A club with 20 women and 17 men needs to form a committee of size six. How many committees are possible if the committee must have three women and three men

The interpretation for the slope of the linear regression prediction equation is change in y with a unit change in x.

The linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Consider the slope of the line as m

m= Change in y coordinate / Change in x coordinate

When change in x coordinate is 1 unit

Then,

m= Change in y coordinate

If the change in x is 1 unit, then slope of the line will change depends on change in y coordinate

Hence, The interpretation for the slope of the linear regression prediction equation is change in y with a unit change in x.

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Answer:

I don't think he moves away from is starting position.

Because he goes forward 3ft, than goes back 4.6ft, and moves forward 4.6ft.

Hope this helps.

Factor analysis and Principal Component Analysis (PCA) are statistical techniques used to reduce the dimensionality of data sets, identify underlying patterns, and simplify data interpretation. In both methods, sample size plays a critical role in determining the accuracy and reliability of the results.

An appropriate sample size is essential for several reasons:

1. Adequate Representation: A larger sample size helps ensure that the data is representative of the population, capturing a wide range of variability and improving the generalizability of the results.

2. Statistical Power: Larger sample sizes increase the statistical power of the analysis, enabling the detection of smaller effects and providing more reliable estimates of the underlying factors or components.

3. Stability: In factor analysis and PCA, larger sample sizes lead to more stable factor structures or component loadings, increasing the likelihood that the results are replicable in different samples or across time.

4. Error Minimization: A sufficient sample size helps minimize errors and distortions in the analysis, reducing the chance of overfitting the data or extracting spurious factors or components.

While there is no one-size-fits-all rule for determining an optimal sample size, some guidelines can help. A widely cited rule of thumb is a minimum of 10 to 20 observations per variable, with more complex models or data structures requiring larger sample sizes. Another approach is to perform a power analysis or Monte Carlo simulation, considering the desired level of statistical power, effect size, and specific model parameters.

In summary, selecting an appropriate sample size for factor analysis or PCA is crucial to ensure accurate, reliable, and generalizable results. Following guidelines and considering the context of the data and research question can help make informed decisions about sample size.

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The required value of x for the given proportion is 45.31

What is proportion?

Proportion is a mathematical relationship or ratio between two or more values. It is used to compare the size, quantity, or degree of two or more objects or measurements. Proportion can be expressed as a fraction, decimal, or percentage. It is often used in geometry, algebra, and calculus to determine the size of a shape or to solve an equation. Proportion is also used in statistics to compare data sets. In everyday life, proportion is used to make sure that items are in good balance with each other. For instance, proportions are used when baking a cake or making a recipe to ensure that the ingredients are properly combined.

Given, the proportion

x : 15 = 29 : 9.6

or, x = \(\frac{29}{9.6}\) × 15

or, x = 45.31

Hence, the required value of x for the given proportion is 45.31

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Answer:

30°

Step-by-step explanation:

x = atan(5.6/9.7) = atan(.5773) = 30.00° (to the nearest hundredth)

Answer:

x=29.7°

Step-by-step explanation:

take x degree as reference angle

using tan rule

tan x=opposite/adjacent

tan x=5.6/9.7

tan x =0.57

x=\(tan^{-1}\)0.57

x=29.68°

x=29.7° (after converting to the nearest tenth).

the new coordinates of the rhombus W'X'Y'Z' after a dilation with scale factor k=3 are: \(W'(3,0), X'(12,-3), Y'(15,-12), Z'(6,-9)\)

To find the new coordinates of the image after dilation, we need to multiply the coordinates of each vertex by the scale factor k = 3.

Let's start with vertex W(1,0):

Multiply the x-coordinate by  \(3: 1 *\times 3 = 3\)

Multiply the y-coordinate by \(3: 0 \times 3 = 0\)

So the new coordinates of W' are \((3,0).\)

Next, let's look at vertex X(4,-1):

Multiply the x-coordinate by \(3: 4 \times 3 = 12\)

Multiply the y-coordinate by \(3: -1 \times 3 = -3\)

So the new coordinates of X' are \((12,-3).\)

Now for vertex Y(5,-4):

Multiply the x-coordinate by \(3: 5 \times 3 = 15\)

Multiply the y-coordinate by \(3: -4 \times3 = -12\)

So the new coordinates of Y' are  \((15,-12).\)

Finally, let's consider vertex Z(2,-3):

Multiply the x-coordinate by  \(3: 2 \times 3 = 6\)

Multiply the y-coordinate by  \(3: -3 \times3 = -9\)

So the new coordinates of Z' are \((6,-9)\)  .

Therefore, the new coordinates of the rhombus  \(W'X'Y'Z'\) after a dilation with scale factor k=3 are:

\(W'(3,0)\)

\(X'(12,-3)\)

\(Y'(15,-12)\)

\(Z'(6,-9)\)

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Answer: y = -5x+2

Step-by-step explanation:

Slope = \(\frac{rise}{run}\) or \(\frac{y_{2}-y_{1}}{x_{2}-x{1}}\)

therefore, given those two points,

Slope = \(\frac{(-3)-7}{1-(-1)}\)

Slope = \(\frac{-10}{2}\)

Slope = -5

Since the m value is the slope, m = -5

In order to find the b value, just substitute the values in the equation with any of the two points given. I'll use (-1,7) but you can use the other one just fine.

let x =1, y = -3

-3=-5(1)+b

-3 = -5+b

-3+5 = b

b = 2

Plug b in the equation:

y=-5x+2

The solution must be concise, the maximum value of y can be found by following the above steps. To find the maximum value, you'll need to analyze the resulting function for any critical points or turning points. The maximum value of y will occur at the highest turning point in the given interval.

To find the maximum value of y in the given initial value problem y'' + y = -sin(2x) with the conditions y(0) = 0 and y'(0) = 0, we can follow these steps:
1. Identify that the given problem is a second-order homogeneous linear differential equation with constant coefficients.
2. Find the complementary function by solving the homogeneous equation y'' + y = 0.
3. Apply the method of variation of parameters to find the particular solution for the non-homogeneous equation.
4. Combine the complementary function and the particular solution to obtain the general solution of the given problem.
5. Apply the initial conditions y(0) = 0 and y'(0) = 0 to find the constants in the general solution.
6. Analyze the solution to determine the maximum value of y.
Since the solution must be concise, the maximum value of y can be found by following the above steps. To find the maximum value, you'll need to analyze the resulting function for any critical points or turning points. The maximum value of y will occur at the highest turning point in the given interval.

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To express the ratio of the given questions in the fraction form are as follow:

1. (2 / 3)  hours

2. (2/3) year

3. 3/2  

4. (3/2) of 20years

5. 1/6

6. 2/4

7. 4/3

8. 1/7

9. 10/3

10. 2/1

As given in the question,

Ratio of the given expression in fraction form is given by:

1. 40 minutes = (120 minutes/3)

                      = (2 / 3)  hours

2. 8 months = (12months) ×( 2/3)

                    = (2/3) year

3. 45 members of sports to the 30 members of dance club

= 45/ 30

= 3/2

4. 3decades = (3 × 10)years

                    = (3/2) of 20years

5. Number of buses to the number of wheels

= 10 / ( 10×6)

= 1/6

6. Projects to quarters

= 2/4

7. Ratio of mango to the apple tree

= 4/3

8. Ratio of number of boxes to the t-shirts

= 1/7

9. ratio of banana to the apples

= 10/3

10. Ratio of girls to the boys

= 20/10

= 2/1

Therefore, the ratio of the given questions in the fraction form are as follow:

1. (2 / 3)  hours

2. (2/3) year

3. 3/2  

4. (3/2) of 20years

5. 1/6

6. 2/4

7. 4/3

8. 1/7

9. 10/3

10. 2/1

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Answer:

We know that the prize of 6 bags of marbles is $18.

Then if each one of the bags costs C, the 6 bags will cost a total of 6 times C.

Then the cost is:

6*C

and this is equal to $18

6*C = $18

Now we want to solve this for C, remember that we can divide both sides of the equation by the same number, then let's divide both sides by 6:

6*C/6 = $18/6

C = $18/6 = $3

Each bag costs $3.

Below you can see a double number line, where above is the number of bags and below is the prize:

Answer:kepler's 3rd law

Step-by-step explanation:

Answer:

\(\sf 9.6\:hours \:\: or \:\: 576\: minutes\)

Explanation:

\(\sf Time \ taken : \dfrac{Distance}{Speed}\)

Here given:

Applying formula,

\(\sf Time \ Taken = \dfrac{48}{5} = 9.6 \ hours = 576 \ minutes\)

3birds would have=2(3)=6legs

Cats have:-

Each cat has 4legs.

Total cats:-

\(\\ \sf\longmapsto \dfrac{24}{4}=6cats\)

The graph of the equation 7x² + 3 = y² is symmetric with respect to B. X-axis and y-axis only.

To test for symmetry with respect to the x-axis, y-axis, and the origin, we need to check if replacing 'x' with '-x', 'y' with '-y', or both leaves the equation unchanged.

For the given equation, when we replace 'x' with '-x', the equation becomes 7(-x)² + 3 = y², which simplifies to 7x² + 3 = y². This indicates that the equation remains the same, so the graph is symmetric with respect to the y-axis.

When we replace 'y' with '-y', the equation becomes 7x² + 3 = (-y)², which simplifies to 7x² + 3 = y². Again, the equation remains the same, indicating symmetry with respect to the origin.

However, when we replace both 'x' with '-x' and 'y' with '-y', the equation becomes 7(-x)² + 3 = (-y)², which simplifies to 7x² + 3 = y². Here, the equation does not remain the same, indicating that the graph is not symmetric with respect to the x-axis.

To visually verify these symmetries, one can use a graphing calculator to plot the graph of the equation. The graph will exhibit symmetry with respect to the y-axis and the origin, but not with respect to the x-axis. Therefore, the correct answer is B. X-axis and y-axis only.

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Answer:

Step-by-step explanation:

as you see the top "moves" like

2,4,6,8, and next will be 10

the bottom adds 3 to the previos answer

5,8,11,14,  next will be 15

5th card is 10/15

To find the volume of the inscribed cube, we need to determine the edge length of the cube first. Let's denote the edge length of the inscribed cube as "x".

In a cube inscribed in a sphere, the diameter of the sphere is equal to the diagonal of the cube. Therefore, the diameter of the sphere is equal to the space diagonal of the large cube, which is given as 9 inches.

The space diagonal of a cube with edge length "a" can be found using the Pythagorean theorem:

Diagonal² = a² + a² + a²

Diagonal² = 3a²

Since the diameter of the sphere is 9 inches, we can write:

3a² = 9²

3a² = 81

a² = 81 / 3

a² = 27

a = √27

a = 3√3

Now we know the edge length of the large cube, which is 3√3 inches. The volume of a cube is given by V = a³, where "a" is the edge length.

Volume of the inscribed cube:

V = (3√3)³

V = 3³ * (√3)³

V = 27 * 3

V = 81 cubic inches

Therefore, the volume of the inscribed cube is 81 cubic inches.

The volume of the cube inscribed in the sphere, given the sphere is inscribed in a cube with an edge length of 9 inches, is 81 cubic inches.

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Answer:

D

Step-by-step explanation:

to be a function you cannot have different y values for the same x, in B for example when x = 3 you have two different values for y (3,7) and (3,8)

D is the only choice where each value of x only has one value for y

The area of the region enclosed by the functions f(x) = √x and g(x) = √x is 2/3 square units

The two functions f(x) = √x and g(x) = √x are identical, so they coincide with each other. Therefore, the region enclosed by the two functions is simply the area under the curve of one of the functions, from x = 0 to x = 1.

To find this area, we can integrate the function f(x) over the interval [0, 1]

∫₀¹ √x dx

We can simplify this integral by using the power rule of integration

∫₀¹ √x dx = [2/3 x^(3/2)] from 0 to 1

Plugging in the limits of integration, we get

[2/3 (1)^(3/2)] - [2/3 (0)^(3/2)] = 2/3 square units

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The given question is incomplete, the complete question is:

Find the area of the region enclosed by f(x)=√x and and g(x)=√x, Write an exact answer (fraction).

Answer:

D

Step-by-step explanation:

3x + y = 10

x - 4y = -1

Multiply the 2nd equation by -3

-3x +12y = 3

Add the 1st equation to the 3rd equation:

13y = 13

Divide both sides by 13:

y = 1

Answer: A) 1

The real distance between towns X and Y measuring 11.2 cm apart on a map with a scale 1: 100,000 is 11.2 km.

Given the scale = 1: 100,000, which means that 1 cm on the map represents 100,000. Thus, 11.2 cm on the map represents 11.2* 100,000 = 1,120,000cm.

We know that 1 km = 100,000cm

Therefore 1,120,000 cm = 1,120,000/100,000

= 11.2 km

Therefore, the real distance between towns X and Y is 11.2km.

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Utilizing the Sieve of Eratosthenes method is simple. In order to encircle the remaining numbers, we must cancel all multiples of each prime number starting with 2 (including the number 1, which is neither a prime nor a composite).

The Sieve of Eratosthenes can be used to locate all prime numbers that are less than 100, as seen in the example below. In ten rows, start by writing the numbers 1 through 100.

Therefore, based on the preceding table, we can conclude that the prime numbers 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are. There are ten prime numbers between 50 and 100 in all. The required prime numbers are those that are surrounded.

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Step-by-step explanation:

so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.

cost1(x) = 19x + 50

cost2(x) = 23x + 42

to get the value for x we know that the cost is the same either way.

that means

cost1(x) = cost2(x) = 19x + 50 = 23x + 42

19x + 50 = 23x + 42

50 = 4x + 42

8 = 4x

x = 2

so, she orders 2 small arrangements.

the total cost is

19×2 + 50 = 38 + 50 = $88

cross check with the other function :

23×2 + 42 = 46 + 42 = $88

correct

The completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

According to the given question.

We have a polynomial

x^3 + 4x^2 - 9x -36

Since for finding the roots of the above polynomial, first we randomly substitute any value of x and find for which value of x the above polynomial gives 0.

So, for x = 3

The above polymonial gets 0.

So, the one factor of the given polynomial is (x -3).

To find the other factors or completely factored form of the given polynomial we will divide x^3 + 4x^2 - 9x -36 by x - 3, which is called long division.

From the attatched solution or log division we can see that

The factored form of x^3 + 4x^2 - 9x -36 is (x -3)(x^2 + 7x + 12).

Now, the foctorization of x^2 + 7x + 12 is given by

x^2 + 7x + 12

= x^2 + 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

Therefore, the completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

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Answer:

C) (x + 3)(x – 3)(x + 4)

Included the whole page!
☆
EDGE2022; Good Luck :D!!!

Answer:

B

Step-by-step explanation:

[z^4/6²]^-3 = z^-12/6^-6 = 6^6/z^12

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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The value of x from the expression is 12

Given the first five terms of a Fibonacci sequence expressed as:

a, 2a, 3a and 5a

If the sum of the first five terms is 228, hence;

a + 2a + 3a  + 5a + 8a = 228

19a = 228

a = 228/19

a = 12

Hence the value of x from the expression is 12

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8

Trent's expression:

2.2x + 8

Ling's expression:

5x

Where,

Number of hours= x

Number of hours Ling Jog than Trent =Ling's expression - Trent's expression

= 5x - (2.2x + 8)

= 5x - 2.2x - 8

= 2.8x - 8

Therefore, Ling jog 2.8x - 8 miles than Trent.

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