Simplify the expression. Write your answer as a power.

4. 5⁵/4. 5³

The simplified expression is

Answer:

32 cm³

Step-by-step explanation:

Volume of a sphere is:

\(V_{s}=\frac{4}{3}\pi r^{3}\)

Volume of a cylinder is:

\(V_{c} = \pi r^{2} h\)

The volume of the cylinder is 48 cm³.

The cylinder has the same radius (r) and height (2r) as the sphere.

\(48 = \pi r^{2} (2r)\\48 = 2\pi r^{3}\\24 = \pi r^{3}\)

Therefore, the volume of the sphere is:

\(V_{s}=\frac{4}{3} (24)\\V_{s}=32\)

The Volume of sphere is 32 cm³.

Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.

We have,

The volume of the cylinder is 48 cm³.

As, Volume of cylinder = πr²h

Volume of Sphere = 4/3πr³

Now, the height h=2r

Then, Volume of cylinder = πr²(2r) = 2πr³

and, Volume of sphere = 4/3πr³

So, we can write

πr³ = 3 ( Volume of sphere)/4

Volume of Cylinder = 3 (Volume of sphere) / 2

48 =  3 (Volume of sphere) / 2

96 /3 = Volume of sphere

Volume of sphere = 32 cm³

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1. The radius of convergence, R, of the series is 1.

2. The interval of convergence, I, is [-1, 1).

To find the radius of convergence, we'll use the ratio test. Let's apply the ratio test to the given series:

lim(n→∞) |(5(n+1))/(5n) * x| = lim(n→∞) |x|

For the series to converge, the limit above must be less than 1. Therefore, we have:

|x| < 1

This implies that the radius of convergence, R, is 1.

To find the interval of convergence, we need to consider the endpoints of the interval. For |x| < 1, the series converges.

At x = 1, the series becomes:

∑ (5n)/(5^n) = ∑ 1/n

This is the harmonic series, which diverges.

At x = -1, the series becomes:

∑ (-1)^n (5n)/(5^n)

This is the alternating harmonic series, which converges.

Therefore, the interval of convergence, I, is [-1, 1) in interval notation.

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Answer:

b = -18

Step-by-step explanation:

to find be you need to isolate the variable. First, you have to multiply both sides by 13 to cancel the denominator. Then, add 8 to both sides to cancel the negative 8 on the left. You should be left with what x equals.

-8+b/13(13) = -2(13)

-8+b = -26

+8       +8

b = -18

Answer:

b = -18

Step-by-step explanation:

First multiply 13 on both sides which will give you

-8 + b = -26

Then add 8 to both sides and will give the answer

b = -18

Answer:

2x+20+x+10+2x-5 = 180

5x + 25 = 180

x=31

brainliestpls

The equation of the ellipse in standard form is (x - 9)² / 64 + (y + 2)² / 100 = 1.

In this problem we must determine the equation of the ellipse in standard form, whose foci are (15, - 2) and (3, - 2) and co-vertices are (9, 6) and (9, - 10). The ellipse is defined by the following equation:

(x - h)² / b² + (y - k)² / a² = 1

Where:

First, determine the center of the ellipse:

(h, k) = 0.5 · (15, - 2) + 0.5 · (3, - 2)

(h, k) = (9, - 2)

Second, determine distance between a focus and the center of the ellipse:

(c, 0) = (15, - 2) - (9, - 2)

(c, 0) = (6, 0)

c = 6

Third, determine the length of the minor semiaxis:

(0, b) = (9, 6) - (9, - 2)

(0, b) = (0, 8)

b = 8

Fourth, determine the length of the major semiaxis:

a = √(b² + c²)

a = √(8² + 6²)

a = 10

Fifth, write the equation of the ellipse:

(x - 9)² / 64 + (y + 2)² / 100 = 1

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Answer:

\(15.0118^o\)

Step-by-step explanation:

\(\mathrm{We\ use\ the\ sine\ law\ to\ solve\ this\ question.}\\\mathrm{\frac{a}{sinA}=\frac{c}{sinC}}\\\\\mathrm{or,\ \frac{31}{sin138^o}=\frac{12}{sinC}}\\\\\mathrm{or,\ sinC=\frac{12}{31}sin138^o}\\\mathrm{or,\ sinC = 0.259}\\\mathrm{or,\ C=sin^{-1}0.259=15.0118^o}\)

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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Answer:

He would recognize Lincoln's accomplishments which a good amount was about his documents like the Emancipation document.

Step-by-step explanation:

Also, he did his "I have a dream" speech on the Lincoln Memorial.

Answer:

see below

Step-by-step explanation:

−6x+3y=18.9

To find the x intercept, set y=0 and solve for x

−6x+3*0=18.9

−6x=18.9

Divide each side by -6

-6x/-6 = 18.9/-6

x =-3.15

The x intercept is -3.15

To find the x intercept, set x=0 and solve for y

−6*0+3y=18.9

3y=18.9

Divide each side by 3

3y/3= 18.9/3

y =6.3

The y intercept is 6.3

Answer:

x-intercept= -3.15

y-intercept= 6.3

Step-by-step explanation:

k12

Answer:

9 inches

Step-by-step explanation:

i divided 36 by 4

Answer:

9 inches

Step-by-step explanation:

You divide 36 by 4 which gives you 9 inch

Mark Brainliest Pls :(

Answer:

a pyramidal prism is 1/3 the volume of a similar rectangular prism of same base and height

so V=(1/3)bh

V=36

H=6

find area of base

36=(1/3)b6

36=2b

divide both sides by 2

18=b

the area of the base is 18 square units

Step-by-step explanation:

the answer is : V= B.h

A normal sampling distribution can be used for testing the claim. The hypotheses are stated as Hp: p ≤ 0.37, Ha: p > 0.37.

To determine whether a normal sampling distribution can be used to test the claim, we need to verify if the conditions for using a normal approximation are satisfied. The conditions are as follows:

Random Sample: The sample should be selected randomly from the population.

Independence: The sample observations should be independent of each other.

Sample Size: The sample size should be sufficiently large, typically requiring np ≥ 10 and n(1-p) ≥ 10, where n is the sample size and p is the estimated population proportion.

Given the information provided:

Claim: p > 0.45 - 0.08

Sample statistics: p = 0.40, n = 130

To determine if a normal sampling distribution can be used, we can check the sample size condition:

Calculate np and n(1-p):

np = 130 * 0.40 = 52

n(1-p) = 130 * (1 - 0.40) = 78

Since both np (52) and n(1-p) (78) are greater than 10, the sample size condition is satisfied.

Therefore, we can conclude that a normal sampling distribution can be used for testing the claim.

Next, we need to state the hypotheses for testing the claim.

H0: p ≤ 0.37 (Null hypothesis)

Ha: p > 0.37 (Alternative hypothesis)

Based on the claim, we are testing if the population proportion (p) is greater than 0.37.

Therefore, the correct choice for stating the hypotheses is:

OC. Hp: p ≤ 0.37, Ha: p > 0.37

To further analyze the data and test the claim, we can perform a hypothesis test using the sample proportion and significance level (α = 0.05).

We can calculate the test statistic, which in this case is a z-score:

z = (p - p0) / sqrt((p0 * (1 - p0)) / n)

= (0.40 - 0.37) / sqrt((0.37 * (1 - 0.37)) / 130)

= 0.03 / sqrt(0.2339 / 130)

≈ 1.437

Using a standard normal distribution table or calculator, we can find the critical value for a one-tailed test with a significance level of 0.05. The critical value corresponds to a z-score of approximately 1.645.

Since the calculated test statistic (1.437) does not exceed the critical value (1.645), we do not have sufficient evidence to reject the null hypothesis.

Therefore, based on the data provided, we do not have convincing statistical evidence to support Jenna's claim that the average texting time at her high school is greater than 94 minutes.

In summary, a normal sampling distribution can be used for testing the claim. The hypotheses are stated as Hp: p ≤ 0.37, Ha: p > 0.37. However, based on the hypothesis test, the data does not provide convincing statistical evidence to support Jenna's claim.

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The student that has the greatest percent error is Ebony.

The percentage error will be calculated as:

= Change in value / Initial values × 100

From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:

= (Measured length - Actual length) / Actual length × 100

= (2.1 - 1.6)/1.6 × 100

= 0.5 / 1.6 × 100

= 31.25%

Ebony had the higher percentage error.

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Electronic verification of Medicaid eligibility under the Affordable Care Act simplifies the application process, improves accuracy, and reduces administrative burdens. By following a three-step procedure, individuals can efficiently determine their eligibility for Medicaid, contributing to a more effective and user-friendly healthcare system.

Most states are now transitioning from paper-based systems to electronic verification of Medicaid eligibility. This process involves the use of advanced technology to streamline the process of verifying eligibility, which is critical to ensuring that only those who qualify for Medicaid benefits receive them. The electronic verification process typically involves cross-checking the applicant's information against multiple databases to ensure accuracy. This helps to reduce the likelihood of fraud and error in the system.

There are three main benefits to moving to electronic verification of Medicaid eligibility. First, it is faster and more efficient than traditional paper-based systems. This means that individuals who qualify for benefits can receive them more quickly, which can be critical for those who need immediate medical care. Second, electronic verification reduces the risk of errors and fraud, which can help to ensure that the Medicaid program remains financially sustainable over the long term. Finally, electronic verification can help to ensure that only those who are truly eligible for Medicaid benefits receive them, which helps to reduce costs and ensure that resources are targeted to those who need them most.

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The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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Answer:

w = 12

Step-by-step explanation:

3w = 11 + 25

3w = 36

w = 12

Hope that helps!

In the system of equations, the value of the variable 'b' will be 3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the equations is given below.

Equations 1: - 4 = 9a - 3b + c

Equation 2: 14 = 9a + 3b + c

Equation 3: - 4 = c

Put the value of c in equations 1 and 2, then we have

- 4 = 9a - 3b - 4

9a - 3b = 0                 ...4

14 = 9a + 3b - 4

9a + 3b = 18               ...5

Subtract equation 4 from 5,

9a + 3b - 9a + 3b = 18 - 0

6b = 18

b = 3

In the system of equations, the value of the variable 'b' will be 3.

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Answer:

Length will be 46 ft and width will be 16 ft

Explanation:

Let the width be x.

then the length will be 3x - 2

using the rectangle perimeter formula:

2( length + width )

2(x + 3x-2) = 124

2(4x-2) = 124

8x - 4 = 124

8x = 128

x = 16 ft

Width will be 16 ft and

Length: 3x - 2

           : 3(16)-2

           : 46 ft

ATQ

\(\\ \tt\hookrightarrow 2(n+3n-2)=124\)

\(\\ \tt\hookrightarrow 2(4n-2)=124\)

\(\\ \tt\hookrightarrow 4n-2=62\)

\(\\ \tt\hookrightarrow 4n=64\)

\(\\ \tt\hookrightarrow n=16\)

Answer:

3d + f -2

Step-by-step explanation:

= 4f+4+3d-6-3f

= f+3d-6

= 3d+ f - 6

In the linear equation -1/4(x -1) = 2/3x + 2, the value of x is -21/11

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

In the given equation -1/4(x -1) = 2/3x + 2, we can solve for the value of x

-1/4(x -1) = 2/3x + 2

collect like terms

-1/4x + 1/4 = 2/3x + 2

2/3x + 1/4x = 1/4 - 2

(11/12)x = - 7/4

x = - 21 / 11

The value of x is -21/11

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A higher confidence level would lead to a wider confidence interval.

The confidence interval represents the range of values within which the true population parameter is likely to fall. It is constructed based on the sample data and the desired level of confidence.

The confidence level refers to the probability that the interval contains the true population parameter.

When we increase the confidence level, we are asking for a higher level of certainty or confidence in our estimation.

This means that we want to be more confident that the interval captures the true population parameter. To achieve a higher confidence level, we need to widen the interval to encompass a larger range of possible values.

On the other hand, if we decrease the confidence level, we are willing to accept a lower level of certainty and are willing to tolerate more uncertainty in our estimation.

In this case, we can construct a narrower interval since we are allowing for a greater chance of the true parameter falling outside the interval.

Therefore, a higher confidence level would lead to a wider confidence interval, while a lower confidence level would result in a narrower confidence interval.

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Answer:

24 pieces.

Step-by-step explanation:

I take it that the question is how many pieces does she get?

I'll answer that. If it is wrong, leave a note.

1 foot will give 6 pieces - each 1/6 of a foot which is 12/6 = 2 inches.

4 feet will give 4 * 6 = 24 pieces.

The answer for this question is 24 pieces.

Answer:

The answer is 36°.

Hope it helps.

Step-by-step explanation:

• • •

Answer:

work is shown and pictured

Classroom objects can be categorized as vertical or horizontal. Examples of vertical objects include doors, bookshelves, and clocks, while horizontal objects include desks, tables, and chairs.

In a classroom, there are many objects that are vertical and horizontal. Here are ten examples of each:

Vertical objects in a classroom:

1. Door                     6. Clock

2. Cabinet               7. Electrical outlets

3. Bookshelf            8. Light switches

4. Whiteboard         9. Window blinds

5. Flagpole             10. Bulletin board

Horizontal objects in a classroom:

1. Desks                  6. Keyboard trays

2. Chairs                 7. Carpet tiles

3. Tables                 8. Ceiling tiles

4. Countertops       9. Whiteboard markers

5. Shelves              10. Paper trays

These are just a few examples of vertical and horizontal objects that can be found in a classroom.

It is important to recognize the different shapes and orientations of objects in our environment, as they can affect the way we perceive and interact with them.

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Answer:

i didn't understand what your question is

Answer:

I'm not sure, but maybe try

\((1, -\frac{3}{4} ) or (2,- \frac{3}{2})\)

Plz click the Thanks button!

<Jayla>

Answer:

The answer to y=3x+5 is Only(2,110

For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?