The diagonals of a rectangle intersect at (0, 0). The rectangle is 6 units long and 4 units wide. Find the coordinates of the four corners of the rectangle

If you have 174 assignments and complete 4 assignments per week, it would take you 43 weeks to finish your work. That is roughly 294 days, given that there are approximately 7 days in a week.

If this is the actual amount of work you need to complete, I applaud you mate. Good luck.

Answer:

Step-by-step explanation:

We must divide the frequency of F grades by the total number of pupils in the class to get the likelihood that a student would receive an F.

The frequency distribution being what it is:

Level: A B C D F

28 35 56 14 7 times each year

You can determine the total number of pupils by adding the frequencies:

Students total: 28 + 35 + 56 + 14 + 7 = 140.

We can now determine the probability:

P(F) = Number of students overall / Frequency of F grades

P(F) = 7 / 140 P(F) = 0.05

As a result, the likelihood that a student will receive a F is 0.05, or 5%.

Answer: The required equation is 100/12 = 8 1/3 which shows 100 ounces of soda divided equally among 12 people.

Step-by-step explanation:

There are 100 ounces of soda divided equally among 12 people.

According to the given information, the algebraic form would be as:

⇒ 100/12 = 25/3

Expressing the solution as a mixed number.

⇒ 100/12 = 8 1/3

Therefore, the required equation is 100/12 = 8 1/3 which shows 100 ounces of soda divided equally among 12 people.

The answer will be 180 .

Given,

15% × 1200.

Firstly convert 15% to fraction form.

Percentage to fraction;

15% = 15/100

Now,

15/100 × 1200

15 × 12

180.

Thus the value of 15% of 1200 is 180.

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You need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

First, 5% of the total cost for four years.

= 0.05 x ($14,895.00/yr x 4 years)

= 0.05 x $59,580.00

= $2,979.00

Second, Divide the total amount you need to pay over four years by the number of years.

= $2,979.00 / 4

= $744.75

Therefore, you need to pay $744.75 for each year of attending college.

Now, the total contribution goal.

= Amount to pay each year x 4 years

= $744.75 x 4

= $2,979.00

and, Monthly savings required

= Total contribution goal / 48 months

= $2,979.00 / 48

= $62.06

Therefore, you need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

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Answer:

Step-by-step explanation:

The expected value E(X) of a random variable X is -1.04

The expected value of a random variable is a measure of its central tendency. It represents the average value that would be obtained if the experiment or process that generates the variable is repeated many times.

To find the expected value of a discrete random variable X with probability distribution P(X), we multiply each possible value of X by its corresponding probability and then sum these products. Symbolically, this can be written as:

E(X) = Σ[x * P(X)]

In words, this formula says that we take each possible value of X, multiply it by its probability, and then add up these products to get the expected value.

In the given problem, we are given the probability distribution of X and asked to find its expected value. We can use the formula above to do this, by plugging in the values of x and P(X):

E(X) = (-9 * 0.16) + (-7 * 0.11) + (-5 * 0.14) + (-3 * 0.17) + (-1 * 0.10) + (1 * 0.32)

E(X) = -1.04

Therefore, the expected value of X is -1.04.

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We have that about 50% of percentage of the students had scores between 485 and 695.

Option B is correct.

A Box-and-Whisker Plot  is  described as a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles.

The box in the plot represents the interquartile range, therefore  the percentage of students who scored between the lower quartile and the upper quartile of the distribution, are those  between the edges of the box.

We take a look at the percentile ranks associated with those scores. and find the  estimate of percentile ranks by drawing a horizontal line at the score values and then reading the corresponding percentile ranks off the y-axis.

With reference from the plot, a score of 485 appears to be at or below the 50th percentile, while a score of 695 appears to be around the 100th percentile.

We then have that the percentage of students with scores between 485 and 695 is likely to be between 100% - 50% = 50%.

The interquartile range represents the middle 50% of the data and the box covers this range.

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Answer:

1260 is the answer

Step-by-step explanation:

you solve for the area of the rectangle and multiply it by 3 because there are three sides so 17x20=340x3=1020 then, you solve for the area of a triangle which is 1/2 x base x height so, 1/2 x 16 x 15 = 120 then you multiply that by 2 since there are 2 triangles so 120 x 120=240 finally, you add 1020+240 = 1260

So we've shown that every pair of vertices in S is connected by an edge in the subgraph induced by S. Therefore, the subgraph induced by S is a complete graph.

To start with, let's clarify what we mean by some of these terms. A graph is just a collection of vertices (or nodes) and edges connecting them. In this case, we're dealing with the complete graph kn, which means that there are n vertices and every possible edge connecting them is included in the graph. So there are a total of n(n-1)/2 edges in the graph.

Now, we're interested in subgraphs of kn. A subgraph is just a subset of the vertices and edges from the original graph. In this case, we're interested in subgraphs induced by nonempty subsets of the vertex set. So if we take some subset of the n vertices in kn, we can look at the edges connecting them and see if they form a complete graph.

So let's say we take some subset of the vertices and call it S. We want to show that the subgraph induced by S is a complete graph. In other words, every pair of vertices in S is connected by an edge.

To see why this is true, let's consider the complement of S, which we'll call S'. This is just the set of vertices in kn that are not in S. Since S is nonempty, S' is also nonempty.

Now, consider any pair of vertices in S. Call them v and w. Since v and w are both in S, they are not in S'. This means that there is an edge connecting v and w in kn, since kn is a complete graph. But since we're only looking at the vertices in S, this edge is also in the subgraph induced by S.

So we've shown that every pair of vertices in S is connected by an edge in the subgraph induced by S. Therefore, the subgraph induced by S is a complete graph.

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The source of bias most relevant to this situation is "perceived lack of anonymity."

When both members of a couple are asked to indicate if they have remained monogamous in their current relationship, they may be hesitant to answer truthfully due to concerns about their privacy or potential repercussions. They might feel that their responses could be traced back to them, which could lead to negative consequences in their relationship. This fear of not being anonymous can result in participants providing inaccurate or dishonest responses.

In a study asking couples about their monogamy, the most relevant source of bias is perceived lack of anonymity, as it may affect the accuracy and honesty of participants' responses.

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The value of the variable 'x' will be 8, 8.1, 9, and 13.

Given that:

Inequality, - x ≤ - 8

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Simplify the inequality, then we have

- x ≤ - 8

x ≥ 8

The value of 'x' is greater than or equal to 8.

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After considering all the given options we conclude that all the options have a greater value than √3.15 except for π/3, then the greatest value from the lot is Option D, which is  6.2 - √(2/2)

In order to evaluate the greatest expression from the lot that has a higher value than √3.15, we have to apply simplification for every option.

Therefore,

π /3) = 1.04

5 - √(3) = 2.2679

1 1/2 - √(2) = 0.0857

6.2 - √(2/2) = 5.2

Therefore, the expression that is  greater than rest of the option and higher in value in comparison to √3.15 is 6.2 - √(2/2)

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Answer:

Have a Nice Best Day : ) Please Give Me Brainliest

The probability of spinning "C" and flipping "heads" is 0.125 or 12.5%.

Assuming the spinner is fair and has 4 equal-sized sections, the probability of spinning "C" is 1/4 or 0.25.

Assuming the coin is fair, the probability of flipping "heads" is 1/2 or 0.5. To find the probability of both events occurring, we multiply the individual probabilities:

The probability of spinning "C" and flipping "heads" is calculated as,

P = (Probability of spinning "C") × (Probability of flipping "heads")

P = 0.25 × 0.5

P = 0.125

Therefore, the probability is 0.125.

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The answer is B. Normal. For a normal distribution, the mean, median, and mode are all equal to each other.

- Mean: The mean of a normal distribution is the center of the distribution, which is also the highest point of the bell-shaped curve.

- Median: The median of a normal distribution is the same as the mean, since the distribution is symmetric around the center.

- Mode: The mode of a normal distribution is also the same as the mean and median, since the highest point of the curve (i.e. the mode) is at the center of the distribution.

For the other probability distributions:

- A. Uniform: A uniform distribution has no mode (or multiple modes), and the mean and median are equal but different from the mode (if it exists).

- C. Exponential: An exponential distribution has a mode of 0, a median of ln(2)/λ, and a mean of 1/λ. Therefore, the mean, median, and mode are not equal.

- D. Poisson: A Poisson distribution has a mode of the integer part of λ (i.e., the highest probability mass function value). The mean and median are both equal to λ. Therefore, the mode is not necessarily equal to the mean and median.

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The general solution of the given system of equations is:

x = Ae^(7t), where A is a non-zero constant.

To find the general solution of the given system of equations, we need to solve the system and express the solutions in terms of the variables.

Given the system:

x' = (13 - 2 - 4)x

We can rewrite the system as:

x' = 7x

This is a linear first-order homogeneous system. The general solution can be found by solving the differential equation.

Separating variables, we have:

dx/x = 7 dt

Integrating both sides, we get:

ln|x| = 7t + C

Taking the exponential of both sides, we have:

|x| = e^(7t + C)

|x| = e^(7t) * e^C

Since e^C is a constant, we can write it as A, where A is a non-zero constant. So we have:

|x| = A * e^(7t)

Now, we consider the sign of x:

If x > 0, then x = A * e^(7t)

If x < 0, then x = -A * e^(7t)

Therefore, the general solution of the given system of equations is:

x = Ae^(7t), where A is a non-zero constant.

To describe the behavior of the solutions as t approaches infinity, we look at the exponential term e^(7t). As t increases, the exponential term grows exponentially, which means the solutions will also grow exponentially. Therefore, as t approaches infinity, the solutions will approach infinity or negative infinity, depending on the sign of the constant A.

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An equation for the parabola that has its x-intercepts at (-2, 0) and (-5, 0) and its y-intercept at (0, -4) is y = -2/5(x² + 7x + 10).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the y-intercept and x-intercepts, we can write the quadratic function and determine the value of "a" as follows:

f(x) = (x + 2)(x + 5)

f(x) = x² + 2x + 5x + 10

f(x) = x² + 7x + 10

f(x) = a(x² + 7x + 10)

-4 = a(x² + 7x + 10)

-4 = a(0² + 7(0) + 10)

-4 = 10a

a = -4/10

a = -2/5

Therefore, the required quadratic function is given by:

y = a(x - h)² + k

y = -2/5(x² + 7x + 10)

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We can use the error bound formula for the midpoint rule to find the smallest value of N for which the error is less than 10^-9:

Error ≤ K(b-a)^3/(12N^2) where K is the maximum value of the absolute value of the second derivative of f on the interval [a,b]. In this case, we have f(x) = x^(4/3) and we need to integrate from 1 to 2.

First, we find the second derivative of f:

f''(x) = (4/3)(1/3)x^(-2/3)

To find the maximum value of the absolute value of the second derivative on [1,2], we evaluate it at the endpoints and at critical points in the interval. Since the second derivative is decreasing on the interval, its maximum value occurs at the left endpoint, x=1:

|f''(1)| = (4/3)(1/3)(1)^(-2/3) = 1.5874

Next, we need to choose N such that the error bound is less than 10^-9:

K(b-a)^3/(12N^2) ≤ 10^-9

Plugging in the values we have:

(1.5874)(2-1)^3/(12N^2) ≤ 10^-9

Solving for N:

N^2 ≥ (1.5874)(2-1)^3/(12(10^-9))

N^2 ≥ 1.3245×10^9

N ≥ √(1.3245×10^9)

N ≥ 36413.89Since N must be an integer, we round up to get:N = 36414

Therefore the smallest value of N for which Error(SN) 10^-9 is 36414.

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We can use the error bound formula for the midpoint rule to find the smallest value of N for which the error is less than 10^-9:

Error ≤ K(b-a)^3/(12N^2) where K is the maximum value of the absolute value of the second derivative of f on the interval [a,b]. In this case, we have f(x) = x^(4/3) and we need to integrate from 1 to 2.

First, we find the second derivative of f:

f''(x) = (4/3)(1/3)x^(-2/3)

To find the maximum value of the absolute value of the second derivative on [1,2], we evaluate it at the endpoints and at critical points in the interval. Since the second derivative is decreasing on the interval, its maximum value occurs at the left endpoint, x=1:

|f''(1)| = (4/3)(1/3)(1)^(-2/3) = 1.5874

Next, we need to choose N such that the error bound is less than 10^-9:

K(b-a)^3/(12N^2) ≤ 10^-9

Plugging in the values we have:

(1.5874)(2-1)^3/(12N^2) ≤ 10^-9

Solving for N:

N^2 ≥ (1.5874)(2-1)^3/(12(10^-9))

N^2 ≥ 1.3245×10^9

N ≥ √(1.3245×10^9)

N ≥ 36413.89Since N must be an integer, we round up to get:N = 36414

Therefore the smallest value of N for which Error(SN) 10^-9 is 36414.

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The end behaviour of the graph of the Polynomial as required to be determined in the task content is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

By observation of the polynomial equation; the degree is 3 which is odd and the leading coefficient is; positive.

Therefore, it follows that the end behaviour is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

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The end behavior of the polynomial y = 2x³ + x² - 45 is:

As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

The degree of the polynomial and the sign of the leading coefficient  describe the end behavior.

Below are rules for determining the end behavior of a function:

a. Even and Positive: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches positive infinity

b. Even and Negative: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches negative infinity

c. Odd and Positive: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

d. Odd and Negative: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches negative infinity.

Given: y = 2x³ + x² – 45

The degree (largest exponent) of the polynomial = 3 (odd)

Leading coefficient (coefficient of largest exponent) = 2 (positive)

Since the degree and leading coefficient are positive and negative respectively.

Therefore, the end behavior of the graph of the polynomial is:

As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

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The solution is, the root of the equation is: (x, y) = (8, 5)

Here, we have,

The equations are:

−5x+8y=0 ...1

−7x−8y=−96 ....2

Adding (1) and (2), we get:

-12x = -96

or, x = 8

⇒ x = 8

Substituting x = 8, in Equation (1), we get:

8y = 5x

8y = 40

⇒ y = 5

Therefore, the root of the equation: (x, y) = (8, 5).

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Answer:

B) 2x12=24 2x7=14

This equals to 24+14

The rate of the boat in still water is approximately 4.67 miles per hour.

Let's assume that the speed of the boat in still water is x miles per hour. Since Kerrie traveled 14 miles upriver and back in a total of 5 hours, we can use the formula:

distance = rate x time

to create two equations:

Upstream: 14 = (x - 3) * t

Downstream: 14 = (x + 3) * (5 - t)

where t is the time it takes to travel upstream.

We can solve for t in the first equation:

t = 14 / (x - 3)

and substitute it into the second equation:

14 = (x + 3) * (5 - 14 / (x - 3))

Simplifying this equation, we get:

14 = (x + 3) * (2x - 7) / (x - 3)

Multiplying both sides by (x - 3), we get:

14(x - 3) = (x + 3) * (2x - 7)

Expanding and simplifying this equation, we get:

2x² - 5x - 45 = 0

Solving for x using the quadratic formula, we get:

x = (5 + √(205)) / 4 or x = (5 - √(205)) / 4

Since the speed of the boat cannot be negative, we reject the negative solution and conclude that the rate of the boat in still water is approximately 4.67 miles per hour.

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The simplified value of log 64 (with base 10) is approximately 2.5.

To solve the logarithm equation log 64, we need to determine the base of the logarithm. Assuming the base is 10 (common logarithm), we can rewrite the equation as: log₁₀ 64

The logarithm function asks the question: "To what power must we raise the base (10) to obtain the given number (64)?" In this case, we need to find the exponent that produces 64 when the base 10 is raised to that power.

To simplify, we recall that 10 to the power of 2 is equal to 100:

10² = 100

Similarly, 10 to the power of 3 is equal to 1000:

10³ = 1000

Since 64 is between 10² and 10³, we can conclude that the exponent will be between 2 and 3. We can estimate that the exponent is closer to 2.5.

Thus, the simplified value of log 64 (with base 10) is approximately 2.5.

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This recursive definition defines the first two terms of the sequence as a1 = 3 and a2 = 6.

A recursive definition for the sequence {an} with closed formula an = 3 * 2^n is:

a1 = 3

an = 2 * an-1 for n ≥ 2

This recursive definition defines the first term of the sequence as a1 = 3, and then defines each subsequent term as twice the previous term. For example, a2 = 2 * a1 = 2 * 3 = 6, a3 = 2 * a2 = 2 * 6 = 12, and so on.

A recursive definition that makes use of two previous terms and no constants is:

a1 = 3

a2 = 6

an = 6an-1 - an-2 for n ≥ 3

This recursive definition defines the first two terms of the sequence as a1 = 3 and a2 = 6, and then defines each subsequent term as six times the previous term minus the term before that. For example, a3 = 6a2 - a1 = 6 * 6 - 3 = 33, a4 = 6a3 - a2 = 6 * 33 - 6 = 192, and so on.

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A 90% confidence interval for the difference in means of two populations with sample sizes of 32 and 43, respectively, can be constructed using the formula [tex]$CI = (\bar{x}_1 - \bar{x}2) \pm t{\alpha/2} * SE$[/tex], where [tex]$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$[/tex] and [tex]$t_{\alpha/2} = \pm 1.695$[/tex].

To construct a confidence interval for the difference in means of two populations, we can use the formula:

[tex]$CI = (\bar{x}_1 - \bar{x}2) \pm t{\alpha/2} * SE$[/tex]

where:

[tex]$\bar{x}_1$[/tex] and [tex]$\bar{x}_2$[/tex] are the sample means for populations X and Y, respectively

tα/2 is the critical value of the t-distribution with degrees of freedom (df) equal to the smaller of [tex](n_1 - 1)[/tex] and [tex](n_2 - 1)[/tex] and α/2 as the level of significance

SE is the standard error of the difference in means, which is calculated as follows:

[tex]$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$[/tex]

Given that a random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y, we can compute the sample means and standard deviations:

Sample mean for population X: [tex]$\bar{x}_1$[/tex]

Sample mean for population Y: [tex]$\bar{x}_2$[/tex]

Sample standard deviation for population X: [tex]s_1[/tex]

Sample standard deviation for population Y: [tex]s_2[/tex]

Sample size for population X: [tex]n_1[/tex] = 32

Sample size for population Y: [tex]n_2[/tex] = 43

Assuming a 90% level of confidence, we can find the critical value of the t-distribution with [tex]$df = \min(n_1-1, n_2-1) = \min(31, 42) = 31$[/tex]. We can use a t-distribution table or software to find the value of tα/2 = t0.05/2 = ±1.695.

Next, we can compute the standard error of the difference in means using the formula [tex]$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$[/tex]

Once we have computed the standard error and the critical value, we can construct the confidence interval:

[tex]$CI = (\bar{x}_1 - \bar{x}2) \pm t{\alpha/2} * SE$[/tex]

This confidence interval will give us an estimate of the true difference in means of the two populations, with 90% confidence that the true difference falls within the interval.

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Rounding off the solution obtained by solving an integer programming problem as a linear programming problem can provide a feasible solution, but it does not guarantee optimality and may require additional analysis

When solving an integer programming problem, we must consider that the decision variables can only take on integer values. However, solving an integer programming problem directly can be computationally challenging. One approach is to first solve the problem as a linear programming problem, which allows for non-integer values of the decision variables. Then, the solution can be rounded off to obtain integer values.

However, rounding off the solution obtained by solving the problem as a linear programming problem does not guarantee optimality. In fact, the values of decision variables obtained by rounding off may be sub-optimal or might violate some constraints. Therefore, it is important to carefully check the feasibility of the rounded off solution before using it in practice.

In summary, rounding off the solution obtained by solving an integer programming problem as a linear programming problem can provide a feasible solution, but it does not guarantee optimality and may require additional analysis.

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A) Null hypothesis (H₀): The mean-life of the light bulbs is equal to 743 hours. Alternative hypothesis (H₁): The mean-life of the light bulbs is less than 743 hours. B)  The critical value for α = 0.05 and 20 degrees of freedom (n-1) to be -1.725. C) The standardized test statistic (t-score) is -2.157. D) Sufficient evidence to reject the manufacturer's claim that the mean-life of the light bulbs is at least 743 hours.

The sample mean of 714 hours, along with the population standard deviation of 57 hours and a significance level of 0.05, leads us to reject the null hypothesis in favor of the alternative hypothesis, indicating that the mean-life of the light bulbs is less than 743 hours.

B) To determine the critical values, we need to consider the significance level (α) of 0.05 and the one-tailed test since the alternative hypothesis is less than. Using a t-distribution table or software, we find the critical value for α = 0.05 and 20 degrees of freedom (n-1) to be -1.725.

C) The rejection region is the left tail of the distribution, where the test statistic is smaller than the critical value. In this case, since it's a one-tailed test, the rejection region corresponds to test statistics less than -1.725.The standardized test statistic (t-score) can be calculated using the formula:t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))[tex]= (714 - 743) / (57 / \sqrt{} (21))[/tex]= -2.157.

D) Since the standardized test statistic of -2.157 falls in the rejection region (-2.157 &lt; -1.725), we can reject the null hypothesis. The evidence suggests that the mean-life of the light bulbs is less than 743 hours. This means there is enough evidence to reject the manufacturer's claim and conclude that the mean-life of the light bulbs is below the guaranteed value.

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The function that represents the situation is y = 125 sin(πt/20).

To construct the graph, we need to first find the equation of the circle that represents the Ferris wheel.

We know that the center of the circle is at the origin and one point on the circle is (125, 0).

Since the radius of the Ferris wheel is not given, we can assume it to be 100 feet (a common value for Ferris wheels).

Using the standard form of the equation of a circle, we get:

x² + y² = r²

Substituting the coordinates of the point (125, 0), we get:

125² + 0² = r²

Simplifying, we get:

r = 125

So the equation of the circle is:

x² + y² = 125²

To find the distance between the car and the horizontal axis at any given time, we need to find the y-coordinate of the point on the circle that corresponds to the angle swept out by the car in that time.

We know that the car takes 40 seconds to make a complete revolution around the Ferris wheel, so the angle swept out in t seconds is:

θ = 2πt/40

Using this angle, we can find the y-coordinate of the point on the circle as:

y = r sin(θ) = 125 sin(πt/20)

We can now plot a graph of y versus t from t=0 to t=40 seconds using a graphing calculator or spreadsheet software.

The resulting graph will show the relationship between the amount of time the car is in motion and the distance in feet between the car and the horizontal axis.

The graph will be a sinusoidal wave with a period of 40 seconds, an amplitude of 125 feet, and a vertical shift of 125 feet (since the lowest point of the Ferris wheel is at y=-125).

The graph will start at y=0 feet when t=0 seconds and will complete one cycle (from y=0 feet to y=0 feet) when t=40 seconds.

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Answer: To solve this problem, we will use the formula d = a2 - a1, where d is the common difference and a1 and a2 are two consecutive terms in the sequence.

Step 1: Identify two consecutive terms in the sequence.

In this case, the two consecutive terms are 13 and 18.

Step 2: Substitute the two consecutive terms into the formula d = a2 - a1.

d = 18 - 13

Step 3: Simplify the equation to calculate the common difference.

d = 5

Therefore, the common difference of the arithmetic sequence 13, 18, 23, 28,... is 5.

Step-by-step explanation: