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The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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The minimum amount of plastic wrap needed to completely wrap 8 containers is  794. 4 in². Option D

The area of each circular end is:

A = πr²

A = 3.14 × (2.75)²

A = 23.68in²

The area of the rectangular side is:

A = h * circumference

circumference = 5.5in * π

circumference = 17.27in

Using the given height of 3 inches, we get:

A = 3in * 17.27

A = 51.81in²

Therefore, the total surface area of each container is:

A = 2 * 23.68 + 51.81

A = 98.17in²

To wrap 8 containers, we need to multiply the surface area of each container by 8:

Total surface area = 8 × 98.17

Total surface area = 794. 4 in²

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Step-by-step explanation:

Simplifying

f(x) = 2cos(3x)

Multiply f * x

fx = 2cos(3x)

Remove parenthesis around (3x)

fx = 2cos * 3x

Reorder the terms for easier multiplication:

fx = 2 * 3cos * x

Multiply 2 * 3

fx = 6cos * x

Multiply cos * x

fx = 6cosx

Solving

fx = 6cosx

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.

f = 6cos

Simplifying

f = 6cos

The linear regression equation is y = -5x + 21

The points are given as:

(-5,14), (1,-16)

The equation is then calculated using:

\(y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1\)

This gives

\(y = \frac{14 + 16}{-5 - 1} * (x - 1) + 16\)

Evaluate

y = -5 (x - 1) + 16

Expand

y = -5x + 5 + 16

Evaluate the sum

y = -5x + 21

Hence, the linear regression equation is y = -5x + 21

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Answer:

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

Step-by-step explanation:

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

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Sample of 252 customers, 208 are satisfied:

This means that \(n = 252, \pi = \frac{208}{252} = 0.8254\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8254 + 2.575\sqrt{\frac{0.8254*0.1746}{252}} = 0.8870\)

As a percentage:

100%*0.8870 = 88.70%

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

Answer:

Step-by-step explanation:

Each term is being multiplied by -0.5

How did I know?

Divide the second term by the first.

-50 divided by 100 = -1/2

Find the last four terms.

-12.5 x -1/2 = 6.25

6.25 x -1/2 = -3.125

-3.125 x -1/2 = 1.5625

1.5625 x -1/2 = -0.78125

Answer:

Future amount (A) = $1,258.77 (Approx)

Step-by-step explanation:

Given:

Amount deposit (p) = $693

Rate of interest monthly (r) = 4.9% / 12 = 0.003833

Number of month (n) = 13 × 12 = 156

Find:

Future amount (A)

Computation:

\(A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77\)

Future amount (A) = $1,258.77 (Approx)

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ? [Hint: Let Y = the number among the 1000 intervals that contain μ. What kind of random variable is Y?]

(Round your answer to four decimal places.)

Answer:

The expected value is

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

\(P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

There is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients.

From the above information, we know that,

n = 1000

p = 0.98

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

The expected value is given by

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and p is also greater than 0.50.

n×p ≥ 10

1000×0.98 ≥ 10

980 ≥ 10  (satisfied)

n×(1 - p) ≥ 10

1000×(1 - 0.98) ≥ 10

20 ≥ 10 (satisfied)

Let Y be the random number among the 1000 intervals that contain μ

\(P(970 < Y < 990) = P(Y < 990) - P(Y < 970) \\\\P(970 < Y < 990) = P( Z < \frac{Y - \mu}{\sigma}) - P( Z < \frac{Y - \mu}{\sigma} )\\\\\)

Where the mean is

\(\mu = 980\)

and the standard deviation is

\(\sigma = \sqrt{n \times p(1-p)} \\\\\sigma = \sqrt{1000 \times 0.98(1-0.98)} \\\\\sigma = 4.4272\)

Finally, the required probability is

\(P(970 < Y < 990) = P( Z < \frac{990 - 980}{4.4272}) - P( Z < \frac{970 - 980}{4.4272} )\\\\\)

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution)  to approximate discrete probability distribution (Binomial distribution).

\(P(970 < Y < 990) = P( Z < \frac{989.5 - 980}{4.4272}) - P( Z < \frac{969.5 - 980}{4.4272} )\\\\P(970 < Y < 990) = P( Z < \frac{9.5}{4.4272}) - P( Z < \frac{-10.5}{4.4272} )\\\\P(970 < Y < 990) = P( Z < 2.15) - P( Z < -2.37 )\\\\\)

From the z-table, the z-score corresponding to 2.15 is 0.9842

From the z-table, the z-score corresponding to -2.37 is 0.0089

\(P(970 < Y < 990) = 0.9842 - 0.0089\\\\P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

Therefore, there is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

1.3(3)+7=16

9+7=16

16=16

So option 1 is correct

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer:D

Step-by-step explanation:

The length is 6.8 meters and the width is 8.2 meters.

Represent the length and the width with x and y

So, we have:

y = 1.2x

P = 2(x + y)

The perimeter is 30.

So, we have:

2(x + y) = 30

Divide by 2

x + y = 15

Substitute y = 1.2x

x + 1.2x = 15

This gives

2.2x = 15

Divide by 2.2

x = 6.8

Substitute x = 6.8 in y = 1.2x

y = 1.2 * 6.8

Evaluate

y = 8.2

Hence, the length is 6.8 meters and the width is 8.2 meters.

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Answer:

\(\displaystyle 8\)

Step-by-step explanation:

List all the factors of twenty-seven, then sum them up:

\(\displaystyle 1, 3, 9, 27; 40 = 27 + 3 + 9 + 1\)

Now, the clue tells you that forty is the fifth multiple of some quantity, so divide by five to get your result, and it MUST be a whole number, or elce we have no solution here:

\(\displaystyle 8 = \frac{40}{5}\)

Eight is the quantity you are looking for, and sinse it is a whole number, it is valid.

I am joyous to assist you at any time.

Answer:

i got 48

Step-by-step explanation:

2(5*2)

2(2*5)

2(2*2)

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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The algebraic equation represents the words: Twenty percent of Tom's grade is 80 points would be 0.20x = 80. thus, option D is correct.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let the tom's grade represneted by x.

so,

Twenty percent of Tom's grade is 80 points means

20%x = 80

20x / 100 = 80

Or 0.20x = 80

Hence, algebraic equation represents the words: Twenty percent of Tom's grade is 80 points would be 0.20x = 80. thus, option D is correct.

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Answer:

13 hours

Step-by-step explanation:

Since Kiara has already written 37 pages she only needs 13 more to get to 50 pages. If she takes one hour per page then it will take her 13 hours to write 13 pages.

Answer: A

Step-by-step explanation:

if rachel is 'x' and jovanna ran 30 more miles than her, then jovanna ran 30+x miles

we know that jovanna ran 47 miles so we set both values equal to each other

30 + x = 47

which is option A :))

Answer:

2

Step-by-step explanation:

3x2=6

s=2

Plz brainly and like :D

Answer: 2

Step-by-step explanation: Hope this help :D

The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.

Histogram Illustration

135  137   136  137  138  139

140  139   137  140  142  146

148  145    139  140  142  143

144   143   141  139   137  138

139   136   133   134  132  132

Her weight should be a histogram.

Answer

131.5-133.5

133.5-135.5

135.5-137.5

137.5-139.5

139.5-141.5

141.5-143.5

143.5-145.5

145.5-147.5

147.5-149.5

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There is a significant difference in stress levels between dog owners and non-dog owners.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves techniques for designing experiments, surveys, and observational studies to gather data, as well as methods for summarizing, visualizing, and drawing conclusions from the data.

Step 1: State the null and alternative hypotheses:

Null hypothesis: There is no significant difference in stress levels between dog owners and non-dog owners.

Alternative hypothesis: There is a significant difference in stress levels between dog owners and non-dog owners.

Step 2: Determine the level of significance (alpha) and the degrees of freedom :

Alpha = 0.01 (given in the problem)

Degrees of freedom = n₁ + n₂ - 2, where n1 and n2 are the sample sizes of the two groups.

n₁ = 20 (from the table)

n₂ = 15 (from the table)

Degrees of freedom = 20 + 15 - 2 = 33

Step 3: Calculate the sample means and standard deviations:

For dog owners:

Sample mean (x₁) = 28.25

Sample standard deviation (s₁) = 9.24

For non-dog owners:

Sample mean (x₂) = 36.20

Sample standard deviation (s₂) = 7.96

Step 4: Calculate the t-statistic:

t = (x₁ - x₂) / √[(s₁²/n₁) + (s₂²/n₂)]

t = (28.25 - 36.20) / √[(9.24²/20) + (7.96²/15)]

t = -2.75

Step 5: Determine the critical t-value:

Using a t-table with 33 degrees of freedom and a one-tailed alpha of 0.01, the critical t-value is -2.449.

Step 6: Make a decision:

Since the calculated t-value (-2.75) is less than the critical t-value (-2.449), we reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in stress levels between dog owners and non-dog owners.

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If the original amount is 390 and the new amount is 546, the amount of increase is 156 and the percent increase is 40%. This indicates that the new amount is 156 units higher than the original amount, representing a 40% increase.

To find the amount of increase and the percent increase between the original amount and the new amount, we can follow these steps:

1. Start with the original amount: 390.

2. Determine the increase by subtracting the original amount from the new amount: 546 - 390 = 156.

3. The amount of increase is 156. This means that the new amount is 156 units greater than the original amount.

4. To calculate the percent increase, divide the amount of increase by the original amount and then multiply by 100: (156 / 390) * 100 = 40.

5. The percent increase is 40%. This means that the new amount is 40% greater than the original amount.

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Answer:

Step-by-step explanation:

increase ≤ 55-43.5

increase ≤ 11.5

Elanor can increase her speed by 11.5 miles per hour.

Answer:

x=106

Step-by-step explanation:

Let's solve your equation step-by-step.

−12+x−34=60

Step 1: Simplify both sides of the equation.

−12+x−34=60

−12+x+−34=60

(x)+(−12+−34)=60(Combine Like Terms)

x+−46=60

x−46=60

Step 2: Add 46 to both sides.

x−46+46=60+46

x=106

Answer:

$3.49

Step-by-step explanation:

If 1 yard = 3 foot

then A 2-yard piece of twine = 6-foot piece of twine.

20.94 per foot is 3.49

as 20.94/3.49.

thus the price per foot is $3.49

Answer:

90

Step-by-step explanation:

I'm not sure about the answer

Answer:

£26.77

Step-by-step explanation:

450(100% + 2%)^6

= 450 (1.02)^6

= 506.77.

506.77 - 480 - 26.77.

Riley had £26.77 left.

Check the picture below.

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

In circle L with m/KLM = 60 and KL = 18 units, the length of arc KM is approximately 18.85 units.

What is circle?

A circle is a geometrical shape that is defined as the set of all points in a plane that are equidistant from a given point called the center of the circle. The distance between the center of the circle and any point on the circle is called the radius of the circle.

We can use the formula for the length of an arc of a circle:

L = rθ

where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the center of the circle (in radians).

In this problem, we are given the measure of the central angle m/KLM = 60 degrees, which is equal to 60/360 = 1/6 of a full revolution (360 degrees). Therefore, the angle θ subtended by the arc KM is:

θ = (1/6) * 2π = π/3 radians

To find the length of arc KM, we need to know the radius of circle L. Since we are not given this information directly, we can use the fact that KL is a chord of the circle and the perpendicular bisector of KL passes through the center of the circle. Let O be the center of circle L, and let N be the midpoint of KL. Then ON is the radius of the circle, and KN = KL/2 = 9 units.

We can use the Pythagorean theorem to find ON:

ON² = OM² + MN²

where OM is the distance from O to the midpoint of LM. Since OM is perpendicular to LM, it is also the altitude of triangle KLM, and we can use the formula for the altitude of an equilateral triangle to find that OM = (\(\sqrt{3}\)/2)KL = 9\(\sqrt{3}\) units.

Since MN = KL/2 = 9 units, we have:

ON^2 = \((9*\sqrt{3} )^2 + 9^2\) = 243 + 81 = 324

so ON = 18 units.

Now we can find the length of arc KM using the formula:

L = rθ = 18 * (π/3) = 6π units

Rounding to the nearest hundredth, we get:

L ≈ 18.85 units.

Therefore, the length of arc KM is approximately 18.85 units.

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