50PTS 50PTS don’t explain just answer.

Curved surface area of frustum is 1000.82 cm² and

Volume of frustum is 2756.754 cm³.

Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum.

Frustum is a Latin word which means ‘piece cut off’. When a solid (generally a cone or a pyramid) is cut in such a manner that base of the solid and the plane cutting the solid are parallel to each other, part of solid which remains between the parallel cutting plane and the base is known as frustum of that solid.

Height of frustum = h = 30 cm

Diameter of top of frustum = 6 cm

Radius of top = R = 6/2 = 3cm

Diameter of bottom of frustum = 15 cm

Radius of bottom = r = 15/2 = 7.5 cm

Slant Height = l = √h²+ (r - R)²

                       ⇒ l = √30² + (7.5 - 3)²

                       ⇒ l = √900 + 20.25 = √920.25 = 30.34 cm

A) Curved surface area of frustum = π(r + R)l

                                                         = 3.1416 × (7.5+3) × 30.34

                                                         = 3.1416 × (10.5) × 30.34

Curved surface area of frustum = 1000.82 cm²

B) Volume of frustum = (πh/3)(r²+R²+r.R)

                                   = (3.1416 × 30/3)(7.5² + 3² + 7.5×3)

                                   = (31.416) × (56.25 + 9 + 22.5)

                                   = 31.416 × 87.75

Volume of frustum = 2756.754 cm³

Hence, the curved surface area and volume of given conical frustum are 1000.82 cm² and  2756.754 cm³ respectively.

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Answer:

the correct answer is 60° and 30°( for the two angles that have the ratio 2:3)

The other angle will be 90°

Answer:

send the picture clearly i will help uou surely

The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).

Given equation,

[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]

= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]

= [tex]-3x^{2}-9x+3[/tex]

Hence, coefficient of [tex]x^{2}[/tex] is -3.

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Answer:

820 [tex]m^{2}[/tex]

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

check the above attachment to verify the answer.

Answer:

0.796 (simplified) 10π (not simplified)

Step-by-step explanation:

The formula for the circumference of a circle is

2πr so we have to do is plug in 5 for our radius:

2π(5) equals .796 or can be left as 10π.

The exact circumference of a circle that has a radius of 5 cm will be 31.4 centimeters.

The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle.

Then the circumference of the circle will be

Circumference = 2πr  units

The radius of the circle is 5 centimeters.

Then the circumference of the circle will be

Circumference = 2πr

Circumference = 2π (5)

Circumference = 10π

We know that the value of π will be 3.14 approximately. Then we have

Circumference = 10 x 3.14

Circumference = 31.4 centimeters

The exact circumference of a circle that has a radius of 5 centimeters will be 31.4 centimeters.

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Answer:

It's A 100% I got it right!!

Step-by-step explanation:

Answer:

($0.5 x 2) + ($1.25 x 3) + ($0.75 x 3) = $7

Answer: ($0.5*2) + ($1.25*3) + ($0.75*3) = $7

Step-by-step explanation: Since Laurie orders 2 fruit, 3 drinks, and 3 popcorn, we multiply the cost of each item by the number of items purchased.

For example, one fruit costs $.50. Since Laurie orders 2 fruits, we multiply .50 by 2, to get $1.

For future reference, the equation representing this problem would be

.50f+.75p+1.25d=c(total cost).

Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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Answer:

She bought 10 apples and 10 bananas

Step-by-step explanation:

10 apples - $1.50 each x 10 apples = $15.00

10 bananas - $1.25 each x 10 bananas = $12.50

15.00+12.50=$27.50

x+y=28.00

1.50x+1.25y=28

Answer:  First three terms are 1/25, 1/5, and 1 in that order.

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

Explanation:

The fifth term is 25, which makes the fourth term to be 25*(1/5) = 5. We multiply any term by the reciprocal of the common ratio to move back to the previous term.

The third term is 5*(1/5) = 1. The second term is 1*(1/5) = 1/5. The first term is (1/5)*(1/5) = 1/25

Therefore, the first five terms are:

1/25, 1/5, 1, 5, 25

As we move from left to right, we multiply each term by 5. Going in reverse, we multiply by 1/5.

The first three terms of the sequence are 0.04, 0.2, and 1.0.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

To find the first three terms of a geometric sequence, we need to use the formula for the nth term of a geometric sequence:

[tex]a_n = a_1 \times r^{n-1}[/tex]

where [tex]a_n[/tex] is the nth term of the sequence, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of the term we want to find.

We are given that,

[tex]a_5[/tex] = 25 and r = 5.

We can use this information to find [tex]a_1[/tex]:

[tex]a_5 = a_1 \times r^{5-1}[/tex]

[tex]25 = a_1 \times 5^4[/tex]

25 = [tex]a_1[/tex] x 625

[tex]a_1[/tex] = 25/625

[tex]a_1[/tex] = 0.04

Now that we have found [tex]a_1[/tex], we can use the formula to find the first three terms of the sequence:

[tex]a_1[/tex] = 0.04

[tex]a_2[/tex] = 0.04 x 5 = 0.2

[tex]a_3[/tex] = 0.04 x 5² = 1.0

Therefore,

The first three terms of the sequence are 0.04, 0.2, and 1.0.

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Answer:

[tex]x = \sqrt{87}[/tex]

Step-by-step explanation:

So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's  [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:

[tex]13^{2} + x^{2} = 16^{2}[/tex]

Now, we will simplify the equations:

[tex]169 + x^{2} = 256[/tex]

Then, we will subtract 169 from both sides, giving us:

[tex]x^{2} = 87[/tex]

Square rooting both sides gives us:

[tex]x = \sqrt{87}[/tex]

And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.  

Hope this helped

Answer:

31.2 lbs

Step-by-step explanation:

Let 2x = weight of oranges

5x = weight of apples

6x = weight of pears

2x + 5x + 6x = total weight

2x = 4.8

x = 2.4

4.8 + 5(2.4) + 6(2.4) = 4.8 + 12 + 14.4

= 31.2 lbs

Answer:

16,126 ft

Step-by-step explanation:

Using the net change theorem and letting s(t) represent the aircraft's position, and s(0) be the aircraft's position at time t = 0, s(0) = 15000 ft  and s(15 be the aircraft's position at time, t = 15 minutes respectively, then,

s(15) - s(0) = ∫₀¹⁵f(t)dt

s(15) - s(0) = ∫₀¹⁵[[tex]e^{0.4t} + 8[/tex]]dt

s(15) - 15000 = [[tex]\frac{e^{0.4t}}{0.4} + 8t[/tex]]₀¹⁵

s(15)  - 15,000 ft = [tex]\frac{e^{0.4X15}}{0.4} + 8X15 - \frac{e^{0.4 X 0}}{0.4} + 8(0)\\\frac{e^{6}}{0.4} + 120 - \frac{e^{0}}{0.4} + 0\\\frac{403.43}{0.4} + 120 - \frac{1}{0.4} + 0\\1008.57 + 120 - 2.5\\1126.07[/tex]

s(15) = 15,000 ft + 1126.07 ft

s(15) = 16,126.07 ft

s(15) ≅ 16,126 ft to the nearest foot

If the freight elevator lifts goods the same height in 2 minutes and 30 seconds, it will travel at a pace of 6.4 feet per second.

Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number. The sign for speed is v (italic), whereas the symbol for velocity is v. (boldface). A bar is placed over the symbol to represent average values. Speed is defined as the rate at which distance changes over time. It has a distance by time dimension. Thus, the SI unit of speed is defined as a combination of the fundamental units of distance and time. As a result, the SI unit of speed is the metre per second.

Here,

Given that a passenger elevator in the sears tower in Chicago can lift people 960 feet in 1 minute and 30 seconds (1.5 minutes). This means that the lift is travelling with a speed of:

=960/1.5

=640 ft/min

If the elevator lifts cargo through the same height in 2 minutes and 30 seconds (2.5 minutes), then the speed is given by:

=640/2.5

=384 ft/min

=384/60

=6.4 ft/second

The freight elevator be traveling at the speed of 6.4 ft/second if it lifts cargo the same height but in 2 minutes and 30 seconds.

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The distance from point A to point B is 781.5 ft.

Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,

tan(15°) = x / 862

Solve for x.

x = 862 (tan(15°))

Similarly, let y be the distance from point B to the lighthouse,

tan(8°) = x / y

Solve for y.

tan(8°) = 862 (tan(15°)) / y

y = 862 (tan(15°)) / tan(8°)

y = 1643.45 feet

Subtract 862 from 1643.45 to get the distance from point A to point B.

distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft

Therefore, the distance from point A to point B is 781.5 ft.

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Answer:

k = -7

Step-by-step explanation:

Let's put the side with the variables on the left.

-k+16-2k-9=28

Now we need to isolate the variable, which is k in this case.

-k+16-2k-9=28

-k-2k+16-9=28

-3k+7=28

(-3k+5) -7 = 28 -7

-3k = 21

k = -21/3

That's your answer:

k = -7

Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.

given

The correct response is 4 less than 7, since 4 is less than 7.

Thus, 7-4=3 could be considered.

The first section of 7–4 appears to be answer B.

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).

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Answer:

x + 5 = 10

Step-by-step explanation:

False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.

Cost per pound = $12.00 / 8 pounds = $1.50

5 pounds of apples cost = 5 pounds x $1.50 = $7.50

The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.

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The logarithmic function y log x is defined as

[tex]$\log_b \text x = \text y \leftrightarrow \text b^y= \text x[/tex].

An exponent that is expressed in a unique way is called a logarithm. As an illustration, we are confident that the exponential formula 32 = 9 is correct. In this instance, the base is 3, and the exponent is 2. The formula will be written as log3 9 = 2 in the logarithmic form.

This is expressed as "9 divided by base 3 is 2" in words. The exponent has been effectively lowered to the mainline in this case. However, despite the fact that this was done to make division and multiplication easier, logarithms are still very useful in mathematics.

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Answer:

the answer would be A, or 5.3%

Step-by-step explanation:

you start by finding the z-score of 200, so 200-144.05 = 55.95/34.52 = 1.62 (rounded to the nearest ) Then you use a z-score table to find the probability that a customer will spend less than 200 dollars and subtract the decimal probability from one. then you convert the decimal probability to a percent and get 5.3%.

Answer:

Number of smaller ropes she can make from the larger rope = 2/3

Step-by-step explanation:

Total length of rope = 2/5 ft

Length of smaller rope = 3/5 ft

How many smaller ropes can she make from the larger rope?

Number of smaller ropes she can make from the larger rope = Total length of rope / Length of smaller rope

= 2/5 ÷ 3/5

= 2/5 × 5/3

= (2*5)/(5*3)

= 10/15

= 2/3

Number of smaller ropes she can make from the larger rope = 2/3