Problem 12 (8 Points) Simplify each expression (if possible), then express the set in set builder notation 1. AU AUB 2. B-(B - A) 3. (B-B) - A 4.B - C - A) SC- Problem 12 continued on Dext page 3 CSE: 14 Homework

The standard error of the mean is approximately $115.63.

The standard error of the mean (SEM) measures the variability or uncertainty in the sample mean compared to the true population mean. It indicates the average amount that the sample mean differs from the population mean.

To calculate the standard error of the mean, we use the formula:

SEM = σ / √n

Where:

SEM: Standard error of the mean

σ: Population standard deviation

n: Sample size

Given information:

Population standard deviation (σ) = $1,850.00

Sample size (n) = 256

Plugging in the values into the formula, we can calculate the standard error of the mean:

SEM = 1850 / √256

To simplify the calculation, let's first calculate the square root of 256:

√256 = 16

Now, we can divide the population standard deviation by the square root of the sample size:

SEM = 1850 / 16

Simplifying the fraction, we have:

SEM = 115.625

Therefore, the standard error of the mean is approximately $115.63.

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The Law of Detachment states:

If a ⇒ b is true and a is true, then b is true

if two figures are congruent, their areas are equal.

a = two figures are congruent

b = their areas are equal

We are given b

The area of ABCD equals the area of PQRS.

We cannot use the law of detachment in this case because we need to be given a for the law of detachment to apply.

ABCD could be a rectangle with area 10

PQRS could be a rhombus with area 10

They are not congruent

Answer:

a) To find the points of intersection, P and Q, of the tangents and the circle, we can use the fact that a tangent line is perpendicular to the radius at the point of tangency. Therefore, the slope of the tangent line is the negative reciprocal of the slope of the radius.

We know that the equation of the circle is (x-3)² + (y + 3)² = 52. To find the slope of the radius, we can differentiate the equation of the circle with respect to x and y.

dx/dt = 2(x-3) and dy/dt = 2(y+3)

We know that the slope of the tangents is a. So, the slope of the radius is -1/a

Now we can use the point slope form of a line to find the equation of the tangent line.

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We can substitute the point of tangency, which is on the circle, into the point slope form.

y + 3 = -1/a(x - 3)

We can now substitute the point (3, -3) and the slope -1/a into the point slope form to find the equation of the line

y + 3 = -1/a(x - 3)

y = -1/a

Step-by-step explanation:

Not sure if this helps, hope it does!

Answer:

question 9

= –12

while question 11=, x= –72

Step-by-step explanation:

question 9=

u= –16+4= –12

question 11=

cross multiplication

x = -36 multiplied by 2 =

-72

I HOPE THIS HELPED IF WRONG IM SORRY

The non parametric equation described by the parametric equation is given as follows:

D. y = 324(x - 3)^4 - 7.

The parametric curve is defined as follows:

Isolating t on the first equation, we have that:

\(\frac{1}{3}\sqrt{t} = x - 3\)

\(\sqrt{t} = 3(x - 3)\)

t = 9(x - 3)² -> applying the square root to both sides.

Replacing on the second equation, the equation of the non parametric function is given as follows:

y = 4t² - 7

y = 4[9(x - 3)²]² - 7.

y = 324(x - 3)^4 - 7.

Meaning that option D is the correct option.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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a) To find E(0.1X + 0.9)-1, Var 2.45. and b) By minimizing the variance, we can find the optimal combination of assets that balances risk and return. This can help investors make informed decisions and construct portfolios that align with their risk tolerance and investment objectives.

(a) To find E(0.1X + 0.9), we can use the linearity of expectation. We multiply the constants with the respective expectations:
E(0.1X + 0.9) = 0.1 * E(X) + 0.9 * E(Y) = 0.1 * 1 + 0.9 * 1 = 0.1 + 0.9 = 1.

To find Var(0.1X + 0.9Y), we need to use the properties of variance. Since X and Y are independent, Var(0.1X + 0.9Y) = (0.1)^2 * Var(X) + (0.9)^2 * Var(Y) = 0.01 * 2 + 0.81 * 3 = 0.02 + 2.43 = 2.45.

(b) To minimize Var(wX + (1-w)Y), we need to find the value of w that minimizes the expression. We can do this by taking the derivative of Var(wX + (1-w)Y) with respect to w and setting it to zero. By solving this equation, we can find the value of w that minimizes the variance.

Minimizing Var(wX + (1-w)Y) would be useful when selecting a portfolio of assets. A lower variance indicates lower risk. By minimizing the variance, we can find the optimal combination of assets that balances risk and return. This can help investors make informed decisions and construct portfolios that align with their risk tolerance and investment objectives.

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The perimeter of the hexagon with 7 congruent circles of radius 4 are packed into it, so hexagon sides are tangent to 6 circles is -

6s, or approximately 60.72.

Let's begin by drawing a diagram:

       ______

    /        \

   /    o     \

  /            \

 /     o o o    \

/     o o o o    \

\     o o o o    /

 \     o o o    /

  \            /

   \__________/

Each circle is tangent to two sides of the hexagon, so the distance between two opposite vertices of the hexagon is equal to the diameter of a circle, which is 8.

Let's call the side length of the hexagon "s".

Then we can draw a right triangle with legs of length s/2 and s/4, and hypotenuse of length 8.

Using the Pythagorean theorem, we can solve for s:

(s/2)^2 + (s/4)^2 = 8^2

5s^2/16 = 64

s^2 = 102.4

s = sqrt(102.4) = 10.12 (rounded to two decimal places)

Therefore, the perimeter of the hexagon is 6s, or approximately 60.72.

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The values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

To determine the values of W and X that make NOPQ a parallelogram, we need to find the conditions under which the opposite sides of the quadrilateral are parallel.

The coordinates of the points N, O, P, and Q are given as follows:

N: (w+7, 5w-5)

O: (3/2x, 3)

P: (?, ?)

Q: (?, ?)

For NOPQ to be a parallelogram, the vector from N to O should be equal to the vector from P to Q, and the vector from O to P should be equal to the vector from Q to N.

The vector from N to O is:

NO = (3/2x - (w+7), 3 - (5w-5))

   = (3/2x - w - 7, -5w + 8)

The vector from O to P should be equal to the vector from Q to N. Thus:

OP = (P_x - (3/2x), P_y - 3)

QN = ((w+7) - Q_x, (5w-5) - Q_y)

Equating the corresponding components, we get the following equations:

3/2x - w - 7 = P_x - (3/2x)

-5w + 8 = P_y - 3

w + 7 = (w+7) - Q_x

5w - 5 = (5w-5) - Q_y

Simplifying these equations, we find:

P_x = 3x

P_y = -5w + 11

Q_x = w + 7

Q_y = 5w

Therefore, the values of W and X that make NOPQ a parallelogram are:

W = -5w + 11

X = 3x

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Please find attached photograph for your answer. Hope it is alright.

Answer:

(5x + \(\frac{3}{10}\) )(3x - \(\frac{7}{10}\))

Step-by-step explanation:

The expression is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

Then

(4x - \(\frac{1}{5}\) )² - (x + \(\frac{1}{2}\) )²

= (4x - \(\frac{1}{5}\) + x + \(\frac{1}{2}\) )(4x -

= (5x + \(\frac{3}{10}\) )(3x - \(\frac{7}{10}\) )

By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.

If there is a reduction, then 0 < k < 1.

If there is an enlargement, then k > 1.

So, you have

Therefore, the correct answer is

Answer:

The first one

Step-by-step explanation:

The area of the front of the book be after the book is enlarged = 121.5 in²

The correct option is C.

A figure that totally resides in one plane is referred to as a plane figure or a two-dimensional figure. Two-dimensional figures are drawn when you sketch, whether by hand or with a computer program. Two-dimensional models of actual objects can be found in blueprints.

A book is 6 inches wide

A book is 9 inches tall.

scale factor of 1.5 to enlarge a book.

6 inches enlarged by 1.5 = 9 inches

9 inches enlarged by 1.5 = 13.5 inches

We know that area of rectangle :

area = length x wight

area = 9 × 13.5

= 121.5 square inches

The area of the front of the book be after the book is enlarged = 121.5 in²

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Answer: 7

Step-by-step explanation:

-x^2 -6y+13x+7

The constant is the term with no variable attached to it

7 is the constant

Answer:

7

Step-by-step explanation:

The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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Answer:

504

Step-by-step explanation:

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The probability that Bob is the last customer to leave the post office comes out as (1 - e^(-λx))^2. The probability that Bob is the last customer to leave the post office can be calculated using the exponential distribution formula.

The exponential distribution is a continuous probability distribution used to model the time between events in a Poisson process. The formula for the exponential distribution is: P(X=x) = λe^(-λx)

Where X is the random variable representing the time between events, λ is the rate parameter, and e is the base of the natural logarithm.


P(Bob is the last customer to leave) = P(Bob's serving time > Alice's serving time) * P(Bob's serving time > Claire's serving time). Since the serving times follow an exponential distribution with parameter λ, we can use the formula to calculate the probabilities:

P(Bob's serving time > Alice's serving time) = ∫_0^∞ λe^(-λx) dx = 1 - e^(-λx)
P(Bob's serving time > Claire's serving time) = ∫_0^∞ λe^(-λx) dx = 1 - e^(-λx)

P(Bob is the last customer to leave) = (1 - e^(-λx))^2
Therefore, the probability that Bob is the last customer to leave the post office is (1 - e^(-λx))^2.

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Answer:

B - ∠b and ∠f

Step-by-step explanation:

Corresponding angles are the angles in matching corners of the intersections in the traversal. Since ∠b and ∠f are in the same position relative to the intersection, they are corresponding.

Answer:

  27

Step-by-step explanation:

Let a represent Amanda's age. Then Jordan's age is 2a+5, and the combined ages are ...

  a +(2a+5) = 38

  3a = 33

  a = 11

So, Jordan's age is ...

  2(11) +5 = 27

Toni's numbers are 11 and 6.

To solve this problem, we need to assign variables to Toni's numbers. Let's call the second number "x." Then, according to the statement, the first number is "five more than the second," which can be written as "x + 5."
Now we can use the second piece of information to create an equation: "if you add the first to three times the second you get 29." This can be written as:
x + 5 + 3x = 29
Simplifying the equation:

4x + 5 = 29
Subtracting 5 from both sides:
4x = 24
Dividing by 4:
x = 6
Now that we know x, we can use the first equation (x + 5) to find the first number:
x + 5 = 6 + 5 = 11
So Toni's numbers are 11 and 6.
To solve the problem of guessing Toni's numbers, we can use variables and equations. By assigning x to the second number, we can write the first number as x + 5, based on the clue that it is "five more than the second." The next piece of information tells us that "if you add the first to three times the second you get 29," which translates to the equation x + 5 + 3x = 29. Simplifying this equation, we combine like terms to get 4x + 5 = 29. Then, we subtract 5 from both sides to get 4x = 24. Dividing by 4, we get x = 6. To find the first number, we use the equation x + 5, which equals 6 + 5 = 11. Thus, Toni's numbers are 11 and 6. By using variables and equations, we were able to solve the problem and find Toni's numbers.

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Answer:

The answer would be, C.)

Step-by-step explanation:

The reason is because the red graph has the same trajectory as the blue graph, it just is a negative version. And the choice C proves this picture right.

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

The range is the best measure of variability, and it equals 9.

Based on the information provided, the best measure of variability for the given data is the range. The range is calculated by subtracting the minimum value from the maximum value in a dataset.

In this case, the minimum value is 1 (as indicated by the dot above 1) and the maximum value is 10 (as indicated by the dot above 10). Therefore, the range can be calculated as:

Range = Maximum Value - Minimum Value

Range = 10 - 1

Range = 9

So, the best measure of variability for the data is the range, and its value is 9. Therefore, the correct option is:

The range is the best measure of variability, and it equals 9.

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Answer:

Step-by-step explanation:

36/$15 = $2.04 per pound

Answer:

36/$15 which equals $2.04 per pound

Step-by-step explanation:

Answer:

I think its

2.4, square root of 5, 1/2, -7/4, -2

hope this helps :D

Answer:

$ 8.86  = $2.95 + 0.85 m

Step-by-step explanation:

The above equation can be used to determine the original cost  m of the sandwich.

Step-by-step explanation:

Here, the cost of 1 drink = $2.95

The discount in the price of the sandwich  = 15%

The total bill of Mitchell  = $8.86

Let us assume the original cost of the turkey sandwich = $m

Now, the discount is always applied on the original price.

⇒ 15% of the original price = 15% of m =  

So, the discount offered on the sandwich = 0.15 m

Reduced price of the Sandwich = Original Price - Discounted amount

                                                    = m - 0.15 m  = 0.85 m

Now, Total Bill = Cost of Drink + Reduced cost of sandwich

⇒ $ 8.86  = $2.95 + 0.85 m

Here, the equation   $ 8.86  = $2.95 + 0.85 m  can be used to determine the original cost  m of the sandwich.

Answer:

2; 3; 4.

Step-by-step explanation:

Li - 2 (two circles); Na - 3 (three circles); K - 4 (four circles).

Answer: 157.5

"Of" means to multiply. When multiplying percentages by whole numbers, the percentage becomes smaller. The commonly asked question in scenarios just like this is, "what is x% of y?" where x is the percentage and y is your number you want a percentage out of. This question requires you to use multiplication, because it uses the word, "of".

\(\bold{Step-by-step}\)

\(\mathrm{"What}\) \(\mathrm{is}\) \(\mathrm{x\%}\) \(\mathrm{of}\) \(\mathrm{y?"}\)

\(P = (x\% \times y)\\P = (75\% \times 210)\\p = 75\% = 0.75\\P = (0.75 \times 210)\\P = 157.5\)

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