Multiply 12×1/8 . Simplify the answer and express it as a mixed number.

The equation of the hyperbola with centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0) is (x²/7) - (y²/20) = 1.

The equation of a hyperbola centered at the origin with vertices on the x-axis is, (x²/a²)-(y²/b²) = 1.

The asymptotes' distance is b, while the distance between the origin and vertex is a. In this case, a = √7 and c = √27, distance from the origin to a focus is c. We can use the relationship a² + b² = c² to solve for b:

b² = c² - a² = 27 - 7 = 20

So, we get, the equation of the hyperbola to be,

(x²/7) - (y²/20) = 1.

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A hyperbola centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0). Write the equation of this hyperbola.

The calculated value of tyhe volume of the cone is 235.71 cubic feet

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

Height = 9 feet

Radius = 5 feet

Using the above as a guide, we have the following:

Volume = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 22/7 * 5² * 9

Evaluate

Volume = 235.71

HEnce, the volume is 235.71

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Answer:

  235.6 ft³

Step-by-step explanation:

You want the volume of a cone with radius 5 ft and height 9 ft.

The formula for the volume of a cone is given:

  V = 1/3πr²h

The values of the variables are given: r = 5, h = 9.

Put these values in the corresponding places in the formula and do the arithmetic.

  V = 1/3π(5 ft)²(9 ft) ≈ 235.6 ft³

The volume of the cone is about 235.6 cubic feet.

Answer:

x≤20

Step-by-step explanation:

He spent no more than $20 so it is 20 or less.

The solution is: the value of x is : x = 98.5.

Formula

<x = 1/2 (arc 1 + arc2)

This is the basic angle formula for the way two chords intersect.

Givens

arc1 = 96

arc2 = 101

Solution

<x = 1/2 (arc1 + arc2)                 Substitute values

<x = 1/2(96 + 101)

<x = 1/2(197)

<x = 98.5

Answer

x = 98.5

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Answer:

Step-by-step explanation:

Brahmagupta's solution to a quadratic equation of the form ax² + bx = c is given by x = (-b ± √(b² - 4ac)) / 2a.

For the equation 3x² + 4x = 6, we have a = 3, b = 4, and c = 6. Plugging these values into the formula, we get:

x = (-4 ± √(4² - 4(3)(6))) / 2(3)

x = (-4 ± √(16 - 72)) / 6

x = (-4 ± √(-56)) / 6

Since the square root of a negative number is not a real number, the quadratic equation has no real solutions. Therefore, Brahmagupta would not have found a solution for this particular equation using his method.

The indefinite integral will be ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C

Lets say u = x⁶ - 4 and du/dx = 6x⁵

it then becomes ∫x⁵e^(x⁶ - 4) dx = ∫e^(x⁶ - 4 * 1/6)du

e^(x⁶ - 4) = ∫(1/6)e^(x⁶ - 4)du = (1/6) ∫e^(x⁶ - 4) du = (1/6)e^(x⁶ - 4) + C

= ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C

An indefinite integral that when you differentiate it will give you the main  or first function.

The above answer is based on the question below as seen in the photo;

Find the indefinite integral (Use C for the constant of integration)

∫x⁵e^(x⁶ - 4) dx

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Answer:

68400

Step-by-step explanation:

Is the final answer to the question the first time first to and the from a the most other way interesting to in the a of long term

The range of equation represented by the graph is [1, ∞}.

The set of all potential values that a function could output or produce is known as its range. To put it another way, it is the collection of all values that the function "hits" or "reaches" when given various input values.

It's crucial to remember that not every function has a range that encompasses all potential values. For instance, the set [-1, 1] is the range of the function g(x) = sin(x), which only returns values between -1 and 1.

The range of the function are all the output values of the of the function or the y-coordinates of the graph.

For the given graph we see that the y-coordinates corresponding to the graph are from: 1 to ∞.

Hence, the range of equation represented by the graph is [1, ∞}.

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Answer:

Radius: 14

Step-by-step explanation:

We know

Circumference of circle = 2 · r · π

Circumference = 28π

Find radius!

Let's solve

28π = 2 · r · π

14π = r · π

r = 14

So, the radius is 14

Answer:

The radius is 14.

Step-by-step explanation:

Since the circumference is 28pi, we can find the diameter.

C = pi•d

C = 28pi

28pi = pi•d

divide both sides by pi.

d = 28

The diameter is 28.

So, cut it in half to find the radius. 28/2 is 14. The radius is 14.

Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.

The annual rate of interest that is charged on a loan or generated on an investment is known as the APR (Annual Percentage Rate), and it is stated as a percentage. Compounding, which is the practise of adding interest to the principal amount of a loan or investment, is not taken into account.

On the other hand, APY (Annual Percentage Yield) does consider the impacts of compounding. The annual percentage yield, or APY, is the rate of return that an investor receives on an investment over the course of a year. Both the interest gained on the initial sum and the interest earned on any prior interest that has been reinvested are considered.

The compound interest is given by the formula:

[tex]A = P * (1 + r/n)^{(n*t)}[/tex]

Now, isolating the value of P we have:

[tex]P = A / (1 + r/n)^{(n*t)}[/tex]

Now, substituting the value we have:

[tex]P = 35000 / (1 + 0.028/1)^{(1*10)} = $290,109.79[/tex]

Hence, Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.

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Answer:

If this helpful

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The type of transformation shown with polygons ABCD and A'B'C'D' would be C. Horizontal translation.

The image displays the preimage of a polygon ABCD, alongside a second figure to its right, titled A' B' C' D'. Each point sustains the same positioning within both images.

This suggests that the second image was established by shifting the preimage from left to right. In contrast, the other transformations cited - reflection across the x-axis, 90° clockwise rotation, and vertical translation - would lead to a different placement and orientation of each point in the subsequent portrait.

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Answer:

The type of transformation shown with polygons ABCD and A'B'C'D' would be C. Horizontal translation.

Step-by-step explanation:

Answer: 25.461 cm

Step-by-step explanation:

The circumference of a circle can be found using the formula C = πd, where d is the diameter and π (pi) is a constant value of approximately 3.14159.

Substituting d = 8.1 cm into the formula, we get:

C = πd

C = 3.14159 x 8.1 cm

C = 25.461 cm (rounded to 3 significant figures)

Therefore, the circumference of the circle with diameter 8.1 cm is approximately 25.461 cm.

Answer:

So, we can write the equation:

2.2x = 132

To solve for x, we can divide both sides by 2.2:

x = 132 ÷ 2.2

x = 60

Therefore, 220% of 60 is 132

There total of 126 ways in which nine people can sit on chairs in the room when four of these people be chosen to stand up.

The problem is asking how many ways we can choose 4 people out of 9 to stand up. This is a combination problem since the order in which the people are chosen is irrelevant. We can utilize the combination formula, which is,

n choose k = n!/(k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, we have n=9 people and k=4 people to choose. Putting all the values in formula,

9 choose 4 = 9!/(4!(9-4)!)

9 choose 4 = 362880/(24 x 120)

9 choose 4 = 126.

Therefore, there are 126 ways to choose 4 people out of 9 to stand up.

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Answer: The length of the field is 100 feet and the width is 60 feet.

Step-by-step explanation:

a. The perimeter of a rectangle is the sum of the lengths of all its sides. For a soccer field, the perimeter is the sum of the lengths of two adjacent sides, which are equal in length, and the sum of the lengths of the other two adjacent sides, which are also equal in length. Therefore, we can write the equation:

2l + 2w = 320

b. According to the problem, the length of the field is 20 less than twice the width. In equation form, this is:

l = 2w - 20

c. To solve the system of equations, we can substitute the expression for l from equation b into equation a, and then solve for w:

2(2w - 20) + 2w = 320

Simplifying:

4w - 40 + 2w = 320

6w - 40 = 320

6w = 360

w = 60

Now that we know the width is 60 feet, we can substitute this value into equation b to find the length:

l = 2w - 20

l = 2(60) - 20

l = 100

Therefore, the length of the field is 100 feet and the width is 60 feet.

Step-by-step explanation:

that sounds like the sequence does not matter (e.g. the selection of Democrat A and Democrat B is the same as the selection of Democrat B and Democrat A).

and repetition is not possible (there cannot be a single person appearing twice in a selection).

so, we have combinations without repetition.

how many options do we have to select the 3 Democrats out of 11 ?

C(11, 3) = 11! / (3! × (11 - 3)!) = 11! / (3! × 8!) = 11×10×9/(3×2) =

= 11×5×3 = 165

how many options do we have to select the 2 Republicans out of 10 ?

C(10, 2) = 10! / (2! × (10 - 2)!) = 10! / (2! × 8!) = 10×9/2 =

= 5×9 = 45

how many optics now to build the committee ?

for each of the Democrat selections we have all Republican options.

so, we have

165 × 45 = 7,425

different ways to build the committee.

This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.

Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.

The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (π) with the square of the radius. Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = πr2h. In this case, the height is h = Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)2(Sin) = 4πSin in3. This can be rounded to the nearest tenths place, giving us a final answer of V = 4πSin in3, rounded to the nearest tenths place.

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This can be rounded to the nearest tenths place, giving us a final answer of V = 4mSin in³,

What is area?

Area is the size of a two-dimensional surface or shape. It is usually measured in square units such as square feet, square meters, or acres. Area can be used in a variety of ways, such as for measuring the size of a garden or calculating the amount of paint needed for a wall. Area can also be used to measure the area of a circle, triangle, or other shapes. Area is an important concept in mathematics, as it is used in a variety of formulas and equations.

The volume of a cylinder is calculated by multiplying the base area with the height. The base area is calculated by multiplying pi (n) with the square of the radius.

Therefore, the volume of a cylinder with a height of h and a base radius of r is calculated by the formula V = mr²h.

In this case, the height is h Sin and the base radius is r = 2in. Applying these values to the formula, we get V = π(2in)²(SinA) = 4πSinA in³.

This can be rounded to the nearest tenths place, giving us a final answer of V = 4mSinA in³, rounded to the nearest tenths place.

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Answer:

45 cm

Step-by-step explanation:

The area of a rectangle can be found by multiplying its breadth and width together.

Since the length of the rectangle is usually taken to be the longer side of the rectangle, we can assume that the ratio of the measure of the breadth to its length is 4:5.

Let the breadth of the rectangle be 4 units, where units shall be written as 'u' for simplification.

Thus, the length of the rectangle is 5u.

Area= length ×breadth

125 cm²= (4u)(5u)

125 cm²= 20u²

Divide both sides by 20:

u²= 6.25 cm²

Square root both sides:

u= 2.5 cm

Length= 5(2.5)= 12.5 cm

Breadth= 4(2.5)= 10 cm

The perimeter is the sum of the length of all its sides, i.e. 2(length +breadth).

Perimeter of the rectangle

= 2(12.5 +10)

= 2(22.5)

= 45 cm

The unused length of the ribbon is 3 inches.

Given that, Luann has a piece of ribbon that is 1 yard long she cuts off 33 inches to tie a gift box,

We need to find the unused length of the ribbon,

Since, 1 yard = 36 inches

Therefore, Luann has 36 inches long ribbon, in which she used 33 inches,

So, the left length = 36 - 33 = 3 inches.

Hence, the unused length of the ribbon is 3 inches.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{41.7\% of 35670}}{\left( \cfrac{41.7}{100} \right)35670}\implies 14874.39~\hfill\underset{ \textit{marked down price} }{\stackrel{ 35670~~ - ~~1487.39 }{\text{\LARGE 20795.61}} }[/tex]

About 21% of the animals at an animal shelter are dogs, which can be written as the fraction 21/100 or simplified to 3/14.

To convert the percentage of dogs at the animal shelter to a fraction, we can write 21% as a ratio of 21 dogs for every 100 animals.

This means that for every 100 animals at the shelter, there are 21 dogs. To express this as a fraction, we can write 21/100.

So, about 21/100 of the animals at the shelter are dogs. This fraction can be simplified to 3/14, which means that out of every 14 animals at the shelter, there are 3 dogs.

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The first method to find GCF for numbers 34 and 85 is to list all factors for both numbers and pick the highest common one:

All factors of 34: 1, 2, 17, 34

All factors of 85: 1, 5, 17, 85

So the Greatest Common Factor for 34 and 85 is 17

The second method to find GCF for numbers 34 and 85 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 34: 2, 17

All Prime Factors of 85: 5, 17

As we can see there is only one Prime Factor common to both numbers. It is 17. So 17 is the Greatest Common Factor of 34 and 85

The probability of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1618.

The likelihood of selling more than 2 pineapple pies in at least one hour can be computed through the application of the complement rule:

P(at least two hours with a minimum of two pies dispersed) = 1 - P(less than two hours meeting the criterion of having more than two pies sold)

P(X < 2) = P(X = 0) + P(X = 1) = (e^(-4)*4^0)/0! + (e^(-4)*4^1)/1!

= 0.0183 + 0.0732 = 0.0915

Consequently, the probability of vending more than two pineapple pies during a given hour is 1 - 0.0915 = 0.9085.

Finally, we can calculate the probability of trading beyond seven pineapple pies total with Poisson distribution parameters λ = 4:

P(X > 7) = 1 - P(X <= 7) = 1  -[P(X=0) + P(X=1) + ... + P(X=7)]

= 1 - [e^(-4)(4^0)/0! + e^(-4)(4^1)/1! + ... + e^(-4)*(4^7)/7!]

= 1 - (0.0183 + 0.0732 + 0.1465 + 0.1954 + 0.1954 + 0.1563 + 0.1042 + 0.0595)

= 0.1472

Therefore, the likelihood of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1472/0.9085 = 0.1618.

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Answer:

Step-by-step explanation:

That is rounded to the nearest cent.

if you want to round to the nearest dollar it is $35

sinθ=y/r

cosθ=x/r

tanθ=y/x

x^2 + y^2 = r^2

r^2(sin^2 θ + cos^2 θ) =r^2

sin^2 θ + cos^2 θ=1

The average velocity for 0.5 seconds: -11 ft/s

The average velocity for 0.1 seconds is -33.6 ft/s

The average velocity for 0.05 seconds: -34 ft/s

The average velocity for 0.01 seconds : -16 fts

change in position using the height function y = 50t - 16t² for the given time intervals.

(i) 0.5 seconds:

y(2) = 50(2) - 16(2²) = 100 - 64 = 36 ft

y(2.5) = 50(2.5) - 16(2.5²) = 125 - 100 = 25 ft

Average velocity = (25 - 36) / 0.5 = -11 ft/s

(ii) 0.1 seconds:

y(2) = 36 ft (calculated before)

y(2.1) = 50(2.1) - 16(2.1²) ≈ 32.64 ft

Average velocity = (32.64 - 36) / 0.1 = -33.6 ft/s

(iii) 0.05 seconds:

y(2) = 36 ft (calculated before)

y(2.05) = 50(2.05) - 16(2.05²) ≈ 34.32 ft

Average velocity = (34.32 - 36) / 0.05 = -34 ft/s

(iv) 0.01 seconds:

y(2) = 36 ft (calculated before)

y(2.01) = 50(2.01) - 16(2.01²) ≈ 35.84 ft

Average velocity = (35.84 - 36) / 0.01 = -16 ft/s

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The population is normally distributed is 90 %.

Given that

C = 0.90,

x = 13.7,

s = 3.0,

n = 10

Use the following formula is necessary:

CI = x t*(s /[tex]\sqrt{n}[/tex])

Where CI stands for confidence interval, x represents sample mean, s represents sample standard deviation, n represents sample size, and t represents the desired level of confidence and the t-value from the t-distribution with n-1 degrees of freedom.

According to the information given, we have:

Since alpha + C equals 1, C = 0.90,

which means that alpha is 0.10. x = 13.7 s = 3.0 n = 10

The t-distribution must be used in place of the z-distribution because n is small (n 30).

Which has a degree of freedom of n-1 = 9 and a confidence level of 90%. About 1.833 is the t-value.

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12 or 128

by the way question is not complete

the answer is 128 , if repetition is allowed

and answer is 12 , if repetition is not allowed