems is by breaking them up into the difference shapes you see

A. Semi-sphere

The volume of a sphere is \(\frac{4}{3} \pi r^3\). Since we have a semi-sphere, we divide this by 2 and get:

\(V=\frac{4}{6} \pi r^3\\\\V= \frac{4}{6} \pi (12)^3\\\\V=3619.115\)

B. Cone

The volume of a cone is \(\pi r^2\frac{h}{3}\)

\(V = \pi (12)^2\frac{30.5}{3}\\V = 4599.292\)

C. Add

Add these two values:

3619.115 + 4599.292 = 8218.406

The sequence is arithmetic. The common difference is 6. Answer: b

If a sequence is arithmetic, there exists a common difference d that is added to each term to get the next term. For instance, given the sequence 2, 5, 8, 11, 14, ...  to get each of the subsequent terms, we add 3. 2 + 3 = 5; 5 + 3 = 8, and so on.

The given sequence is 2,7,13,20, ...To determine whether it is an arithmetic sequence, we need to find the common difference d.

Subtract each subsequent term from its preceding term;7 - 2 = 513 - 7 = 620 - 13 = 7

Therefore, the common difference d is 6.

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Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level \(\alpha = 0.04\)

Given:

\(H_0: \mu = 8.2 \text{ seconds}, \, H_a: \mu < 8.2 \text{ seconds}\)

\(\alpha = 0.04\)

\(z_0 = -1.75\)

\(p = 0.0401\)

If p value is greater than level of significance alpha then we accept null hypothesis otherwise we reject null hypothesis.

Here \(p = 0.0401\) which is greater than the alpha \(0.04\), hence do not reject null hypothesis.

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Answer:

100 and 101

Step-by-step explanation:

Hi there!

Let x be equal to the smaller number.

Let x + 1 be equal to the larger number, which is consecutive to the smaller number.

We are given that the sum of the two numbers is 201:

\(x+(x+1)=201\\x+x+1=201\\2x+1=201\\2x=200\\x=100\)

Therefore, the smaller number is 100. Because the larger number is x + 1, it is 101.

I hope this helps!

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9x^2 + 24x + 16 = 0

(3x + 4)(3x+4)=0

3x + 4 = 0

3x = -4

x = -4/3

3x + 4 = 0

3x = -4

x = -4/3

Answer:

Γ = 15

Step-by-step explanation:

Given

f(x) = x² - 8x + Γ

with a = 1, b = - 8 and c = Γ , then

sum of zeros α + β = - \(\frac{b}{a}\) = - \(\frac{-8}{1}\) = 8

product of zeros = αβ = \(\frac{c}{a}\) = Γ

Given α - β = 2 , then

(α - β)² = 2²

α² - 2αβ + β² = 4 → (1)

and

(α + β)² = 8²

α² + 2αβ + β² = 64 → (2)

Add (1) and (2) term by term

2α² + 2β² = 68 ( divide through by 2 )

α² +β² = 34

Substitute α² + β² = 34 into (1)

34 - 2αβ = 4 ( subtract 34 from both sides )

- 2αβ = - 30 ( divide both sides by - 2 )

αβ = 15

Now

αβ = Γ = 15

Thus

f(x) = x² - 8x + 15

Answer: 10 wreaths

Step-by-step explanation:

First identify the terms.

She has a booth that cost $200. This price will not change thus making it a Fixed cost.

Making a wreath would cost her $10 each time so this is a Variable cost.

She sells the wreath for $30 so this is the selling price.

Breakeven = Fixed Cost / Contribution margin

Contribution margin = Selling price - Variable cost

= 30 - 10

= $20

Breakeven point = 200/20

= 10 wreaths

Answer:

887.74

Step-by-step explanation:

Answer:

the answer is

\( \sqrt{221} \)

\( {10}^{2} + {11}^{2} = 221\)

14.86606875

Answer:

Step-by-step explanation:

If you change the bases to the same number, the exponents must equal each other.

Answer: I believe the answer is 6.3 I will research more and get a definite answer just dam me for the answer!

Step-by-step explanation:

:)

True.An example of a variable input on a college campus would indeed be the number of instructors needed.

The number of instructors required can vary based on factors such as the number of courses being offered, the size of the student population, class sizes, faculty-student ratios, and other factors that affect the teaching workload and staffing needs of the institution.

The number of instructors needed is a variable input because it can change over time and in response to different circumstances. For example, at the beginning of a semester, when a college campus experiences high enrollment, more instructors may be required to meet the demand for teaching courses. On the other hand, during summer or holiday breaks when fewer courses are offered or when the student population is reduced, fewer instructors may be needed.

The number of instructors needed is an important consideration for colleges and universities to ensure the smooth functioning of academic programs and the provision of quality education. It plays a crucial role in determining the faculty-student ratio, class sizes, course availability, and overall academic experience for students.

In terms of solution, determining the number of instructors needed involves careful planning and analysis by the college administration or academic departments. They need to consider various factors, such as the number of courses being offered, the size and nature of the courses, the expertise required for specific subjects, and any contractual or workload obligations of the instructors.

The process typically involves forecasting student enrollments, analyzing historical data on course registrations, and considering factors such as class sizes, faculty workload policies, and teaching responsibilities. The administration may use mathematical models, scheduling software, or historical data analysis to estimate the number of instructors required for each semester or academic year.

Based on this analysis, the college can make decisions about hiring new instructors, assigning existing faculty members to courses, or adjusting course offerings to ensure that the staffing needs are met. It is crucial to strike a balance between the number of instructors and the workload to ensure that instructors have a manageable teaching load while meeting the needs and expectations of students.

In conclusion, the number of instructors needed is a variable input on a college campus. It can fluctuate based on factors such as student enrollments, course offerings, class sizes, and other factors. Determining the appropriate number of instructors requires careful planning, analysis, and consideration of various factors to ensure the effective functioning of academic programs and the provision of quality education to students.

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Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Answer: Option D 9(3)^x

Step-by-step explanation:

3^x+2 = 9(3)^x

9= 3^2

whenever there are same 2 numbers in multiplication, there powers are added.

Therefore, 3^2(3^x) = 3^(x+2)

Answer:

x = 19

Step-by-step explanation:

180-123 = 57

x = 57/3

x = 19

Answer:

x=19

Step-by-step explanation:

180°-123°=3x

3x=57°

x=19

The equation of the problem is \(5(n+7)\)

The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.

The equation of the line parallel to the x-axis and passing through the points (1,1,2) and (2,1,1) is x = 1.

To determine the equation of a line parallel to the x-axis, we know that the y-coordinate and z-coordinate will remain constant.

Given the points (1,1,2) and (2,1,1), we can see that the y-coordinate is always 1. Therefore, the equation of the line will be of the form y = 1.

Since the line is parallel to the x-axis, the x-coordinate can vary but the y-coordinate and z-coordinate remain constant.

To find the equation, we can consider any point on the line. Let's use the point (1,1,2). Since the y-coordinate and z-coordinate remain constant, the equation becomes x = 1.

Therefore, the equation of the line parallel to the x-axis and passing through the points (1,1,2) and (2,1,1) is x = 1.

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Answer:

c

Step-by-step explanation:

Answer:

MOM

TOOT

Step-by-step explanation: