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AfilCa [17]
3 years ago
13

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on con

structing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 94%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.
Mathematics
1 answer:
Naddika [18.5K]3 years ago
8 0

Answer:

The sample size is    n = 68

Step-by-step explanation:

From the question we are told that

    The margin of error is  E = 5 \ years

     The standard deviation is  \sigma = 22

From the question we are told the confidence level is  94% , hence the level of significance is    

      \alpha = (100 - 94 ) \%

=>   \alpha = 0.06

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

   Z_{\frac{\alpha }{2} } =  1.881

Generally the sample size is mathematically represented as  

   n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2

=>  n = [\frac{1.881 } *  22 }{5} ] ^2

=>  n = 68

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Solve the following Simultaneous equation<br>Using any suitable method<br> x+6y=2, 3x +2y =10​
uranmaximum [27]

Answer:

x = 0.5

y = -1/4 or -0.25

Step-by-step explanation:

x + 6y = 2

3x + 2y = 10

Multiply a number by any of the equations to get numbers of the same variable

3x + 18y = 6

3x + 2y = 10

3x - 3x = 0

NB: subtract evenly if u subtract down from top make sure u subtract down from top throughout

16y = -4

16y/16 = -4/16

y = -1/4 or -0.25

to find the x value, any where you see y u put in the y value(-0.25)

So u'll pick just one of the equations above

x + 6(0.25) = 2

x + 1.5 = 2

x = 1.5 + 2

x = 0.5

5 0
3 years ago
Solve y=x2 +7 fоr x.<br> ОА. x = t /у +7<br> ОВ. x= y +7<br> Ос. x=y-7<br> OD. х = + y -7
elena55 [62]

Answer:

x = ± \sqrt{y-7}

Step-by-step explanation:

Given

y = x² + 7 ( subtract 7 from both sides )

y - 7 = x² ( take the square root of both sides, thus

x = ± \sqrt{y-7}

5 0
3 years ago
The 4th term of an arithmetic sequence is 12 and the 8th term is 36. Find the 17th term of the sequence.
Blizzard [7]

Answer: 90

Step-by-step explanation:

The formula for calculating the nth term of a sequence is given as :

t_{n} = a + ( n - d )

Where a is the first term

d is the common difference and

n is the number of terms

This means that the 4th term of an arithmetic sequence will have the formula :

t_{4} = a + 3d

And the 4th term has been given to be , 12 ,substituting into the formula we have

12 = a + 3d .............................. equation 1

Also substituting for the 8th term , we have

36 = a + 7d .............................. equation 2

Combining the two equations , we have

a + 3d = 12  ................... equation 1

a + 7d = 36 ------------ equation 2

Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is

a = 12 - 3d ................... equation 3

substitute a = 12 - 3d into equation  2 , equation 2 then becomes

12 - 3d + 7d = 36

12 + 4d = 36

subtract 12 from both sides

4d = 36 - 12

4d = 24

divide through by 4

d = 6

substitute d = 6 into equation 3 to find the value of a, we have

a = 12 - 3d

a = 12 - 3 ( 6)

a = 12 - 18

a = -6

Therefore , the 17th term of the sequence will be :

t_{17} = a + 16d

t_{17} = -6 + 16 (6)

t_{17} = -6 + 96

t_{17} = 90

Therefore : the 17th term of the sequence is 90

6 0
3 years ago
What is the sum of the areas of circle C and circle D?
Yanka [14]

Answer:

98pi

Step-by-step explanation:

Area of circle: pi(r)^2

A1=pi(7)^2

A2=pi(7)^2

A2+A1=98pi

4 0
3 years ago
In the past year and a half, Gnarly the dog lost an average of 29pound each month. Today, Gnarly weighs 14 pounds. How much did
tatyana61 [14]

Answer:

449pounds

Step-by-step explanation:

29x15months=435

435+15=449 pounds

P.S. That was one BIG dog.

7 0
3 years ago
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