What is the volume of a sphere with a radius of 31.6 cm, rounded to the nearest tenth of a cubic centimeter?

The transformation that maps the pre-image (red) onto the image (blue) is reflection

Given that

the pre-image (red) and the image (blue)

From the figure, we can see that

Both triangles are mirrors of one another

As a general rule

When two shapes with the same orientation and properties mirror one another, then the transformation between the shapes is the reflection transformation

This means that the transformation of the two triangles is a reflection transformation

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An experience that I had outside the academia was when I worked as a marketing coordinator for a small start-up company.

A product launch event had been planned by the team for several weeks, and everything appeared to be going according to plan. However, we learned the day before the event that our keynote speaker, who was an important component of it, had unexpectedly become unwell and would not be able to attend.

I had to evaluate the situation as the marketing coordinator and decide right away. Either we could cancel the event or we could locate a another speaker.

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Check the picture below.

The solution of the equation is x=0.08813 or 3.90664.

We have,

2x² / 3  + 9[tex]x^{1/3[/tex] = -4

Now, solving the equation for x

2x² + 27[tex]x^{1/3[/tex] = -12

Now, taking cube on both side we get

(2x² + 27[tex]x^{1/3[/tex] )³= -12³

Now, simplifying we get

19683x = -1728 -864x² -144[tex]x^4[/tex]-8[tex]x^6[/tex]

So, x=0.08813 or 3.90664

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The graph of the inequality is added as an attachment

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

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

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The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

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All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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The amount to be invested now is  $173.9.

The amount to be invested now can be calculated using the formula for future value of an annuity as shown below;

FV = A x ((1 + r)ⁿ⁻¹) / r

where:

Monthly rate becomes;

r = 6% / 12 = 0.5% = 0.005

The amount is calculated as;

80,000 = A x ((1 + 0.005)¹⁶⁸ ⁻ ¹) / 0.005

80,000 =460A

A = 80,000/460

A = $173.9

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The 25th percentile for the math scores is 71.65.

In Mathematics and Geometry, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Note: 25th percentile for the math scores is the same as the first quartile for the math scores.

Based on the z-score table A, 25th percentile (0.25) is equal to a z-score of -0.67;

0.2514 = -0.67

By substituting the parameters, we have:

Z-score, z = (x - μ)/σ

-0.67 = (x - 75)/5

x = 75 - 3.35

x = 71.65

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Answer:

Step-by-step explanation:

hello :

6x  the greatest common factor from the polynomial.

 12x² + 30x

Answer:

20%  (D)

Step-by-step explanation:

Answer:

-x³ + 4x²

Step-by-step explanation:

-x^2(x-4)

Distribute

-x³ + 4x²

So, the answer is -x³ + 4x²

The parabola for the expression are given in attachment.

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix

y=2x(x-7)

Let us take few values of x and y and draw the parabola

Similarly we draw the graph for (x+4)(x-4)

Hence, the parabola for the expression are given in attachment.

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Answer:

0

Step-by-step explanation:

a. The definite integral ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx = πr²/2

A definite integral is an integral evaluated on an interval.

Given the figure, to evaluate the definite integral ∫₀²f(x)dx and ∫₂⁴f(x)dx, we proceed as follows.

a.  The definite integral ∫₀²f(x)dx

Observe the graph, the integral ∫₀²f(x)dx is the area occupied by the square on the interval (0, 2).

So,  ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx

Observe the graph, the integral ∫₂⁴f(x)dx is the area occupied by the circle on the interval (2, 4).

So,  ∫₂⁴f(x)dx = πr²/2

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Answer:

  C. 10

Step-by-step explanation:

You want to know the bin size in a histogram with bin boundaries 10.5, 20.5, 30.5, ....

The size of the bin is the difference between its boundary values. Here, all of the bins are the same size:

  20.5 -10.5 = 10

The bin size is 10.

__

Additional comment

The bin boundaries are typically chosen so that no data value can fall on the boundary, but must be unambiguously allocated to one bin or another. When the data values are integers, it is not uncommon to have the bin boundary be halfway between two integers.

Here, the boundary being 20.5 means a score of 20 will be counted in the bin to the left, and 21 will be counted in the bin to the right.

The boundary value shown at the right edge of the graph is not 100.5, as we might expect. However, we can reasonably assume that a test score of 100 would be counted in the bin with upper boundary 100, without any ambiguity.

Answer: 10

Step-by-step explanation:

The size of each value marker

Check the picture below.

Step-by-step explanation:

use the formula V=1/3hπr².

V=1/3×3 π 2×2

V=1/3×12π

V=4πcm3

The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;

Parallel lines or line segments are line segments that have the same slope.

1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5

The slope of the segment [tex]\overline{CD}[/tex] is;  (3 - 0)/(10 - (-5)) = 3/15 = 1/5

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

[tex]\overline{AB}[/tex] ⊥  [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is perpendicular to  [tex]\overline{CD}[/tex]

2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3

The slope of the segment [tex]\overline{CD}[/tex] is;  (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]

3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2

The slope of the segment [tex]\overline{CD}[/tex] is;  (-7 - 11))/(5 - (-1)) = -18/6 = -3

The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1

The slope of the segment [tex]\overline{CD}[/tex] is;  (2 - 6)/(-8 - (-4)) = -4/(-4) = 1

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]

5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4

The slope of the segment [tex]\overline{CD}[/tex] is;  (6 - (-3))/(12 - 0) = 9/12 = 3/4

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║  [tex]\overline{CD}[/tex]

6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2

The slope of the segment [tex]\overline{CD}[/tex] is;  (7 - (-5))/(-4 - 2)) = 12/(-6) = -2

The slope of  [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and  [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.

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In the initial value problem the value of f(π/5) ≅ -5.26

Given the initial value problem f"(x) = -25sin(5x) and f'(0) = 3 and f(0) = -2, we desire to find f(π/5). We proceed as follows

f"(x) = -25sin(5x)

Integrating both sides of the equation, we have that

∫f"(x) = ∫-25sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25(-cos(5x))/5 + C

f'(x) = 5cos(5x) + C

Given that f'(0) = 3, substituting the values of the variables into the equation, we have that

f'(x) = 5cos(5x) + C

f'(0) = 5cos(5(0)) + C

3 = 5cos(0) + C

3 = 5(1) + C

3 = 5 + C

C = 3 - 5

C = -2

So, we have that f'(x) = 5cos(5x) - 2

To find f(x), we integrate f'(x). So, we have that

f'(x) = 5cos(5x) - 2

∫f'(x) = ∫(5cos(5x) - 2)dx

f(x) = ∫5cos(5x)dx - ∫2dx

= 5sin(5x)/5 - 2x + C'

f(x) = sin(5x) - 2x + C'

Since f(0) = -2, we have that

f(0) = sin(5(0)) - 2(0) + C'

-2 = sin0 - 0 + C'

- 2 = 0 - 0 + C'

- 2 = 0 + C'

C' = -2

So, substituting C' into the equation, we have that

f(x) = sin(5x) - 2x + C'

f(x) = sin(5x) - 2x - 2

So, to find f(π/5), substituting this into the equation, we have that

f(π/5) = sin(5π/5) - 2(π/5) - 2

f(π/5) = sin(π) - 2π/5 - 2

f(π/5) = 0 - 2π/5 - 2

f(π/5) = - 2π/5 - 2

f(π/5) = (- 2π - 10)/10

f(π/5) = - 2(π + 10)/10

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(3.142 + 10)/5

f(π/5) = - 2(13.142)/5

f(π/5) = - 26.284/5

f(π/5) = -5.2568

f(π/5) ≅ -5.26

So, f(π/5) ≅ -5.26

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The account's total value is $498,174.72.

The total interest paid is $174,174.72.

We can utilize the calculation for the future value of a compound interest annuity to resolve this issue:

FV = P*(((1 + r/n)(n*t))-1) / (r/n).

where

When we enter the values, we obtain:

FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72

After the 60th deposit, the account's total value is $498,174.72.

We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:

Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72

Therefore, the total interest paid is $174,174.72.

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The value of the expressions are;

a. 4n - 8

b. 64

c. 18

d. 5(n + 3)

Algebraic expressions are described as expressions that consists of terms, constants, coefficients, factors and variables.

They are also identified to consist of mathematical operations which includes;

Using the distributive property, we have;

a. 4(n - 2)

expand the bracket, we get;

4n - 8

b. . 8(2+6)

8(8)

expand the bracket

64

c. 6•8-6•5

48 - 30

Subtract

18

d. 5n+15

factorize the expression

5(n + 3)

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The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

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Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.

The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.

This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is

3.14×30= 94.2 meters

The circumference of the Kiddie Land ferris wheel is

3.14 ×10= 31.4 meters

Here, 94.2-31.4 =62.8 meters

Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

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The rectangular coordinate from the given polar coordinate is (2.73, -0.73)

To find the rectangular coordinate from the polar coordinates, we can rewrite this as;

x = r cosθ

y = r sinθ

x = r cosθ

Let's substitute the values into it;

x = (2√2)* cos(-π/12)

x =(2√2)cos(-15)

x = √3 + 1

x = 2.73

y = r sin θ

y = (2√2)sin(-π/12)

y = (2√2) * sin (-15)

y = -√3 + 1

y = -0.73

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The lower quartile, the median, and the upper quartile are 22, 31 and 90

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

11, 18, 22, 22, 31, 31, 63, 86, 90, 92, 98

Split the data values into 2

So, we have

11, 18, 22, 22, 31,

31,

63, 86, 90, 92, 98

The middle of each set is the quartiles

So, we have

Lower = 22

Median = 31

Upper = 90

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Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

Circumcenter : The point of intersection of the three perpendicular bisectors.

Incenter : The point of intersection of the three angle bisectors.

Centroid : The point of intersection of the three medians.

Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.

In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

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Answer :

Step-by-step explanation :

It's given that :

The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters.

Formula of volume of cylinder = πr²h

where,

By substituting the values of values of height and volume in the above formula we'll get the required value of the radius.

[tex]:\implies [/tex] 180π = πr² 11.25

[tex]:\implies [/tex] 180π = r² × 11.25 π

[tex]:\implies [/tex] 180π/11.25 π = r²

[tex]:\implies [/tex] 16 = r²

[tex]:\implies [/tex] r² = √16

[tex]:\implies [/tex] r = 4

Hence, Radius of the cylinder is 4 meters.