Simplify the following and write your answer in simplest form

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Volume formula for cone: V=1/3(π)(b)(h)

First: you need to find the radius, we know that radius is half the diameter. The diameter is 12, so the radius is 6.

Second: Now we substitute b for 6 and h for 12, since the height is 12. We will substitute π for 3.14.

Third: V=1/3(3.14)(6)(12). When you simplify: 1/3x3.14x6x12=452.16

Final answer=452.16in³

I hope this helps! :)

A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of [tex]9[/tex] centimeters. If the surface area of the pyramid is [tex]140.4[/tex]square centimeters, the slant height of the pyramid  is [tex]Slant height= 2*(140.4-81\sqrt{3} )/27[/tex]

To find the slant height of the pyramid, we first need to determine the lateral area of one of the triangular faces of the pyramid.

Since all sides of the equilateral triangle have a length of [tex]9[/tex] centimeters, we can use the formula for the area of an equilateral triangle, which is:

[tex]A=\sqrt{3} /4*side length^{2}[/tex]

Substituting the given side length [tex]9[/tex] centimeters into the formula:

[tex]A=\sqrt{3} /4*9^{2} \\A=\sqrt{3} /4*81\\ A=81\sqrt{3}/4[/tex]

Now, since there are four equilateral triangular faces on the pyramid, the total lateral area of the pyramid is [tex]4*81\sqrt{3}/4=81\sqrt{3}[/tex] square centimeters.

Given that the total surface area of the pyramid is [tex]140.4[/tex] square centimeters, we subtract the area of the base (which is also an equilateral triangle) from the total surface area to find the lateral surface area:

[tex]Lateral surface area=Total surface area-Area of base\\Lateral surface area=140.4-81\sqrt{3}[/tex]

Now, the lateral surface area of a pyramid can be calculated using the formula:

[tex]Lateral surface area=12*perimeter of base*slant[/tex]

For an equilateral triangle, the perimeter is [tex]3*side length=3*9= 27[/tex]centimeters.

So, we have:

[tex]140.4-81\sqrt{3} =1/2*27*slant height\\140.4-81\sqrt{3} =27/2*slant height\\Slant height=2*(140.4-81\sqrt{3} )/27[/tex]

Calculating this expression gives us the value of the slant height of the pyramid.

COMPLETE QUESTION:

A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of [tex]9[/tex] centimeters. If the surface area of the pyramid is [tex]140.4[/tex]square centimeters, what is the slant height of the pyramid?

Final answer:

Fossil evidence, morphological, and genetic similarities are key factors in determining common ancestry of species, with fossil evidence being particularly definitive for extinct life forms.

Explanation:

To determine common ancestry of two different species of plants, scientists would most likely consider fossil evidence as a primary source. Fossils provide concrete evidence about extinct life forms and can give more accurate dates of divergence. Morphological (form and function) and genetic evidence are other crucial factors in establishing evolutionary connections among organisms. Similar physical features and genomes usually indicate a closer relationship, with homologous structures stemming from common evolutionary paths. Therefore, similar ecological niches or habitats may suggest a relationship, but they are not as definitive as morphological and genetic similarities and fossil evidence in determining a shared ancestry.

Answer:

11

Step-by-step explanation:

Answer:

Four quarters a pound is four multiply that by 100 you get 400

Step-by-step explanation:

The area of the circle with a circumference of 3/2 π cm is 9/16 π cm².

The question is asking about finding the area of a circle when the circumference is given. The formula to find the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle. Given that the circumference is 3/2 π cm, we can use this information to find the radius.

From the circumference equation, r = C/2π = (3/2π)/ 2π = 3/4 cm. Having the radius, we can then use the formula for the area of a circle, which is A = πr². As a result, the area of the given circle is π(3/4)² cm² which simplifies to 9/16 π cm².

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No, a quadrilateral with perpendicular diagonals is not always a rhombus. While a rhombus has perpendicular diagonals, other quadrilaterals like a square share this property.

While a rhombus does have perpendicular diagonals, other quadrilaterals, such as a square, also possess this property.

Therefore, if the diagonals of a quadrilateral are perpendicular, it does not exclusively imply that the quadrilateral is a rhombus.

Additional conditions, such as equal side lengths, are necessary to establish the quadrilateral as a rhombus.

Thus, perpendicular diagonals are a characteristic of both rhombuses and squares, but not solely indicative of a rhombus.

Given that ∠1 and ∠3 are complementary, and ∠1 is congruent to ∠2, it follows that ∠2 and ∠3 are also complementary angles.

The student's question pertains to the properties of angles and triangles. When it is stated that

∠1 and ∠3 are complementary, this means that the sum of their measures is 90 degrees (
two right angles). And if

∠1
≅
∠2, then these two angles are congruent, having the same measure. Given these conditions, the following statement will always be true:

∠2 and ∠3 are also complementary angles. This is because the measure of

∠2 will be equal to the measure of

∠1 (since they are congruent), and thus their combined measure with

∠3 will also add up to 90 degrees, making them complementary as well.

Answer:

13,000 People

Step-by-step explanation:

65,000 (0.1) = 6500

6500 (2) = 13,000

You multiply by 2 to get 10% above or below the announced attendance.

Answer:

6,500

Step-by-step explanation:

If you think you can guess the attendance within 10% of the actual value, then your guess would have to be within 6,500 of the actual attendance of 65,000 in order for you to support your claim. This is because 10% of 65,000 is 6,500. So if your guess is within 6,500 of the actual attendance, then you can support your claim.

Answer:

$925.00

Step-by-step explanation:

Answer:

The smallest possible number this could have been = 455500

Step-by-step explanation:

456000 has been rounded to the nearest thousand.

If the value is more than 456500 the value rounded to the nearest thousand is 457000.

If the value is less than 455500 the value rounded to the nearest thousand is 455000.

In between 455500 and 456500 the value rounded to the nearest thousand is 456000.

So,  The smallest possible number this could have been = 455500

Answer: The area of the circular wooden table = 50.24 ft²

Step-by-step explanation:

Given: The radius of the circular table = 4 feet

We know that area of a circle is given by :-

[tex]\text{Area}=\pi r^2[/tex]

Therefore, the area of circular wooden table is given by :-

[tex]\text{Area}=3.14(4)^2\\\Rightarrow\ 3.14\times16\\\Rightarrow\text{Area=}50.24\ ft^2[/tex]

The area of the circular wooden table = 50.24 ft²

Answer: 50.24

Step-by-step explanation:

We know: The radius = 4 feet and that the area of a circle = πr^2

Next: (π) 3.14 (4)^2

which we can simplify to be 3.14 * 16

= 50.24

(just took the test hope this helped)