when using your calculator, please indicate the function used and the parameters you entered for the function. 1. The selling prices of various homes in a community follow a normal distribution with a mean of $276,000.00 and standard deviation of $32,000.00. a. Calculate the probability that the next home in the neighborhood will sell for less than $220,000.00. Label the mean, standard deviation, and indicate the appropriate area on the included graph of a normal distribution. b. Calculate the probability that the next home in the community will sell for less than $350,000.00 but more than $250,000.00. Label the mean, standard deviation, and indicate the appropriate area on the included graph of a normal distribution.

Answer:

xy*(2x^2 + 7x^2 - y^2)

Step-by-step explanation:

You can get xy out of the expression since all have xy

Answer:

Step-by-step explanation:

\(|-5-4| - |1+-3|\)

|-9| - |-2|

9-2

7

The two groups have the same ratio of students with solo to total students.

We should know that ration is the quotient of two numbers. In mathematics ration is defined as  as the number of times one number contains another number

The given parameters are

25 choir students

5 solo students from the choir

20 Orchestra students

4 solo orchestra students

Expressing the ratio of total choir students to total orchestra students and solo choir  students to solo orchestra students we have

25:20 = 5:4

Dividing the left hand side by 5

5:4 = 5:4

In conclusion the ratio of total choir students to total orchestra students and solo choir students to solo orchestra students are the same = 5:4

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Answer:

2

Step-by-step explanation:

Answer:

It is 2

Step-by-step explanation:

I do not have a true explanation its just quick math to my brain.

75 represents the total minutes spent running and biking

The given parameters are:

The equation is given as:

x + y = 75

The above means that when the minutes spent running and the minutes spent biking are added, the total is 75

Hence, the 75 represents the total minutes spent running and biking

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Answer:

C. Point P

Step-by-step explanation:

sqrt(92) = 9.59

The point closest to 9.59 is point P.

The length of CF is CF = 5y + 9, based on the given parameters, and the complete lengths are:. CD = 2y - 2, DF = 3y + 11 and CF = 5y + 9

The given parameters are:

CD = 2y - 2

DF = 3y + 11

To calculate the length CF, we use the following equation

CF = CD + DF

Substitute the known values in the above equation

CF = 2y - 2 + 3y + 11

Evaluate the like terms

CF = 5y + 9

Hence, the length of CF is CF = 5y + 9, based on the given parameters.

So, the complete lengths are:.

CD = 2y - 2

DF = 3y + 11

CF = 5y + 9

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Answer:

Umm, no

Step-by-step explanation:

Answer:

No, that is definitely impossible.

Step-by-step explanation:

The only way you would be able to afford something that costs more than what you have, is by applying a coupon or getting it on sale. If you're online shopping, I recommend using something such as Honey, the extension.

Answer:

3 ways

Step-by-step explanation:

Since 6 will remain constant throughout the testing, we just need to find all prime numbers 1-6.

1 - is not prime nor composite

2 - is prime

3 - is prime

4 - 2x2=4, so composite

5 - is prime

6 - 2x3=6, so composite

Therefore, 2, 3, and 5 are prime numbers, and there are 3 of them.

Answer:

3 ways

Step-by-step explanation:

2 , 3 and 5 are prime numbers.

Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

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To maintain the CG and balance in the system, the third box weighing 20 pounds should be placed 4 feet forward of the CG.  The CG is the point where the weight of the object is evenly distributed, and it is crucial for maintaining balance.

First, let's calculate the total weight of the system. We have two boxes weighing 15 pounds and 10 pounds, and a third box weighing 20 pounds. The total weight is 15 + 10 + 20 = 45 pounds.
Next, we need to find the moment caused by the two boxes already placed. The moment is the product of the weight and its distance from the CG.
For the 15-pound box, the moment is 15 pounds * 4 feet = 60 pound-feet.
For the 10-pound box, the moment is 10 pounds * 2 feet = 20 pound-feet.

To keep the CG unchanged, the total moment of the system must be zero. This means that the moment caused by the third box must balance out the moments of the other two boxes.

Let's denote the distance from the CG to the third box as 'x' feet. The moment caused by the third box is 20 pounds * x feet.
So, to maintain balance, the equation becomes:
60 pound-feet + 20 pound-feet = 20 pounds * x feet.
Simplifying this equation, we get:
80 pound-feet = 20x feet.
To solve for 'x', we divide both sides by 20:
4 = x.
Therefore, the third box should be placed 4 feet forward of the CG to maintain balance.

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Answer:

B. 20

Step-by-step explanation:

Using the Pythagorean Theorem, you have:

\(a^2 + b^2 = c^2\\24^2 + 32^2 = c^2\\576 + 1024 = c^2\\1600 = c^2\\c = 40\)

So you know side AB is 40 inches long. It asks the length of the midpoint to point A, so you have to do 40/2 = 20 inches

The maximum value of T occurs at the vertex (x, y) = (0, 0). One way to approach this is to use the method of partial derivatives.

To find the vertex that results in the maximum value of the function T = x - 3y, we need to use a technique called optimization.

One way to approach this is to use the method of partial derivatives. We can take the partial derivative of T with respect to x and set it equal to zero to find the critical point:

∂T/∂x = 1 = 0

Solving for x, we get:

x = 0

Next, we can take the partial derivative of T with respect to y and set it equal to zero:

∂T/∂y = -3 = 0

Since there is no value of y that satisfies this equation, there are no critical points with respect to y.

Therefore, the maximum value of T occurs at the vertex (x, y) = (0, 0).

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The volume V obtained by rotating the region bounded by the curves y = 3 sin x, y = 3 cos x, 0 ≤ x ≤ (pi/4) about y = 3 is (105/48)π or 6.9025.

To find the volume V obtained by rotating the region bounded by the curves y = 3 sin x, y = 3 cos x, 0 ≤ x ≤ (pi/4) about y = 3, we can use the disk method.

First, we need to find the equation of the line y = 3, which is the axis of rotation. Since the axis of rotation is a horizontal line, we can simply use y = 3.

Next, we need to find the radius of each disk at each value of x. The radius is the distance between the curve and the axis of rotation. Since we are rotating around y = 3, the radius is given by:

r = 3 - y

Now, we need to integrate the area of each disk over the given interval [0, pi/4]. The area of each disk is given by:

A = πr^2

Substituting r = 3 - y, we have:

A = π(3 - y)^2

The volume V is then given by integrating the area A over the interval [0, pi/4]:

V = ∫[0,pi/4] π(3 - y)^2 dy

V = π ∫[0,pi/4] (9 - 6y + y^2) dy

V = π [9y - 3y^2 + (1/3)y^3] |[0,pi/4]

V = π [(9(pi/4)) - 3((pi/4)^2) + (1/3)((pi/4)^3)]

V = (27/4)π - (9/16)π + (1/48)π

V = (105/48)π

Therefore, the volume V obtained by rotating the region bounded by the curves y = 3 sin x, y = 3 cos x, 0 ≤ x ≤ (pi/4) about y = 3 is (105/48)π.

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D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.

Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.

We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:

(PDP^(-1))^2 = PDP^(-1) + 1.

Expanding the square and applying the matrix multiplication rules, we get:

PD^2P^(-1) = PDP^(-1) + 1.

Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:

P(D^2)P^(-1) = PDP^(-1) + 1.

Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:

D^2 = D + 1.

This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.

Therefore, the correct answer is D) A^2 = A + 1.

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Answer:is that smallest is (small) while minimum is to the lowest degree

Step-by-step explanation:

Answer:

1/2 (1 and a half)

Step-by-step explanation:

We get this because 2/3  are half of a whole. If we take half of 2/3 and multiply it by 2 we get a whole number. In this case it is 1.

The conversion of  730 km into miles is 456.70 miles so Maria drives 456.70 miles.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

Distance = 730 kilometers.

Since given that,

1 mile =1.609 kilometers

So,

1 kilometer = 1/1.609 miles

So,

730 kilometers = 730 × 1/1.609 miles

⇒ 456.70 miles

Hence "The conversion of  730 km into miles is 456.70 miles so Maria drives 456.70 miles".

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ok                                                         its 11 sqrt 6                                    

because if sqrt 6 is x, and 5x +6x=11x

so its 11 sqrt 6              

The area of the shaded region is 9198.11 in³ - 112.5 in².

We have,

Sphere:

Diameter = 26 in

Radius = 26/2 = 13 in

Volume.

= 4/3 πr³

= 4/3 x 3.14 x 13 x 13 x 13

= 9198.11 in³

Now,

The unshaded region is a trapezium.

Height = 5 in

Parallel sides = 19 in and 26 in

Area = 1/2 x height x (sum of the parallel sides)

= 1/2 x 5 x (19 + 26)

= 1/2 x 5 x 45

= 1/2 x 225

= 112.5 in²

Now,

The area of the shaded region.

= Volume of the sphere - Area of the trapezium

= 9198.11 in³ - 112.5 in²

Thus,

The area of the shaded region is 9198.11 in³ - 112.5 in².

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Answer:

  c:  8,20,25

Step-by-step explanation:

You want to know which set of side lengths can form a triangle from the sets ...

A set of lengths can form a triangle if and only if the sum of the shorter two exceeds the longest.

In sets a, b, d, the sum of the shorter two is equal to the longest. These lengths will form a line segment, not a triangle.

A triangle can be formed by ...

  c: 8,20,25 . . . . . . 8+20=28 > 25

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The exact value of y is \(\sqrt{3}\)

The correct answer is an option (c)

Let us assume that in the attached diagram of right triangle the angle A measures 45 degrees.

Here, the hypotenuse measures \(\sqrt{6}\)

We know that in right triangle, the sine of angle θ is nothing but the ratio of opposite side of angle θ to the hypotenuse.

Consider the sine of angle A

sin(A) = opposite side of angle A / hypotenuse

sin(45°) = y / ( \(\sqrt{6}\))

We know that from the standard trigonometric table the value of sin(45°) is \(\frac{1}{\sqrt{2} }\)

Substitute this value in above equation we get,

\(\frac{1}{\sqrt{2} }\) =  y / ( \(\sqrt{6}\))

We solve this equation to find the value of y.

y =  \(\sqrt{6}\) ×  \(\frac{1}{\sqrt{2} }\)

y = \(\frac{\sqrt{3}\sqrt{2} }{\sqrt{2} }\)

y = \(\sqrt{3}\)

Therefore, the correct answer is an option (c)

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The maximum weight in kilograms is approximately 56.7 kg. Hence, the correct option is (a) 56.7 kg.

The maximum weight of a shipping container is 125 pounds.

We need to find out what is the maximum weight in kilograms.

Step 1: Find out 1 pound weight in kilograms We know that 1 pound = 0.45359237 kilograms (we already know that)

Step 2: Convert the maximum weight in pounds to kilograms

Maximum weight in pounds = 125 Maximum weight in kilograms

= 125 x 0.45359237

= 56.69904625≈ 56.7 kg

Therefore, the maximum weight in kilograms is approximately 56.7 kg.

Hence, the correct option is (a) 56.7 kg.

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The examples of a function from Z to Z that are f(x) = 2x, g(x) = x², h(x) = 3x and k(x) = x³

Example 1: One-to-One but not Onto Function

Consider the function f: Z to Z defined by f(x) = 2x, where Z represents the set of integers. This function is one-to-one (injective) but not onto (surjective).

However, this function is not onto. For a function to be onto, every element in the codomain must have a corresponding element in the domain. In this case, not all integers in the codomain Z have a preimage in the domain Z. For instance, there is no integer x such that f(x) equals 1 or f(x) equals 3, as the function only produces even integers. Thus, the function f is not onto.

Example 2: Onto but not One-to-One Function

Consider the function g: Z to Z defined by g(x) = x², where Z represents the set of integers. This function is onto (surjective) but not one-to-one (injective).

However, the function g is not one-to-one. A function is one-to-one if distinct elements in the domain map to distinct elements in the codomain. In this case, there are multiple domain elements that map to the same codomain element. For instance, both -2 and 2 map to the same output 4, as (-2)² = 2² = 4. Therefore, the function g is not one-to-one.

Example 3: Both Onto and One-to-One Function (Not the Identity Function)

Consider the function h: Z to Z defined by h(x) = 3x, where Z represents the set of integers. This function is both onto (surjective) and one-to-one (injective), but it is not the identity function.

Additionally, the function h is onto. For any integer y in the codomain Z, we can find an integer x in the domain Z such that 3x = y. For example, if we choose y = 6, we can set x = 2, as 3 * 2 = 6. This shows that every element in the codomain has a corresponding element in the domain, fulfilling the onto property.

Example 4: Neither Onto nor One-to-One Function

Consider the function k: Z to Z defined by k(x) = x³, where Z represents the set of integers. This function is neither onto (surjective) nor one-to-one (injective).

Moreover, the function k is not one-to-one. It fails the one-to-one property because different elements in the domain can map to the same output in the codomain. For example, both -2 and 2 map to the same output -8, as (-2)³ = 2³ = -8. Therefore, the function k is not one-to-one.

By examining these four examples, you can observe the distinct combinations of properties that a function from Z to Z can possess. It is important to explore these properties to understand the behavior and characteristics of various functions.

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(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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The simplified expression for the function f(x+h) - f(x) / h is 10x + 5 + h.

To evaluate and simplify the expression f(x+h) - f(x) / h, we first substitute the given function f(x) = 5x² - x. Let's expand the expression and combine like terms.

       = 5(x² + 2xh + h²) - x - h

       = 5x² + 10xh + 5h² - x - h

Next, we subtract f(x) from f(x+h):

             = 5x²2 + 10xh + 5h² - x - h - 5x² + x

             = 10xh + 5h² - h

Finally, we divide the result by h:

                   = 10x + 5h - 1

Thus, the simplified expression for f(x+h) - f(x) / h is 10x + 5h - 1.

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