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adoni [48]
2 years ago
8

Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate​ planes, usi

ng triple integrals.
Mathematics
1 answer:
dem82 [27]2 years ago
3 0

First,

9x+15y+15z=45\implies 3x+5y+5z=15

The volume is given by the integral (one of 6 possible combinations),

\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}

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Voting age
Levart [38]

Answer:

\frac{17}{64}\approx 0.27

Step-by-step explanation:

We have been given a table to voters and their ages. We are asked to find the probability that a voter is younger than 45.

Voting age         Voters

17-29                       9

30-44                      8

45-64                    32

65+                        15

We can see from our given table that age of 17 (9+8) voters is between 17 to 44 years.

To find the probability that a voter is younger than 45, we will divide 17 by total number of voters.

\text{Total voters}=9+8+32+15=64

\text{Probability that a voter is younger than 45}=\frac{17}{64}

\text{Probability that a voter is younger than 45}=0.265625

\text{Probability that a voter is younger than 45}\approx 0.27

Therefore, the probability that a voter is younger than 45 is 0.27.

4 0
2 years ago
What is -45+30-(-60)=?
Rasek [7]

Answer:

45

Step-by-step explanation:

-45 + 30 gives you -15. When subtractinf a negative number, it actually turning into addition/positive. This changes it into -15 + 60, which is 45.

8 0
2 years ago
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Jessie bought f bags of potting soil for $2.00 each. Write an expression to show how much Jessie paid.
pav-90 [236]
I believe it is x = 2f

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8 0
3 years ago
Solve for x. 3/x-1 - 1/x^-1=5/x-1<br><br> Please show all work
navik [9.2K]

3/(x-1) - 1/(x^2-1) = 5/(x-1)

Subtract 3/(x-1) from both sides

-1/(x^2-1) = 2/(x-1)

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-1/[(x-1)(x+1] = 2/(x-1)

Multiply by (x-1)(x+1) on both sides

-1 = 2 (x+1)

-1 = 2x + 2

Subtract 2 from both sides

-3 = 2x

Divide by 2 on both sides

-3/2 = x

5 0
2 years ago
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What is the common ratio of the sequence?<br><br> -2, 6, -18, 54,...
navik [9.2K]
The common ratio is the multiplicity of -3

hope this helps
8 0
2 years ago
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