Given l||m||n, find the value of x

The answer is 3√3ln|√3x^2-13|+C, where C is the constant of integration. Evaluating this at the limits of integration (0 and 2), we get 3√3ln(2√3-13)-3√3ln(-13)+C, which simplifies to approximately 1.728. Therefore, the answer in numerical is 1.728.
To evaluate the integral ∫(6x dx)/(√(3x²-13)), first, we need to recognize that this is an integral of the form ∫(f'(x) dx)/f(x). Here, f(x) = √(3x²-13) and f'(x) = 6x. This means we can use the natural logarithm rule to solve the integral.

∫(6x dx)/(√(3x²-13)) = ∫(f'(x) dx)/f(x) = ln|f(x)| + C

Now, substitute f(x) back in:

= ln|√(3x²-13)| + C

Now, we can rewrite the square root as a power of 1/2:

= ln|(3x²-13)^(1/2)| + C

This is the general solution to the integral.

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From the calculation, you are 100 m away from the plateau.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards, or the angle between the horizontal and the line of sight when an observer is looking upward.

We know that;

Angle of elevation = 35°

Height of the Plateau = 70 m

Thus;

Tan 35 =70/x

x = Your distance from the plateau.

x = 70/Tan 35

x = 100m

In trigonometry and geometry, the angle of elevation—which can be expressed in degrees, radians, or other angular units—is frequently employed to address issues with heights and distances.

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Answer:

m=2

Step-by-step explanation:

The area of the shaded portion of the circle which is a sector of the circle would be = 11/9π

To calculate the area of the shaded portion, the radius of the circle should first be determined through tye formula of the length of an arc.

That is;

Length of an arc = 2πr(∅/360)

But length of an arc = 11/9π

∅ = 110°

That is:

11/9π = 2×π×r(110/360)

π will cancel out on both sides;

11/9 = 2×r× 0.3056

11/9 = 0.6111r

r = 11/9×0.6111

r = 2

Area of the shaded sector of the circle = ∅/360×πr²

radius = 2

area = 110/360× π × 2×2

= 110/90π

= 11/9π

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The remaining piece of board is 8 and 5/12 inches long, and it is long enough to make a 7-inch by 7-inch square.

The total length of the board is 23 and 4/16 inches, which can be simplified to 23 and 1/4 inches.

To replace the shelf, Cindy needs a piece of board that is at least 7 and 15/16 inches long, which is the length of the shelf minus the width of the board (7 and 1/4 inches) and the width of the replacement square (7 inches).

So, the minimum length of the board needed for the shelf and the square is 7 and 15/16 + 7 = 14 and 15/16 inches.

Therefore, the remaining length of the board is 23 and 1/4 - 14 and 15/16 = 8 and 5/12 inches.

To determine if this remaining length is long enough for the 7-inch by 7-inch square, we need to calculate the diagonal of the square, which is √(7^2 + 7^2) = 9.899 inches (rounded to three decimal places).

Since the remaining length of the board is longer than the diagonal of the square, it is long enough to make the square.

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The discount amount of the bike Sarah wants to buy is $60. The calculation was done by using the formula: Discount = Original price x Percent off.

To find the discount amount of the bike, we need to use the formula

Discount = Original Price x Discount Rate

where Discount Rate = Percent Off / 100

We know that the original price of the bike is $150 and it is now 40% off. So, the discount rate is

Discount Rate = 40 / 100 = 0.4

Substituting these values in the formula, we get:

Discount = $150 x 0.4 = $60

Therefore, the discount amount of the bike is $60.

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It would take approximately one minute and a half (or 1.6 minutes) to reach 100 jumping jacks at this rate.

What was the activity?

The dependent variable is the number of jumping jacks completed in a specific time period. In this case, the number of jumping jacks completed in one minute is the dependent variable.

The independent variable is the time in minutes. This means that the number of jumping jacks completed is influenced by the time spent doing the activity.

The relationship between the dependent variable (number of jumping jacks completed) and the independent variable (time in minutes) is directly proportional, with a ratio of approximately 63 jumping jacks per minute. This means that for every one minute spent doing jumping jacks, approximately 63 jumping jacks can be completed.

To calculate how much of the activity would be completed if this rate was maintained for 12 minutes, we can multiply the rate (63 jumping jacks per minute) by the time (12 minutes), which gives us 756 jumping jacks.

To find out how long it would take to reach 100 jumping jacks, we can set up a ratio:

63 jumping jacks / 1 minute = 100 jumping jacks / x minutes

We can solve for x by cross-multiplying:

63x = 100

x = 100 / 63

x ≈ 1.6

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68 – 0. 2 = T and 0. 2(68) = T equation can be written to model this scenario. The correct options are A and C.

The equation 68 – 0.2(68) = T is correct since it represents the total cost after the 20% discount is applied.

The equation 68 – 0.2 = T is not correct since it does not correctly calculate the total cost after the discount.

The equation 68 – 20 = T is not correct since it subtracts the discount amount from the original price, which would give the discounted price before the discount, not the total cost after the discount.

The equation 0.8(68) = T is not correct since it calculates the discounted price, not the total cost after the discount.

Therefore the correct options are a and c.

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Answer:

2π/3 or 120°

Step-by-step explanation:

To find a reference angle, we either subtract 2π or 360°

For this one we do 8π/3 - 2π

Which is equal to 2π/3 which is equivalent to 120° which I assume is what the question is asking for

The circumference of a circle with a diameter of 8.7 units is approximately 27.318 units, calculated using the formula Circumference = πd. So, the correct answer is D).

The formula for the circumference of a circle is given by

Circumference = πd

where d is the diameter of the circle.

Substituting the given value of the diameter of circle a, we get:

Circumference = π x 8.7

Using the approximation of π = 3.14, we get

Circumference = 3.14 x 8.7

Circumference = 27.318 units (rounded to three decimal places)

Therefore, the circumference of the circle with a diameter of 8.7 units is approximately 27.318 units. So, the correct option is D).

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--The given question is incomplete, the complete question is given

" The diameter of circle a is 8.7 units. find the circumference of the circle.

a. 17.4 units

b. 75.69 unit

c. 8.7 units

d. 27.318 units "--

If all three conditions are met, then the two-sample t-test can be used to test the hypotheses.

For testing the hypotheses in part A, a two-sample t-test for independent means can be used to compare the mean speed of the baseball line drive using the old technique to the mean speed using the new technique. The conditions for the t-test are:

Independence: The 42 hits using the new technique should be independent of the hits using the old technique.

Normality: The speeds using the new and old techniques should be normally distributed. This can be checked by creating a histogram of the speeds and checking for a roughly bell-shaped curve.

Equal variances: The variance of the speeds using the new technique should be approximately equal to the variance of the speeds using the old technique. This can be checked by using a statistical test for equal variances, such as Levene's test.

If all three conditions are met, then the two-sample t-test can be used to test the hypotheses.

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The area of the circle is approximately 202.03 square feet

If the circumference of a circle is 50.4 ft, we can use the formula for the circumference of a circle to find its radius:

C = 2πr

C = circumference

r = radius

r = C / (2π)

Substituting C = 50.4 ft, we get:

r = 50.4 / (2π)

Using a calculator, we can approximate this value to be:

r =25.2/π ft

A circle's area can be calculated using the following formula:

A = πr²

Substituting r = 25.2/π ft, we get:

A = π(25.2/π)²

= 635.04/3.14

= 202.03

Therefore, the area of the circle is approximately 202.03 square feet.

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We need a sample size of at least n = 214 students to estimate the population mean score if we wish to be 99% confident that the sample mean score is within 1. 8 points of the population mean score for students who are high on the need for closure

We are given that the population standard deviation is σ = 8.19 and the sample mean is X = 177.30 for a sample of n = 78 students in the highest quartile of the "need for closure" scale.

We want to determine the sample size needed to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.

Since we do not know the population mean score, we will use a t-distribution to calculate the margin of error. We can use the formula:

margin of error = t_(α/2) * (σ/√n)

where t_(α/2) is the critical value from the t-distribution for a 99% confidence level with (n - 1) degrees of freedom. We can find this value using a t-table or a calculator, and we get t_(α/2) = 2.64 (rounded to two decimal places) for n - 1 = 77 degrees of freedom.

Substituting the given values into the formula, we have:

1.8 = 2.64 * (8.19/√n)

Solving for n, we get:

n = [2.64 * (8.19/1.8)]^2 = 214 (rounded up to the nearest whole number)

Therefore, we need a sample size of at least n = 214 students to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.

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Drawing a number line is a useful way to visualize the relationship between tons and pounds and can help make conversions easier to understand.

If we were to draw a number line that shows the relationship between tons and pounds, we would start with the fact that one ton is equivalent to 2000 pounds. We would then draw tick marks on the number line for every whole number from 0 to 10, with each tick mark representing 100 pounds. So, the tick mark at 0 would represent 0 pounds, the tick mark at 1 would represent 100 pounds, the tick mark at 2 would represent 200 pounds, and so on. The tick mark at 20 would represent 2000 pounds, or one ton.

We could then continue the number line past 20 to show larger quantities of tons and pounds, with each additional tick mark representing another ton (2000 pounds). For example, the tick mark at 30 would represent 3000 pounds, or 1.5 tons, the tick mark at 40 would represent 4000 pounds, or 2 tons, and so on.

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Answer:

**Statement | True or False**

---|---

**1. The higher the percentile rank of a score, the greater the percent of scores above that score.** | True

**2. A mark of 75% always has a percentile rank of 75.** | False. A mark of 75% could have a percentile rank of 75 if it is the median score. However, it could also have a percentile rank of 60, 65, 80, or any other percentile rank, depending on the distribution of scores.

**3. A mark of 75% might have a percentile rank of 75.** | True. See above.

**4. It is possible to have a mark of 95% and a percentile rank of 40.** | True. For example, if there are 100 students in a class, and 95 of them get 100% on a test, then the student who gets 95% will have a percentile rank of 40.

**5. The higher the percentile rank, the better that score is compared to other scores.** | True. A higher percentile rank indicates that a score is better than more of the other scores.

**6.A percentile rank of 80, indicates that 80% of the scores are above that score.** | False. A percentile rank of 80 indicates that 80% of the scores are **at or below** that score.

**7. PR50 is the median.** | True. The median is the middle score in a distribution. By definition, half of the scores will be at or below the median, and half of the scores will be at or above the median. Therefore, the percentile rank of the median is 50.

**8. Two equal scores will have the same percentile rank.** | True. Two equal scores will always have the same percentile rank.

Step-by-step explanation:

The critical value is approximately 2.681. Since the absolute value of the test statistic (4.114) is greater than the critical value (2.681), we can reject the null hypothesis at the 0.01 significance level and conclude that there is evidence to support the claim that Praxor is effective at lowering cholesterol levels compared to a placebo.

Hypothesis testing is a statistical method used to determine whether there is enough evidence to support a claim about a population.

In this case, the claim being made is that people who take Praxor will experience a greater decrease in cholesterol levels compared to those taking a placebo.

The first step in hypothesis testing is to state the null and alternative hypotheses. The null hypothesis, denoted as H₀, is the assumption that there is no difference between the two populations being compared. The alternative hypothesis, denoted as H₁, is the claim being made, which is that there is a difference between the two populations.

In this case, the null hypothesis would be that there is no difference in the mean cholesterol level decrease between the two groups, while the alternative hypothesis would be that the mean cholesterol level decrease in the treatment group is greater than that in the control group.

Next, a significance level, denoted as α, is chosen. This represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. In this case, a significance level of 0.01 is chosen.

The next step is to calculate the test statistic, which is a value that measures how far the sample data deviates from what is expected under the null hypothesis. The test statistic used in this case is the two-sample t-test. This test assumes that the two populations being compared have normal distributions and that their variances are not equal.

The formula for the two-sample t-test is:

t = (x₁ - x₂) / √√(s₁²/n1 + s₂²/n₂)

Where x₁ and x₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes for the two groups being compared.

Substituting the values in the formula we get,

= (19.9 - 19.3) / √((3.9²/32) + (1.3²/36))

t ≈ 4.114

Finally, we compare the test statistic to a critical value from a t-distribution table with degrees of freedom equal to n₁ + n₂ - 2 and a significance level of 0.01. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

In this case, the critical value is approximately 2.681. Since the absolute value of the test statistic (4.114) is greater than the critical value (2.681), we can reject the null hypothesis at the 0.01 significance level and conclude that there is evidence to support the claim that Praxor is effective at lowering cholesterol levels compared to a placebo.

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To answer this question, we need to know the driver's reaction time. Let's assume the reaction time is 1.5 seconds, which is a typical average for most drivers.

To find how far the car traveled during the reaction time, we can use the formula:

distance = speed × time

Plugging in the given speed of 72.08 feet per second and the assumed reaction time of 1.5 seconds, we get:

distance = 72.08 ft/s × 1.5 s

distance = 108.12 ft

Therefore, the car traveled 108.12 feet during the driver's reaction time. Rounded to two decimal places, the answer is 108.12.

Answer

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

Answer

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

The car model that is least likely to have a brake failure is model d, and the probability of brake failure for this model is 0.0029%.

The given table provides the probabilities of brake failure for different car models. We need to identify the car model that has the lowest probability of brake failure and the corresponding probability.

From the table, we can see that the probability of brake failure is the lowest for model d, which is 0.0029%. To find this, we simply need to compare the probabilities given in the table and identify the smallest one.

It's worth noting that the total probability of brake failure across all car models is 0.0048%, which means that the probability of brake failure for any individual car model is quite low.

To express this in a more tangible way, we could say that out of 1000 new cars of model d, we can expect only about 2 or 3 to have brake failure. The low probabilities of brake failure suggest that new cars in general are quite safe and reliable when it comes to braking performance.

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The domain and range of f(x) = 2(x-8)² - 10 are Domain: (-∞, ∞) ,Range: [-10, ∞)

The given function, f(x) = 2(x-8)² - 10, is a quadratic function in the form of f(x) = a(x-h)² + k. In this case, a = 2, h = 8, and k = -10. Since the coefficient of the squared term (a) is positive, the parabola opens upwards.

The domain of a quadratic function is always all real numbers, so the domain is (-∞, ∞).

For the range, we need to find the minimum value of the function. Since the parabola opens upwards, the vertex of the parabola represents the minimum point. The vertex is located at (h, k), which in this case is (8, -10). Thus, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is [-10, ∞).

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The solutions for the cube function are x=64 or x= -64.

The main power rules are presented below.

The question gives the equation [tex]x^{2/3}[/tex]=16, you can rewrite it as: [tex]\sqrt[3]{x^2}[/tex]=16.

For eliminating the cubic root, you should apply the power 3 ib both sides. See:

[tex](\sqrt[3]{x^2})^3[/tex]= 16³

x²= 4096

Finally, you have x=64 or x=-64

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After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

To compute the first 10 iterations of Newton's method for the given function and initial approximation, follow these steps:

1. Write down the function and its derivative:

[tex]f(x) = 4 * tan(x) - 6 * x  

f'(x) = 4 * sec^2(x) - 6[/tex]
2. Define the initial approximation, X₀ = 1.4.

3. Apply Newton's method formula to find the next approximation, X₁:
  X₁ = X₀ - f(X₀) / f'(X₀)

4. Repeat steps 3-4 for a total of 10 iterations (X₁ to X₁₀).

Note that I'm unable to perform calculations on this platform, but I'll provide a general outline for performing the iterations:

Iteration 1 (X₁):
[tex]X₁ = 1.4 - (4 * tan(1.4) - 6 * 1.4) / (4 * sec^2(1.4) - 6)[/tex]

Iteration 2 (X₂):
[tex]X₂ = X₁ - (4 * tan(X₁) - 6 * X₁) / (4 * sec^2(X₁) - 6)[/tex]

Repeat these steps up to the 10th iteration (X₁₀).

After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

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The required answer is P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)

a. To find the long-term average number of people in line, we will use the following formula:

Average number of people in line = λ * a

Here, λ is the arrival rate of customers following a Poisson process, and a is the average time taken by the chef to process an order.

b. To find the long-term probability that there are at least two people in line, we first need to calculate the probability that there is at least one person in line. Then, we will subtract this probability from 1 to find the probability of having at least two people in line.

Probability of at least one person in line = 1 - Probability of no one in line

Since the arrival of customers follows a Poisson process, the probability of having no one in line is given by:

P(0) = e^(-λ * a)

Thus, the probability of at least one person in line is:

P(at least 1) = 1 - e^(-λ * a)

Now, we can calculate the probability of having at least two people in line by considering that the second person joins the line with probability 1/(1 + 1) = 1/2. So, the probability of at least two people in line is:

P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)

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The statement "if point b is on ac and between points a and c, then mab + mbc = mac" describes the angle addition postulate in geometry.

In geometry, an angle is formed by two rays that share a common endpoint called a vertex. The measure of an angle is the amount of rotation between the two rays, usually measured in degrees or radians. The angle addition postulate states that if point B is on line segment AC and between points A and C, then the sum of the measures of angles MAB and MBC is equal to the measure of angle MAC. This postulate is used in various proofs and constructions in geometry, and it is also useful in real-world applications such as navigation, surveying, and engineering. The postulate is based on the fact that a straight angle measures 180 degrees, so if we know the measures of two angles that share a common ray, we can find the measure of the third angle by subtracting the sum of the first two angles from 180 degrees.

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Answer:

ben earns $9 per hour and $6 for each delivery he makes

Step-by-step explanation:

The width of a small paving stone is 0.62 m or 62 cm

Length of path = 4 sides of a large paving stone = 3.72 m

Width of large paving stone: 3.72 m ÷ 4 = 0.93 m

Width of small paving stone: 1.55 m − 0.93 m = 0.62 m

or: Length of path = 6 sides of a small paving stone = 3.72 m

Width of small paving stone: 3.72 m ÷ 6 = 0.62 m

or: Let the width of the small paving stone be x and the width

of the large paving stone be y.

Then in cm: x + y = 155 cm,

and 2x + 3y = 372 cm

We can see from the diagram that y = 372 cm – 2 × (x + y)

so y = 372 cm − 2 × 155 cm = 372 cm – 310 cm = 62 cm

Therefore, the width of a small paving stone is 0.62 m or 62 cm.

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Each cook made 109 pizzas.

The total number of pizzas ordered is 4 + 97 + 335 = 436.

If the 4 cooks each made an equal number of pizzas, then we can divide the total number of pizzas by the number of cooks to find out how many pizzas each cook made.

436 pizzas / 4 cooks = 109 pizzas per cook.

Therefore, each cook made 109 pizzas.

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Estimated  large sample size need to be selected for the 90%  of confidence level with standard deviation of $900 is equal to 24.

Standard deviation = $900

Confidence level = 90%

Estimate the required sample size,

Use the formula for the margin of error,

Margin of Error = Z × (standard deviation / √(sample size))

where Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For 90% confidence level, Z = 1.645.

Rearrange the formula to solve for the sample size,

Sample size = (Z × standard deviation / margin of error) ^ 2

Substituting the given values, we get,

⇒ Sample size = (1.645 × 900 / 300) ^ 2

⇒ Sample size = 24.35

Round up to the nearest whole number = 24

Therefore, need a sample size of at least 28 to ensure that it is large enough to achieve the desired level of confidence level.

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Answer:

$2,240

Step-by-step explanation:

1400×3=4,200

4200×20=84,000

84,000÷100=840

840+1400=2,240

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Using regression analysis, we get the following quadratic function:

y = 557[tex]x^{2}[/tex] + 1,690x + 60,000

We can use the data given and fit a quadratic equation in the form of y = a[tex]x^{2}[/tex] + bx + c, where y represents the number of flu cases and x is the number of years since 2012.

x (years since 2012) y (number of flu cases)

0 60,000

1 62,000

2 63,000

3 64,000

4 65,000

5 66,000

6 67,000

7 68,000

8 69,000

9 70,000

10 71,000

11 72,000

12 73,000

13 74,000

14 75,000

15 76,000

Next, we can use this table to find the coefficients a, b, and c that give us the best-fit quadratic function.

Using a regression analysis, we get the following quadratic function:

y = 557[tex]x^{2}[/tex] + 1,690x + 60,000

Here, the coefficient of x is 1,690, which represents the linear term in the quadratic equation. It tells us how much the number of flu cases changes with each year since 2012, assuming a quadratic relationship.

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Year Number of Flu Cases

2000 20,000

2001 22,000

2002 25,000

2003 28,000

2004 32,000

2005 35,000

2006 38,000

2007 42,000

2008 45,000

2009 50,000

2010 55,000

2011 58,000

2012 60,000

2013 62,000

2014 63,000

2015 64,000

Find a quadratic function that models the number of cases of flu each year, where y is years since 2012. What is the coefficient of x?