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Answer: 12√3 square inches

Step-by-step explanation:

By the property of equilateral triangle,

Apothem = √3/2 × Side

⇒ Side = 2/√3 × Apothem

Here, apothem = 6 inches

Thus, the side of the given equilateral triangle =  [tex]\frac{2}{\sqrt{3}}\times 6[/tex]

= [tex] \frac{12}{\sqrt{3}}[/tex]

= [tex]4\sqrt{3}[/tex]  unit

Since, For an equilateral triangle,

[tex]\text{ Area} = \frac{\sqrt{3}}{4}\times (\text{ side})^2[/tex]

⇒ The area of the given equilateral triangle = [tex] \frac{\sqrt{3}}{4}\times (4\sqrt{3})^2[/tex]

[tex]=\frac{\sqrt{3}}{4}\times 48[/tex]

[tex]=12\sqrt{3}[/tex]  square inches

Answer:

Standard error = 5.4

Step-by-step explanation:

We are given that Population Mean, [tex]\mu[/tex] = 150 and Population Standard deviation, [tex]\sigma[/tex] = 27  and sample size, n = 25

Standard error formula for the sampling distribution of this sample mean is given by;

 Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{27}{\sqrt{25} }[/tex] = 5.4

By dividing Domingo's annual salary of $29,640 by the total number of hours worked in a year (2080 hours), we find that his hourly rate is $14.25.

To determine how much Domingo was paid per hour, we need to follow these steps:

Therefore, Domingo was paid $14.25 per hour.

The measure for the angle of the slices that are left is 160°.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Mario cut a circular pizza into 9 equal slices.

Angle of a circle = 360°

If Mario cut into 9 pieces.

360° / 9 = 40°

That means, the angle measure of each slice is 40°.

And he put a slice of pizza on each of 5 plates.

That means, he left 9 - 5 = 4 slice on the plate.

So, the angle measure;

4 x 40° = 160°

Therefore, the angle measure of the 4 slices are 160°

To learn more about the multiplication;

https://brainly.com/question/19634536

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Answer:

f(n) = –6.5n + 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5

Step-by-step explanation:

The nth term of an arithmetic sequence is given as

Tn = a + (n-1)d

where a is the first term and d is the common difference between two consecutive terms

From the given sequence,

a = 8, d = 1.5 - 8

d = -6.5

As such, Tn = f(n) = 8 + (n-1)-6.5

= 8 - 6.5n + 6.5

= 14.5 - 6.5n

f(1) = 8

f(n + 1) - f(n) = – 6.5

f(n + 1) = f(n) – 6.5

The weight of the aquarium when it's full of water is 294.66 pounds.

To get the weight of the aquarium we first calculate the volume of the aquarium.

[tex]Volume=(length\times width\times height)[/tex]

[tex]V=30\times 14\times18[/tex]

[tex]V=7560 \ in^3[/tex]

But weight of water is such that for every cubic inches, the weight is [tex]0.036\ lb[/tex]

thus the weight of water will be:

[tex]0.036×7560=272.16 lb[/tex]

Thus the total weight of the aquarium is:

[tex]272.16+22.5[/tex]

[tex]=294.66 \l b[/tex]

The weight of the aquarium when it's full of water is 294.66 pounds.

The height of the monument is approximately 253.2 feet.

To find the height of the monument, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the height and distance from the observation point.

Step-by-Step Solution:

Identify the given values:

Use the tangent function:

tan(θ) = opposite / adjacent

Where θ is the angle of elevation, the opposite side represents the height of the monument (h), and the adjacent side represents the distance from the point (405 feet).

Set up the equation and solve for h:

tan(32°) = h / 405 feet

Using a calculator, find tan(32°):

tan(32°) ≈ 0.6249

So the equation is:

0.6249 = h / 405

Multiply both sides by 405 to solve for h:

h ≈ 0.6249 * 405

h ≈ 253.2 feet

Thus, the height of the monument is approximately 253.2 feet.

Answer:

3 seconds is the time when the object hits the ground.

Step-by-step explanation:

Given the height of a free falling object at time t can be found using the function is given by:

[tex]h(t)=-12t^2+36t[/tex]         ....[1]

where,

h(t) is the height in feet

t is the in seconds.

We have to find the time when the object hits the ground.

⇒h(t) = 0

Substitute this in [1] we have;

[tex]-12t^2+36t =0[/tex]

⇒[tex]12t^2-36t = 0[/tex]

⇒[tex]12t(t-3) = 0[/tex]

⇒t = 0 and t = 3

Since, time cannot be 0.

⇒t = 3 seconds

Therefore, the time when the object hits the ground is, 3 seconds

Answer:

  144 ft²

Step-by-step explanation:

There are a number of ways you can solve this problem. One is to figure the leg lengths, and use those to compute the area of the triangle in the usual way.

  AC = (24 ft)·sin(45°) = 12√2 ft

  BC = (24 ft)·cos(45°) = 12√2 ft

Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²

___

Another is to recognize that the altitude from the hypotenuse of this isosceles right triangle is half the length of the hypotenuse, or 12 ft. Then the triangle area formula gives the area as ...

Area = (1/2)·AB·(AB/2) = (1/2)·(24 ft)·(12 ft) = 144 ft²

___

Along the same lines, the triangle is half a square whose diagonals are both 24 ft. The area of the square is half the product of those diagonals:

  square area = (1/2)·(24 ft)² = 288 ft²

The triangle area is half of that, or

Area = (1/2)(288 ft²) = 144 ft²

Answer:

 144 ft²

Step-by-step explanation:

AC = (24 ft)·sin(45°) = 12√2 ft

BC = (24 ft)·cos(45°) = 12√2 ft

Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²

Answer: [tex]195.74\ ft^2[/tex]

Step-by-step explanation:

From the given picture, the length of the garden = 16 ft

The width of the garden = 14 ft

Now, the area of the whole garden is given by :-

[tex]\text{Area of whole garden}=length\times width\\\\\Rightarrow\text{Area of  whole garden}=16\times14=224\ ft^2[/tex]

Also, the radius of the circular pond (r)= 3 ft

The area of the circular pond is given by :-

[tex]\text{Area of pond}=\pi r^2\\\\\Rightarrow\text{Area of pond}=(3.14)(3)^2\\\\\Rightarrow\text{Area of pond}=28.26\ ft^2[/tex]

Now, the area of the Japanese garden around the koi pond

= Area of the whole garden - Area of the Koi pond

=[tex]224-28.26=195.74\ ft^2[/tex]

Hence, the area of the Japanese garden around the koi pond is [tex]195.74\ ft^2[/tex]

Answer:

x=-4,1,2+5i,2-5i

Step-by-step explanation:

Given is an algebraic expression g(x) as product of two functions.

Hence solutions will be the combined solutions of two quadratic products

[tex]g(x) = (x^2 + 3x - 4)(x^2 - 4x + 29)\\[/tex]

I expression can be factorised as

[tex](x+4)(x-1)[/tex]

Hence one set of solutions are

x=-4,1

Next quadratic we cannot factorize

and hence use formulae

[tex]x=\frac{4+/-\sqrt{16-116} }{2} =2+5i, 2-5i[/tex]

Answer:

The answer above is correct:

B. 1

C. 4

E. 2+5i

F. 2-5i

Step-by-step explanation:

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