what is 250 divided by 17

To prove that the sequence defined by the recurrence relation satisfies the formula sn = 3 + n(n + 1), we need to show that the base case holds and then prove the inductive step.

To prove that the sequence defined by the recurrence relation satisfies the formula , we need to show that the base case holds and then prove the inductive step.

Base case:

When , we have . This matches the formula, so the base case holds.

Inductive step:

Assume that the formula holds for some . We want to show that it holds for .

Using the recurrence relation, we have:

sn+1 = sn + 2(n+1)

Using the induction hypothesis, we can substitute  in the expression:

sn+1 = (3 + n(n + 1)) + 2(n+1)

Expanding the expression:

sn+1 = 3 + n(n + 1) + 2n + 2

Combining like terms:

sn+1 = 3 + n(n + 1) + 2(n+1)

sn+1 = 3 + (n+1)((n + 1) + 1)

This matches the formula for , so the inductive step holds. Therefore, the formula holds for all integers .

To construct a 95% confidence interval for the difference between the average number of daily intrusion attempts before and after changing firewall settings, you determine the standard deviation and mean for both periods. Use these in the formula for the confidence interval. If the interval doesn't include zero, it indicates a significant difference in the average number of daily intrusion attempts, and thus, potentially a significant reduction in intrusion attempts.

To perform this analysis, we first need to calculate the mean of the numbers of intrusion attempts for both periods - before and after the change of firewall settings. Then, we need to calculate the standard deviation for the numbers of intrusion attempts for both periods. The formula for the confidence interval is Mean Difference ± (Z*Standard Error). Where Z is a standard score value retrieved from the Z distribution table for a particular confidence level, in this case, 95%. The confidence levels you will be working with depend on the number of samples, in this case 14 and 20 respectively.

Once you have the confidence interval, it will give you the range in which the actual difference between the two means lies with 95% certainty. If the interval does not include zero, it indicates a significant difference between the means. By observing whether the values are predominantly positive or negative, we can infer about the significant reduction in the rate of intrusion attempts.

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We have been given that a sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction.

We are asked to find the area of the sector to nearest square foot.

We will use area of sector formula to solve our given problem.

[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where,

[tex]\theta[/tex] = Central angle of sector,

[tex]r[/tex] = Radius.

For our given problem [tex]\theta = 225^{\circ}[/tex] and [tex]r=11[/tex].

[tex]\text{Area of sector}=\frac{225^{\circ}}{360^{\circ}}\times \pi (11)^2[/tex]

[tex]\text{Area of sector}=0.625\times 121\pi[/tex]

[tex]\text{Area of sector}=237.5829444277281137[/tex]

[tex]\text{Area of sector}\approx 238[/tex]

Therefore, the sprinkler can water approximately 238 square feet.

To find the area of the sector, we need to find the central angle, find the fraction of the circle covered by the sector, and then multiply it by the area of the entire circle with a radius of 11 feet.

To find the area of the sector, we need to find the central angle first. Since the sprinkler can only rotate 225∘ in each direction, the total angle covered is 225∘+225∘=450∘.

Next, we need to find the fraction of the circle covered by the sector. We can do this by finding the ratio of the central angle to the total angle of a circle, which is 360∘. This can be calculated as (450/360).

Finally, we multiply the fraction by the area of the entire circle with a radius of 11 feet, which is π(11)^2, to find the area of the sector.

Using the concept of stratified sampling, it is found that 10 people will be selected from those who responded yes.

In a stratified sample, the population is divided into groups, and the same number of elements of each group is surveyed.

In this problem:

A similar problem is given at https://brainly.com/question/24188753

To decide how many participants who answered 'yes' to include in a stratified random sample of 20, use the proportion of 'yes' answers out of 300 to calculate the sample from that stratum.

In a stratified random sample, the population is divided into groups, or strata, and a sample is taken from each group to ensure that each subgroup of the population is adequately represented. To determine the number of people that will be selected from those who responded yes in a stratified random sample, we need to find the proportion of 'yes' responses among the 300 respondents and then apply that proportion to the sample size of 20.

Assuming we know the exact number of people who responded 'yes', let's call that number 'Y'. The number of 'yes' responses in the stratified sample would then be (Y/300) * 20. Without the actual number of 'yes' responses, we cannot compute the exact number of people that should be selected from the 'yes' group. However, this formula demonstrates how you would calculate it once the value for 'Y' is known.

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Answer:

A: 6 Units

Step-by-step explanation:

Answer:

is there more to the question?

Step-by-step explanation:

Answer:

1. is 56

2. is 82

Step-by-step explanation:

Just took the quiz and got it right (Like it please so people know its the correct answer)

Answer:

  ∠3 = ∠4 = 60°

Step-by-step explanation:

Angles 1 and 3 are "remote interior angles" with respect to angle 2, so ...

  ∠2 = ∠1 + ∠3

  120° = 60° + ∠3 . . . fill in known values

  60° = ∠3 . . . . . . . . . subtract 60°

__

Since two of the interior angles in the triangle ABC are 60°, the third one is also. The interior angle at B (supplementary to angle 2) is corresponding to ∠4, so has the same measure as angle 4.

  ∠4 = 60°

Answer: A) 32÷6x5=S

B) 30 sheets of chart paper.

Step-by-step explanation:

we have 32 students.

he puts 6 students into each group.

he gives each group 5 pieces of chart paper.

32/6 will give us the number of groups

32/6 = 5.33

This means that we have 5 complete groups 6 students, and one group with 2 students. (a total of 6 groups)

And each of these groups need 5 pieces of paper, so we have the equation:

(32/6)*5 = S

and S = 26.66

now, for the 5 complete groups we need 5 pieces of paper for each, and 5*5 = 25 pieces of papper.

For the group of 2 persons we have the oter 1.66 ( or 2 if we round up) pieces of papper.

but this is a group, so they also should receive 5 pieces of papper regardless that they are only 2 integrants, then the total number of paper pieces is 30.

Rejection region(s)

t > 2.998

Test statistic value

t = 2.89

Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Option B is the right choice.

State the hypotheses

H0: μD = 0

Ha: μD > 0

State the rejection region

Since the alternative hypothesis is one-sided, we use a one-tailed test. The rejection region for a one-tailed t-test with significance level 0.01 and 7 degrees of freedom is:

t > 2.998

Compute the test statistic

The test statistic for a paired t-test is calculated as follows:

t = ([tex]\bar x[/tex]D - μD) / (sdD / √n)

where:

[tex]\bar x[/tex]Dis the mean difference between the unabraded and abraded breaking loads

sdD is the standard deviation of the difference between the unabraded and abraded breaking loads

n is the sample size

Calculating the mean difference:

[tex]\bar x[/tex]D = (36.3 - 28.5) + (55.0 - 20.0) + (51.2 - 46.0) + (38.6 - 34.0) + (43.2 - 36.5) + (48.8 - 52.5) + (25.6 - 26.5) + (49.6 - 46.5) = 6.85

Calculating the standard deviation of the difference:

sdD = √[((36.3 - 28.5)^2 + (55.0 - 20.0)^2 + (51.2 - 46.0)^2 + (38.6 - 34.0)^2 + (43.2 - 36.5)^2 + (48.8 - 52.5)^2 + (25.6 - 26.5)^2 + (49.6 - 46.5)^2) / 7] = 10.87

Calculating the test statistic:

t = (6.85 - 0) / (10.87 / √8) = 2.89

Make a decision

Since the test statistic (2.89) is less than the critical value (2.998), we fail to reject the null hypothesis.

The correct choice is option d. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

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Question:-

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H0: ?D = 0 versus Ha: ?D > 0 at significance level 0.01. (Use ?D = ?U ? ?A.)
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)

t ? _______

t ? ________

Compute the test statistic value. (Round your answer to three decimal places.)

t = _____

State the conclusion in the problem context.

a.Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to b.reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. c.Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

d.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions

Answer:

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Step-by-step explanation:

The equation of a circle in standard form is

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

You are given

[tex] x^2 + y^2 - 18x + 45 = 0 [/tex]

In order to put the equation in standard from, we need to complete the square. Since there is no y term, the y part is simply y^2, and there is no need to complete the square for y. For x, we do have an x term, so we must complete the square in x.

Start by grouping the x terms and subtracting 45 from both sides.

[tex] x^2 - 18x + y^2 = -45 [/tex]

Now we need to complete the square for x.

[tex] x^2 - 18x ~~~~~~+ y^2 = -45 [/tex]

The number that completes the square will go in the blank above, and it will also be added to the right side of the equation.

To find the number you need to add to complete the square, take the coefficient of the x term. It is -18. Divide it by 2. You get -9. Now square -9 to get 81. The number that completes the square in x is 81. Now you add it to both sides of the equation.

[tex] x^2 - 18x + 81 + y^2 = -45 + 81 [/tex]

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Answer: [tex] (x - 9)^2 + y^2 = 36 [/tex]

Answer:

82.8 centimeters

Step-by-step explanation:

Chandler has 828 millimeters of fabric.

Expressing as a ratio

[tex]\dfrac{1}{x}= \dfrac{10}{828}\\10x=828\\x=828\div 10\\x=82.8 cm[/tex]

Therefore, Chandler has 82.8 centimeters of fabric.

Answer:

82.8 centimeters of fabric

Step-by-step explanation:

1 centimeters= 10 millimeters;

828mm x 1cm ÷10 mm=82.8cm ;centimeters of fabric

The exercise is performed by conversion factor and a smaller unit is transferred to a larger unit that is centimeters.

Answer:

Step-by-step explanation:

if x= -2

and P(x)=x^4+4x^3+6x^2-8

then P(-2)=(-2)^4+4*(-2)^3+6*(-2)^2-8=16-32+24-8=0

so P(x)=(x+2)* Q(x)   and P(x) is divisible by x+2

Answer:

1/4

Step-by-step explanation:

2/4 ÷ 2

Copy dot flip

2/4 * 1/2

We can cancel the 2 in the numerator and denominator

1/4 * 1/1

1/4

Answer:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Step-by-step explanation:

We have the following data given:

62 63 68 72 79 80 83 93 94 95

And we need to begin finding the mean with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]

Now we can find the mean absolute deviation like this:

[tex] |62-78.9| = 16.9[/tex]

[tex] |63-78.9| = 15.9[/tex]

[tex] |68-78.9| = 10.9[/tex]

[tex] |72-78.9| = 6.9[/tex]

[tex] |79-78.9| = 0.1[/tex]

[tex] |80-78.9| = 1.1[/tex]

[tex] |83-78.9| = 4.1[/tex]

[tex] |93-78.9| = 14.1[/tex]

[tex] |94-78.9| = 15.1[/tex]

[tex] |95-78.9| = 16.1[/tex]

And finally we can find the mean abslute deviation with the following formula:

[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]

And replacing we got:

[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]

And the best anwer is

10.12

Answer:

8.5

Step-by-step explanation:

To find mean, we simply take the average of all the numbers in the data set, and divide in by the amount of values!

[tex]8+10+6+4+12+6+8+14= 68\\[/tex]

68 ÷ 8 = 8.5!

Answer:

[tex]8\frac{1}{2}[/tex]

Step-by-step explanation:

First add up all the numbers:

8+10+6+4+12+6+8+14=68

Now you have to divide the sum by the amount of numbers. There are 8 numbers.

[tex]\frac{68}{8}=\frac{34}{4}=\frac{17}{2}[/tex]

[tex]\frac{17}{2}=8\frac{1}{2}[/tex]

Answer: -28

Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.

On the left side, the -4's will cancel

and on the right side, 7(-4) is -28.

So x = -28.

Please do not try to do this problem in your head.

Show the work that it takes to get x by itself.

Answer:

x= - 28

Step-by-step explanation:

-4/1[x/-4 = 7]

x = -28

Answer:bruh

Step-by-step explana

The radius of the table, rounded to the nearest half-foot, is 3.5 feet.

To determine the radius of the circular dining room table, we can use the formula for the circumference of a circle, which is:

C = 2 π r

where:

C - circumference

r - radius

Given that each person has about 2 feet of space along the edge of the table, the circumference of the table must be able to accommodate the seating for 11 people. Each person occupies 2 feet of space, so the total space needed around the edge of the table is:

11 × 2 = 22 feet

We can set up an equation using the circumference formula:

C = 2 π r = 22

To find the radius (r), we divide both sides of the equation by 2π:

r = [tex]\frac{22}{2 \pi}[/tex]

Now, let's calculate the value:

r = [tex]\frac{22}{2 \pi}[/tex] = [tex]\frac{22}{2 \times 3.14}[/tex] = [tex]\frac{22}{6.28}[/tex] = 3.503

Rounding to the nearest half-foot, we get:

r = 3.5 feet

Answer:

1/12

Step-by-step explanation:

hope this helps you

Final answer:

The probability of rolling a 2 on a single 12-sided die is 1/12, which is approximately 8.33%.

Explanation:

If a single 12-sided die is tossed once, the probability of rolling a 2 is calculated by dividing the number of ways to roll a 2 by the total number of possible outcomes on the die. Since there is only one way to roll a 2, and there are 12 different possible outcomes on a 12-sided die, the probability is calculated as follows:

Count the number of favorable outcomes for rolling a 2: There is 1 way to roll a 2.

Count the total number of possible outcomes on a 12-sided die: There are 12 possible outcomes (1, 2, 3, ... 12).

Divide the number of favorable outcomes by the total number of possible outcomes to get the probability: P(rolling a 2) = 1/12.

Therefore, the probability of rolling a 2 on a 12-sided die is 1/12, which can also be expressed as approximately 8.33%.

Answer:

13 meters

Step-by-step explanation:

The perimeter is the sum of all the sides.

As a square has four identical sides, to calculate the length of one side you would simply divide 52 by 4,which gives you 13.

1) Divide 52 by 4.

[tex]52/4=13meters[/tex]

Answer:

13m

Step-by-step explanation:

52/4 = 13

Answer:

7

Step-by-step explanation:

formula for circumference of a circle is [tex]\pi[/tex]d

7[tex]\pi[/tex] = [tex]\pi[/tex]d

d = 7

Answer:

The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 200, \pi = \frac{58}{200} = 0.29[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 - 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.2372[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 + 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.3428[/tex]

The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).

Answer:

[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]

[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]

And the confidence interval for this case would be (0.237; 0.343).

Step-by-step explanation:

We can begin find the proportion estimated of responded that they felt that quality standards have been maintained with the following formula:

[tex]\hat p = \frac{X}{n}[/tex]

And replacing we got:

[tex] \hat p =\frac{58}{200}= 0.29[/tex]

The confidence interval is given by 90%, and the significance level would be [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]

The confidence interval for the true proportion is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the values we got:

[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]

[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]

And the confidence interval for this case would be (0.237; 0.343).

Answer:

She drove [tex]\frac{147}{2} miles/ hour[/tex]

Step-by-step explanation:

We are given that Lydia drove 441 miles in 6 hours.

We are supposed to find how fast did she drive in miles per hour

Distance covered by Lydia in 6 hours = 441 miles

Distance covered by Lydia in 1 hour =[tex]\frac{441}{6}[/tex]

Distance covered by Lydia in 1 hour =[tex]\frac{147}{2} miles/ hour[/tex]

Hence She drove [tex]\frac{147}{2} miles/ hour[/tex]

Answer:b

Step-by-step explanation:

a. The point estimate of the mean price of college textbooks is $145. b. A 90% confidence interval for the mean price is ($133.49, $156.52).

Given a sample of 25 comparable textbooks with a mean price of $145 and a known population standard deviation of $35, the following steps will help answer the questions:

a. Point Estimate:

The point estimate of the mean price of all such college textbooks is simply the sample mean, which is $145.

b. 90% Confidence Interval:

To construct a 90% confidence interval for the mean price of college textbooks, we follow these steps:

Thus, the 90% confidence interval for the mean price of all college textbooks is ($133.49, $156.52).

Answer:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Step-by-step explanation:

Data provided

1.9, 2.4, 3.0, 3.5, and 4.2

We can calculate the sample mean and deviation from this data with these formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}[/tex]

And we got:

[tex]\bar X= 3[/tex]

s=0.903 represent the sample standard deviation

n=5 the sample size

Confidence=95% or 0.95

Confidence interval

We need to begin finding the confidence interval for the population variance is given by:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

The degrees of freedom given by:

[tex]df=n-1=5-1=4[/tex]

The Confidence level provided is 0.95 or 95%, the significance is then[tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical values for this case are:

[tex]\chi^2_{\alpha/2}=11.143[/tex]

[tex]\chi^2_{1- \alpha/2}=0.484[/tex]

And the confidence interval would be:

[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]

[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

[tex] 0.541 \leq \sigma \leq 2.595[/tex]

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Answer:

The train ride is 3.5 hours

Step-by-step explanation:

We know that distance is equal to rate times time

d = rt

We know the distance and the rate

420 = 120*t

Divide each side by 120

420/120 = 120t/120

3.5 =t

The train ride is 3.5 hours

Answer:

3.5 hrs

3 hrs and 30 min

210 min

Answer:

  y = x^2 +8x +16

Step-by-step explanation:

t can be written in terms of x, then substituted into the equation for y.

  x = t -4

  x + 4 = t

  y = t^2 = (x +4)^2

  y = x^2 +8x +16

Answer:

B

Step-by-step explanation:

You can see that the dashes on the number line are going up by 1/4 which is equal to 2/8 (when you multiply 1/4 by 2). At point C your already at 6/8 which is a little larger than 5/8 so when you do a little less than 6/8 you get to point B which is the best answer.

Answer:

Used car have the highest range of 75

Step-by-step explanation:

Yeah the type of car that have the highest range In monthly sales.

we know that

The range is the difference between the highest and the lowest value

First we,

calculate the range in monthly sales for the new car

highest value=51

lowest value=20

range=51-20

range=31

Secondly,we

calculate the range in monthly sales for used car

highest value=87

lowest value=12

range=87-12

range=75

Answer:

My answer: "The car that had the largest range in monthly sales was a used. Through finding the range by subtracting the highest and lowest data points, i was able to find the range for used cars being 75, and for new cars was 31. 75 is larger then 31, so therefore the used cars have the largest monthly range in sales. "

Their sample answer: Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger."

Select all that you included in your explanation.

The range for new cars was 31.

The range for used cars was 75.

Subtract the highest and lowest numbers.

Step-by-step explanation:

edg2020

Answer:

Answer is 2

Step-by-step explanation:

If it shows a graph with Frog Population on top