Mr. Fry is building a fence around his pool.

•Length of the fence is 60 feet.
•Width of the fence is 30 feet.

How many yards of fence will Mr. Fry build?

The number of combinations which are possible according to the specifications is; 119,700.

It follows from the task content that the 5ember teams to be formed must contain 3 girls and 2 boys.

On this note, it follows that the combinations possible are as follows

20C(3) × 15C2 = 1140 × 105 = 119,700.

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Answer:

b

Step-by-step explanation:

We are given the first derivative

To find the antiderivative, we must think of functions whose derivative is sin x. That happens when we have f(x) = cos u. Recall:

So we can assume that:

So we know that u must be 17.5t, which gives us u' = 17.5. Therefore there must be a multiplier before u' for us to get -210.

So, the antiderivative must be:

Let's check:-

To find the value of c, we will use i(0) = 0.

The complete equation for i(t) is:

Using the equation we found for 1(t), we can calculate i(5).

The current when t = 5 is 1.98 amperes.

To find the time when the current is zero again, we substitute once more.

The next time that current is zero again is at t = 0.359 seconds.

The rate of change of di/dt when t = 0.5 is equal to its derivative (the second derivative of the original function).

The rate of change of di/dt at t = 0.5 is 3,632 amps/second^2.

42 is the answer to x3 y3 z3 K in sum of cubes problem.

In mathematics, completely by accident, there is a polynomial equation whose solution, 42, has similarly baffled mathematicians for decades. The "sum of cubes problem" refers to the equation x3+y3+z3=k.

The "sum of cubes problem" refers to the equation x3+y3+z3=k. The most brilliant mathematicians in the world have been baffled by a mathematical problem for decades. A Diophantine equation known as "summing of three cubes" is x3+y3+z3=k, where k is the sum of all the numbers between one and 100. ∴ 3xyz will be the necessary outcome.

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Answer:

64

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

\(10x - 30\)

\(10 \times 5 - 30\)

\(50 - 30\)

\( = 20\)

We can show similarity in the two sides of the display in the following ways:

1. Neither set of data has any outliers.

2. The majority of observations are between 5 and 9 MPa for both sets of data.

However, the statement "Both sets of data have outliers in the data" is contradictory to the first statement, and the statement "The majority of observations are between 10 and 14 MPa for both sets of data" is contradictory to the second statement. Therefore, these statements cannot be used to describe the similarities between the two sides of the display.

Based on the given options, the similarity between the two sides of the display is that the majority of observations are within a similar range for both sets of data. Specifically, option B states that "the majority of observations are between 5 and 9 MPa for both sets of data." Therefore, this is the common similarity between the two sides of the display.

The other options suggest differences between the two sets of data, such as the presence or absence of outliers and differences in the range of values observed.

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Answer:

16 play only basketball

5 play only baseball

19/29 + 5/29 = 24/.29

Step-by-step explanation:

Answer:

\(3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30\)

m<DGI = 80°

\(3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81\)

The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The ray GI bisects ∠DGH.

It implies that the new angles are equal in measurement.

⇒ m∠DGI = m∠IGH

⇒ 3x - 9 = 2x + 21

⇒ x = 30

Then, in order to calculate m∠DGI, plug x = 30 in  3x - 9 as,

3 × 30 - 9 = 81

Hence, the measure of angle ∠DGI is given as 81°.

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The variance of the bedroom areas in the five-bedroom house is 864, and the standard deviation is approximately 29.39 square feet.


Mean: (100 + 100 + 120 + 120 + 180) / 5 = 620 / 5 = 124
Squared differences: (24^2, 24^2, 4^2, 4^2, 56^2) = (576, 576, 16, 16, 3136)
Mean of squared differences: (576 + 576 + 16 + 16 + 3136) / 5 = 4320 / 5 = 864
Variance: 864
Standard deviation: √864 ≈ 29.39


Hence, The variance of the bedroom areas in the five-bedroom house is 864, and the standard deviation is approximately 29.39 square feet.

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The hidden compartment of the jewelry box has a volume of 1005.459 cubic centimeters.

According to the statement, we find the case of a jewelry box, whose is form is a rectangular prism, divided into two compartments. The volume of the hidden compartment is defined below:

V = w · l · (H - h)

Where:

If we know that w = 12.7 cm, l = 20.3 cm, H = 10.2 cm and h = 6.3 cm, then the volume of the hidden compartment is:

V = (12.7 cm) · (20.3 cm) · (10.2 cm - 6.3 cm)

V = 1005.459 cm³

The volume of the hidden compartment of the jewelry box is equal to 1005.459 cubic centimeters.

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(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation.

How to Translate a Triangle

Step 1: Identify the coordinates of each of the vertices of the triangle.

Step 2: Translate each point by adding the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. For these translations, add a negative number if the horizontal translation is to the left or if the vertical translation is downward.

Step 3: Plot the three translated points and draw the triangle by connecting each pair of points with a straight line.

Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axis.

Given data

(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

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Answer:

B, 71

Step-by-step explanation:

Triangles have 180 total degrees. 180 - (23+86) gives 71.

Answer:

The answers are options A and C.

They are (-2,0) and (0,0).

Step-by-step explanation:

x-intercept

(-2,0) and (0,0)

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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Answer:

The answer is 1/5

Step-by-step explanation:

Answer:

The height of the skyscraper is 1,459 ft. Choice c

Step-by-step explanation:

Right Triangles

The ground and the building form a right angle (90°). In the right triangles, the trigonometric ratios are satisfied. To solve the problem we use the tangent ratio, defined as:

\(\displaystyle \tan\theta=\frac{\text{opposite side}}{\text{adjacent side}}\)

The angle of elevation from which the skyscraper can be seen is θ=12°. The opposite side of this angle is the height of the skyscraper H and the adjacent side is the distance from the ground X=1.3 miles.

Converting miles to feet: X=1.3*5,280 = 6,864 ft

Applying the tangent ratio to the angle of elevation:

\(\displaystyle \tan 12^\circ=\frac{H}{6,864}\)

Solving for H:

\(H=6,864\tan 12^\circ\)

Calculating:

H = 1,459 ft

The height of the skyscraper is 1,459 ft. Choice c

Answer:

We can start by using the Pythagorean identity to simplify the expression for cos J:

cos^2(J) + sin^2(J) = 1

Since we are given the value of sin J, we can substitute and solve for cos J:

cos^2(J) + (4/√82)^2 = 1

cos^2(J) + 16/82 = 1

cos^2(J) = 66/82

cos(J) = ±√(66/82)

We want to express cos J in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:

cos(J) = ±√[(2311)/(2*41)]

cos(J) = ±(√2/2) * (√33/√41)

Since J is in the first or second quadrant (based on the given value of sin J), we know that cos J is positive, so we can drop the negative sign:

cos(J) = (√2/2) * (√33/√41)

Therefore, the exact value of cos J in simplest radical form is (√2/2) * (√33/√41).

The equivalence classes of the partition induced by the relation R on X={1,2,...,20}, defined as x≡y(mod5), are {{1,6,11,16},{2,7,12,17},{3,8,13,18},{4,9,14,19},{5,10,15,20}}. These equivalence classes group elements based on their remainder when divided by 5.

In this relation, elements in each equivalence class share the same remainder when divided by 5. For example, the first equivalence class {{1,6,11,16}} consists of elements that leave a remainder of 1 when divided by 5. Similarly, the second equivalence class {{2,7,12,17}} comprises elements that leave a remainder of 2 when divided by 5, and so on.

Each equivalence class represents a distinct residue class modulo 5. The partition created by the equivalence classes ensures that every element in X is assigned to exactly one equivalence class, and every pair of elements in the same equivalence class are related by R.

Thus, the equivalence classes of the partition induced by R on X are {{1,6,11,16},{2,7,12,17},{3,8,13,18},{4,9,14,19},{5,10,15,20}}.

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The poles of the transfer function are s = -1 and s = -5/2. The poles of a transfer function are the values of s that make the transfer function equal to zero. In this case, the transfer function is equal to zero when s = -1 and s = -5/2. Therefore, the poles of the transfer function are s = -1 and s = -5/2.

The transfer function is given by:

\(\frac{s-2}{\left(s^{2}+2 s+5\right)(s+1)} = \frac{s-2}{(s+1)(s+5/2)(s+1)} = \frac{s-2}{(s+5/2)(s+1)^2}\)

The denominator of the transfer function is equal to zero when s = -1 or s = -5/2. Therefore, the poles of the transfer function are s = -1 and s = -5/2.

The poles of a transfer function are important because they determine the stability of the system. If a pole is located in the right-hand side of the complex plane, then the system is unstable. If all of the poles of a transfer function are located in the left-hand side of the complex plane, then the system is stable. In this case, the poles of the transfer function are located in the left-hand side of the complex plane, so the system is stable.

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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A statement that correctly compares the areas of these two rectangles is that the area of the yellow rectangle is greater than the area of the blue rectangle by 8 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

Based on the information provided about these rectangles, we have the following:

Area of blue rectangle = 10 × 4

Area of blue rectangle = 40 square units.

Area of yellow rectangle = 6 × 8

Area of yellow rectangle = 48 square units.

Difference = Area of yellow rectangle - Area of blue rectangle

Difference = 48 - 40

Difference = 8 square units.

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Thus, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

The equation of exchange is an economic equation that relates the money supply (M) with the price level (P), the velocity of money (V), and the real output of the economy (Q). The equation is M x V = P x Q.

Using the given values of M = $1.5 trillion, V = 7, and P = 1.05, we can solve for Q by rearranging the equation as Q = M x V / P.

Plugging in the numbers, we get:

Q = ($1.5 trillion x 7) / 1.05 = $10 trillion

Therefore, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

It's worth noting that the equation of exchange is a theoretical model and may not reflect actual economic conditions. In practice, changes in any one of the variables (M, V, P, or Q) can affect the others, and there may be other factors at play that influence the economy.

Nonetheless, the equation of exchange provides a useful framework for thinking about the relationship between the money supply, prices, and economic activity.

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Complete question

in the equation of exchange, if m = $1.5 trillion, v = 7, and p = 1.05, then:

Find real output.

The expression 2x^3 x^2 2x can be simplified to 4x^6. Since this is a polynomial of degree 6, it does not have critical points, which are only present in functions that have derivatives. So, the function 2x^3 x^2 2x has a critical point at x = 0.

Critical points are points where the derivative of a function is equal to zero or undefined.
Yes, the function 2x^3 x^2 2x has critical points.
To find the critical points, we first need to find the derivative of the function with respect to x. The function is f(x) = 2x^3 * x^2 * 2x.
Step 1: Combine like terms.
f(x) = 4x^6
Step 2: Calculate the derivative.
f'(x) = 24x^5
Step 3: Set the derivative equal to zero and solve for x.
24x^5 = 0
Step 4: Solve for x.
x = 0
So, the function 2x^3 x^2 2x has a critical point at x = 0.

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Answer:

x= -2

Step-by-step explanation:

15x + 6 = 6x - 12

6 = -9x -12

18 = -9x

2 = -x

-2 = x

Answer:

The answer is 8.3

Step-by-step explanation:

(I'm not that good at explaining things so bear with me please. I checked on Khan Academy so it's right)

I split the box on the right diagonally and got the equation

\(4^{2}\) + \(2^{2}\) = \(x^{2}\)

=16 + 4 =\(\sqrt{20}\)

≈4.5

The new triangle will help solve what d is

\(4.5^{2}\) + \(7^{2}\) = \(d^{2}\)

=20.25 +49 = \(\sqrt{69.25}\)

≈8.3

The diagonal of the rectangular prism shown is 8.3.

A polygonal is a closed, two-dimensional structure that is flat or plane and seems to have excellent dimensional.

A diagonal is a line segment that joins 2 opposing polygonal vertices.

In another word, a diagonal is an inclined line that connects two orthogonal lines to become a complete triangle.

Diagonal is the use for the idea of the length of sides, for example, if you want to measure the height of a tower knowing diagonal will surely help to do this.

Given a rectangular prism

Let x is the diagonal of the sides 7 and 4 then

By Pythagoras theorem

4² + 7² = x²

x² = 65

x=8.06

Now in the right-angle triangle of sides d,x and 2

d² = 65 + 4

D = √(69)

d  = 8.30 hence, the correct answer is 8.30.

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To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Average love of cats is not significantly different from average love of school, but increased love of cats is associated with increased love of school.

If there were zero correlation, the probability of increased love of cats being reliably associated with increased love of school on this 5-point scale would decrease.

The answer to question 1 is: The result of this analysis shows that, on this 5-point scale, the average love of cats is probably not significantly different from the average love of school, but increased love of cats is reliably associated with increased love of school.

The answer to question 2 is: If there were zero correlation between the love of cats and the love of school on this 5-point scale, the average love of cats is probably significantly different from the average love of school, and increased love of cats is probably not reliably associated with increased love of school compared to the observed correlation (R = 0.03) or a larger correlation between the two variables.

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Answer:

QR = 8

Step-by-step explanation:

      4x            x + 6

Q ------------ R ------------S

find: QR

QR = QS

4x = x + 6

4x - x = 6

3x = 6

x = 6/3

x = 2

solve for QR:              solve for QS:

QR = 4x                       QS = x + 6

QR = 4(2)                     QS = 2 + 6

QR = 8                         QS = 8