The radius of a circular stage is 15 feet. Katie wants to lay down tile to cover the stage. If Katie pays $12.50 per square foot of tile, how much would it cost to tile the entire stage floor? Round to the nearest whole dollar.

Answer:

The equation of the line with a slope of 3 that passes through (-4,-7) is;

Explanation:

We want find the equation of the line with;

Using the point slope form of linear equation;

substituting the given values into the equation above we have;

Above is a point slope form of the equation.

solving further we have;

The equation of the line with a slope of 3 that passes through (-4,-7) is;

If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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Answer- The rabbit population decreased in 2013 and 2015 in some areas of up to 80%

After simplifying the trigonometric expression 2 cos (3 x) sin (3 x), we get the value as sin (6 x).

We are given the expression as:

2 cos (3 x) sin (3 x)

Now, we know the trigonometric identity as:

2 sin θ cos θ = 2 sin (2 θ)

Using this identity in the expression where θ = 3 x, we get that:

2 cos (3 x) sin (3 x) = sin ( 2 × 3 x) ( value of θ substituted in the expression)

2 cos (3 x) sin (3 x) = sin (6 x)

Therefore, after simplifying the trigonometric expression 2 cos (3 x) sin (3 x), we get the value as sin (6 x).

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Answer:

I have a feeling that the answer is B. table 2

Check the picture below.

we know the diameter MK is 9 units, so the radius must be half that, or 4.5.

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4.5\\ \theta =218 \end{cases}\implies \begin{array}{llll} s=\cfrac{(218)\pi (4.5)}{180}\implies s=5.45\pi \\\\\\ s\approx 17.1 \end{array}\)

Answer:

80 -14=66 and 66-80=52 if we check the 66-52 the difference will be 14

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

D

Step-by-step explanation:

You are given the two sides and the abgle inbetween.

The area of the rectangle is approximately 3.32 square meters.

We must multiply the length by the width of the rectangle to determine its area.

The length of the rectangle is given as 2 meters and 13 centimeters, which can be written as 2.13 meters.

The width of the rectangle is given as 1 meter and 56 centimeters, which can be written as 1.56 meters.

Therefore, the area of the rectangle is:

Area = length x width

= 2.13 meters x 1.56 meters

= 3.3208 square meters

Rounding to the nearest hundredth, we get:

Area ≈ 3.32 square meters

Therefore, the area of the rectangle is approximately 3.32 square meters.

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Answer:

Step-by-step explanation:

\(a_1=8\\a_2=48\\a_3=288\\\\288:48=6\\48:8=6\\\\ \dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}= 6\)

Therefore it's geometric sequence with common ratio of 6

\(a_n=a_1\cdot r^{n-1}\\\\a_1=8\\r=6\\\\a_n=8\cdot6^{n-1}\)

The chi-square goodness of fit test is used to determine whether a sample comes from a population with a specific distribution.

It is used to test hypotheses about the probability distribution of a random variable that is discrete in nature.What is the chi-square goodness of fit test?The chi-square goodness of fit test is a statistical test used to determine if there is a significant difference between an observed set of frequencies and an expected set of frequencies that follow a particular distribution.

The chi-square goodness of fit test is a statistical test that measures the discrepancy between an observed set of frequencies and an expected set of frequencies. The purpose of the chi-square goodness of fit test is to determine whether a sample of categorical data follows a specified distribution. It is used to test whether the observed data is a good fit to a theoretical probability distribution.The chi-square goodness of fit test can be used to test the goodness of fit for several distributions including the normal, Poisson, and binomial distribution.

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Answer: each time you roll a 6-sided die is 1/6 percent to get any number  

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

This question wants the formula for the line that travels through (7, -8) and (-4, 6). The equation should be in point-slope form, using (-4, 6) as the point. Steps to find the equation are:  Calculate the slope and plug all values into point-slope form formula.

Point-slope form formula: \(y-y_1 = m(x - x_1)\)

\(m = \frac{6-(-8)}{-4-7} = -\frac{14}{11} \\\)

Plug this into the formula.

\(y - y_1 = -\frac{14}{11} (x - x_1)\)

Substitute in the point (-4, 6).

\(y - (6) = -\frac{14}{11}(x - (-4)) \\y - 6 = -\frac{14}{11}(x +4)\)

So Option B is the correct answer.

Answer:

y=-4x/5-3

Step-by-step explanation:

a. The equation representing the cost of buying and operating the Super Cool X1400 is: C = 800 + 60m. b. The equation representing the cost of buying and operating the Efficient Energy X2000 is: C = 1200 + 40m. c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase. d. Figuring your family will only use the air conditioner for four months each year, you would have to wait 5 years to start saving money overall.

a. The cost of buying the Super Cool X1400 is a one-time expense of $800. Additionally, the cost of operating it is $60 per month. Therefore, the equation representing the cost C as a function of months m is C = 800 + 60m.

b. The cost of buying the Efficient Energy X2000 is a one-time expense of $1200. The operating cost is $40 per month. Hence, the equation representing the cost C as a function of months m is C = 1200 + 40m.

c. To compensate for the additional cost of the original purchase (which is $400), we equate the two cost equations and solve for m:

800 + 60m = 1200 + 40m

20m = 400

m = 20

Therefore, your family would have to use the Efficient Energy model for 20 months (or 10 months more than the Super Cool X1400) to compensate for the additional cost.

d. Considering your family only uses the air conditioner for four months each year, we divide the total number of months (20) by four to find the number of years needed to start saving money overall:

20 months / 4 months/year = 5 years

Hence, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

a. The cost of buying and operating the Super Cool X1400 is represented by the equation C = 800 + 60m.

b. The cost of buying and operating the Efficient Energy X2000 is represented by the equation C = 1200 + 40m.

c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase.

d. Assuming your family uses the air conditioner for four months each year, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

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complete question- Your family plans to buy a new air conditioner. They can buy the Super Cool X1400 for $800, or they can buy the Efficient Energy X2000 for $1200. Both models will cool your home equally well, but the Efficient Energy model is less expensive to operate. The Super Cool X1400 will cost $60 per month to operate, while the Efficient Energy X2000 costs only $40 per month to operate. a. Write an equation to represent the cost of buying and operating the Super Cool X1400 where C= cost and m= months. b. Write an equation to represent the cost of buying and operating the Efficient Energy X2000. c. How many months would your family have to use the Efficient Energy model to compensate for the additional cost of the original purchase? d. Figuring your family will only use the air conditioner for four months each year, how many years ill you have to wait to start saving money overall?

a. The appropriate hypothesis test for this situation can be formulated as follows: Null Hypothesis (H₀) and Alternative Hypothesis (H₁)

b. To test the hypothesis, we can use the z-test for proportions.

c. We can find the p-value associated with z = 5.1493.

d. Conclusion:

If the p-value is less than α, we reject the null hypothesis.

If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

A hypothesis known as the null hypothesis states that sample observations are the result of chance.

(a) Hypothesis Test:

The appropriate hypothesis test for this situation can be formulated as follows:

Null Hypothesis (H₀): The proportion of children with autism is equal to 5% (p = 0.05).

Alternative Hypothesis (H₁): The proportion of children with autism is different from 5% (p ≠ 0.05).

(b) Test Procedure:

To test the hypothesis, we can use the z-test for proportions. The steps for this test procedure are as follows:

1. Formulate the null and alternative hypotheses as stated in part (a).

2. Set the significance level (α) to determine the threshold for rejecting the null hypothesis.

3. Collect a random sample of children and record the number of children showing signs of autism.

4. Calculate the sample proportion (\(\bar p\)) of children with autism.

5. Calculate the standard error of the proportion (SE):

  SE = √((p₀ * (1 - p₀)) / n),

  where p₀ is the hypothesized proportion (0.05 in this case) and n is the sample size.

6. Calculate the test statistic (z):

  z = (\(\bar p\) - p₀) / SE

7. Calculate the p-value associated with the test statistic using a standard normal distribution table or a statistical software.

8. Compare the p-value with the significance level (α).

  - If the p-value is less than α, reject the null hypothesis.

  - If the p-value is greater than or equal to α, fail to reject the null hypothesis.

(c) Perform the Test and Calculate the p-value:

In this case, the sample size is 384, and the number of children showing signs of autism is 46.

\(\bar p\) = 46/384 = 0.1198

SE = √((0.05 * (1 - 0.05)) / 384) ≈ 0.0134

z = (0.1198 - 0.05) / 0.0134 ≈ 5.1493

Using a standard normal distribution table or a statistical software, we can find the p-value associated with z = 5.1493. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the assumption that the null hypothesis is true.

(d) Conclusion:

Based on the calculated p-value and the chosen significance level (α), we can draw a conclusion:

If the p-value is less than α, we reject the null hypothesis.

If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

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As x approaches negative or positive infinity, the term with the highest degree (x⁴) dominates the other terms. The highest exponent in the polynomial is 4.

To write the given polynomial function in standard form, we arrange the terms in descending order of their exponents:
y = -7x⁴ + x⁴ + 3x² + 9

Now, let's classify the polynomial by degree and number of terms.

Degree:  Therefore, the degree of the polynomial is 4.

Number of terms: The polynomial has four terms separated by addition and subtraction. Hence, the number of terms is 4.

Since the coefficient of the leading term (-7) is negative, the end behavior of the polynomial is as follows:
- As x approaches negative infinity, the polynomial decreases without bound.
- As x approaches positive infinity, the polynomial increases without bound.

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The equivalent expression of \(\frac{(2mn)^4}{6m^{-3}n^{-2}}\) is \(\frac{(2mn)^4}{6m^{-3}n^{-2}}\)

The expression is given as:

\(\frac{(2mn)^4}{6m^{-3}n^{-2}}\)

Evaluate the expression on the numerator

\(\frac{16m^4n^4}{6m^{-3}n^{-2}}\)

Divide 16 by 6

\(\frac{8m^4n^4}{3m^{-3}n^{-2}}\)

Apply the law of indices

\(\frac{8m^7n^6}{3}\)

Hence, the equivalent expression of \(\frac{(2mn)^4}{6m^{-3}n^{-2}}\) is \(\frac{(2mn)^4}{6m^{-3}n^{-2}}\)

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Answer:

118

Step-by-step explanation:

:)

Step-by-step explanation:

\(\sf Books\begin{cases}\sf Mathematics\leadsto 4 \\ \sf English \leadsto 3 \\ \sf Science \leadsto 6\end{cases}\)

\(\tt {:}\longrightarrow Total\:books=3+4+6=13\)

\(\tt {:}\longrightarrow |S|=13\)

\(\tt {:}\longrightarrow E=\:\{3\:English\:books\}\)

\(\tt {:}\longrightarrow |E|=3\)

\(\sf P(E)\begin{cases}\tt {:}\longrightarrow \dfrac{|E|}{|S|} \\ \tt {:}\longrightarrow \dfrac{3}{13}\end{cases}\)

Answer:

1/286

Step-by-step explanation:

got it right on edge :)

The domain of the function can be written in the form of interval as  (-∞, ∞).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The function is given as y = aˣ.

Its domain can be found as follows,

For x = 0, y is a⁰ = 1.

For x = n, where n > 0, y is given as,

y = aⁿ, which is greater than zero.

For x = n, where n < 0, y is given as,

y = a⁻ⁿ

⇒ y = 1/aⁿ

Thus, the given function is valid for all real numbers.

Which implies its domain is (-∞, ∞).

Hence, the domain of the given function is obtained as (-∞, ∞).

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The height of the tree is h = 40 ft.  We can set up a proportion based on the similarity of the triangles formed by the man and the tree.

To find the height of a tree given the length of its shadow and the height and shadow length of a man, we can use similar triangles. By setting up a proportion, we can solve for the height of the tree.

Let's consider the given information: the height of the man is y = 5 ft, the shadow length of the man is x = 7 ft, and the shadow length of the tree is b = 56 ft. We can set up a proportion based on the similarity of the triangles formed by the man and the tree:

y/x = h/b

Substituting the given values, we have:

5/7 = h/56

To solve for h, we can cross-multiply:

7h = 5 * 56

7h = 280

Dividing both sides by 7, we get:

h = 40

Therefore, the height of the tree is h = 40 ft.

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The tree shown below casts a shadow 56 feet long when a man 5 feet tall casts a shadow 7 feet long. Find the height h of the tree. (Let y = 5 ft, x = 7 ft, and b = 56 ft.) ft h = h x  

Step-by-step explanation:

To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8. Notice that the symbol for cube root is the radical sign with a small three (called the index) above and to the left .Other roots are defined similarly and identified by the index given. (In square root, an index of two is understood and usually not written.) Following is a list of the first eleven perfect (whole number) cube roots.

To find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for square root is √0.

Answer:

Below

Step-by-step explanation:

Formula for an arithmetic sequence is an = 4n - 5

First 4 terms are

-1, 3, 7, 11.

10th term = 4(10) - 5

= 35.

Answer:

1,000 lightbulbs that day were tested

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We start with the second line;

3x -2y + 4 = 0

3x + 4 = 2y

divide through by 2

3x/2 + 2 = y

Comparing this with standard form of y = mx + c

where m is slope

This means 3/2 is slope of the line

Since this line is perpendicular to the other line, then the product of their slopes is -1

3/2 * slope of second line = -1

Slope of second line = -1 divided by 3/2 = -2/3

We use the point slope form to find the equation of the other line

y-y1 = m(x-x1)

where m = -2/3 and (x1,y1) = (2,-3)

y-(-3) = -2/3 (x-2)

y + 3 = -2/3 (x -2)

3(y + 3) = -2(x-2)

3y + 9 = -2x + 4

3y + 5 = -2x

3y + 2x + 5 = 0

The sample size which is required for the maximum error of 0.03 mg and 90% confidence level is equal to approximately 307.

Confidence level = 90%

Maximum error = 0.03mg

To determine the sample size needed to estimate the nicotine content with a maximum error of £0.03 mg at a 90% confidence level,

Use the formula for sample size determination,

n = (Z × σ / E)²

Where,

n = required sample size

Z = Z-value for the desired confidence level (corresponding to a 90% confidence level, Z ≈ 1.645)

σ = standard deviation of the population ( 0.32 mg)

E = maximum error or margin of error ( £0.03 mg)

Plugging in the values, we have,

⇒n = (1.645 × 0.32 / 0.03)²

⇒n ≈ (0.5264 / 0.03)²

⇒n ≈ 17.5098²

⇒n ≈ 306.5

Rounding up to the nearest whole number, the required sample size is approximately 307.

Therefore, a sample size of at least 307 cigarettes would be needed to estimate the nicotine content with a maximum error of £0.03 mg at a 90% confidence level.

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