If x-y = 40 and x+y = 70, then what is the value of x squared -y squared ?

Answer:

B

Step-by-step explanation:

Circumference is equal to \(\pi d\)

\(C=\pi d\)

\(C=\pi \times 8\)

Answer:

there u go

Step-by-step explanation:

DCM, this is the solution:

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.

Therefore,

KJ = 2 * GH

KJ = 2 * 30

KJ = 60 and FJ = 30

JL = 2 * FG

JL = 2 * 37

JL = 74

To convert a nominal value to a real value in dollar terms, the base year index must be set at 100.The answer: True

1. Nominal value represents the face value or stated value of a currency, security, or financial instrument without considering the effects of inflation or changes in the purchasing power of money.
2. Real value is the value adjusted for inflation, reflecting the purchasing power of a currency in a given base year.
3. To convert a nominal value to a real value in dollar terms, we need to adjust the nominal value for inflation using a price index.
4. The base year index is typically set at 100, which allows for easy comparison and calculation of the real value.
5. To convert the nominal value to a real value, divide the nominal value by the price index in the current year and then multiply by the base year index (100). This will give you the real value in dollar terms.

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To convert a nominal value to a real value in dollar terms, the base year index must be set at 100.The answer: True

1. Nominal value represents the face value or stated value of a currency, security, or financial instrument without considering the effects of inflation or changes in the purchasing power of money.
2. Real value is the value adjusted for inflation, reflecting the purchasing power of a currency in a given base year.
3. To convert a nominal value to a real value in dollar terms, we need to adjust the nominal value for inflation using a price index.
4. The base year index is typically set at 100, which allows for easy comparison and calculation of the real value.
5. To convert the nominal value to a real value, divide the nominal value by the price index in the current year and then multiply by the base year index (100). This will give you the real value in dollar terms.

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Answer:

Max area = 100

10 10 sides

Step-by-step explanation:

here given perimeter for fencing is 40 feet

for it to have maximum area sides

sides length is perimeter / 4

so l = 40/4 = 10

so it is 10 × 10 square

Area = 100

This is the maximum area

Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.

A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.

given, a function f(x) = √ (x² - 4x +4)

now for every input value of x we will get an output value for f(x).

we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}

when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]

                                                                            f(-3) = √25 =5

     similarly, f( -2) = 4

                            f(-1) = 3

                             f(0) = 2

                               f(1) = 1

                            f(2) =0

                           f(3) = 1

the range of function is {5, 4, 3, 2, 1, 0,1}

The range of function indicates that it is neither increasing nor decreasing.

hence the function is a monotonous function.

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

18 pounds

Step-by-step explanation:

5 x 3 3/5 =18

Answer:

18(D)

Step-by-step explanation:

The proof of every positive integer k that divides the order of g, there exists a subgroup h of g of order k is shown below:

A subgroup is a group nested inside another group. The subgroup test is used on subsets of a group to determine if they are subgroups. A proper subgroup is a subgroup that does not contain all of the original group, while a trivial subgroup contains only the identity.

Suppose k ∣ g ⟹n=dk:

If h(g)=⟨g⟩ is cyclic then

clearly K:=|⟨g^d⟩|=k .

Suppose now we have

1≠H≤h(g),

|H|=k and

let r>0 be the minimal natural number s.t.

g^r ∈ H , then

1=(g ^ r)^k = g^(r k)

⟹n ∣ r k ⟹ r k=ns =d ks ⟹ r= ds ⟹ s ∣ d

and from here we have

g^ r=(g^ d)^ s ∈K

Also,  |H|=||K|

we get equality and thus uniqueness of K.

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Answer:

The population is 40,269 as of the 2020 Census, a 1.2% decrease from 2010. Crystal Lake is the largest city in McHenry County, part of the Chicago metropolitan

Step-by-step explanation:

The interval for mean sale price is $582

According to statement

The given rates are 560, 468, 685, 534, 658, 593

Now,

Sample mean = X / n

Put the values in it and then

(560+ 468+ 685+ 534+ 658+ 593) / 6 = 582.1667

and use this formula S = sqrt [ X2 - n 2 / (n-1) ]

and put the values in these and

S = sqrt [ X2 - n 2 / (n-1) ] = 95.97179

So, The interval for mean sale price is $582

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a.  The marginal pdf f1(x) of X is 0

b. the conditional pdf f2(y∨x) is 0

c. The  P(Y>13∨X=x) for any x>13 is  0

a. To find the marginal pdf f1(x) of X, we integrate f(x,y) over y from 0 to x:

f1(x) = ∫ f(x,y) dy from 0 to x

= ∫ 15xy^2 dy from 0 to x

= 5x^4

So, f1(x) = 5x^4 for 0 ≤ x ≤ 1, and f1(x) = 0 otherwise.

b. To find the conditional pdf f2(y∨x), we use the formula:

f2(y∨x) = f(x,y) / f1(x)

So, we have:

f2(y∨x) = 15xy^2 / (5x^4) = 3y^2 / x^3 for 0 ≤ y ≤ x ≤ 1, and f2(y∨x) = 0 otherwise.

c. To find P(Y > 13 ∨ X = x) for any x > 0, we need to integrate the joint pdf f(x,y) over the region where y > 13 and x = x. This region is a triangular region with vertices at (x,13), (x,x), and (1,x). So, we have:

P(Y > 13 ∨ X = x) = ∫∫ f(x,y) dy dx over the triangular region

= ∫ x∫13^x 15xy^2 dy dx / (5x^4)

= ∫ x [(13x^3)/2 - (x^4)/4] dx / (5x^4)

= 15/8 - (13/8)x

So, P(Y > 13 ∨ X = x) = 15/8 - (13/8)x for 0 < x ≤ 1, and P(Y > 13 ∨ X = x) = 0 otherwise.

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Answer: 33.2

Step-by-step explanation:

The constant of proportionality is the coefficient in the equation.

The length of arc AB in terms of pi is 16pi.

We have,

To find the length of the arc AB in terms of pi, we can use the formula:

Length of arc = (angle intercepted by arc / 360 degrees) * (circumference of the circle)

Given:

Diameter = 32 (which means the radius is half of the diameter, so the radius is 32/2 = 16)

Angle intercepted by arc AB = 180 degrees

First, we need to find the circumference of the circle using the formula:

Circumference = 2 x pi x radius

Circumference = 2 x pi x 16 = 32 x pi

Now, we can calculate the length of arc AB:

Length of arc AB = (180 / 360) x (32 x pi)

Simplifying:

Length of arc AB = (1/2) x (32 x pi)

Length of arc AB = 16 x pi

Therefore,

The length of arc AB in terms of pi is 16pi.

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Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

Answer: 1327.3 feet cubed\(V=\pi\cdot r^2\cdot h\\V=\pi\cdot(6.5)^2\cdot10\\V=\pi\cdot 42.25\cdot10\\V=422.5\pi ft^3\\or\\V\approx 1327.3 ft^3\)

Step-by-step explanation:

Volume of a cylinder:

Complete question :

A circular swimming pool has a radius of 28 ft. There is a path all around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path.

About how many feet of fencing are needed to go around the pool path

Answer:

201 feets

Step-by-step explanation:

The Circumference of a circle, C :

C = 2 * pi * r

r = Radius ; pi = 3.14

The entire Radius = pool radius + pathnaroind the pool = 28 + 4 = 32

Hence, the Circumference, which gives the value of fencing required is :

C = 2 * 3.14 * 32

C = 200.96 ft

C = 201 feets

Answer:

D. 201

Step-by-step explanation:

Answer:

m< -4/3 and m>-4

Step-by-step explanation:

Based on the characteristics of the line and parabola, the correct answer is:

A. \(\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)\)

Based on the given information, let's analyze the characteristics of the line and parabola to determine the correct representation:

1. Line: In the context of graphing, a line appears as a straight line that can extend in any direction across the coordinate plane. It can have a positive or negative slope, or be horizontal or vertical.

- The line passes through the points \((1,1), (2,0), (4,-2), and (8,-6).\)

- It extends along the first and fourth quadrants.

- A closed dot is shown at the point (1,1).

2. Parabola: In the context of graphing, a parabola appears as a curved line. It can open upward or downward and can be concave or convex. The vertex of the parabola represents the lowest or highest point on the curve, and the axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two symmetric halves.

- The parabola passes through the points \((1,3), (-2,6), and (10,-3).\)

- It extends along the first and second quadrants.

- An open dot is shown at the point (1,3).

- The vertex of the parabola lies at (0,2).

Given these characteristics, we can determine the correct representation:

The correct answer is:

A. \(\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)\)

Explanation: The equation \(\(y = x^2 + 2\)\) represents the parabola, and the equation \(\(y = -x + 2\)\) represents the line. The closed dot at (1,1) corresponds to the parabola, and the open dot at (1,3) corresponds to the line.

Therefore, the correct answer is A.

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The procedure for approximating sampling distributions when the shape is unknown is the bootstrap method.

When theory cannot provide information about the shape of the sampling distribution, the bootstrap method is commonly used. The bootstrap is a resampling technique that allows us to estimate the sampling distribution by repeatedly sampling from the original data.

Here's how the bootstrap method works:

1. We start with a sample of data from the population of interest.

2. We randomly select observations from the sample, with replacement, to create a resampled dataset of the same size as the original sample.

3. We repeat this process numerous times, creating multiple resampled datasets.

4. With each resampled dataset, we calculate the statistic of interest (e.g., mean, median, standard deviation).

5. The distribution of these calculated statistics from the resampled datasets approximates the sampling distribution of the statistic.

By generating an empirical approximation of the sampling distribution through resampling, the bootstrap allows us to construct confidence intervals and make statistical inferences even when the underlying distribution is unknown or cannot be determined through theoretical means.

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Answer:

AB ≈ 5.2

Step-by-step explanation:

given ∠ CAD = ∠ BAD = Θ

then AD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is

\(\frac{BD}{CD}\) = \(\frac{AB}{AC}\) ( substitute values )

\(\frac{4.1}{4.3}\) = \(\frac{AB}{5.5}\) ( cross- multiply )

4.,3 AB = 4.1 × 5.5 = 22.55 ( divide both sides by 4.3 )

AB ≈ 5.2 ( to one decimal place )

Answer: To differentiate this function, we need to use the product rule and the chain rule.

First, we will simplify the function:

f(y) = (1/y^2 - 3/y^4) * y(y + 9y^3)

f(y) = (y + 9y^3) / y^3 - (3y + 27y^3) / y^5

f(y) = y^-3 * (y^4 + 9y^6 - 3y^4 - 27y^6)

f(y) = 6y^4 / y^3

f(y) = 6y

Now we can differentiate:

f'(y) = 6

Therefore, the derivative of f(y) is 6.

Using product rule and power rule of differentiation, the derivative of the function f(y) = 1/y² - 3/y⁴ * (y + 9y³) is f'(y) = 12/y⁷ - 6/y⁶ - 54/y⁵.

To differentiate the given function,

We need to use product rule and the power rule of differentiation

use product rule to differentiate two terms in the function;

Let's consider the first term: 1/y²

The derivative of 1/y² with respect to y is:

d(1/y²)/dy = -2/y³

Now, let's consider the second term: -3/y⁴ * (y + 9y³)

The derivative of -3/y⁴ with respect to y is:

d(-3/y⁴)/dy = 12/y⁵

The derivative of (y + 9y³) with respect to y is:

d(y + 9y³)/dy = 1 + 27y²

Let's use product rule to differentiate the expression

Using the product rule, the derivative of the entire expression f(y) = 1/y₂- 3/y⁴ * (y + 9y³) is:

f'(y) = (1/y²) * (d(-3/y⁴ * (y + 9y³))/dy) + (-3/y⁴ * (y + 9y³)) * (d(1/y²)/dy)

Let's plug the value into the previous expression

f'(y) = (1/y²) * (12/y⁵) + (-3/y⁴* (y + 9y³)) * (-2/y³)

Simplifying further:

f'(y) = 12/y⁷ - 6(y + 9y³)/y⁷

      = 12/y⁷ - 6(y/y⁷ + 9y³/y⁷)

      = 12/y⁷ - 6/y⁶ - 54y²/y⁷

      = 12/y⁷ - 6/y⁶ - 54/y⁵

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To determine the combined output of the old and new mixers over time, we need to consider their individual capacities and mixing times.

Let's define the variables:

The old mixer has a capacity of 50 gallons and can fill in 40 minutes, which means it has an output rate of 50 gallons / 40 minutes = 1.25 gallons per minute.

The new mixer has a capacity of 20 gallons and can fill in 15 minutes, which means it has an output rate of 20 gallons / 15 minutes = 1.33... (repeating decimal) gallons per minute.

To calculate the combined output at time t, we need to determine the proportion of time each mixer has been running.

Since both mixers are loaded and started at the same time, we can express the proportion of time each mixer has been running as a fraction of t.

Now, we can calculate the combined output at time t using the proportions:

C(t) = (1.25 gallons per minute) * to + (1.33... gallons per minute) * tn

So, the function C(t) representing the combined output of the two mixers is:

C(t) = 1.25 * min(t, 40) + 1.33... * min(t, 15)

Note: The repeating decimal 1.33... indicates that the new mixer's output rate remains constant at 1.33... gallons per minute regardless of the time.

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Answer:

-3

Step-by-step explanation:

Answer:

The answer is x=26

Step-by-step explanation:

8x-71=5x+7 (because they are congruent you make them equal each other)

Add 71 to both sides

8x=5x+78

subtract 5x

3x=78

divide 3 from both sides

x=26

Answer:

9.5

Step-by-step explanation:

Using the intersection of sets we find that A ∩ B = {1, 3}

A set is a collection of well ordered items.

Givent hat set A = {x| x is an od number greater than 0 and less than 10} and set B = {1, 2, 3, 4}, we desire to find A ∩ B. We proceed as follows.

First since set A = {x| x is an odd number greater than 0 and less than 10}, its elements are A = {1, 3, 5, 7, 9}

Also, set B =  {1, 2, 3, 4}

Since we require A ∩ B which is the intersection of both sets and is  the elements that both sets have in common. Since both sets have element 1 and 3 in common, we have that

A ∩ B = {1, 3}

So, A ∩ B = {1, 3}

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I think it's answer this .

Answer:

x = -8

Step-by-step explanation:

4(1 - 5x) + 2 ≤ 166

4 - 20x + 2 ≤ 166

6 - 20x ≤ 166

-20x ≤ 166 - 6

- 20x ≤ 160. divide both sides by -20

x = -8