If X(t) and Y(t) are 2 zero-mean, independent random processes with the following autocorrelation functions RXX​(τ)=e−∣τ∣ and RYY​(τ)=cos(2πτ) Verify through the first two properties, that they are WSS

Answers

Answer 1

To verify that X(t) and Y(t) are wide-sense stationary (WSS) random processes, we need to check two properties: time-invariance of the mean and autocorrelation functions. X(t) and Y(t) are independent zero-mean random processes with specific autocorrelation functions. We will examine these properties to confirm if they satisfy the WSS conditions.

1. Time-invariance of the mean: For a process to be WSS, its mean must be constant over time. Since both X(t) and Y(t) are zero-mean random processes, their means are constant and equal to zero, independent of time. Therefore, the first property is satisfied.

2. Autocorrelation functions: The autocorrelation function of X(t) is given by RXX(τ) = e^(-|τ|), which is a function solely dependent on the time difference τ. Similarly, the autocorrelation function of Y(t) is RYY(τ) = cos(2πτ), also dependent only on τ. This indicates that the autocorrelation functions of both processes are time-invariant and only depend on the time difference between two points. Consequently, the second property of WSS is satisfied.

Since X(t) and Y(t) fulfill both the time-invariance of the mean and autocorrelation functions, they meet the conditions for being wide-sense stationary (WSS) random processes.

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Related Questions

i need help pleaseeeeeee

i need help pleaseeeeeee

Answers

Answer:   \(2^x + 4\)

==================================================

Explanation:

We simply add the expressions we are given, though we cannot combine the terms (as they aren't like terms). There's not much to show in terms of steps, though I guess you could have the following:

\(h(x) = f(x)+g(x)\\\\h(x) = 2^x+4\\\\\)

Adding 4 onto 2^x means we shift the 2^x curve up four units.

Tianna is designing a quilt block. She will cut from two different sizes of
rectangular fabric scraps to create a spiral pattern. Which rectangular
scrap has the longer diagonal?
V149 in.
7 in.
12.2 in.
2.2 in.
10 in.
12 in
1. What does the problem ask you to do?

Answers

Answer: uh I think its a carrot, sorry i hope this could maybe help :)

Step-by-step explanation:

if 4a + 6 = 12 - 2a what is 6a

Answers

___________________________

Hey!!

Solution

4a+6=12-2a

or,4a+2a=12-6

or,6a=6

or,a=6/6

a=1

The value of a is 1.

hope it helps...

Good luck on your assignment

_________________________

value of 6a = 6* 1 = 6

What is linear equation ?

In a linear equation coefficients can be positive or negative values and in which the highest power of the variable is always 1 .

according to question the linear equation given is :

4a + 6 = 12 - 2a

find = 6a ?

4a + 6 = 12 - 2a

6a = 12 - 6

6a = 6

a = 1

since , substituting value of a

6a = 6* 1 = 6

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What is an equation of the line that is parallel to the one shown and passes through (6, −5)?

A. y=−23x−1
B. y=32x−4
C. y=23x+1
D. y=−32x+4

What is an equation of the line that is parallel to the one shown and passes through (6, 5)? A. y=23x1

Answers

Answer:

D is the answer

The equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. \(\mathbf{y = -\frac{3}{2} x + 4}\)

Recall:

Slope of two lines that are parallel to each other will always be the same value.Slope = rise/run

From the graph shown, the slope (m) of the line is \(-\frac{3}{2}\).

Thus, the line that passes through (6, -5) and is parallel to the line in the graph will have the same slope of \(-\frac{3}{2}\).

Write the equation in point-slope form by substituting (a, b) = (6, -5) and m = -3/2 into y - b = m(x - a).

Thus:

\(y - (-5) = -\frac{3}{2} (x - 6)\\\\y +5 = -\frac{3}{2} (x - 6)\)

Rewrite in point-slope form as y = mx + b

\(y +5 = -\frac{3}{2} (x - 6)\\\\y + 5 = -\frac{3}{2} x + 9\\\\y = -\frac{3}{2} x + 9 - 5\\\\\mathbf{y = -\frac{3}{2} x + 4}\)

Therefore, the equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. \(\mathbf{y = -\frac{3}{2} x + 4}\)

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The reporting station originating this Aviation Routine Weather Report has a field elevation of 620 feet. If the reported sky cover is one continuous layer, what is its thickness (tops of OVC are reported at 6,500 feet)?

Answers

The reported sky cover is one continuous overcast layer, its thickness is 5,780 feet.

To calculate the thickness of a cloud layer, you need to subtract the cloud base height from the cloud top height. In this case, the sky cover is reported as one continuous layer, and the cloud top is reported at 6,500 feet.

Aviation Routine Weather Reports (METARs) typically include cloud height information in increments of 100 feet above ground level (AGL). If the sky cover is reported as overcast (OVC) with no height information, it is assumed to be at or below 6,000 feet AGL.

Therefore, the thickness of the cloud layer in this scenario can be calculated as follows:

Cloud base height = 620 feet (field elevation) + 100 feet = 720 feet AGL

Cloud thickness = Cloud top height - Cloud base height

= 6,500 feet - 720 feet

= 5,780 feet

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A new school will have three playgrounds. Two playgrounds will be large and one playground will be small. The district administrator had 3 5/8 truckloads of concrete delivered for each of the two large playgrounds and 1 9/10 truckloads of cement delivered for small playground. If the cost of the concrete is $2,000 per 1/2 truckload, the concrete for the three playgrounds will cost $_____.


Blank options

-18,300

-22,100

-32,600

-36,600


plz help I don't understand this at all.

Answers

Answer:

you multiple two numbers and you devide both sides you get the answer

Shelly and Terrence completed a different number of tasks in a game. Shelly earned 90 points on each task. Terrence's total points were 20 less than Shelly's total. The expression below shows Terrence's total points in the game:

90x − 20

What does the factor x of the first term of the expression represent? (2 points)

Group of answer choices

The total number of tasks Terrence completed

The total number of tasks Shelly completed

The sum of Shelly's and Terrence's total points

The difference between Shelly's and Terrence's total points

Answers

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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What is the difference between frequency distributions and percentage distributions, and how are they used differently

Answers

Frequency distributions, count the number of times each value or range of values appears in a dataset, while percentage distributions show the proportion or percentage of times each value or range of values appears in the dataset.

Frequency distributions are useful for summarizing and describing the distribution of a variable in a data set, while percentage distributions are useful for comparing different variables or subgroups within the data set.

For example, a frequency distribution could be used to show the number of hours of sleep each participant in a study gets per night, while a percentage distribution could be used to compare the number of hours of sleep between males and females in the study.

Frequency distributions and percentage distributions provide different perspectives on the same data set and can be used together to gain a more complete understanding of the data.

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a client shows you the greek vanilla yogurt he eats for breakfast most mornings. determine the calories from protein if the client eats 3/4 cup. 54 calories 72 calories 122 calories 162 calories

Answers

The number of calories from protein if the client eats 3/4 cup is 54 calories. So, the correct option is 54 calories.

Calories are a unit of energy. The energy needed to raise the temperature of 1 gram of water through 1 °C is equal to one calorie. Calories are the energy that food supplies to the body.

Calories from protein: Protein supplies 4 calories per gram. To calculate the total number of calories from protein, you must first know the amount of protein that the food item contains.

To calculate the calories from protein in Greek vanilla yogurt: Greek vanilla yogurt contains about 10 grams of protein per cup.

Therefore, Calories from protein = Protein x 4 = 10 x 4 = 40 Calories per 1 cup Greek vanilla yogurt

If the client eats 3/4 of a cup of Greek vanilla yogurt, the number of calories from protein would be:

Calories from protein = 40 Calories x 3/4 cup = 30 Calories

Hence, the correct answer is 54 calories.

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Please help me out! ​

Please help me out!

Answers

Answer:

a

Step-by-step explanation:

I think its A sorry if u get it wrong

A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test three brands: Powerade, Gatorade and Vitaminwater. He will have each of the athletes complete a 400 meter run and record their times.

Which of the following represents a confounding variable? Mark all that apply.

A. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater.
B. He allows each athlete to choose their favorite drink from a cooler.
C. He has some of the athletes drink the sports drink two hours before running,others one hour before running, and the rest 30 minutes before running.
D. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running.

Answers

Step-by-step explanation:

A confounding variable is a variable that affects the independent and dependent variables and may cause a false association between them. Therefore, in this case:

A. Giving males a different sports drink than females could be a confounding variable since gender may affect their performance.

C. The timing of the sports drink consumption could also be a confounding variable since it may affect the athlete's performance.

D. Giving different brands of sports drinks to the athletes can be a confounding variable since the different formulas in the sports drinks might affect the results.

Therefore, options A, C, and D represent confounding variables. Option B does not represent a confounding variable since allowing athletes to choose their preferred drink from a cooler is a valid way to ensure that each athlete is comfortable with their sports drink.

What is the formula for the indicated variables? A-lw wh + lh, for w

Answers

Hello there. To solve this question, we have to remember some properties about solving equations for a variable.

Given the following equation:

\(A=lw+wh+lh\)

We want to solve it for w.

First, notice we can group some factors

\(A=w\cdot(l+h)+lh\)

Subtract lh on both sides of the equation

\(A-lh=w\cdot(l+h)\)

Assuming l + h is not equal to zero, divide both sides of the equation by this factor

\(w=\dfrac{A-lh}{l+h}\)

This is the answer to this question.

Determine the given equation is a linear equation write yes or no. If yes, write the equation in standard form.
7n - 8m = 4 - 2m.
Use Standard form

Answers

Answer:

The equation is linear. Standard form:

7n - 6m - 4 =0

Step-by-step explanation:

Linear Equations

The linear equations are identified because all terms form a polynomial of degree 1 or zero (no variable).

The standard form of a linear equation is:

ax+by+cz+d=0

where x, y, z are the variables, and a,b,c are constants.

The equation:

7n - 8m = 4 - 2m

Is linear, both variables have an exponent of 1 and there is an independent term. Moving all terms to the left side:

7n - 8m - 4 + 2m =0

Simplifying:

7n - 6m - 4 =0

Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)

Part B: Write a verbal expression for 3(n + 8). (5 points)

Answers

The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

Linear Expression

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

Part A

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word more will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

Part B

The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

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If you fit a slope and intercept at the same time, then their errors will be correlated. True or False?

Answers

The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

What is the intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

The errors of a slope and an intercept will be connected if you fit them simultaneously.

By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.

Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.

Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

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A local salesman receives a base salary of $500 monthly. He also receives a commission of 10% on all sales over $1850. How much would he have to sell in a month if he needed to have a monthly income of $2800 ?

Answers

If the local salesman needed to have a monthly income of $2,800, and receives a base salary of $500 monthly plus a commission of 10% on all sales over $1,850, the sales revenue he must generate is $24,850.

How the sales revenue is computed:

The total sales revenue that can yield a monthly income of $2,800 for the salesman can be computed following these steps:

The base monthly salary of the local salesman = $500

Commission received on all sales over $1,850 = 10%

Expected monthly income = $2,800

a) Total commission received (in dollars) = $2,300 ($2,800 - $500)

b) Sales revenue above $1,850 recorded = $23,000 ($2,300/10%)

c) The total sales to be made = $24,850 ($23,000 + $1,850)

Thus, the salesman's monthly income is based on the sales revenue of $24,850.

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Express 6 1/2 in simplest radical form

Answers

Answer in picture below:

Express 6 1/2 in simplest radical form

The conversion of the exponent into the simplest radical form will be √6.

How do convert the exponent into the simplest radical form?

If an is a true figure and n is a numeric value bigger than 1, then \(\sqrt[\rm n]{\rm a} =\left ( \rm a \right ) ^{\frac{1}{ \rm n}}\), where the symbol is referred to as the radical, and is referred to as the dividing a large, and n is referred to as the index.

If the power of the variable "a" is b/c.

Then the simplest radical form of the expression will be

\(\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}\)

The expression is given below.

\(\rightarrow \left (6 \right ) ^{\frac{1}{2}}\)

The conversion of the exponent into the simplest radical form will be

\(\left (6 \right ) ^{\frac{1}{2}} = \sqrt[2]{(6)^1} = \sqrt6\)

The conversion of the exponent into the simplest radical form will be √6.

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A car travels 22 miles for every gallon of gasoline used. The table below represents the relationship.

Answers

Answer:

22/1 = x/3

Step By Step:

Hope this helps you out in figuring the answer ;]

Answer: i looked up the table so the equation is... 22/1=x/3

x=66

Step-by-step explanation:

Next time include the table but at least it was online!

How to solve: 22 miles per 1 gallon (unit rate) = _(x/?)_ miles per 3 gallons

Cross multiply: 66=1x

x=66

OR 22*3=66, x=66


Can someone pleaseeee help and if you’re correct i’ll give brainliest

 Can someone pleaseeee help and if youre correct ill give brainliest

Answers

Answer:

The total cost would be $208

Step-by-step explanation:

First, we have to find the area of the square office which would be 4yards times 4yards which equals 16yd^2

Next, we'll multiply the area of the square office by $13 (since each square yard of new carpet costs that much).

So 16yd^2 times $13= $208

Hope I helped :)

find the exact value of cos-1 (sqrt 3/2)

Answers

The exact value of cos^-1( √3/2) = 30°

What is trigonometric ratio?

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Integration by Parts Part 1 of 4 Evaluate the integral [(9x (9x + 4)cos(8x) dx. First, decide on appropriate u and dv. U-9x +4 9x + 4 dv = cos(8x) Part 2 of 4 Since u = 9x + 4 and dv = cos(8x) dx, find du and v. du = 9 dx V= sin (8x) sin(8x) 9 Part 3 of 4 Given that du = 9 dx and v= sin(8x), apply Integration By Parts formula. J (9x + 4)cos(8x) dx = dx cos (8x) dx

Answers

It seems there is an error in the given information for integration by parts. Let me correct and complete the steps for you:

Integration by parts formula states that ∫ u dv = uv - ∫ v du.

Part 1 of 4: Evaluate the integral ∫ (9x)(9x + 4)cos(8x) dx.

We need to choose appropriate u and dv:

Let u = 9x + 4 (function with polynomial term)

Let dv = cos(8x) dx (function with trigonometric term)

Part 2 of 4: Find du and v.

Taking the derivatives and antiderivatives:

du = 9 dx

To find v, we need to integrate dv:

∫ dv = ∫ cos(8x) dx = (1/8) sin(8x)

Part 3 of 4: Apply the integration by parts formula.

∫ (9x)(9x + 4)cos(8x) dx = uv - ∫ v du

∫ (9x)(9x + 4)cos(8x) dx = (9x + 4)(1/8) sin(8x) - ∫ (1/8) sin(8x) (9 dx)

Part 4 of 4: Simplify the result.

∫ (9x)(9x + 4)cos(8x) dx = (9x + 4)(1/8) sin(8x) - (1/8) ∫ 9 sin(8x) dx

∫ (9x)(9x + 4)cos(8x) dx = (9x + 4)(1/8) sin(8x) - (9/8) ∫ sin(8x) dx

∫ (9x)(9x + 4)cos(8x) dx = (9x + 4)(1/8) sin(8x) + (9/64) cos(8x) + C

Therefore, the evaluated integral is ∫ (9x)(9x + 4)cos(8x) dx = (9x + 4)(1/8) sin(8x) + (9/64) cos(8x) + C, where C is the constant of integration.

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can someone explain this to me please

can someone explain this to me please

Answers

Answer:

Explanation:

Let x represent the number of call in the first evening, y represent the call in the second evening, and z represent the call in the third evening.

x + y + z = 98 (given)

She received 8 more call (+8) in the first evening more than the second evening.

x = y + 8

She received 4 times (multiply 4) the call in the 3rd evening than the 2nd.

z = 4y

Substitute:

x + y + z = 98
y + 8 + y + 4y = 98
6y + 8 = 98
6y = 98 - 8
6y = 90
y = 15

x = 15 + 8 = 23
y = 15
z = 4(15) = 60

A bleach and water solution with a 2:3 ratio means: A 1/3 part bleach and 2/3 part water B 2 cups of bleach and 3 cups of water C 3 cups of bleach and 2 cups of water

Answers

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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HIII can some ONE PLEASEEEEE help plzzzz

HIII can some ONE PLEASEEEEE help plzzzz

Answers

Answer:5^(-1))^(5)

The third one

Step-by-step explanation:

You make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece of wood. What is the area of the photo prop?

Answers

The area of the photograph when cropped by 10 square inches is,

31.99 ft².

Use the concept of quadrilateral defined as:

A quadrilateral is a shape with four sides, four vertices, and four angles that is only two-dimensional. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Given that,

The height of the photo is = 8 ft

The width of the photo is = 4 ft

The cropped area  = 10 square inches,

Since we know that,

1 square inch  = 0.007 square foot

Therefore,

10 square inches = 0.007 x 10 square foot

10 square inches = 0.07 square foot

The area of the photograph = 8x4

The area of the photograph = 32 square ft

Now the area of the photo after cropping:

32 - 0.07  = 31.99 square ft

Hence,

The required area of the photograph is 31.99 ft².

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The complete question is:

You make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece of wood. What is the area of the photo prop?

You make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece

Ninety-three percent of a town’s population owns cars. If the number of cars owned is 5,208, what is the population of the town?

Answers

Answer:

5600 people is the population is the town

Step-by-step explanation:

Simplify this expression, 3y+14+5y-9

Answers

Answer:

8y+5

Step-by-step explanation:

combine like terms

Answer:

8y+5

Step-by-step explanation:

3y+14+5y-9

we first add 5y+3y

= 8y+14-9

then we do 14-9

=8y+5

giving 5 stars to right person

giving 5 stars to right person

Answers

Answer:

12/40

Step-by-step explanation:

12/40=3/10

Which expressions are equivalent? Choose ALL that apply.
9 to the fourth power
36
9•9.9•9
4 to the ninth power
94

Answers

For the given expressions , the equivalent expressions are as follow:

9 to the fourth power9•9.9•99⁴

As given in the question,

Given expressions are given below:

9 to the fourth power369•9.9•94 to the ninth power9⁴

Simplify and find the equivalent expression from the following given expressions:

9 to the fourth power

=9⁴

= 9 × 9 × 9 × 9

= 6561

36

36 = 6²

    ≠ 6561

9•9.9•9

=9⁴

= 9 × 9 × 9 × 9

= 6561

4 to the ninth power

= 4⁹

= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

=262144

≠6561

9⁴

= 9⁴

= 9 × 9 × 9 × 9

= 6561

Therefore, for the given expressions , the equivalent expressions are as follow:

9 to the fourth power9•9.9•99⁴

The complete question is :

Which expressions are equivalent? Choose ALL that apply.

9 to the fourth power369•9.9•94 to the ninth power9⁴

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Question 19 / 50
In a class of forty students, one fifth of the students also play on the school's
football team. If four more students from the class join the football team, what
percentage of students in the class will be on the football team?
25%
30%
0 33%
O 35%
40%
Submit Answer

Answers

Answer: 30%

Step-by-step explanation:

1/5th of students = 1/5 x 40 = 8

If 4 more students join, they will be (8+4) 12 students

Percentage will be 12/40 x 100 = 30%

Other Questions
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