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nekit [7.7K]
2 years ago
12

It takes 6 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder wi

th the same base and height as the cone? 
A.18
B.24
C.2
D.12
Mathematics
1 answer:
frosja888 [35]2 years ago
5 0
The volume of a cone is equal to
Volume = pi * r^2 * h / 3

The volume of a cylinder is equal to
Volume = pi * r^2 * h

The cone is filled with 6 cubic inches colored sand.
As you observed, the volume of the cone is 1 / 3 of the volume of the cylinder.

Cone = Cylinder / 3
6 = Cylinder / 3
Cylinder = 18

So the answer is A. 18.
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3 years ago
During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi
Afina-wow [57]

The second question:

Consider the division expression 7\frac{1}{2} / 2. Select all multiplication equations that correspond to this division expression.

2 * ? = 7\frac{1}{2}     7\frac{1}{2} * ?= 2     ? * 2  = 7\frac{1}{2}

2* 7\frac{1}{2} = ?    ?  * 7\frac{1}{2} = 2

Answer:

1. See Explanation

2. 2 * ? = 7\frac{1}{2}     and     ? * 2  = 7\frac{1}{2}

Step-by-step explanation:

Solving (a):

Given

Students = 60

Group = Equal\ Sized

Required

Interpret \frac{60}{5} in 2 ways

<u>Interpretation 1:</u> Number of groups if there are 5 students in each

<u>Interpretation 2:</u> Number of students in each group if there are 5 groups

<u>Solving the quotient</u>

Quotient = \frac{60}{5}

Quotient = 12

<u>For Interpretation 1:</u>

The quotient means: 12 groups

<u>For Interpretation 2:</u>

The quotient means: 12 students

Solving (b):

Given

7\frac{1}{2} / 2

Required

Select all equivalent multiplication equations

Let ? be the quotient of t 7\frac{1}{2} / 2

So, we have:

7\frac{1}{2}/2 = ?

Multiply through by 2

2 * 7\frac{1}{2}/2 = ? * 2

7\frac{1}{2} = ? * 2

Rewrite as:

? * 2 = 7\frac{1}{2}  --- This is 1 equivalent expression

Apply commutative law of addition:

2 * ? = 7\frac{1}{2}  --- This is another equivalent expression

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There was a 12.35% increase in the price.
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Customer: "I see that the amount I owe has been reduced from $90.00 to $75.00." Employee: "Yes, the discount has saved you _____
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Answer:

15 dollers or 22.5%

Step-by-step explanation:

thank you i hope this helps

3 0
2 years ago
Read 2 more answers
What is 4log1/2^w(2log1/2^u-3log1/2^v written as a single logarithm?
IrinaK [193]
Given:

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

 log 1/2 (w^4)  + 2 log 1/2 (u) - 3 log 1/2 (v) 
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3) 

then use the quotient property of logarithms which is log of b (x)  - log of b (y) = log of b (x/y)

Therefore, 

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

log of 1/2 (u^2 w^4 / v^3)  
8 0
2 years ago
Read 2 more answers
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