Question 6
A square is placed within a rectangle. Find the area of the shaded region.
Select one:
O
✪
✪
O
559 ft²
640 ft²
721 ft²
604 ft²
32 ft
19A
9 ft
20 ft

Answer:

53,352 cm

Step-by-step explanation:

1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.

2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.

3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.

If I made a mistake or if have any questions feel free to tell me!

-Mathematics and Science Major for Middle School Students at Harvard University

Answer:

Im pretty sure its the third one

Step-by-step explanation:

It all depends on the square root to find the nearest tenth and rounding it all up.

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 area of the shaded region is  π(R + 3)² - 9π where R is teh radius of the outer circle

The circumference of the inner circle is 18.84 feet

So, we have

2πr = 18.84

Divide by 2π

r = 18.84/2π

Evaluate

r = 3.0

So, the area of the inner circle is

A = πr²

This gives

A = π * 3²

Evaluate

A = 9π

The shaded area is

Area of big - Area of inner circle

So, we have

Shaded area = π(R + 3)² - 9π where R is teh radius of the outer circle

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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:

poor photo quality.

Step-by-step explanation:

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.

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 total interest paid is $58.52.

We are given that;

P = 800

r = 0.015

n = 18

Now,

We can plug in the values given in question:

EMI = 800 x 0.015 x (1+0.015) ^ 18 / { (1+0.015) ^ 18-1}

EMI = 47.64

This means that your monthly payments are $47.64.

To find the total interest paid, we can multiply the EMI by the number of months and subtract the loan amount12:

Total interest paid = EMI x n - P

Total interest paid = 47.64 x 18 - 800

Total interest paid = 58.52

Therefore, by the given interest the answer will be $58.52.

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The height of 3 meter to the left of the center of arch is -2.7 meters which is found by the evaluation of the given equation when x = -3.

We can solve it through

The Height at x = -3 meters on the left of the center = [tex](1/10)(-3^2 - 36) [by Substituting x = -3]= (1/10)(9 - 36)= (1/10)(-27)= -2.7 meters[/tex]

At the end height of the arch at 3 meters to the left of the center when x = -3 is -2.7 meters. This negative value means the point is actually below the ground level at that position. So the height is -2.7 meters where - insists negative value.

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The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.

Given that:

sin(2x) – sin(x) = 0

Simplify the equation, then the value of 'x' is calculated as,

sin(2x) – sin(x) = 0

sin(2x) = sin(x)

2 sin x cos x = sin x

cos x = 1/2

cos x = cos (π/3, 5π/3)

x = π/3, 5π/3

The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.

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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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Check the picture below.

Answer:

D

Step-by-step explanation:

We know that the residual is the difference between the observed value and the predicted value for a given point. Let's assume that the predicted values for the three points in the data set are denoted by ŷ₁, ŷ₂, and ŷ₃, and the observed values are denoted by y₁, y₂, and y₃.

We can write the residuals as:

e₁ = y₁ - ŷ₁

e₂ = y₂ - ŷ₂

e₃ = y₃ - ŷ₃

We are given that two of the residuals are -7 and 4.
Let's assume that e₁ = -7 and e₂ = 4.

We can use these values to find the third residual e₃.Since the sum of residuals is always equal to zero, we have:

e₁ + e₂ + e₃ = 0

Substituting the values of e₁ and e₂, we get

:-7 + 4 + e₃ = 0

Simplifying, we get:

e₃ = 3

Therefore, the third residual is 3, which is option D.

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 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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Answer:

approximately 7.07 square feet

Step-by-step explanation:

To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius of the circle.

Given the radius of the circle is 1.5 ft, we can substitute this value into the formula:

A = π(1.5)^2

A = 7.07 square feet (rounded to the nearest hundredth)

Therefore, the area of the circle is approximately 7.07 square feet.

Answer:

A= 1.77 units squared.

Step-by-step explanation:

To find your answer, you would first need the formula. It would be A=πr2. In your image, 1.5cm is the diameter, twice the radius. How to find the radius is easy. To do that, you would divide by two.

1.5/2 <---- shown here (which would equal 0.75)

A=πr2

A=π(0.75)2

A=π(0.5625)

A= 1.76625

However, to round your answer, you would get 1.77

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 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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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

The requreid, the joint probability function f(x, y) is:

f(0,0) = 3/14

f(0,1) = 9/28

f(0,2) = 3/28

f(1,0) = 9/28

f(1,1) = 9/28

f(2,0) = 3/14

f(2,1) = 3/14

f(3,0) = 1/14

To evaluate the joint probability function f(x, y), we need to determine the probability of selecting x black balls and y blue balls out of a sample of 4 balls. We can do this using the hypergeometric probability distribution formula:

f(x,y) = P(X = x, Y = y) = (C(3, x) * C(2, y) * C(3, 4-x-y)) / C(8, 4)

where C(n, k) represents the number of combinations of k items chosen from a set of n items.

Plugging in the values, we get:

f(0,0) = (C(3,0) * C(2,0) * C(3,4-0-0)) / C(8,4) = 3/14

f(0,1) = (C(3,0) * C(2,1) * C(3,4-0-1)) / C(8,4) = 9/28

f(0,2) = (C(3,0) * C(2,2) * C(3,4-0-2)) / C(8,4) = 3/28

f(1,0) = (C(3,1) * C(2,0) * C(3,4-1-0)) / C(8,4) = 9/28

f(1,1) = (C(3,1) * C(2,1) * C(3,4-1-1)) / C(8,4) = 9/28

f(2,0) = (C(3,2) * C(2,0) * C(3,4-2-0)) / C(8,4) = 3/14

f(2,1) = (C(3,2) * C(2,1) * C(3,4-2-1)) / C(8,4) = 3/14

f(3,0) = (C(3,3) * C(2,0) * C(3,4-3-0)) / C(8,4) = 1/14

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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 function that is most likely increase exponentially is f(x). Because it eventually exceeds g(x)

To determine which function is most likely increasing exponentially, we need to compare the rate at which the two functions are increasing.

Looking at the table, we can see that as x increases, f(x) increases at a faster rate than g(x). In fact, f(x) eventually exceeds g(x) for x values greater than or equal to 5. This suggests that f(x) is increasing at an exponential rate.

On the other hand, g(x) is increasing at a much slower rate than f(x). Although g(x) is also increasing, it does not appear to be increasing exponentially. In fact, g(x) will never exceed f(x), because f(x) grows at a faster rate.

Therefore, the function that is most likely increase exponentially is f(x).

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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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The statement "70 decreased by twice chai’s height" as an expression is 70 - 2c

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

70 decreased by twice chai’s height

Represent chai’s height with c

So, we have the following representation

70 decreased by 2c

When the above statement is then represented as an expression, we have the following

Expression: 70 - 2c

Hence, the expression of the statement "70 decreased by twice chai’s height"  is 70 - 2c

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Answer:

-x³ + 4x²

Step-by-step explanation:

-x^2(x-4)

Distribute

-x³ + 4x²

So, the answer is -x³ + 4x²

Answer:

20%  (D)

Step-by-step explanation: