In independent random samples of 10 men and 10 women in a coed basketball league, the numbers of points scored per season are given by the back-to-back stemplot below: Row 1 contents are Men; bar; blank; bar; Women. Row 2 contents are 2; bar; 0; bar; 3. Row 3 contents are 8, 5, 4; bar; 1; bar; 4, 7. Row 4 contents are 8, 3, 1; bar; 2; bar; 2, 3, 6, 7. Row 5 contents are 9, 4; bar; 3; bar; 0, 5. Row 6 contents are 6; bar; 4; bar; 1. Part A: Describe the shape of each data set. (3 points) Part B: Michaela analyzed the data and stated that the better measure of center for the women is the mean. Is Michaela correct? Explain your reasoning. (3 points) Part C: Michaela decided there are no outliers in the women's data set. Is she correct? Justify your answer mathematically. (4 points) (10 points)

The debt-to-income ratio is the division between the sum of all debts and the sum of income.

Debt: $1,982 + $258 + $184 + $237 = $2,661.

Income: $4,115 + $700 + $1,000 + $95 = $5,910.

Then,

The correct option is for the value of c,  such that f(c) is the average value of the function on the interval [0, 2], is D.

The average value of a function on an interval [a, b] is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is [0, 2], then:

f(2) = √(2 + 2) = 2

f(0) = √(0 + 2) = √2

Then here we need to solve the equation:

√(c + 2) = (f(2) - f(0))/(2 - 0)

√(c + 2) = (2 + √2)/2

Solving this for c, we will get:

c = [ (2 + √2)/2]² - 2

c = 0.9

Them tjhe correct option is D.

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Answer:

reflex angle

Step-by-step explanation:

A reflex angle is the larger angle, it's always more than 180° (half a circle) but less than 360° (A full circle).

Answer:

REFLEX ANGLE !!

Step-by-step explanation:

The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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The volume of the solid obtained by rotating the region bounded by y = 2x and y = x² about the x-axis can be found using the method of cylindrical shells.

In the first paragraph, it is stated that the problem involves finding the volume of a solid obtained by rotating a region bounded by two curves, y = 2x and y = x², about the x-axis.

To find the volume, we divide the region into infinitely thin vertical strips parallel to the y-axis. Each strip acts as a cylindrical shell when rotated about the x-axis. The height of each cylindrical shell is given by the difference between the y-values of the two curves at a particular x-value. In this case, the height is \((2x - x^2)\).

The radius of each cylindrical shell is simply the x-value at which it is located. Thus, the radius is x.

To calculate the volume of each shell, we use the formula for the volume of a cylinder: \(V = 2\pi x(2x - x^2)dx\), where dx represents an infinitely small width of each shell.

Integrating this expression over the interval where the curves intersect, we can find the total volume of the solid obtained by rotating the region.

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Using Simpson's Rule, the cardiac output can be estimated by approximating the area under the curve formed by the dye concentration readings at two-second intervals.

Simpson's Rule is a numerical method used to approximate definite integrals by dividing the interval into subinterval and applying a weighted average of function values. In this case, we have the time (t) and dye concentration (c(t)) readings at two-second intervals.

To estimate the cardiac output, we need to find the integral of the concentration function over the given time interval. Simpson's Rule can be applied by dividing the interval into subintervals (in this case, 0-12 seconds) and using the given function values to calculate the approximate integral.

By applying Simpson's Rule to the given data, the cardiac output can be estimated by calculating the weighted average of the function values and multiplying it by the width of the subintervals.

Please note that since the table is incomplete, providing the exact calculation and result of the cardiac output is not possible without additional data.

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Answer:

I'm not a hundred percent sure but I think 6 teacups were bought for 60$

The dimensions of the box that minimize surface area are L = 25√2, W = √2/10, and H = √2/10.

The minimum surface area is given as  (50 + 1)√2 square inches

The length of one side of the base is W = √2/10, and the height of the box is H = √2/10

Let L, W and H be the length, width, and height of the rectangular box, respectively.

volume of the box is 500 \(in^3\)

V = LWH = 500

To minimize the surface area

A = 2LW + 2LH + 2WH

Use the method of Lagrange multipliers

f(L, W, H) = 2LW + 2LH + 2WH + λ(LWH - 500)

Take partial derivatives with respect to L, W, H, and λ and setting them equal to zero

∂f/∂L = 2W + WHλ = 0

∂f/∂W = 2L + LHλ = 0

∂f/∂H = 2L + LWλ = 0

∂f/∂λ = LWH - 500 = 0

we have either W = 0 or Hλ = -2.

we are looking for positive dimensions, so

Hλ = -2.

Similarly, From the second equation, we have either L = 0 or Hλ = -2.  we discard the possibility of L = 0 and conclude that

Hλ = -2.

From the third equation, we have either L = 0 or Wλ = -2.

Wλ = -2.

From the fourth equation, we have

LWH = 500.

Multiplying the first equation by W and the third equation by H, and substituting the resulting expressions into the equation for A

A = 2LW + 2LH + 2WH = -4/λ

Multiplying this equation by λ and substituting LWH = 500

-λA/2 = 1000/λ

Solving for λ, we get:

λ = ±10√2

Since we want positive dimensions, we can discard the negative value of λ.

Therefore, we have

Hλ = -2 => H = 2/λ = 2/(10√2) = √2/10

Wλ = -2 => W = 2/λ = 2/(10√2) = √2/10

LWH = 500 => L = 500/WH = 500/(2/λ)(√2/10) = 25√2

Hence, the dimensions of the box that minimize surface area are L = 25√2, W = √2/10, and H = √2/10.

The length of one side of the base is W = √2/10, and the height of the box is H = √2/10.

The minimum surface area is given by (50 + 1)√2 square inches.

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Answer:3.33%

easy

Step-by-step explanation:

A = true value = 60

B = estimated or measured value = 62

C = percent error

C = ( |A-B|/A ) * 100%

C = ( |60-62|/60 ) * 100%

C = (2/60)*100%

C = 0.0333*100%

C = 3.33%

17,242 rounded to the nearest 10,000 is 20,000.

The given number is 17,242.

We need to round the given number to the nearest 10,000.

To round a number to the nearest 10,000, check the thousands of digits to decide whether to round up or round down. If the thousands are 5000 or more, round up. If they are 4999 or less, round down. In the given number the thousands are greater than 5000.

So, 17,242 rounded to the nearest 10,000 is 20,000.

Therefore, 17,242 rounded to the nearest 10,000 is 20,000.

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The point q = (4, 8, 1, 3) is located approximately 3.46 units away from the hyperplane in R4 passing through the point p = (1, 2, -1, 3) with the normal vector N = (1, 0, 2, 2).

To calculate the distance between the point q and the hyperplane, we can use the formula for the distance from a point to a plane. The formula is given by:

distance = |(q - p) · N| / ||N||

where q - p represents the vector connecting the point q to the point p, · denotes the dot product, and ||N|| represents the magnitude of the normal vector N.

Calculating the vector q - p:

q - p = \((4 - 1, 8 - 2, 1 - (-1), 3 - 3) = (3, 6, 2, 0)\)

Calculating the dot product (q - p) · N:

(q - p) · N = \(3 * 1 + 6 * 0 + 2 * 2 + 0 * 2 = 7\)

Calculating the magnitude of the normal vector N:

||N|| = \(\sqrt{(1^2 + 0^2 + 2^2 + 2^2)} = \sqrt{9} = 3\)

Substituting the values into the distance formula:

distance = |7| / 3 ≈ 2.33 units

Therefore, the point q is approximately 2.33 units away from the hyperplane in R4 passing through the point p with the normal vector N.

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Answer:

73.8 g

Step-by-step explanation:

57.4/7 = 8.2 per cake

8.2 x 9 = 73.8 g

Answer:

I'm pretty sure the answer would be 73.8g

Step-by-step explanation:

(a) The equilibrium output (Y*) in this closed economy is 17,000.

(b) Since Yp < Y*, there is a recessionary gap.

(c) The change in government expenditure necessary to move the economy back to its potential is an increase of $1,800.

(a) To calculate Y, we need to use the equation for equilibrium in a closed economy: Y = C + I + G + NX. Since there is no trade (NX=0), we can simplify the equation to Y = C + I + G. Substituting the given values, we get:

Y = 400 + 0.8Y + 1800 + 1200

0.2Y = 3400

Y* = 17,000

(b) To determine if there is an inflationary or recessionary gap, we need to compare the actual output (Yp) with the potential output (Y*). If Yp > Y*, then there is an inflationary gap, and if Yp < Y*, then there is a recessionary gap. Substituting the given value of Yp, we get:

Yp = 8000

Y* = 17,000

Since Yp < Y*, there is a recessionary gap.

(c) To calculate the change in government expenditure (ΔG) necessary to move the economy back to its potential, we can use the formula for the expenditure multiplier: ΔY/ΔG = 1/(1 - MPC) where MPC is the marginal propensity to consume. In this case, MPC = 0.8 since C = 400 + 0.8Y.

Substituting the values, we get:

ΔY/ΔG = 1/(1 - 0.8) = 5

ΔY = ΔG * 5

To close the recessionary gap of 9,000 (i.e., Y* - Yp), we need to increase output by ΔY = 9,000.

Therefore,

ΔG * 5 = 9,000

ΔG = 1,800

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steps)7-2n=3

then you move the constant to tge right hand side and change its sign

-2n=3-7

then

calculate the difference

-2n=3-7

-2n= -4

Divide both sides

n=2

Answer:

From what I understand n=5

Answer:

\(108\pi\) or approx. \(339.3 m^{2}\)

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, \(SA_{tot} =4\pi r^2\). But we need it for a hemisphere, so multiply the equation by \(\frac{1}{2}\).

\(SA} = (\frac{1}{2}) 4\pi r^2\) => \(SA} =2\pi r^{2}\)

We also need the area of the base, which is circle. \(A_{circle}=\pi r^{2}\).

Now add these equations together to get our equation.

\(SA_{tot} =2\pi r^2 +\pi r^{2}\) => \(SA_{tot} =3\pi r^2\)

Now we have the proper equation for total surface area of a hemisphere, \(SA_{tot} =3\pi r^{2}\). Plug in the value of \(r\) which is given in the problem, \(r=6m\).

=> \(SA_{tot} =3\pi (6)^{2}\) => \(SA_{tot} =3\pi (36)\) => \(SA_{tot} =108\pi m^{2}\) or approx. \(339.3 m^{2}\)

Use the bar diagram section

From the question

The probability a student at school A is in grade 10 is

From the table

Number of students in grade 10 at school A = 25

Total number of students in School A = 120

Therefore

The probability a student at school A is in grade 10 is

Hence, The probability a student at school A is in grade 10 is 5/24

The probability a student at school B is in grade 10 is

From the table

Number of students in grade 10 at school B = 20

Total number of students in School A = 80

Therefore

The probability a student at school B is in grade 10 is

Hence, The probability a student at school B is in grade 10 is 1/4

Since, the probability a student at school B is in grade 10 is greater than the probability a tudent at school A is in grade 10 then

It is less like

section = 210/360 = 7/12

Area = pi*r^2

Area = 12^2*pi

Area = 144*pi

Area = 7/12*144*pi

Area = 1008/12*pi

Area = 84~pi this is the result

The correct statement is: The margin of error is plus or minus 3%.

To determine the margin of error based on the given confidence interval, we can calculate half the width of the interval. The margin of error is the maximum likely difference between the true proportion and the sample estimate.

The given confidence interval is (40%, 46%), so the width of the interval is 46% - 40% = 6%.

The margin of error is half of the width of the interval, so the margin of error is 6% / 2 = 3%.

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Answer:

Step-by-step explanation:

First we can determine that this is a special 45-45-90 triangle, since the two legs are congruent, meaning the two unknown angles are congruent as well:

180 = 90 + 2(theta)

theta = 45

Knowing this, we can remember that the hypotenuse of this special triangle is equal to the leg*sqrt(2).

This means that 1 = x(sqrt(2)).

\(x=\frac{1}{\sqrt{2} }\)

Hope this helps!

The number of movie bewteen 25 and 29 are 5.

The statement is false.

The correct statement is "A postulate is a statement that is assumed true without proof."

Answer:

The answer is 55g+10

Step-by-step explanation:

first you use distributive property then add like terms.

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.

Let's call DE = x. Then, we have:

CE/FG = x/142.1

Solving for x, we have:

x = (CE * 142.1) / FG

CE = CF + FD = 130 + 60 = 190m

x = (190 * 142.1) / 142.1 = 190m

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

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The complete question is :

To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.

The total cost is $132

From the question, we have

the dimensions of the fence are 20 feet long and 6 feet high.

if each piece of wood is 72 inches tall and 4 inches wide

the wood costs $1.10 per square foot.

total number of woods =(total area of fence) /(area of each wood)

=(20*6)/(6*0.33)

= 60

cost per plank = 2 * $1.10 =$2.20.

total cost =  60*2.20= $132

The total cost is $132

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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Answer:

x y

1 2

2 2

3 2

4 2

5 2

To write the equation y = -2x + 6 as a table, we need to substitute different values of x into the equation and solve for y. Here is an example of a table with some values of x and the corresponding values of y:

x y

1 4

2 2

3 0

4 -2

5 -4

Step-by-step explanation: