The area, A, of a circle is given by A = π r2, where r is the radius of the circle. Round all values to the nearest whole number before substituting into the formula in order to estimate the area of a circle with radius 11.3 centimeter

Answer:

• Width: 56 yards.

• Length: 232 yards.

Explanation:

Let the width of the rectangular field = w

Quadruple the width = 4w

The length is 8 yards longer than quadruple the width. Therefore:

The perimeter of the field is 576 yards.

We solve the equation for w.

The width of the rectangular playing field is 56 yards.

Next, we find the length.

The length of the rectangular playing field is 232 yards.

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

\(180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113\)

Answer:

6/8, 9/12, 12/16, 15/20

Step-by-step explanation:

If you simplify the fractions it will all equal 3/4.

Simplify by finding the Greatest Common Factor and dividing both numbers by the GCF.

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info

Where \($\mu=205$\) and \($\sigma=1.5$\)

Let the probability be

\($P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$\)

For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:

\($\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$\)

To simplify this problem is utilizing the normal standard distribution and the z score given by:

\($z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$\)

To find the z scores for each limit and we got:

\($z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$\)

\($z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$\)

To find this probability:

P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)

simplifying the above equation, we get

= 0.962 - 0.0377

= 0.9243

The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:

P = 1 - 0.9243 = 0.0757

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

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The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

C.The equation has a positive y-intetcept

Step-by-step explanation:

def not lying

The mass of the thin bar is \((\pi/2) - 1\).

To find the mass of the thin bar with the given density function, we need to integrate the density function over the length of the bar.

The length of the bar is given as L = SA - SX = \(\pi/2 - 0 = \pi/2.\)

So, the mass of the bar is given by the integral:

M = ∫(SX to SA) p(x) dx

Substituting the given density function, we get:

M = ∫(0 to \(\pi/2\)) (1 + sin x) dx

Using integration rules, we can integrate this as follows:

M = [x - cos x] from 0 to \(\pi/2\)

M = \((\pi/2) - cos(\pi/2) - 0 + cos(0)\)

\(M = (\pi/2) - 1\)

Therefore, the mass of the thin bar is \((\pi/2) - 1.\)

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It will take them about 26 days to complete the expedition

According to the information, the team of explorers is to travel 19.12km in 12 hours

If they are expected to travel 1014.15km in total, the total time taken is given as:

1014.15km = x

Take their proportions:

\(\frac{19.12}{1014.15} = \frac{12}{x} \\ 19.12x = 12,169.8\\ x = 636.495hours\)

Convert the time taken to days;

\(x =\frac{636.495}{24}\\ x \approx 26.5 days\)

This shows that it will take them about 26 days to complete the expidition.

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The distance between two points can be calculated using the formula;

For points;

Given the points;

The distance between the two points can be calculated using the above formula;

The distance between the two points is;

Answer:

1

Step-by-step explanation:

x+6y=20-10y

x+6y+10y=20

x+16y=20

Given x=4,

=> 4+16y=20

16y=20-4=16

y=1

So, the missing value is 1.

Answer:

we will have to multiply the second equation by 3 to eliminate the y variable by adding.

Step-by-step explanation:

Given the equations

4x – 3y = 6              →   (1)

6x + 2y = 10             →   (2)

As the first equation is multiplied by 2,

2(4x – 3y) = (2)6

8x - 6y = 12               →  (3)

As we have to eliminate y,

so multiply the second equation by 3,

6x + 2y = 10

3(6x + 2y) = 3(10)

18x + 6y = 30              →  (4)

So now adding the new equations (3) and (4) will eliminate the y variable by adding

8x - 6y = 12

18x + 6y = 30

--------------------

26x + 0y = 42

26x = 42

x = 42/26

x = 21/13

Therefore, we will have to multiply the second equation by 3 to eliminate the y variable by adding.

The volume of the box is 210 cubic inches.

Given that the height of the box is 7 inches and the base of the box has an area of 30 square inches. We need to find the volume of the box. The volume of the box can be found by multiplying the base area and height of the box.

So, Volume of the box = Base area × Height of the box

We know that

base area = length × breadth

Area of rectangle = length × breadth

30 = length × breadth

Now we know the base area of the rectangle which is 30 square inches.

Height of the rectangular prism = 7 inches.

Now we can calculate the volume of the rectangular prism by using the above formula:

The volume of the rectangular prism = Base area × Height of the prism= 30 square inches × 7 inches= 210 cubic inches

Therefore, the volume of the box is 210 cubic inches.

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========================================================

Explanation:

x = sticker price, which is some number larger than 9 (otherwise the store loses money)

x-9 = profit made per speaker

To get the gross margin percentage, we divide the profit over the sales (aka revenue). So we'll divide (x-9) over x

The expression (x-9)/x represents the gross margin in decimal form. Set this equal to 0.80 and solve for x

-----------------

(x-9)/x = 0.80

x-9 = 0.80x

x-0.80x = 9

0.20x = 9

x = 9/0.20

x = 45

The sticker price is $45

-------------------

If the sticker price is $45 per speaker, then the store owner gets 45-9 = 36 dollars in profit per speaker sold. The gross margin would be (profit)/(sales) = 36/45 = 0.80 = 80%

In other words, 80% of the revenue is profit (the remaining 20% is costs or expenses).

(a) The repeated eigenvalue is -1, and the multiplicity of this eigenvalue is 2.

(b) To find a basis for the eigenspace associated with the eigenvalue -1, we need to solve the equation (A₁ - (-1)I)v = 0, where A₁ is the given matrix and I is the identity matrix.

The augmented matrix for the system of equations is:

\(\begin{bmatrix}0 & 2 & -1 \\ -6 & -9 & 2 \\ 2 & 2 & -1\end{bmatrix}\) \(\begin{bmatrix}0 \\ 0 \\ 0\end{bmatrix}\)

Row reducing this augmented matrix, we obtain:

\(\begin{bmatrix}1 & 0 & -\frac{1}{3} \\ 0 & 1 & -\frac{1}{3} \\ 0 & 0 & 0\end{bmatrix}\) \(\begin{bmatrix}0 \\ 0 \\ 0\end{bmatrix}\)

This system of equations has infinitely many solutions, which means that the eigenspace associated with the repeated eigenvalue -1 is not spanned by a single vector but a subspace. Therefore, we can choose any two linearly independent vectors from the solutions to form a basis for the eigenspace.

Let's choose the vectors [1, -1, 3] and [1, 1, 0]. So, the basis for the eigenspace associated with the repeated eigenvalue -1 is {[1, -1, 3], [1, 1, 0]}.

(c) The dimension of the eigenspace is the number of linearly independent vectors in the basis, which in this case is 2. Therefore, the dimension of the eigenspace is 2.

(d) To determine if the matrix is diagonalizable, we need to check if it has a sufficient number of linearly independent eigenvectors to form a basis for the vector space. If the matrix has n linearly independent eigenvectors, where n is the size of the matrix, then it is diagonalizable.

In this case, the matrix has two linearly independent eigenvectors associated with the repeated eigenvalue -1, which matches the size of the matrix. Therefore, the matrix is diagonalizable.

The correct answers are:

(a) Repeated eigenvalue: -1, Multiplicity: 2

(b) Basis for eigenspace: {[1, -1, 3], [1, 1, 0]}

(c) Dimension of eigenspace: 2

(d) The matrix is diagonalizable: True

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The correct option is a b c d.

fd = 2,809

We need to round the given answers to the nearest hundredth.

a. 150, 150, fd = 2,809

Now, we need to find 150 such that it is the same percentage as 2,809 of 150.

150 * (2,809/100) = 4.2135 ≈ 4.21

So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100

b. 150, 150, fd = 2,809

Now, we need to find 150 such that it is the same percentage as 2,809 of 150.

150 * (2,809/100) = 4.2135 ≈ 4.21

So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100

c. 150, 150, fd = 53

Now, we need to find 150 such that it is the same percentage as 53 of 150.

150 * (53/100) = 79.5 ≈ 79.5

So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100

d. 150, 150, fd = 53

Now, we need to find 150 such that it is the same percentage as 53 of 150.

150 * (53/100) = 79.5 ≈ 79.5

So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100

Therefore, the correct option is a b c d.

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Answer:

b pizza hut

Step-by-step explanation:

sorry im wrong

the total number of days spent in Bolivia by Audrey is 7days.

Audrey spent two weeks in Brazil

that mean

the total number of days spent in Brazil by Audrey = 2x7

= 14 days

This is twice as many days as she spent in Bolivia.

2m = 14

m = 14/2

m = 7

so, the total number of days spent in Bolivia by Audrey = 7days

The term "week" most commonly refers to any span of seven continuous days. The term "week" is also frequently used to describe the seven-day period that runs from Sunday through Saturday (though in some places this may be different, with the week considered to begin on Monday, for example)

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Answer: Yes, it does.

Step-by-step explanation: Let x represent the price of gas today. 200% of x=200/100*x, which can be written as 2x because 200/100=2. 2x is x doubled, and therefore, it does mean the price has doubled.

Answer:

yes, the price has doubled

Answer:

.............

Step-by-step explanation:

.............

Answer:

First Problem. 17x , 17 + x, and 7x + 10x

Second Problem. 2 + 12y, 2x1 + 2x6y

Step-by-step explanation:

Given the sequence:

7, -14, 28, -56,

To find the 7th term of the geometric sequence, use the formula below:

where,

a is the first term = 7

n is the number of terms = 7

r = common ratio =

Thus, we have:

The 7th term is -448

ANSWER:

A) -448

Answer:

x=-3

Step-by-step explanation:

First u have to bring te variable to one side and numbers for the other side. so to remove -x from the right side add x and as to balance the eqaution u have to add x for the left side too.

x+1+x=-x+(-5)+x

then it becomes,

2x+1 = -5

Now to remove +1from the left side substract 1 from both sides.

2x+1 -1 = -5-1

Now the equation is like,

2x =-6

Now divide the equation by 2

2x/2 = -6/2

then,

x = -3

So itis simply like this,

x+1 = x-5

2x=-6

x=-3

To find the value of x, we calculate the average of the sample observations. Summing up the observations and dividing by the total number of observations, we get:

x = (125 + 122 + 126 + 100 + 155 + 132 + 121 + 118 + 114 + 125 + 142 + 2 + 130 + 110 + 140 + 129 + 3) / 17 = 114.118 seconds (rounded to three decimal places).b) To find the value of R, we calculate the range of each sample by subtracting the minimum observation from the maximum observation. Then we find the average range across all samples:R = (155 - 100 + 142 - 2 + 140 - 110 + 132 - 114 + 142 - 3) / 5 = 109.2 seconds (rounded to three decimal places).

c) The Upper Control Limit (UCL) and Lower Control Limit (LCL) using 3-sigma can be calculated by adding and subtracting three times the standard deviation from the average:UCL = x + (3 * R / d2) = 114.118 + (3 * 109.2 / 1.693) = 348.351 seconds (rounded to three decimal places).LCL = x - (3 * R / d2) = 114.118 - (3 * 109.2 / 1.693) = -120.115 seconds (rounded to three decimal places).

d) The Upper Control Limit Range (UCLR) and Lower Control Limit Range (LCLR) using 3-sigma can be calculated by multiplying the average range by the appropriate factor:UCLR = R * D4 = 109.2 * 2.115 = 231.108 seconds (rounded to three decimal places).LCLR = R * D3 = 109.2 * 0 = 0 seconds.

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Answer:

12.25

Step-by-step explanation:

You have to work it out like if it was a ratio.

basically you need to make 7/x equal to 4/7

to do this you divide 4 by 7 and the divide 7 by the answer. This will make x equal to 12.25

The error in the statement will be When reporting correlation, one does not report units because correlation has no units that is option D is correct.

The correct statement would be "The correlation between shoe size and height is 0.87." The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 0 indicating no relationship, and 1 indicating a strong positive relationship. The correlation coefficient does not have units because it is a standardized measure of the relationship between the variables. If there is a unit given in any correlation statement then it means that the statement is a wrong statement or it has an error.

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The significance of the mentioned statistics lies in their ability to provide insights into the performance of investment managers who graduated from top business programs.

The significance of the mentioned statistics regarding investment managers' performance and the sample of 400 managers who graduated from top business programs lies in their ability to provide insights into the performance of investment managers who have received education from prestigious business programs.

By focusing on a sample of 400 managers who graduated from top business programs, we can gain valuable information about the capabilities and effectiveness of these managers in the field of investment management. This sample selection suggests a certain level of quality and expertise in the chosen managers, as they have undergone rigorous training and education in renowned business programs.

Analyzing the performance statistics of these investment managers allows us to assess their success in generating returns on investments and making sound financial decisions. It provides a basis for evaluating their skills, expertise, and ability to navigate the complexities of financial markets.

Additionally, studying the performance of investment managers from top business programs can have broader implications. It can shed light on the effectiveness of these programs in equipping graduates with the necessary knowledge and skills to excel in the investment management industry. The statistics obtained from this sample can help identify any patterns or trends in performance, enabling us to evaluate the impact of education from top business programs on the success of investment managers.

Furthermore, these statistics can serve as a benchmark for comparing the performance of investment managers from different educational backgrounds. It allows for comparisons between managers who graduated from top business programs and those who did not, providing insights into the potential advantages or disadvantages of specific educational pathways in the investment management field.

In conclusion, the significance of the mentioned statistics lies in their ability to provide insights into the performance of investment managers who graduated from top business programs. They help evaluate the skills, expertise, and success of these managers while also contributing to our understanding of the impact of education on their performance.

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What is the significance of the mentioned statistics regarding investment managers' performance and the sample of 400 managers who graduated from top business programs?

Answer:

144

Step-by-step explanation:

We can see that every 2 boxes has 24 peaches in it. That means that every single box would have 12 in it. Then it is just simple multiplication from there. 12 * 12 = 144.

Hope that this helps!

The inequality that represents the given condition is "p > 12".

Let p be the amount of cheese produced in kg.

Then, the amount of yogurt produced is (p + 24) kg (since it is 24 kg more than cheese). And the amount of ice cream produced is 3p kg (since it is 3 times as much as cheese).

Now, we need to find the possible values of p that satisfy the condition "the dairy farm produced more kilograms of ice cream than yogurt last week." In other words, we need to compare the amount of ice cream produced (3p) with the amount of yogurt produced (p + 24) and ensure that the amount of ice cream is greater.

So, we can write the following inequality:

3p > p + 24

Simplifying this inequality, we get:

2p > 24

Dividing both sides by 2, we get:

p > 12

Therefore, the possible values of p that satisfy the given condition are all values of p greater than 12.

In summary, the inequality that represents the given condition is "p > 12".

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Answer:

Step-by-step explanation:

The graph choices have not been posted.

There is also a doubt as to what is really wanted, is it

A. f(x) = 100(0.5)^x - 1

or

B. f(x) = 100(0.5)^(x - 1)

I have included a graph for each. Feel free to make a choice between the two, A is red, and B is blue.

Answer:

it's B

Step-by-step explanation:

i literally just did it on ed