What is 80% of 63? Do not round your answer.

The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The function used to find the radius r of a sphere given volume V,

r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]

The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r

The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²

We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)

We have, A(s) = 6s²

Substituting function for s to A(s)

⇒ A(s(r)) = 6(2r)² = 24r²

Substituting function for r into A(s(r)),

⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The question is incomplete. Find the complete question below:

Consider a cube with an inscribed sphere. The function  r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function  s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area,  A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?

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Answer:

Answer is D

Step-by-step explanation:

The sample space for the given experiment is

{ (r,r) , (r,g) , (r,b)

  (g,r) , (g,g) ,(g,b)

  (b,r) , (b,g) , (b,b)}

A sample space is a set of potential results from a random experiment. Events are the subset of possible experiment results. An event is set of possible outcomes.

The die consists of 3 different colors namely red, green and blue

Here, the number of variables is 3 i.e red, green and blue.

The subset will contain

= [tex]2^{3}[/tex]

=8 elements.

The red color is indicated by 'r'

The green color is indicated by 'g'

The blue color is indicated by 'b'

The events that can appear in a single roll is r, b or g.

Sample space for the next 2 rolls

={ (r,r) , (r,g) , (r,b)

  (g,r) , (g,g) ,(g,b)

  (b,r) , (b,g) , (b,b)}

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The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).

In this problem we find a line segment whose endpoints are known: A(x, y) = (- 3, - 6), B(x, y) = (10, 4), and of which we need to find a point C such that it is 3 / 10 of the way from point A to point B, whose exact location can be found by means of the line segment formula:

C(x, y) = A(x, y) + (3 / 10) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 6) + (3 / 10) · [(10, 4) - (- 3, - 6)]

C(x, y) = (- 3, - 6) + (3 / 10) · (13, 10)

C(x, y) = (- 3, - 6) + (3.9, 3)

C(x, y) = (0.9, - 3)

The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).

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Answer:

a  c  e

Step-by-step explanation:

Answer: 2a-2ab+7

Step-by-step explanation:

6a-5ab+8-(4a-3ab+1)=

6a-5ab+8-4a+3ab-1=

2a-2ab+7

Answer:

2a - 2ab - 9b + 7

Step-by-step explanation:

The step here is to collect the like terms available like this;

6a - 5ab - 9b + 8

- 4a - 3ab - 0 + 1

which is = 2a - 2ab - 9b + 7

The function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

We are given that:

The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.

So, we get that:

Parking fees = 3 x for 0 ≤ x ≤ 2

Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is

6 + 4 ( x - 2) for 2 < x ≤ 5

Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be

20 for x > 5

So, the function becomes:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

Therefore, we get that, the function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

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[tex]\huge\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]

Given a point and a slope, we want to write an equation in point-slope form.

The point-slope form is defined as:

[tex]y-y_1=m(x-x_1)[/tex]

In this equation, [tex](x_1, y_1)[/tex] is a known point on the line and [tex]m[/tex] is the line's slope.

Substitute in the values:

[tex]y-(-2)=-\dfrac{4}{3}(x-3)[/tex]

Finally, simplify. Subtracting a negative number is the same as adding a positive number:

[tex]\large\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]

The type of solution to the given simultaneous equations is no solution

When it comes to linear simultaneous equations as given in the question, there are different types such as; one solution, no solution or infinitely many solution.

We are given the simultaneous equations;

y = 5x + 4   ---(1)

y = 5x - 2   ----(2)

Using elimination method, subtract eq 1 from eq 2 to get;

0 = -2 - 4

0 = -6

0 cannot be equal to -6 and as such there is no value of x that makes the simultaneous equations true. Thus, the type of solution to the given simultaneous equations is no solution

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Answer:

8 tacos

Step-by-step explanation:

40 tacos    to     15 students

8 tacos       to      3 students

15/3 =5, so divide 40 by 5 to get 8

The equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is; L = 2t + 10

The general formula for equation of a line in Slope Intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given question, the table of values is;

Number of weeks         Amount of money owed

      0                                   10

      1                                     8

      2                                    6

      3                                    4

Now, since Sophie agreed to pay back her friend $2 per week and originally borrowed $10, it means that;

Slope = 2

y-intercept = 10

Thus, the equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is;

L = 2t + 10

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Answer:

Step-by-step explanation:

Let the speed of the private jet is p and commercial jet is c.

Find c:

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

Work Shown:

[tex]f(\text{x}) = -2\text{x}^2+4\\\\f(4) = -2(4)^2+4\\\\f(4) = -2(16)+4\\\\f(4) = -32+4\\\\f(4) = -28\\\\[/tex]

Explanation:

Replace every x with 4. Then use the order of operations PEMDAS to simplify to a single number.

Answer:

8

Step-by-step explanation:

Given: x=2

Then,

5x-2 = 5(2)-2

= 10-2

=8

Answer:The answer is -0.6

Step-by-step explanation: -15.4-10.4 is -25.8

                                             -25.8+25.2 is -0.6

                           So therefore the answer is -0.6

If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;

F'(-2/4, 8/4) = (-1/2, 2)

G'(4/4, 8/4) = (1, 2)

I'(-6/4, -4/4) = (-1.5, -1) and;

H(8/4, -4/4) = (2, -1)

A scale factor is is a number used to enlarge a shape and each side is multiplied by the same number.

The given trapezoid has the coordinate points F(-2, 8), G(4, 8), I(-6, -4) and H(8, -4).

If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;

F'(-2/4, 8/4) = (-1/2, 2)

G'(4/4, 8/4) = (1, 2)

I'(-6/4, -4/4) = (-1.5, -1) and;

H(8/4, -4/4) = (2, -1)

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Answer:

Below

Step-by-step explanation:

Flower bed A

C = 2πr

C = 2π(5)

C = 2(5)π

C= 10π

A= πr²

A= π(5)²

A= π25

A= 25π

____________________________________________________

Flower bed B

C = 2πr

C = 2π(6)

C = 2(6)π

C = 12π

A = πr²

A = π(6)²

A = π36

A = 36π

Answer:

3

Step-by-step explanation:

2.25×10=22.5

If there is 0 in front of the number:eg(02.25) 0 does not count but it counts if it comes after nonzero digits.

5n² can be expressed as, 5n² =  3² x 5⁵ x x⁶

Given that n can be written as the product of the primes as

n = 3 x 5² x x³

This expression for n is called the prime factorization of n.

We need to express 5n² as such a product of primes.

For that taking square of n, add the power 2 with the existing powers of 3,5 and x,

So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶

So 5n² = 5(3² x 5⁴ x x⁶)

Multiplying 5 with the existing power of 5, 5⁴,

⇒ 5n² = 3² x 5⁵ x x⁶

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Answer:

a) true

b) false

c) false

Step-by-step explanation:

Here are these 4 sets in order of including more numbers to including fewer numbers.

R = all real numbers

Z = all integers

W = all whole numbers

N = all natural numbers

a) true

b) false

c) false

Answer:

i think there both obtuse

Answer:

-4[tex]\leq[/tex]a<7

Step-by-step explanation:

-20[tex]\leq[/tex]5a -10<25  add 10

+10       +10  +10

-20 [tex]\leq[/tex]5a<35  Divide all the way through by 5

-4[tex]\leq[/tex]a<7

Answer:

Step-by-step explanation:

See attachment

The position of the bicyclist at t=8 minutes is 3.2 km

Speed is the rate of change of position of an object in any direction.

position the way in which something or someone is placed or arranged.

when time t = 6 position d = 5

when time t = 5 position d = 2

when time t = 8 position d = x

therefore we can say

8 / x = 5 / 2

x = 8 * 2 /5

  = 3.2 km.

Hence the position of the bicyclist at t=8 minutes is 3.2 km.

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complete question:

The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.

Answer:

12

Step-by-step explanation:

[tex] \frac{3}{8} = \frac{?}{32} [/tex]

8*4=32

3*4=12