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e-lub [12.9K]
3 years ago
6

Solve the problem as directed.

Mathematics
1 answer:
Alex17521 [72]3 years ago
4 0

The algebraic equation for the given statement is v = cd^3

<h3><u>Solution:</u></h3>

Given that The volume (v) of a sphere varies directly as the cube of its diameter (d)

To find: statement in algebraic language using an equation with the variables c, v, and d

Let "v" be the volume of sphere

Let "d" be the diameter of sphere

From given information,

volume of sphere varies directly as the cube of its diameter

\text{ volume of sphere } \alpha \text{ cube of its diameter}

\text{ v} \alpha d^3

v = cd^3

Where "c" is the constant of proportionality

Then the algebraic equation for the given statement will be :-

v=cd^3 , where c is the proportionality constant.

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The national mean sales price for a new one-family home is $181,900. A sample of 40 one-family homes in the south showed a sampl
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Answer:

a

The  null hypothesis is  \mu  =  \$181,900

The alternative hypothesis is  \mu <  \$ 181.900

b

t = -2.92

c

p-value  =  0.0016948

d

There no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900

Step-by-step explanation:

From the question we are told that

   The  population mean is  \mu  =  \$ 181, 900

    The  sample size is  n =  40

    The  sample  mean is  \=  x  =  \$ 166,400

      The  sample  standard deviation is s= \$ 33, 500

The  null hypothesis is  \mu  =  \$181,900

The alternative hypothesis is  \mu <  \$ 181.900

 

Generally the test statistics is mathematically represented as

      t =  \frac{ \= x  -  \mu }{ \frac{s}{\sqrt{n} } }

=>    t =  \frac{  166400  - 181900 }{ \frac{33500}{\sqrt{40} } }

=>    t = -2.92

Generally the p-value is obtain from the z-table  the value is  

      p-value  =  P(Z < t ) = P(Z  <  -2.93) = 0.0016948

=>    p-value  =  0.0016948

From the calculation we see that  

     p-value  >  \alpha  hence we fail to reject the null hypothesis

Thus there no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900

3 0
3 years ago
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