State the power function that the graph of f resembles for large values of x. Find the end-behavior for the function. Write your results using limit notation

Answers

Answer 1

Notice that:

[tex]\begin{gathered} \lim _{x\rightarrow\infty}\frac{2x^2(x-5)^2}{x^4}=\lim _{x\rightarrow\infty}\frac{2(x-5)^2}{x^2} \\ =\lim _{x\rightarrow\infty}\frac{2(x^2-10x+25)}{x^2} \\ =\lim _{x\rightarrow\infty}(\frac{2x^2}{x^2}-\frac{10x}{x^2}+\frac{25}{x^2}) \\ =\lim _{x\rightarrow\infty}(2-\frac{10}{x}+\frac{25}{x^2}) \\ =\lim _{x\rightarrow\infty}2-\lim _{x\rightarrow\infty}\frac{10}{x}+\lim _{x\rightarrow\infty}\frac{25}{x^2} \\ =2-0+0 \\ =2 \end{gathered}[/tex]

Which means that, for large values of x:

[tex]2x^2(x-5)^2\approx2x^4[/tex]

Since the function:

[tex]f(x)=2x^4[/tex]

is a 4th degree monomial, with positive coefficient, then it keeps growing as x grows. Then, we know that:

[tex]\lim _{x\rightarrow\infty}2x^2(x-5)^2=\infty[/tex]

Which means that the end behavior is such that f(x) approaches infinity as x approaches infinity.

On the other hand, for large negative values of x, the function is also positive. Then:

[tex]\lim _{x\rightarrow-\infty}2x^2(x-5)^2=\infty[/tex]

Related Questions

the file p02 45.xlsx contains the salaries of 30 business school professors at a (fictional) large state university. if you increased every professor's salary by $4,000, what would happen to the mean and median salary?

Answers

We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be

Y = 1/n∑Yi

Y = 1/n∑(Xi + 4000)

Y = 1/n(∑Xi + ∑4000/n)

Y = X + 4000

Median Xm is the middle most value of the Professor's old salary, since new salary is

Yi = Xi + 4000

then new median salary Ym will be

Ym = Xm + 4000

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Answer:

Step-by-step explanation:The mean and Median salary would increase by $4,000.

Let sum of the salaries be n1+n2+n3+.......... +n30

Mean = sum of observation / no. of observation

Thus,

Initial mean, M1 = n1+n2+n3+.......... +n30 / 30

When $4,000 is added to every salary 4000 is added 30 times to the sum.

Thus,

New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)

= M1 + ( 4000 * 30)

Thus, M2 = M1+ 4000

Therefore, The mean salary increase by $4,000.

We know Median of even number of observation = [(n/2)th term + ((n/2) + 1)th term]/2

Here n/2th term is n15 and (n/2 +1)th term is n16

Thus,

Initial Median, Median 1 = n15 + n16

When $4,000 is increased in each salary

New Median, Median 2 = n15 + 4000 + n16 + 4000

= Median 1 + 2 * 4000

Thus, Median 2= Median 1 + 4000

Therefore, The median salary increases by $4,000

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an urn contains 18 red marbles and 15 blue marbles. 12 marbles are chosen. in how many ways can 7 red marbles be chosen? a) 792 b) 95,567,472 c) 34,827 d) 31,824 e) 126 f) none of the above.

Answers

The total number of ways 7 red marbles can be chosen is 95,567,472 i.e., option b is correct.

12 marbles are chosen in which 7 are red marbles and remaining marbles, which are 5, are blue marbles.

In order to find in how many ways 7 red marbles can be chosen we will follow the steps mentioned below:

Out of 18 red marbles 7 are chosen and out of 15 blue marbles 5 are chosen. So, we can write

Total number of ways 7 red marbles can be chosen= [tex]18C_{7}[/tex] × [tex]15C_{5}[/tex]

Total number of ways 7 red marbles can be chosen= [tex](\frac{18!}{7! (18-7)!} )[/tex][tex](\frac{15!}{5! (15-5)!})[/tex]

Total number of ways 7 red marbles can be chosen= 31824 × 3003

Total number of ways 7 red marbles can be chosen= 95,567,472

Thus, we can conclude that in 95,567,472 number of ways 7 red marbles can be chosen.

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Use the Distributive
nt Property to find an equivalent
expression:
5(3x-7)

Answers

15x-35 hope this helps

The owner of a restaurant wants to move the restaurant from Braddock Avenue to a new location onKnox Avenue that has more foot traffic. The owner would also like to double the perimeter of therestaurant due to the expected increase in business but keep the overall shape exactly the same, asshown in the coordinate plane.

Answers

We want to find a series of transformations that change the polygon ABCD into the polygon A'B'C'D'.

We see that a counter-clockwise rotation must be necessary, as:

By doing a traslation of 4 units to the right, and a dilation by a scale factor of 2, we obtain the desired figure. This is, the answer is B.

Math
I need an explanation too btw

Answers

The transformation from the graph of f to the graph of g is reflection in the x-axis.

We are given the function f(x) = -4x + 8

Also it says that g(x) = -f(x)

= 4x - 8

Since f(x) is a linear function, the graph of f(x) and hence the graph of g(x), both are straight lines. But the graph of g(x) will be a transformed image of the graph of f(x).

Here, if f(x) = y, then the transformation from f(x) to g(x) can be represented as, (x, y) -------> (x, -y)

This transformation corresponds to the reflection in the x-axis. When reflected along x-axis, the x- co-ordinate does not change, but the y- co-ordinate changes its sign. This is exactly what happens when the function f(x) is transformed to g(x) = -f(x).

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Approximate pi plus the square root of forty to the nearest hundredth.

Answers

To the nearest hundredth, pi + the square root of forty roughly equals 9.47. The best choice is B.

What does it mean to round a number to a particular place?

Rounding a number to a particular value reduces the complexity of the number while increasing readability and accessibility.

When you round to a certain point, the exact digits are maintained on the left side of that point but are rounded or somewhat trimmed from the right.

The limit is set at five.

All right-sided values are made zero if the right-side digit to the digit where we must round off is less than or equal to five; otherwise, it is increased by one and the remaining right-side digits are made zero. If the digit to the right of the decimal point is 5, and there are just zeros or no values after it, we round up (raise by 1 as in 347500 to 34800). (Well there are many detailed rules of rounding)

The following can be used to represent the provided expression, "pi plus the square root of forty to the closest hundredth,"

π + √40

= 3.1416 + 6.3245

= 9.4661 ≈ 9.47

Value is therefore 9.47.

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recall the birthday paradox problem: take a random sample of size k with replacement from the set {1, 2,⋯, 365}. let pk be the probability that there is repetition in the sample (there are at least two people who share a common birthday).

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the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%

In this question, you are asked the probability for any of the 2 person to have the same birthday. To answer this it will be easier to calculate how much the probability for no one has same birthday. Let say the first person birthday is 1. Then the next person birthday should be other than 1, which mean 364 possible days out of 365 days.

Then the calculation for 2 people would be:

(365!/365-2!)/(365^(2)= (365!/363!)/ 365^2= 0.9972=99.72%

Then the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%

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Name two transformation sequences that can be done in any order without changing the outcome and explain how you know.

Answers

Answer:

There are two different categories of transformations: The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.

Step-by-step explanation:

yep sorry if you get it wrong it is

Write an equation that represents your total earnings based on the price of your item and how many you sell.
The price of the item is $3, and I sell 40 items.

Answers

Answer:

y = 3(40)

Step-by-step explanation:

Let's break it down:

Total earnings = y

Price of item = 3

Amount of items sold = x (in this case 40)

For A Brainlist !!Please help its Urgent I need Help I think its C i dont know

Answers

Answer:

It would be 4/(-1) , which is -4

Step-by-step explanation:

You take f(1) and g(1) and then divide them to get f/g of (1)

Hello!

Let's solve:

[tex]\dfrac{f}{g} (1)=\dfrac{f(1)}{g(1)} \\\\\\\\\text{Plug in the value for f(1) and g(1) given by the table}\\\\\dfrac{f(1)}{g(1)}=\dfrac{4}{-1} =-4[/tex]

Answer: -4

Note:

To find value of f(1) and g(1) on the table

Start on the top bar of the chart (value of x)Move horizontally to the right until you reach the number 1. You have just now reached x when it is equal to 1Now move down one step into the box below the '1'. You have just found f(1)Now move down one more step into the box below f(1)'s value. You have just found g(1)

Hope that helps!

b) Solve x^2 + 5x + 6 = 0

Answers

Answer: (x+2)(x+3)

Step-by-step explanation:

1) Try to simplify with the line method

List the multiplicative numbers for a and c.

x^2 + 5x + 6 = 0

1x-----------> 3

1x-----------> 2

3 + 2 = 5

Make sure the two numbers multiply-add to b

Afterward, flip the top and bottom numbers.

1x--------------> 2

1x--------------> 3

Put them into an equation.

(x+2)(x+3)

Convert the following percents to fractions and decimals. SHOW YOUR WORK
1. 89%
2. 35%
3. 64%

Answers

After conversion, the percentages in fractions and decimals are:

89/100, 0.897/20, 0.3514/25, 0.64

Calculations and Parameters

Recall that a percentage is over 100 and the symbol is %

Therefore, for 89%, it would be 89/100.

This is the fraction, then the decimal would be 0.89

For 35%, the fraction would be 35/100

We break it down to the lowest value possible, it would be 7/20. This is the fraction, the decimal is 0.35

For 64%, it would be 64/100

It would be broken down to the lowest value possible which would be 14/25

The decimal would be 0.64

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Tickets for an Amtrak train cost $21 for children and $49 for adults. Josie paid $3,332 for a total of 88 tickets. How many children tickets and how many adult tickets did Josie buy?

Answers

SOLUTION:

Case: System of equation word problem

Required: Find the number of adults and children tickets Josie bought.

First we create a system of equation. One for the total number of tickets, the other for the total cost of tickets.

Assumption: Let the number of adult tickets be a and the number of children tickets c.

Sytems of equations:

[tex]\begin{gathered} a\text{ + c= 88. (ticket equation)} \\ 49a\text{ + 21c = 3332. (Cost equation)} \end{gathered}[/tex]

Solving the system of equation, using substitution method

[tex]\begin{gathered} \text{Make c the isolated variable from ticket equation} \\ c=\text{ 88-a} \\ \text{Substitutute in Cost equation.} \\ 49a\text{ + 21c = 3332. } \\ 49a\text{ + 21(88-a) = 3332. } \\ 49a\text{ + 1848 - 21a = 3332. } \\ \text{Taking like terms} \\ 49a\text{ - 21a = 3332 - 1848} \\ 28a\text{ = }1484 \\ Divide\text{ both sides by 28} \\ a=53 \end{gathered}[/tex]

Next we find the value of c

[tex]\begin{gathered} We\text{ plug in the value }a\text{ in the isolated variable equation} \\ c=\text{ 88 - a} \\ c=\text{ 88 - 53} \\ c=\text{ 35} \end{gathered}[/tex]

Final answers:

The total number of children tickets bought were 35 WHILE

The total number of adult tickets bought were 53.

write an equation for the line shown on the right. answer needs to be in slope-intercept form.

Answers

Answer: [tex]y\text{ = }\frac{3}{8}x\text{ + 2}[/tex]

Explanation:

Given:

A linear graph

To find:

the equation of the line

The formula for linear equation is given as:

y = mx + b

m = slope

b = y-intercept

We need to get the slope and y-intercept of the line. To get the slope, two points will be picked on the line

Using points: (-8, -1) and (0, 2)

[tex]\begin{gathered} slope\text{ = }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=-8,y_1=-1,x_2=0,y_2\text{ = 2} \\ m\text{ = }\frac{2-(-1)}{0-(-8)}=\frac{2+1}{0+8} \\ m\text{ = 3/8} \end{gathered}[/tex]

The y-intercept is the value of y when x = 0. On the graph, it is the value of y when the line crosses or touches the y-axis.

The line crosses the y axis at y = 2

b = y-intercept = 2

The equation of the line in slope-intercept form becomes:

[tex]y\text{ = }\frac{3}{8}x\text{ + 2}[/tex]

Solve the equation 6 = -3(s+2)

Answers

Answer:

-4 = s

Step-by-step explanation:

6=-3(s+2) multiply -3 into the parenthesis.

6=-3s-6 add 6 to the other side

12=-3s divide by -3 on both sides.

-4=s

Which expression is equivalent to 2(−4.1s − 3.4)?

−2.1s − 3.4
−2.1s − 6.8
−8.2s − 3.4
−8.2s − 6.8

Answers

Answer:

D. −8.2s − 6.8

Step-by-step explanation:

Hope this helps you! :))

Action movies make up 80% of Devons movie collection. If she has 40 movies, how many action movies are in Devons collection

Answers

The number of action movies are in Devon's collection are, 32.

What is percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given: Action movies make up 80% of Devon's movie collection. She has 40 movies.

We can find the number of Devon's movie collection by multiplying its percentage by the number of Action movies. That is;

Number of Devon's movie collection = [tex]\frac{80}{100} (40) = 32[/tex]

Therefore, Therefore he has 32 movies that are in Devon's collection.

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help please!!!!!!!!!!!!

Answers

In the estimation, the missing values are 8 and 1 respectively.

How to work out the missing values

Approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up.

Since the number after the digit 8 in 8.41 is 4, we will round down 8.41 to 8

Also, the number after the digit 0 in 0.61 is 6, so we will round up 0.62 to 1

Therefore, the missing values in the estimation are 8 and 1 respectively.

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Please please someone help me on this!!! ( 30 points + brainliest )

Answers

m<A, which is 48 degree.

The values of mL and mJ are 55 and 61 degrees, respectively.

Since vertical angles are equal in magnitude and are created by intersecting two lines, they are known as the opposing angles.

what are the explanation of the problems?

1.Angles in the vertical plane coincide. They are equal in size, thus this indicates. Calculate x x = 4x - 24 by putting them on an equal footing. In the equation, deduct x from both sides.

o = 3x - 24 On both sides, add 24.

24 = 3x Divide both sides by 3

Multiply both sides by 3

8 to get x

m<A, which is 8.

4x-24

=3*8+24=24+24=48 degree

2.We can thus write,

The angles L and Z are vertical.

∠L = 2x + 9 and,

∠Z = 3x - 14.

Given that both angles are vertical,

∠L = ∠Z

2x + 9 = 3x - 14

Continuing to solve

3x - 2x = 9 + 14

x = 23

The value of L is therefore,

= 2(23)+9

= 46+9

= 55°

Angle L has a value of 55°.

2. Y and J are equal because they are both vertical angles.

∠Y = 7x + 12

∠J = 10x - 9

∠Y = ∠J

7x + 12 = 10x - 9

Continuing to solve

3x = 21

x = 7

So, the value of ∠J is, = 10(7) - 9 = 70 - 9 = 61°

The value of ∠J is 61°.

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it has been determined with 95% confidence that the proportion of on-line students at spc who live in pinellas county is between 0.73 and 0.77. determine the margin of error associated with this confidence interval.

Answers

The margin of error associated with the confidence interval is 0.02.

The 95% confidence interval for the population proportion is defined as:

p ± z(0.05 / 2) × √[p ( 1 − p )/ n]

We have,

p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 ----------- ( 1 )

p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.77 ----------- ( 2 )

Adding the above two equations,

p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] + p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 + 0.77

2p = 0.73 + 0.77

2p = 1.5

p = 0.75

Now, Subtracting the equations ( 1 ) and (2),

We get,

p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] - p - z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 - 0.77

−2 × z(0.05 / 2) × √[ p ( 1 − p )/ n ] = -0.44

z( 0.10 / 2) × √[ p ( 1 − p )/ n] = 0.02

The margin of error is defined by the formula:

M E = z(0.05 / 2) × √[ p ( 1 − p )/ n]

Therefore, The margin of error will be:

M E = 0.02

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Find the Highest Common factor of 60 and 96

Answers

Answer: hi someone else answered this but you should report it its not an answer anyway here is the answer. 12

Step-by-step explanation:

write out the factors of both numbers:

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

then find the highest number in both, 12.

and thats the hcf. hope this helped but report that person they are not helping. :)

I’ll give brainliest!! What is the standard form of the equation for a line that passes through (1, 2) and that has a slope of -4?

PLEASE SHOW WORK OR EXPLAIN

Answers

Answer:

[tex]y=-4x+6[/tex]

Step-by-step explanation:

Point Slope Form = Y-y1=m(X-x1)

m=-4, (x1,y1) = (1,2)

y-2=-4(x-1)

y-2=-4x+4

y=-4x+6

(Lol please give Brainliest if I'm correct :] )

I need to show a picture of the problem

Answers

x and y intercepts are the points where lines cut off the x and the y axis respectively.

In this case, the line cuts the x axis at x=-8. It means that the x intercept of the line is (-8,0).

The line also cuts the y axis at y=-6, which means that the y intercept of the line is (0,-6).

Suppose that 3 j of work is needed to stretch a spring from its natural length of 24 cm to a length of 33 cm. (a) how much work is needed to stretch the spring from 29 cm to 31 cm? (round your answer to two decimal places.) (b) how far beyond its natural length will a force of 15 n keep the spring stretched? (round your answer one decimal place.)

Answers

a) 14.81 J of work is needed to stretch the spring from 29 cm to 31 cm.

b) 2 cm far beyond its natural length will a force of 15 N keep the spring in stretched position.

It is mentioned that 3 J of work is needed to stretch a spring from its natural length of 24 cm to 33 cm.

We know the work done on the spring is expressed by the following given equation:

[tex]W=\frac{1}{2} ke^{2}[/tex]

Where, W = workdone that is done on the spring

k = elastic constant

e = extension of the given material

So, Work (W) = 3 J and e = 33 cm - 24cm = 9 cm = 0.09 m

So, putting the above values we calculate the value of 'k' as below:

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ [tex]3=\frac{1}{2} k(0.09)^{2}[/tex]

⇒ 3 x 2 = 0.0081k

⇒ k = [tex]\frac{6}{0.0081}[/tex] N/m

⇒ k = 740.74 N/m

a) Now using the same formula for work, we will determine the amount of work that is needed to stretch the spring from 29 cm to a length of 31 cm.

k = 740.74 N/m

e = 31 cm - 29 cm = 2 cm = 0.02 m

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ W = [tex]\frac{1}{2} (740.74) (0.02)^{2}[/tex]

⇒ W = 14.81 J

The work that is done to stretch the spring from 29 cm length to 31 cm is 14.81 J.

b) From the Hooke's law we have, F = ke, where F is the force applied on the spring. Now here we have been given that a force of 15N is applied and we have to find the 'e' that is the extennsion in the natural length of the given spring.

k = 740.74 N/m

F = 15 N

F = ke

⇒ 15 N = 740.74 x e

⇒ e = [tex]\frac{15}{740.74}[/tex] m

⇒ e = 0.02 m = 2 cm

Therefore the natural length of the spring will be stretched by a length of 2 cm when a force of 15 N is applied.

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PLEASE HELP ASAP!!!!!!!!!!! Point A is one vertex of triangle ABC. Point B is the x-intercept of 6x−4y=−12 and point C is the y-intercept. What are points B and C? Sketch the triangle in the coordinate plane.

Answers

That’s a hell of a question

Ok the line given is equal to y=3/2x+3

Y-intercept is (0,3) = C

X-intercept is (-2,0) = B

And A can go anywhere

What are the slopes of these lines and how are they perpendicular

Answers

Answer:

Line A's slope is 2 and Line B's slope is 1/2.

Step-by-step explanation:

The slope of perpendicular lines is such that the slope of one line is the negative reciprocal of the slope of another line

4/6= ? x 1/6 what number makes the equation

Answers

The first step here is to write out this question as a proper algebraic expression. That means you assign a letter to the question mark and you now have;

4/6 = y * 1/6

(Note that the symbol * represents the multiplication sign)

y * 1/6 can be re-written as y/6 since it is actually y/1 * 1/6

Therefore you now have;

4/6 = y/6

Cross multiply and you now have,

4 * 6 = y * 6

24 = 6y

Divide both sides of the equation by 6 (to eliminate the 6 on the right hand side)

4 = y

Therefore the number that should be in the question mark is 4.

identify the incorrect statement describing the sample sizes and time frames for conducting the various stages of human clinical trials: group of answer choices stage 3: 500-50,000 individuals - usually 4-5 years stage 4: millions of individuals - between 1-2 years stage 1: 5-50 individuals (healthy, young); few weeks to months stage 2: 50-500 individuals (cross section, more cohorts) - months to years

Answers

The incorrect statement is 50-500 individuals (cross section, more cohorts) - months to years

The answer provided above has been developed in a clear step by step manner.

Stage 1: 5-50 individuals (healthy, young); few weeks to months is correct considering the hypothesis

Second option is incorrect

Stage 2: 50-500 individuals (cross section, more cohorts) - months to years

Stage 3: 500-50,000 individuals - usually 4-5 years is also correct

Stage 4: millions of individuals - between 1-2 years is also correct

Appropriate sample size generally depends on the specified statistical hypotheses and a few study design parameters. These include the minimal meaningful detectable difference (effect size), estimated measurement variability, desired statistical power, and significance level

Therefore,50-500 individuals (cross section, more cohorts) - months to years can't be used to describe the sample sizes and time frames for conducting the various stages of human clinical trials

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Solve this inequality:
5w-4>59-2w

Please show working out

Answers

Step-by-step explanation:

5w - 4 > 59 - 2w

add 4 to both sides:

5w - 4 + 4 > 59 - 2w + 4

5w > 63 - 2w

subtract 2w from both sides:
5w - 2w > 63 - 2w - 2w

3w > 63

divide both sides by 3:

3w/3 > 63/3

w > 21

in internal notation: (21, ∞)

The stadium design currently has a 3:2 ratio of premium seats to bleacher seats (12,000 premium seats and 8,000 bleacher seats). If the team wants to keep the total of premium seats and bleacher seats at 20,000 but wants to change the ratio to 4:1, how many of each seat would the stadium have?

Answers

To keep the total seats still at 20,000 but change the ratio to 4 : 1; the number of premium and bleachers seats the stadium would have are; 16,000 and 4,000 respectively.

What number of premium and bleacher seats would the stadium have?

It follows from the task content that the total number of seats which the stadium would have if the ratio is to be changed to 4:1 be determined.

Since the number of seats, 20,000 remains constant.

To divide the number 20,000 in the ratio; 4 : 1;

The number of premium seats would be; (4/5) × 20,000 = 16,000 seats.

And the number of bleacher seats would be; (1/5) × 20,000 = 4,000 seats.