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The value of SS for this population cannot be determined with the given information.

The sum of squares (SS) for a population is calculated by summing the squared differences between each individual score and the population mean.

However, the given information provides the population standard deviation (σx = 12) and the population variance (σx^2 = 54), but it does not provide the population mean (μ).

Without the population mean, we cannot accurately calculate the value of SS. Therefore, the value of SS for this population cannot be determined based on the given information.

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The value of x in the chord intersection is 16 units.

The intersecting chord theorem  states that the products of the lengths of the line segments on each chord are equal. In other words, If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Therefore, lets find the value of x in the intersecting chords as follows:

15 × x = 24 × 10

15x = 240

divide both sides of the equation by 15

x = 240 / 15

x = 16

Therefore,

x = 16 units

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Answer:

$18,480

Step-by-step explanation:

so rate of the car, increases annually by 14%

so in 4 years time it will be 14×4= 56%

new car purchased is $42,000

to find the car's value in 4 years time it would be

100%-56%,which is 44%

then 44% of $ 42,000 will give you

$18,480

The variable T as the subject of the formula is t = √(k/[5a - 2])

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

k-t² = t²[5a-3]

Rewrite as

k - t² = t²[5a - 3]

Add t² to both sides of the equation

So, we have the following representation

k = t² + t²[5a - 3]

Factor out t²

This gives

k = t²[1 + 5a - 3]

Evaluate the like terms

k = t²[5a - 2]

Divide by 5a - 2

So, we have

t² = k/[5a - 2]

Tale the square roots

t = √(k/[5a - 2])

Hence, the solution is t = √(k/[5a - 2])

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Multiply each payout by the corresponding probability and take the total:

E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95

The expected value = 3.92

"It describes the average of a discrete set of variables based on their associated probabilities."

\(E(x)=\Sigma[ xP(x)]\)

Multiply each value of the random variable by its probability and add the products.

For given question,

We have been given a payout probability distribution.

We need to find the expected value of the winnings.

First we multiply each value of the random variable by its probability .

0 × 0.5 = 0

5 × 0.2 = 1

8 × 0.15 = 1.2

10 × 0.1 = 1

15 × 0.05 = 0.75

Now, we find the sum of above products.

0 + 1 + 1.2 + 1 + 0.75 = 3.95

By using the formula of expected value,

\(\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92\)

Therefore, the expected value = 3.92

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The mean of sample means is p=126.5, while the standard deviation (standard error) can be calculated as SE=5.72 using the formula SE=o/sqrt(n), where o is the population standard deviation and n is the sample size.

The mean of the distribution of sample means is equal to the population mean, which is p = 126.5.

The standard deviation of the distribution of sample means, also known as the standard error, can be calculated using the formula:

SE = o / sqrt(n)

where o is the population standard deviation and n is the sample size. Substituting the given values, we get:

SE = 72.6 / sqrt(161) = 5.72

Therefore, the standard deviation of the distribution of sample means is 5.72 (accurate to 2 decimal places).

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The Cov(X,Y) = E(XY) - E(X)E(Y) = 1.26 - 0.76(1.70) = 0.02h) Find ρX,Y.To find the correlation coefficient of X and Y, we use the formula ρX,Y = Cov(X,Y) / (σXσY). We already calculated Cov(X,Y) to be 0.02. Now we need to calculate σX and σY. We calculated σX to be 0.638. We could not calculate σY because the variance was negative. Therefore, we cannot find the correlation coefficient of X and Y.

Find the marginal probability mass function pX(x). Round the answers to two decimal places.a.1) Px(0)a.2) Px(1)a.3) Px(2)We can use the following formula to find the marginal probability mass function: Px(x) = Σy P(x, y) where Σy is the sum of all the values of y for each value of x.

The table shows the joint probability mass function of the random variables X and Y.X/Y|0 |1 |2 |P(X=x)0 |0.12 |0.16 |0.280.6 |1 |0.18 |0.14 |0.320.64 |2 |0.10 |0.12 |0.22Let's now use the formula to find Px(0):Px(0) = Σy P(0, y) = P(0,0) + P(0,1) + P(0,2) = 0.12 + 0.16 + 0.28 = 0.56Now we'll find Px(1):Px(1) = Σy P(1, y) = P(1,0) + P(1,1) + P(1,2) = 0.18 + 0.14 = 0.32Lastly, we'll find Px(2):Px(2) = Σy P(2, y) = P(2,0) + P(2,1) + P(2,2) = 0.10 + 0.12 = 0.22b)

Find the marginal probability mass function pY(y). Round the answers to two decimal places.b.1) Py(0)b.2) Py(1)b.3) Py(2)We can use the following formula to find the marginal probability mass function: Py(y) = Σx P(x, y) where Σx is the sum of all the values of x for each value of y. The table shows the joint probability mass function of the random variables X and Y.X/Y|0 |1 |2 |P(X=x)0 |0.12 |0.16 |0.280.6 |1 |0.18 |0.14 |0.320.64 |2 |0.10 |0.12 |0.22

Let's now use the formula to find Py(0):Py(0) = Σx P(x, 0) = P(0,0) + P(1,0) + P(2,0) = 0.12 + 0.18 + 0.10 = 0.40Now we'll find Py(1):Py(1) = Σx P(x, 1) = P(0,1) + P(1,1) + P(2,1) = 0.16 + 0.14 + 0.12 = 0.42Lastly, we'll find Py(2):Py(2) = Σx P(x, 2) = P(0,2) + P(1,2) + P(2,2) = 0.28 + 0.14 + 0.22 = 0.64c) Find µXTo find µX, we use the formula µX = E(X) = Σx xP(X = x).

We can calculate the expected value of X by using the marginal probability mass function Px(x) that we previously calculated. The formula is: E(X) = Σx xPx(x) = 0(0.56) + 1(0.32) + 2(0.22) = 0 + 0.32 + 0.44 = 0.76Therefore, µX = 0.76d) Find μY.

Round the answer to two decimal places.To find µY, we use the formula µY = E(Y) = Σy yP(Y = y). We can calculate the expected value of Y by using the marginal probability mass function Py(y) that we previously calculated. The formula is: E(Y) = Σy yPy(y) = 0(0.40) + 1(0.42) + 2(0.64) = 0 + 0.42 + 1.28 = 1.70Therefore, µY = 1.70e) Find σX.To find the standard deviation of X, we can use the formula σX = sqrt(V(X)) where V(X) is the variance of X. To find the variance of X, we use the formula V(X) = E(X²) - [E(X)]². We already calculated E(X) to be 0.76. Now we need to calculate E(X²):E(X²) = Σx x²P(X = x) = 0²(0.56) + 1²(0.32) + 2²(0.22) = 0 + 0.32 + 0.88 = 1.20

Therefore, V(X) = E(X²) - [E(X)]² = 1.20 - 0.76² = 0.4064σX = sqrt(V(X)) = sqrt(0.4064) = 0.638f) Find σY.To find the standard deviation of Y, we can use the formula σY = sqrt(V(Y)) where V(Y) is the variance of Y. To find the variance of Y, we use the formula V(Y) = E(Y²) - [E(Y)]².

We already calculated E(Y) to be 1.70. Now we need to calculate E(Y²):E(Y²) = Σy y²P(Y = y) = 0²(0.40) + 1²(0.42) + 2²(0.64) = 0 + 0.42 + 1.28 = 1.70Therefore, V(Y) = E(Y²) - [E(Y)]² = 1.70 - 1.70² = -0.29σY = sqrt(V(Y)) = sqrt(-0.29)This is an invalid result, since the variance cannot be negative. Therefore, there may be an error in the calculations or in the values provided in the table.

We cannot find the standard deviation of Y.g) Find Cov(X, Y).To find the covariance of X and Y, we use the formula Cov(X,Y) = E(XY) - E(X)E(Y). We already calculated E(X) and E(Y) to be 0.76 and 1.70 respectively. Now we need to calculate E(XY):E(XY) = Σx Σy xyP(X = x, Y = y) = 0(0)(0.12) + 0(1)(0.16) + 0(2)(0.28) + 1(0)(0.18) + 1(1)(0.14) + 1(2)(0.00) + 2(0)(0.10) + 2(1)(0.12) + 2(2)(0.22) = 0 + 0 + 0 + 0 + 0.14 + 0 + 0 + 0.24 + 0.88 = 1.26

Therefore, Cov(X,Y) = E(XY) - E(X)E(Y) = 1.26 - 0.76(1.70) = 0.02h) Find ρX,Y.To find the correlation coefficient of X and Y, we use the formula ρX,Y = Cov(X,Y) / (σXσY). We already calculated Cov(X,Y) to be 0.02. Now we need to calculate σX and σY. We calculated σX to be 0.638. We could not calculate σY because the variance was negative. Therefore, we cannot find the correlation coefficient of X and Y.

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Answer: you’re just full of questions today aren’t you :)

Step-by-step explanation:

Just multiply both sides And you should get what you need

have a good day

Answer:

the solution is (5,5)

Step-by-step explanation:

if you plug in (5,5) where the x and y are you will find that the equation will balance out.

The local maximum value of f using both the first and second derivative tests is f(x) = x √4 - x.

To find the maximum value of f, we can substitute x = -4 into

\(f(x) = x(4 - x)^{(1/2)}.f(-4) \\\\f(x)= (-4)(4 - (-4))^{(1/2)}\)

= -4(2)

= -8

Therefore, the local maximum value of f is -8.

The function \(f(x) = x(4 - x)^{(1/2)}\) is given.

We are to find the local maximum value of f using both the first and second derivative tests.

Find f'(x) first .We can use the product rule for differentiation:

Let u = x, then

v = \(v=(4 - x)^{(1/2)}\)

du/dx = 1 and

\(dv/dx-(1/2)(4 - x)^{(-1/2)}(-1)\)

\(= (1/2)(4 - x)^{(-1/2)\)

f'(x) = u dv/dx + v du/dx

\(= x(4 - x)^{(-1/2)} + (1/2)(4 - x)^{(-1/2)\)

Taking the common denominator, we get

\(f'(x) = (2x + 4 - x)/2(4 - x)^{(1/2)\)

\(= (4 + x)/2(4 - x)^{(1/2)\)

To find the critical numbers, we set

f'(x) = 0.4 + x

= 0x

= -4

The only critical number is x = -4.

Next, we find f''(x).We have that \(f'(x) = (4 + x)/2(4 - x)^{(1/2)\).

Let's rewrite f'(x) as \(f'(x) = 2(4 + x)/(8 - x^2)^{(1/2)\)

Now, we can use the quotient rule:

Let u = 2(4 + x),

then v = \((8 - x^2)^{(-1/2)\)

du/dx = 2 and

\(dv/dx = (1/2)(8 - x^2)^{(-3/2)}(-2x)\)

\(= x(8 - x^2)^{(-3/2)\)

Therefore, we get f''(x) = u dv/dx + v du/dx

\(= (2)(x(8 - x^2)^{(-3/2)}) + (4 + x)(-1)(8 - x^2)^{(-3/2)(-2x)}f''(x)\)

\(= (16 - 3x^2)/(8 - x^2)^{(3/2)\)

We know that at a local maximum, f'(x) = 0 and f''(x) < 0.

We have that the only critical number is x = -4 and

\(f''(-4) = (16 - 3(-4)^2)/(8 - (-4)^2)^{(3/2)\)

= -2.17 < 0, f has a local maximum at x = -4.

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Answer:

6

Step-by-step explanation:

Set up the equation to look like this:

6+7x=10x-12

then solve like normal

Owing 175 dollars is more than owing 150 dollars.

Thereby, the correct answer is A) -175 dollars

The area of the composite shape in this problem is given as follows:

A = 104 m².

The figure in the context of this problem is a composite figure, hence we obtain the area of the figure adding the areas of all the parts of the figure.

The figure for this problem is composed as follows:

Hence the area of the figure is given as follows:

A = 8 x 9 + 2 x 0.5 x 8 x 4

A = 104 m².

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We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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There are 24 possible ways the four schools can place 1st, 2nd, 3rd, and 4th in the finals.

We have,

To determine the possible ways the four schools can place 1st, 2nd, 3rd, and 4th in the finals, we can use the concept of permutations.

A permutation is an arrangement of objects in a specific order. In this case, we want to find the permutations of the four schools.

The number of permutations can be determined by multiplying the number of choices for each position.

Since there are four schools, there are four choices for the 1st position, three choices for the 2nd position, two choices for the 3rd position, and one choice for the 4th position.

The total number of permutations is given by:

= 4 × 3 × 2 × 1

= 24

Therefore,

There are 24 possible ways the four schools can place 1st, 2nd, 3rd, and 4th in the finals.

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Answer:

x = 4, y = 5.

Step-by-step explanation:

4x-2=3y-1

y+3=3x-4

Rearranging:

4x - 3y =  1       (A)

-3x + y = -7      (B)

Multiply  B by 3:

-9x + 3y = -21   (C)
Adding A and C:

-5x = -20

x = 4

Substitute for x in equation A:

4(4) - 3y = 1

3y = 15

y = 5.

There are 7 possible positive integers that satisfy the inequality.

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

We can find the positive values of x in the given inequality.

2x + 8 < 22

2x < 22 - 8

2x < 14

x < 7

The solution shows that x < 7

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Answer:

4th option

10x + 32 / x(x+8)

Step-by-step explanation:

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

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Answer:

The legs are a and b, the hypotenuse is c

Step-by-step explanation:

The legs of a right triangle are the two smaller sides. The hypotenuse is the longest side it is also always opposite of the 90-degree angle. If you need to find the lengths of sides remember the Pythagorean theorem, .

Answer:

yes the person above me is correct .

Step-by-step explanation:

good job :)

2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Answer:

Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (2, 4).

Summary:

The unit vector that is parallel to the line tangent to the parabola y = x2 at the point (2, 4) is ±(i + 4j)/√17.

Step-by-step explanation:

Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (2, 4).

Solution:

Given parabola y = x2

Point (2, 4)

The slope of the tangent line to the parabola at (2,4) can be written as

(dy/dx) at (2,4) = 2x at (2,4) =4

So, any line parallel to the tangent line has slope ‘4’

Let us assume the unit vector is ±(i + 4j)

The length of the vector is √(12 + 42) = √17

So, the required unit vectors are ±(i + 4j)/√17

Comparing the two blankets, we find that they have the same perimeter (12 meters) but different areas (9 square meters for the square blanket, 8 square meters for the rectangular blanket).

Let's compare the perimeters and areas of the two blankets.
First blanket (square):
Side length: 3 meters
Perimeter: 4 x side length = 4 x 3 meters = 12 meters
Area: \(side $ length^2 = 3^2 = 9 $ square $ meters\)
Second blanket (rectangle):
Length: 2 meters
Width: 4 meters
Perimeter: 2 x (length + width) = 2 x (2 + 4) meters = 2 x 6 meters = 12 meters
Area: length x width = 2 x 4 = 8 square meters.  

Note: Perimeter refers to the total distance around the boundary of a two-dimensional shape.

It is the sum of the lengths of all the sides of the shape.

Here are some key points about perimeter:

Calculation: The perimeter of a shape can be calculated by adding together the lengths of all its sides.

The formula for perimeter varies depending on the specific shape.

Square: The perimeter of a square is calculated by multiplying the length of one side by 4.

So, the formula for the perimeter of a square is P = 4s, where s represents the length of a side.

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Considering a proportional relationship, it is found that:

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, in the case of a direct relationship, as presented below:

y = kx

In this problem, the cost of each pizza is of $7, hence the constant is of k = 7 and the equation is:

y = 7x.

Then the cost for 12 pizzas is found calculating the numeric value at x = 12, that is, replacing the lone instance of x in equation by 12 as follows:

y = 7(12) = $96.

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35,200,003 is the answer

Answer:

Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

solution :

From these we can get is;

119 = n – 66

=> n = 119 + 66

=> n = 185

So option d ) 185 is the correct answer

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Disclaimer: the question was given incomplete on the portal. Here is the Complete Question.

Question: Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

We get that the value of n is option (d) 185 for the equation n - 66 = 119.

We are given an equation:

n - 66 = 119.

An equation is an expression that has an equality sign in between.

For example: 3 x + 3 y = 6 or 7 x + 5 y = 9

We have to solve the equation to find the value of n.

First, we will add 66 to both the sides of the equation.

n - 66 + 66 = 119 + 66 .

Now simplifying the expression, we get that:

n = 119 + 66

Solving the expression to get the value of n:

n = 185

So, option (d) 185 is correct.

Therefore, we get that the value of n is option (d) 185

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