Simplify the expression: 2√75+ √20

A three-dimensional object has a depth of 8 inches and a triangular base that has an area of 12 square inches, so it has a volum

Lemur [1.5K]

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Area of triangular base = 12 sq. inches

Height of a three dimensional object = 8 inches

We need to find the Volume of that object.

As we know that "Volume = Area of base × Height "

So, it becomes,

$Volume=12\times 8\\\\Volume= 96\ cubic.\ inches$

So, the volume of object is 96 cubic inches.

Hence, Option 'D' is correct.

4 0

3 years ago

Read 2 more answers

Suppose a white dwarf star has a diameter of approximately 1.8083 to the power of 4 km. Use the formula 4n to the power of 2 to

aivan3 [116]

ANSWER:

The surface area of the star is 3.2700 x $10^{8}$ square kilometres.

EXPLANATIONS:

Diameter of the star = 1.8083 x $10^{4}$ Km.

Surface area of the star = 4 $n^{2}$

Where n is the radius of the star.

So that;

n = $\frac{ 1.8083 * 10^{4} }{2}$

= 0.90415 x $10^{4}$

n = 0.90415 x $10^{4}$ Km

Thus,

Surface area = 4 x $(0.90415*10^{4} )^{2}$

= 326994889

Surface area = 3.2700 x $10^{8}$ $km^{2}$

Therefore, the surface area of the star is 3.2700 x $10^{8}$ square kilometres.

4 0

3 years ago

Combine like radicals to get your answer. <br><br> image attached

spin [16.1K]

Answer:

So the final answer is

$-8\sqrt{3}$

Step-by-step explanation:

Radicals:

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher.

The given expression is

$-5\sqrt{3} -3\sqrt{3}$

Now take common radical out so we will get

$\sqrt{3}(-5-3)$

Now add the Parenthesis part.

$\sqrt{3}(-8)$

So the final answer is

$-8\sqrt{3}$

5 0

3 years ago

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

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

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>

5 0

2 years ago

What does 7/18 estimate to 0,1/2,1

DiKsa [7]

Answer: 11/2

Step-by-step explanation:

7 0

3 years ago