A cone has a height of 8 yards and a radius of 3 yards. What is its volume?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

cubic yards
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Yea

The lateral area of the prism is 270cm²

What is the lateral area of a prism?

The lateral area of a prism is defined as the sum of the areas of its lateral faces.

Using the formula;

Lateral area = (a+ b+ c) h

Where a, b, c, are all the lateral faces and h is the height

Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²

Therefore, the lateral area of the prism is 270cm²

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Answer:

hope you can understand

Answer:

3m²n⁴

Step-by-step explanation:

Given :

⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]

=============================================================

Solving :

⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]

⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]

⇒ 3 × m² × n⁴

⇒ 3m²n⁴

Option d is the correct answer. All real numbers are greater than or equal to 2.

Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).

Thus Option d is the correct answer. All real numbers are greater than or equal to 2.

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Answer:

[tex]1.25332[/tex]

Step-by-step explanation:

[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]

Answer:

x= 3/2

Step-by-step explanation:

3/x=2

Multiply x both sides so,

3 =2x

Divide 2 to get the value of x so,

x= 3/2

Answer:

The angle shows 90° so that means

90° - 42° = 48°

Therefore the angle of the depression is 48°

The angle of depression from C to point A 48°. The correct option is c. 48°

From the question, we are to determine the angle of depression from C to point A

The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object

Thus, in the given diagram

The angle of depression is 90° - 42°

Angle of depression = 48°

Hence, the angle of depression from C to point A 48°. The correct option is c. 48°

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Answer: 1

Step-by-step explanation:

First, we will translate this into an algebraic expression.

-> Quotient means we will be using divison

-> Product means we will be using multiplciation

     the quotient of 12 and the product of 3 and 4

     [tex]\displaystyle \frac{12}{\text{the product of 3 and 4}}[/tex]

     [tex]\displaystyle \frac{12}{3*4}[/tex]

Now, I will simplify.

     Given:

      [tex]\displaystyle \frac{12}{3*4}[/tex]

     Multiply:

     [tex]\displaystyle \frac{12}{12}[/tex]

     Divide:

     1

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Answer:

1.43

Step-by-step explanation:

12 tenths ⇒ 1.2

23 hundredths ⇒ 0.23

0.23 + 1.2 = 1.43

Answer:

Hi,

Step-by-step explanation:

sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)

a=45° and b=30°

[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]

Answer:

In terms of Pi: [tex]3\pi + 6[/tex] km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]

We can plug in the values to solve for the perimeter.

In terms of Pi, it is [tex]3\pi + 6[/tex],

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42

Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

Answer:

r = - 18/5

I hope this helps! ^^

( This problem has 13 steps, so it would take a lot of time to type them in ^^)

Answer: x=15, y=3

Step-by-step explanation:

Subtracting the two equations, we get -3y=-9, meaning y=3.

Substituting this into the first equation, we get that x-3=12, and thus, x=15.

The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

The first term of an arithmetic progression can be calculated using the following expression:

Sn = n/2 [2a + (n − 1)d]

Where;

100 = 2 [2a + (4 - 1)4]

100 = 4a + 24

4a = 100 - 24

a = 76/4

a = 19

Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

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The value of this equation is x = 0

The representation of an equation of the first degree - is given by:

[tex] \boxed{ \large \sf ax + b = 0}[/tex]

This representation is also defined in a first degree function.

— To solve this expression, let's: add or subtract the real terms. Then we will do the division.

⚘ Resolution

[tex] \large \sf{-3+8x-5=-8}[/tex]

[tex] \large \sf{-8+8x=-8}[/tex]

[tex] \large \sf{8x=0}[/tex]

[tex] \large \sf{x=0 \div 8}[/tex]

[tex] \green{ \boxed{ \boxed{ \blue{ \large \sf{x=0}}}}} \\ [/tex]

Therefore, the value of this equation will be x = 0

Answer:

10,800 kilograms

Step-by-step explanation:

(24 x 30) x 15 = 10,800

or (24 x 15) x 30

Answer: 0.5 or - 0.834

Step-by-step explanation: Here is the explanation!

Answer:

6

Step-by-step explanation:

The dimensions the rug should have is 20 by 29

The dimension of the rug is given as:

22 ft by 31 ft

The area of the carpet is given as:

Area = 580

Represent the length of the empty space with x.

So, the dimension of the carpet is:

22 - 2x by 31 - 2x

The area is calculated as:

Area = (22 - 2x) * (31 - 2x)

Expand

Area = 682 - 62x - 44x + 4x^2

Evaluate the difference

Area = 682 -106x + 4x^2

Substitute Area = 580

682 -106x + 4x^2 = 580

Subtract 580 from both sides

102 -106x + 4x^2 = 0

Rewrite as:

4x^2 - 106x +102 = 0

Using a graphing calculator, we have:

x = 1 and x = 22.5

Substitute these values in 22 - 2x by 31 - 2x

So, we have:

Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23

Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14

The dimensions cannot be negative.

So, we have:

Length = 20 and Width = 29

Hence, the dimensions the rug should have is 20 by 29

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Answer:

The angle Sita here is called Amplitude

Based on the calculations, the area of the shaded region is equal to 22 square foot.

By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:

Area of shaded region = Area of square - Area of circle.

Note: The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.

Radius = diameter/2 = 10/2 = 5 feet.

For the area of square, we have:

Area of square = S²

Area of square = 10²

Area of square = 100 square foot.

For the area of circle, we have:

Area of circle = πr²

Area of circle = 3.14 × 5²

Area of circle = 78.5 square foot.

Substituting the parameters into the formula, we have;

Area of shaded region = Area of square - Area of circle.

Area of shaded region = 100 - 78.5

Area of shaded region = 21.5 ≈ 22

Area of shaded region = 22 square foot.

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Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.

The algebraic expression of the situation above is 4x - 100 = 400

Let

the amount of ice cream they serve in July = x + 100

the amount of ice cream they serve in June = x

They served twice as many customers in august as they did in June.

Therefore,

the amount of ice cream they serve in August = 2(x)

the amount of ice cream they serve in August = 2x

Therefore,

2x + x  + x + 100 = 400

4x - 100 = 400

4x = 500

x = 500 / 4  

x = 125  

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To expand an expression, use FOIL method.

-7y and y are the first terms in each expression.

(-7y)(y) = -7y²

-7y is the first term in the first expression

-4 is the last term of the second expression

(-7y)(-4) = 28y

-8 is the last term in the first expression

y is the first term in the second expression

(-8)(y) = -8y

-8 is the last term of the first expression

-4 is the last term of the second expression

(-8)(-4) = 32

Combine all simplified terms.

Answer:

Wxndy~~

Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

The surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

[tex]S = \pi r(r+l)[/tex]

Where S is the surface area

r is the radius

and [tex]l[/tex] is the slant height

First, we will calculate the slant height of the cone

[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)

[tex]l^{2}=81+31.36[/tex]

[tex]l^{2}=112.36[/tex]

[tex]l}=\sqrt{112.36}[/tex]

[tex]l=10.6 \ ft[/tex]

∴ The slant height is 10.6 ft

Now, for the surface area

[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]

[tex]S = 90.72\pi \ ft^{2}[/tex]

[tex]S = 285.0053 \ ft^{2}[/tex]

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

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Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

Given the following formula,

w=x-y/2 -z

We need to solve for y.

[tex]w = \dfrac{x-y}{2 -z}[/tex]

By cross multiplication

[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]

subtract x both side

2w - wz -x = x - y -x

y = x - 2w + wz

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Answer:

1) 5
2) 0.8
3)  -1.3

4) -[tex]\frac{4}{9}[/tex]

5) ±10

6) ±[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

All the numbers follow a pattern of division by 2

Therefore the next number is 3/2 which is equal to 1.5