33–44 ■ Values of Trigonometric Functions Find the exact
value. Questions 33., 34., and 35.

The quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point (5,-42) is:

f(x) = -2(x - 7)(x + 2)

The quadratic function has x-intercepts of (-2,0) and (7,0).

The function passes through the point (5,-42).Let's try to find the quadratic equation using the above information:

Since the quadratic function has x-intercepts of (-2,0) and (7,0), the function can be written as:

f(x) = a(x + 2)(x - 7)

Since the quadratic function passes through the point (5,-42), we can substitute the x and y coordinates into the above

equation to get the value of 'a':-

42 = a(5 + 2)(5 - 7)-42 = a(7)(-2)-42 = -14a => a = 3

So, the quadratic equation for the given function is:

f(x) = 3(x + 2)(x - 7)

Simplifying the equation:

f(x) = 3(x² - 5x - 14)f(x) = 3x² - 15x - 42

Therefore, the quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point

(5,-42) is: f(x) = -2(x - 7)(x + 2)

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Ratio of surface area of one of the new spheres to surface area of original sphere is [tex]$\frac{1}{3}\sqrt[3]{3}$[/tex] when a solid metal sphere of radius 9 is melted and transformed into three identical spheres.

How to calculate the ratio of the surface area of one of these spheres to the surface area of the original sphere?

The original sphere has radius 9, so its surface area is:

[tex]$A_1 = 4\pi(9^2) = 324\pi$[/tex]

When the sphere is melted down and formed into three identical spheres, each sphere will have one-third of the original mass and one-third of the original volume. Since the spheres are identical, they will each have the same radius.

Let r be the radius of one of the new spheres. Then the volume of each new sphere is:

[tex]$V_2 = \frac{4}{3}\pi(r^3)$[/tex]

Since the original sphere has been split into three identical spheres, the total volume is:

[tex]$V_{total} = 3(\frac{4}{3}\pi(r^3)) = 4\pi(r^3)$[/tex]

Since the original sphere and the three new spheres have the same total volume, we can set their volumes equal to each other:

[tex]$4\pi(9^3) = 4\pi(r^3)$[/tex]

Simplifying, we get:

[tex]$r = \frac{9}{\sqrt[3]{3}}$[/tex]

Now we can find the surface area of one of the new spheres:

[tex]$A_2 = 4\pi(r^2) = 4\pi(\frac{9}{\sqrt[3]{3}})^2 = \frac{108\pi}{\sqrt[3]{3}}$[/tex]

Finally, we can find the ratio of the surface area of one of the new spheres to the surface area of the original sphere:

[tex]$\frac{A_2}{A_1} = \frac{\frac{108\pi}{\sqrt[3]{3}}}{324\pi} = \frac{1}{3}\sqrt[3]{3}$[/tex]

Therefore, the ratio of the surface area of one of the new spheres to the surface area of the original sphere is [tex]$\frac{1}{3}\sqrt[3]{3}$[/tex].

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The best measure of variability for the data is None of the given options is correct as the range is the best measure of variability, and it equals 7.

The best measure of variability for the given data would be the range, which is the difference between the maximum and minimum values in the dataset.

From the given line plot, we can see that the minimum value is 1 and the maximum value is 8, which gives a range of 8-1 = 7. Therefore, neither of the options that state the range as 3 or 9 is correct.

The IQR (interquartile range) is another measure of variability, which is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the dataset. However, the line plot does not provide enough information to calculate the quartiles or the IQR. Therefore, neither of the options that mention the IQR is correct either.

Hence, the answer is: None of the given options is correct as the range is the best measure of variability, and it equals 7.

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Fraction is a part of whole.Fractions are written in the form of two numbers, one on top of the other, separated by a horizontal line. The number on the top is called the numerator, and the number at the bottom is called the denominator.

What is fraction?

A fraction is a mathematical concept that represents a part of a whole or a group. It is a way of expressing a number that is less than one and greater than zero.

The numerator represents the part of the whole or group that is being referred to, and the denominator represents the total number of parts in the whole or group. For example, if we have a pizza that is cut into eight equal slices, and we eat three slices, we can represent the amount of pizza we ate as the fraction 3/8. In this case, the numerator is 3, which represents the number of slices we ate, and the denominator is 8, which represents the total number of slices in the pizza.

Fractions can be used in a variety of mathematical operations, including addition, subtraction, multiplication, and division. To add or subtract fractions, the denominators must be the same. If they are not, the fractions must be converted into equivalent fractions with the same denominator before they can be added or subtracted.

Multiplying fractions involves multiplying the numerators together and the denominators together. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction, which is obtained by switching the numerator and denominator of the second fraction.

Fractions are commonly used in everyday life, such as when cooking or measuring ingredients, calculating percentages, and dealing with money. For example, if a store is having a sale with a discount of 20%, we can represent the sale price as the fraction 4/5, since the price after the discount is 80% of the original price.

It is important to note that fractions can also be expressed as decimals or percentages. To convert a fraction to a decimal, we divide the numerator by the denominator. To convert a fraction to a percentage, we multiply the fraction by 100.

In conclusion, fractions are an important concept in mathematics and are used in many different areas of our daily lives. They represent a part of a whole or group and are written in the form of a numerator over a denominator. Fractions can be used in a variety of mathematical operations and can be expressed as decimals or percentages.

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Correct question is "What is fraction? Write 358 words about it "

The Average rate of growth is 28589 per year

The Slope of the line connecting is m = 28589 pee year.

The average rate of growth is a measure of how much a quantity or variable changes on average over a certain period of time. It is calculated by dividing the total change in the quantity by the length of the time period. The formula for the average rate of growth is:

Average Rate of Growth = (Final Value - Initial Value) / Time Interval

Average rate of growth = 1611,589-210733 / 2009-1960

= 28589 per year

Slope of the line connecting ( 1960, 210, 733) 4 (2009, 1,611, 589) will be:

m = У2 - y1 / x2 - x1

m = 28589 per year

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The ratio between their radii of cylinder is therefore 1:4.

The distance between a circle's or sphere's centre and its edge is referred to in geometry as its radius1. It is known as "r" and is a crucial component of spheres and circles3.

For instance, if a circle has a radius of 5 cm, that indicates that the circle's center to edge distance is 5 cm3.

When two cylinders have 1:16 ratios for their volumes and heights, it is possible to calculate their radii as follows:

Assume that one cylinder has a radius of r and a height of h. The other cylinder will have a radius of R and a height of 16h.

As the volumes of both cylinders are equal, we may write:

πr²h = πR²(16h) (16h)

r²/R² = 1/16

r/R = √(1/16) = 1/4

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Answer:

2 hours

Step-by-step explanation:

[tex]\frac{5}{10}[/tex] = [tex]\frac{60}{x}[/tex]  Cross multiply and solve for x

5x = 600  Divide both sides by 5

x = 120

This is 120 minutes.  120 minutes is equal to 2 hours.

Helping in the name of Jesus.

Answer:

2 hours

Step-by-step explanation:

If 5 pages in 10 minutes and 60 pages than 60/5, which is 12.  12*10=120 minutes.  120 minutes is equivalent to 2 hours.

The length of the ladder is 14.36 feet. To the nearest tenth of a foot, the length of the ladder is 14.4 feet.

Trigonometric functions such as sine, cosine, and tangent are used to model and describe physical phenomena like waves, sound, and light.

The given problem can be solved using the trigonometric concept. The basic trigonometric equation used is:

Opposite Side (S) = Adjacent Side (L) x Tan(θ)

Where θ is the angle in degrees and L is the length of the ladder.

In this problem,

θ = 62°

S = 27 ft

Using the equation, we can find the length of the ladder (L).

L = S/Tan(θ)

L = 27/Tan(62°)

L = 27/1.88

L = 14.36 ft

The length of the ladder is 14.36 feet. To the nearest tenth of a foot, the length of the ladder is 14.4 feet.

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According to the information, the approximation and exact values are V = 65.45 cubic cm (approximation to the nearest hundredth), Exact value: V = (4/3)π(2.5)^3 = 65.44984695 cubic cm (exact).

The formula for the volume of a sphere is:

V = (4/3)πr^3

Since the diameter of the sphere is given as 5 cm, the radius is half of that, which is:

Substituting this value into the formula, we get:

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the expression 1.01 represents the interest rate applied to the initial amount of 1.005 thousand dollars

In the given expression 1.01 × [tex]1.005^{t}[/tex], the value 1.01 represents the annual interest rate on Carter's savings account. To understand this, let's break down the expression: "1.005" represents the initial amount of money in Carter's savings account, in thousands of dollars. "t" represents the number of years that have passed since he opened the account, and t is the variable that represents this time. "1.01" represents the interest rate on Carter's savings account. The interest rate of 1.01 means that for every 1 dollar in Carter's savings account, he earns an additional 1.01 cents of interest after one year.  Therefore, the expression 1.01 ×[tex]1.005^{t}[/tex]represents the amount of money in thousands of dollars that Carter has in his savings account after t years, with 1.01 being the interest rate applied to the initial amount of 1.005 thousand dollars

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Complete Question

The expression 1.01*1.005(^t) gives the amount of money, in thousands of dollars, in Carter's savings account (t) years after he opens it. What does 1.01 represent in this expression?

The value of m arc Q I=94°

a continuous section of an arc, which is a curved line that forms a portion of a circle of  circumference. a blazing passage of electricity  electrodes through between a gap in a circuit o that called a curved rout

arcs have two properties is the easiest way . They have length as a component of circumference and, based on the associated central angle, they also have a detectable curvature.

Given arc m Y S=180°,m∠Q B I=137°

We know that,

[tex]mQBI =\frac{1}{2} (m arcYS+marcQI)\\137=\frac{1}{2} (180+marcQI)\\274=180+marcQI\\marcQI=274-180\\marcQI=94[/tex]

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Answer:

49.87%

Step-by-step explanation:

We know the following information:

$400 is the average weekly wage

$50 is the standard deviation (from the average wage)

To solve for the probability that a randomly-selected worker makes between $400-550, we have to solve for the standard score of each end of the range.

First, the standard score (Z) of $400:

[tex]Z = \dfrac{\text{value}-\text{average}}{\text{std deviation}}[/tex]

[tex]Z_{400} = \dfrac{400-400}{50} = 0[/tex]

The standard score of $400 is 0, since it is the average (mean) wage.

Second, the standard score of $550:

[tex]Z_{550} = \dfrac{550-400}{50} = 3[/tex]

The standard score of $550 is 3.

The probability that a worker's weekly wage is between $400 and $550 is equal to the probability that the standard score is between 0 and 3.

So, we can plug the standard scores that we just solved for into a distribution calculator to determine both probabilities.

P(0 < Z < 3) ≈ 49.87%

So the equation that represents the function F is F(x) = 2^(x-3) + 1.

None of the above equations represent the function given in the table. To find the equation, we need to look for a pattern in the outputs (f(x)) based on the inputs (x).

Starting with x=3, we see that f(x)=9. Moving to x=4, we see that f(x) increases by 8 to equal 17. Moving to x=6, we see that f(x) increases by 48 to equal 65. Each time we move to the next input value, the output increases by double the previous increase plus 1. This pattern can be written as:

f(x) = 2^(x-3) + 1

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The margin of error would have been much smaller if Dr. Si Sanchez had increased his sample size to 1,000.

A margin of error quantifies the amount of random sampling error in survey results. The smaller the margin of error, the larger the sample size. This is due to the fact that a larger sample size reduces the amount of random variation in the data, allowing the estimate to be more precise.

Dr. Sanchez's margin of error decreases as he increases his sample size from 500 to 1000, because sample size is proportional to margin of error.

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Answer:

1.yes it's a function

a.1,2,3,4,5

b.40,80,120,160,200

The drive-thru is able tο estimate their wait time mοre cοnsistently will be A. Burger Quick, because it has a smaller IQR.

The range οf values in the middle οf the scοres is knοwn as the interquartile range, οr IQR. The apprοpriate measure οf variability is the interquartile range when a distributiοn is skewed and the median is used instead οf the mean tο shοw a central tendency.

The cοrrect οptiοn here is Burger Quick, because it has a smaller IQR (Interquartile Range). IQR is the difference between the third quartile and the first quartile, which is represented by the bοx in the bοx plοt. In this case, the IQR fοr Burger Quick is 24 - 9.5 = 14.5, while the IQR fοr Super Fast Fοοd  is 15.5 - 8.5 = 7. A smaller IQR indicates that the data is mοre cοnsistent and less spread οut.

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The form of "research-data" which is likely to be used by quantitative research study than by a qualitative research study is (c) Economic data.

The Quantitative research depends on numerical data and statistical analysis to answer research questions, while

The Qualitative research depends on non-numerical data such as words, images, or observations to gain an understanding of the context of the phenomenon being studied.

The Economic data, such as data on income, expenditures, or market trends, is typically collected and analyzed using statistical methods, making it more suitable for quantitative research.

Therefore, the correct option is (c) economic data.

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The given question is incomplete, the complete question is

Which of the following forms of research or data would be more likely used by a quantitative research study than by a qualitative research study?

(a) interview data

(b) personal narrative data

(c) economic data

(d) archival data.

Answer:

Therefore, there are 27.04 cubic feet of sand in the container.

Step-by-step explanation:

We can start by calculating the volume of the rectangular container:

Volume = length x width x height

Volume = 6.5 ft x 3.2 ft x 2 ft

Volume = 41.6 cubic feet

Since the sand fills the container to a depth of 1.3 feet, we can calculate the volume of the sand as follows:

Volume of sand = length x width x depth of sand

Volume of sand = 6.5 ft x 3.2 ft x 1.3 ft

Volume of sand = 27.04 cubic feet

Therefore, there are 27.04 cubic feet of sand in the container.

Answer:

Let the number of marbles in the large bag be L. Then we have: 25 : 7S = 7S : L Multiplying both sides by 7S, we get: 25(7S) = (7S)^2 : L 175S = 49S^2 : L L = (49S^2) / 175 L = (7S^2) / 25 Therefore, the number of marbles in the large bag is (7/25) times the number of marbles in the medium bag.

The relationship is non-existent and positive about the plot in terms of the relationships between the two variables.

A scatter plot is a graph that compares two different sets of data by plotting them as points on a graph. A scatter plot is utilized to investigate the degree of correlation between two different data sets. The points' placement on a scatter plot implies a correlation between the two data sets that can be classified as positive, negative, or non-existent.

The following statements are true about the plot in terms of the relationships between the two variables:There is no association between music and living spaces.Therefore, the answer is: non-existent.The majority of students who play an instrument live off-campus.Therefore, the answer is: Positive.There is no association between the Northside and playing an instrument.Therefore, the answer is: Non-existent.

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Answer:

The height of the statue is 152ft.

Step-by-step explanation:

305 = 153 + h

152 = h

Tyler need 24 cups of vanilla for making 6 gallons of mint chocolate ice cream for a bake sale.

We know that the recipe for a gallon of mint chocolate ice cream calls for 4 fluid ounces of vanilla. Tyler is making 6 gallons of mint chocolate ice cream for a bake sale, we need to find how many cups of vanilla does he need:

therefore, first we need to find the ratio according to the statement above:

one gallon of mint chocolate : fluid ounces of vanilla = 1:4

now we need to find how many cups of vanilla does he needs for 6 gallons = 1 x 6 : 4 x 6

= 6 : 24

therefore it is clear that Tyler need 24 cups of vanilla for making 6 gallons of mint chocolate ice cream for a bake sale.

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The statement "bar charts are more versatile than pie charts and line charts" is true.

The statement "bar charts are more versatile than pie charts and line charts" is true. Bar charts are versatile and can be used to compare data, show trends over time, and compare different categories or groups. They are especially useful for showing data with distinct categories, such as nominal data. In contrast, pie charts are limited in their use because they can only represent parts of a whole, while line charts are best suited for showing trends over time. Bar charts can be customized to display a wide range of information and are a valuable tool for communicating data effectively in a variety of contexts.

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We need a sample size of 35 to reduce the margin of error to $25 for a 95% confidence interval, given that we have reason to believe that the population standard deviation of credit card debts for this group is $150.

To determine the sample size needed to reduce the margin of error to $25 for a 95% confidence interval, we can use the following formula:
n = (z * σ / E)²
Where:
n = sample size
z = z-score corresponding to the desired confidence level (1.96 for 95% confidence)
σ = population standard deviation
E = desired margin of error
Substituting in the given values:
n = (1.96 * 150 / 25)²
n = 34.57
Rounding up to the nearest whole number, we get a sample size of 35. Therefore, we need a sample size of 35 to reduce the margin of error to $25 for a 95% confidence interval, given that we have reason to believe that the population standard deviation of credit card debts for this group is $150.

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The tennis ball will hit the ground [tex]5[/tex] seconds after being dropped from an initial height of  [tex]400[/tex]feet.

To determine when the tennis ball hits the ground, we need to find the value of t when h becomes 0, since at that time the height of the ball is zero, which means it has hit the ground.

So, we can set  [tex]h = 0[/tex] and solve for t:

[tex]0 = -16t^2 + 400[/tex]

Adding 16t^2 to both sides:

[tex]16t^2 = 400[/tex]

Dividing both sides by 16:

[tex]t^2 = 25[/tex]

Taking the square root of both sides:

[tex]t = \pm5[/tex]

Since we cannot have a negative time, we can disregard the negative solution.

Therefore, the tennis ball will hit the ground  [tex]5[/tex] seconds after being dropped from an initial height of  [tex]400[/tex] feet.

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Answer: f(x)

Step-by-step explanation: It goes from the lowest elevation to the highest.

The measure of ∠AOB is 80°.

In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.

The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:

An acute angle is less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle is greater than 90 degrees but less than 180 degrees.

A straight angle measures exactly 180 degrees.

A reflex angle is greater than 180 degrees but less than 360 degrees.

A full angle measures exactly 360 degrees.

In a parallelogram, opposite angles are equal, so we have:

∠OAD = ∠OCB = a2 + b2 (1)

∠OAB = ∠ODC = a1 + d1 (2)

∠OAB + ∠OAD = ∠BOC = 180° (3)

∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)

From (1), (2), and (3), we have:

∠AOB = 180° - (a1 + b2 + a2 + d1)

= 180° - (a1 + a2 + b1 + b2 + c1 + d1 + d2)

= 180° - ∠ABD - ∠BCD

Since ABCD is a parallelogram, we have ∠ABD = ∠BCD. Therefore,

∠AOB = 180° - 2∠ABD

Let x be the measure of angle ABD. Then we have:

∠ABD + ∠BCD = 180°

x + (d1 + d2) = 180° (5)

In triangle ADO, we have:

∠ADO + ∠ODA + ∠OAD = 180°

d2 + x + a2 = 180° (6)

From (5) and (6), we get:

d1 + d2 + a2 + x = 180°

Substituting this expression into (3), we obtain:

∠AOB = 180° - 2(d1 + d2 + a2 + x)

= 80°

Therefore, the answer is (d) 80°.

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The measure of ∠AOB is 80°. The required answer for the given question is option (d). 80°.

An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the

rays coming from the vertex and continuing in opposing directions indefinitely.

A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:

Acute angle is one that is less than 90 degrees.

A right angle has a 90 degree angle.

Obtuse angles are those that are greater than 90 degrees and less than 180 degrees.

A straight angle has a 180 degree length.

Greater than 180 degrees and less than 360 degrees is a reflex angle.

360 degrees makes up a whole angle.

Since opposite angles in a parallelogram are equal, we have:

∠OAD = ∠OCB = [tex]a_2+b_2[/tex] (1)

∠OAB = ∠ODC = [tex]a_1+d_1[/tex] (2)

∠OAB + ∠OAD = ∠BOC = 180° (3)

∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)

From (1), (2), and (3), we have:

∠AOB = 180° - [tex](a_1 + b_2 + a_2 + d_1)[/tex]

= 180° - [tex](a_1 + a_2 + b_1 + b_2 + c_1 + d_1 + d_2)[/tex]

= 180° - ∠ABD - ∠BCD

Due to the parallelogram that is ABCD, we have ∠ABD = ∠BCD.

∠AOB = 180° - 2∠ABD

Let x be the measure of angle ABD. Then we have:

∠ABD + ∠BCD = 180°

x + [tex](d_1 + d_2)[/tex] = 180° (5)

In triangle ADO, we have:

∠ADO + ∠ODA + ∠OAD = 180°

[tex]d_2[/tex] + x + [tex]a_2[/tex] = 180° (6)

From (5) and (6), we get:

[tex]d_1 + d_2 + a_2[/tex] + x = 180°

Substituting this expression into (3), we obtain:

∠AOB = 180° - 2[tex](d_1 + d_2 + a_2 + x)[/tex]

= 80°

Therefore, the answer is (d) 80°.

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The approximate probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, assuming the true proportion is 15%, is 0.9693

To solve this problem, we will use the normal approximation to the binomial distribution. We can assume that the number of students who report experiencing extreme levels of stress follows a binomial distribution with parameters n = 160 and p = 0.15, where n is the sample size and p is the true proportion of students who have experienced extreme levels of stress in the population.

The expected value of the number of students who report experiencing extreme levels of stress in the sample is:

E(X) = np = 160 * 0.15 = 24

The variance of the number of students who report experiencing extreme levels of stress in the sample is

Var(X) = np(1-p) = 160 * 0.15 * 0.85 = 18.36

The standard deviation of the number of students who report experiencing extreme levels of stress in the sample is

SD(X) = sqrt(Var(X)) = sqrt(18.36) = 4.28

To calculate the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month, we need to convert the percentage into a number. Since the sample size is 160, 10% corresponds to 16 students. We want to find the probability that X > 16.

To standardize the distribution, we calculate the z-score

z = (16 - 24) / 4.28 = -1.87

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.87, which is approximately 0.0307. Therefore, the probability that more than 10% of the sample would report experiencing extreme levels of stress during the past month is approximately 1 - 0.0307 = 0.9693

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Suppose that 15%, percent of the 1750 students at a school have experienced extreme levels of stress during the past month. A high school newspaper doesn't know this figure, but they are curious what it is, so they decide to ask a simple random sample of 160 students if they have experienced extreme levels of stress during the past month. Subsequently, they find that 10, percent of the sample replied “yes” to the question.Assuming the true proportion is 15, percent, what is the approximate probability that more than 10, percent of the sample would report that they experienced extreme levels of stress during the past month?

The answer is C) (9, 11) which represents the center of the circular track.

A circle is a closed, two-dimensional shape where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the middle.

To find the center of the circular track, we need to convert the given equation into the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

First, we need to complete the square for x and y terms:

x² - 18x + y² - 22x = -177

(x² - 18x + 81) + (y² - 22x + 121) = -177 + 81 + 121

(x - 9)² + (y - 11)² = 25

Now, we can see that the equation is in the standard form of the equation of a circle, where the center is (9, 11) and the radius is √25 = 5.

Therefore, the answer is C) (9, 11) which represents the center of the circular track.

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Answer:

If y varies directly as x, then we can express this relationship using a proportionality constant k, such that:

y = kx

To solve for k, we can use the initial condition given:

y = 21 when x = 3

Substituting these values into the equation above, we get:

21 = k * 3

Solving for k, we get:

k = 7

Now that we have k, we can use the equation to find y when x = 2:

y = kx

y = 7 * 2

y = 14

Therefore, when x = 2, y = 14.

Step-by-step explanation: