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maks197457 [2]
3 years ago
7

What is the circumference of a child's swimming pool that has a radius of 3 feet

Mathematics
1 answer:
Gnom [1K]3 years ago
5 0
Formula for circumference= (2)(pi)(r) or (pi)(d)
diameter=2r=6ft
6ft*3.14=18.84
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What is the nth term rule of the quadratic sequence below?<br> 8,14,22,32 ,44, 58, 74...
DanielleElmas [232]

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

8 0
2 years ago
Find the area of a diameter of 200 ft. What is the radius?
Alecsey [184]
Your answer is 100ft. This is because to find the radius when you already know the diameter you have to divide the diameter by 2.
4 0
3 years ago
Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness
Yakvenalex [24]

Complete Question

Country financials, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more that fair. In Feb 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair.

a

State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

b

What is the sample proportion indicating that their  financial security was more that fair in 2012?In 2010?

c

Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?

Answer:

a

The null hypothesis is  H_o :  p_1 = p_2

The  alternative hypothesis is   H_a :  p_1  \ne  p_2

b

in 2012  \r  p_1  =0.41

in 2010  \r  p_2  =0.35  

c

The  p-value  is  p-value = 0.0072

The conclusion is

There is  sufficient evidence to conclude that the proportion of those indicating that  financial security is more fair in Feb 2010 is different from the proportion of  those indicating that financial security is more fair in Feb 2012.

Step-by-step explanation:

From the question we are told that

   The  sample size in 2012 is  n_1  =  1000

    The  number that indicated that their finance was more than fail is  k  =  410  

     The  sample  size in 2010  is  n_2  =  900

   The  number that indicated that their finance was more than fail is  u  =  315

     The  level of significance is  \alpha  =  0.05[/ex]The null hypothesis is  [tex]H_o :  p_1 = p_2

The  alternative hypothesis is   H_a :  p_1  \ne  p_2

Generally the sample proportion for  2012 is mathematically represented as

     \r  p_1  =  \frac{k}{n_1}

=>   \r  p_1  =  \frac{410}{1000}

=>   \r  p_1  =0.41

Generally the sample proportion for  2010 is mathematically represented as

      \r  p_2  =  \frac{u}{n_2}

=>   \r  p_2  =  \frac{315}{900}

=>   \r  p_2  =0.35    

Generally the pooled sample proportion is mathematically represented as

      \r p =  \frac{k + u }{n_1 + n_2}

=>     \r p =  \frac{410 + 315 }{1000+ 900}

=>      \r p =  0.3816

Generally the test statistics is mathematically represented as

     z =  \frac{( \r p_1 - \r p_2 ) - 0}{\sqrt{\r p (1 - \r p ) ( \frac{1}{n_1} +\frac{1}{n_2} )}  }

 z =  \frac{( 0.41 -0.35 ) - 0}{\sqrt{0.3816 (1 - 0.3816 ) ( \frac{1}{1000} +\frac{1}{900} )}  }    

 

 z =  \frac{( 0.41 -0.35 ) - 0}{\sqrt{0.3816 (1 - 0.3816 ) ( \frac{1}{1000} +\frac{1}{900} )}  }

   z  =  2.688

Generally the p- value  is mathematically represented as  

      p-value = 2 P(Z >2.688  )

From the z -table  

      P(Z > 2.688) = 0.0036

So  

      p-value = 2 *0.0036

        p-value = 0.0072

So from the p-value  obtained we see that p-value  <  \alpha so we reject the null hypothesis

Thus there is  sufficient evidence to conclude that the proportion of financial security is more fair in Feb 2010 is different from the proportion of financial security is more fair in Feb 2012.

5 0
3 years ago
Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.
N76 [4]
The solution is <span>B. π/12+nπ

</span>proof 
sinx cosx = 1/4 is equivalent to  2 <span>sinx cosx = 1/2 or sin2x =1/2
so 2x = arcsin(1/2) = </span>π/6 + 2nπ,  so x = π/12+nπ
8 0
3 years ago
Read 2 more answers
Solve the problem below, simplify, add steps<br> 1/3 √21 minus 2/3 √3 * √7
iogann1982 [59]
Do you want square root? And If so then here is the answer:Rewrite <span><span>√37</span>37</span> as <span><span>√3√7</span>37</span>.<span><span>√3√7</span>37</span>Multiply <span><span>√3√7</span>37</span> by <span><span>√7√7</span>77</span>.<span><span><span>√3√7</span><span>√7√7</span></span><span>37⁢77</span></span>Simplify.        And in the end of, this I put  the decimals.√<span><span>217</span><span>217</span></span>The result can be shown in both exact and decimal forms.Exact Form:<span><span><span>√21</span>7</span></span>Decimal Form:<span>0.65465367<span>… not sure this answer.
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4 0
3 years ago
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