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zlopas [31]
3 years ago
11

G a spherical tank has a capacity of 300 gallons. using the fact that 1 gallon is about 0.1337 ft3, find the radius of the tank

(to the nearest hundredth of a foot).
Mathematics
1 answer:
Paladinen [302]3 years ago
5 0
Volume of a sphere is  V=(4/3)pi r^3
300(.1337)=(4/3)pi r^3
solve for r
r= 2.12 ft
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A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a
laila [671]

Complete Question

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?

Round your answer up to the nearest integer.

sample size = _____

Answer:

The sample size is n = 271    

Step-by-step explanation:

From the question we are told that  

   The margin of error is  E = 5% = 0.05

Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be  

     \^ p =  0.5

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.645

Generally the sample size is mathematically represented as  

    n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>   n = [\frac{1.645 }{0.05} ]^2 * 0.5 (1 - 0.5 )

=>   n = 271    

5 0
3 years ago
2x(3x+7) multiply the expressions.
kolbaska11 [484]

Answer:

6x^2 +14x

Step-by-step explanation:

Multiply using the distributive property.

8 0
3 years ago
1. Find a vector in R^3 which is not in the span of the set S-((1,2, -2), (2, -1, 1). Explain.
pav-90 [236]

Answer:

Step-by-step explanation:

A vector in R^3 which is not in the span of the set S {(1,2,-2) and (2,-1,1)

If a vector is in the span it can be represented as a linear combination of these two vectors

Let S1 = (1,2,-2) and S2 = (2,-1,1)

i.e. any vector which is of the form

\alpha S1+\beta S2\\=(\alpha +2\beta,2\alpha -\beta,-2\alpha +\beta)

Where alpha and beta are any real numbers

Any vector not in this form will not be in the span

i.e. say if alpha = beta =1,

then spanned vector = (3,1,-1)

If we change one coordinate alone say

(3,0,-1) this cannot be represented as a linear combination hence this would be the answer.

8 0
3 years ago
9. Given the following matrices, what is the correct product matrix AB?АBСD[12] [] 15.07opaDa
lesya692 [45]

The product of A and B is:

\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}-1 & 2 \\ 1 & 0\end{bmatrix}=\begin{bmatrix}1 & 2 \\ 1 & 6\end{bmatrix}

Therefore the answer is the third choice.

7 0
1 year ago
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