MATHEMATICS MIDDLE SCHOOL

a manufacturer of cat toys produces three different toys filled with catnip the toys are the shape of a cone cylinder sphere each with radius 3 inches the cone and the cylinder each have a height of 2 inches which statement about the toys are true choose all that apply help ?

Answers

Answer 1

Answer:

Statements A, B, and C are true.

Step-by-step explanation:

Step 1:

A cone, a cylinder and a sphere all have radii of 3 inches. The cone and cylinder have heights of 2 inches.

The volume of the cone, $V=\pi r^(2) (h)/(3).$ Here r = 3 inches and h = 2 inches.

So the volume of the cone $=\pi r^(2) (h)/(3) = \pi (3^(2)) (2)/(3) = 18.85$ cubic inches.

The volume of the cylinder, $V=\pi r^(2) h.$ Here r = 3 inches and h = 2 inches.

So the volume of the cylinder = $=\pi r^(2) h= \pi (3^(2)) (2) = 56.55$ cubic inches.

The volume of the sphere, $V=(4)/(3) \pi r^(3).$ Here r = 3 inches.

So the volume of the sphere $=(4)/(3) \pi (3^(3))= 113.1$ cubic inches.

Step 2:

Now we check to see which statements are true.

A. About 113 cubic inches of catnip will fit inside a sphere-shaped toy so it is true.

B. About 18.8 cubic inches of catnip will fit inside a cone-shaped toy so it true.

C. The sphere-shaped toy holds the most of the three so it is true.

D. No shape holds 169.6 cubic inches, so D is false.

E. The toys shaped like a cone and a cylinder do not hold the same amount of catnip in them. So it is false.

P.S. I couldn't see the options B, D, and E completely.

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Answers

c only one and two is the answer

The sum of 5 consecutive integers is 505.What is the third number in this sequence ?

Answers

Answer: 101

Step-by-step explanation:

1st integer: x

2nd integer: x + 1

3rd integer: x + 2

4th integer: x + 3

5th integer: x + 4

x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 505

5x + 10 = 505

5x = 495

x = 99

3rd integer: x + 2 = (99) + 2 = 101

What is the solution to 4w=2/3

Answers

2/12 or 1/6. You have to divide 2/3 by 4 to get what w equals to.

4w = 2/3 Divide each side by 4 to get w by itself.

w = 2/3 ÷ 4 To divide fractions you multiply the reciprocal

w = 2/3 × 1/4 multiply across

w = 2/12 which reduces

w = 1/6

What is the value of x in this simplified expression? (-j)^-7=1/(-j)^x

Answers

$x=7\n\n\text{because}\n\na^(-n)=(1)/(a^n);\ a\neq0\n\n(-j)^(-7)=(1)/((-j)^7)$

$\text{Minus in a power means inverse.}$

$a^(-1)=(1)/(a)\n\n(-j)^(-7)=(-j)^(7\cdot(-1))=\left[(-j)^7\right]^(-1)=(1)/((-j)^7)\n\n\text{Used:}\n\n(a^n)^m=a^(n\cdot m)$

There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils?

Answers

Answer

Find out the how many packages will be needed for 28 children if each child gets 4 pencils .

To prove

As given

There are 8 pencils in a package .

Total number of childrens = 28

each child gets 4 pencils

Total number of pencils needed for 28 children = 28 × 4

= 112

Now find out the Number of packages for 28 children .

$Number\ of\ packages\ needed\ for\ 28\ children =(Total\ numer\ of\ pencils\ needed)/( pencils\ in\ a\ package)$

Total number of pencils needed = 112

pencils in a package = 8

put in the above

$Number\ of\ packages\ needed\ for\ 28\ children = (112)/(8)$

Number of packages needed for 28 childrens = 14

Therefore the 14packages will be needed for 28 children if each child gets 4 pencils .

The question is asking to state or calculate how many package will be needed for 28 children if each child gets 4 pencils, base on my calculation, I would say that the answer would be 14 pencils. I hope you are satisfied with my answer and feel free to ask for more if you have questions

A batch of chicken required 3 1/3 cups of flour if a fast food restaurant was making 4 3/7 batches, how much flour would they need ?