The doubling time of a cityʹs population is 8 years. How long does it take for the population to quadruple.

Answer:

29.4 degrees

Step-by-step explanation:

i divided sin by 55 degrees

Answer:

1.

A. H0 :  μ1 = μ2 = μ3

Ha : μ1 ≠ 2μ ≠ μ3

2. Test Statistics = 95%

3. Critical F-Value = 3.76

4. P-Value = 2.32

5. Conclusion : Reject the null hypothesis

6. Type of vehicle does effect the amount of green house gas emissions.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

A. H 0  μ1 = μ2 = μ3

Ha  μ1 ≠ 2μ ≠ μ3

2. Test Statistics is 95%

3. Critical F-Value is 3.76.

4. P-Value is 2.32.

5. Conclusion  Reject the null hypothesis.

6. Type of vehicle does effect the amount of green house gas emissions.

The correct order of the steps of a hypothesis test is given below.

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

All steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

For more details on hypothesis test follow the link:

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Answer:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

There are many combinations based on the number you chose to subtract from both sides.

Step-by-step explanation:

Let the number be x.

According to the question,

3 x+7 > 4 x

We get, 3 x+1=4 x-6, after subtracting 6 from both sides.

3 x+1=4 x-6

4 x- 3 x=6+1

x=7

You will get the same answer if you subtract 3 x or 7 or any other number from both sides.

Thank you!

Answer:

18

Step-by-step explanation:

since you want the difference in scores, you want to take the absolute value of the difference

9 - (-9) = 9+9 = 18

The difference in scores between Player A and Player B is 18.

The difference between two numbers is found by subtracting the smaller number from the greater number.

We are informed that Player A finished first in a tournament at a golf club with a score of −9 or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par.

We are asked for the difference in scores between Player A and Player B.

The score of Player A = -9.

The score of Player B = 9

Since Player B's score > Player A's score,

To calculate the difference in their scores, we subtract player A's score from player B's score.

∴ Difference = 9 - (-9)

or,  Difference = 9 + 9

Difference = 18.

∴ The difference in scores between Player A and Player B is 18.

Learn more about the difference at

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Answer:

a

  The null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

The Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

b

     [tex]\sigma_{\= x} = 0.8944[/tex]

c

   [tex]t = -2.236[/tex]

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        [tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]

       [tex]\= x = 19[/tex]

The standard deviation is evaluated as

        [tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]

         [tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]

         [tex]\sigma = 2[/tex]

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         [tex]\alpha = 100 - 90[/tex]

        [tex]\alpha = 10[/tex]%

         [tex]\alpha =0.10[/tex]

Now the null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

the Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

The  standard error of mean is mathematically evaluated as

         [tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]

        [tex]\sigma_{\= x} = 0.8944[/tex]

The test statistic is  evaluated as  

              [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]

              [tex]t = -2.236[/tex]

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   [tex]z_{0.10} = 1.28[/tex]

Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  standard deviation is  [tex]\sigma = 2.45[/tex]  

Step-by-step explanation:

From the given data we can compute the expected mean for each random values as follows

          [tex]E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6[/tex]

So  

          [tex]E(x) = 0 + 0.6 + 0.8 + 0.6[/tex]

          [tex]E(x) = 2[/tex]

The  

             [tex]E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6[/tex]

So  

        [tex]E(X^2) = 0 + 1.2 + 3.2 + 3.6[/tex]

        [tex]E(X^2) = 8[/tex]

Now  the variance is  mathematically evaluated as

         [tex]Var (X) = E(X^2 ) -[E(X]^2[/tex]

Substituting value  

        [tex]Var (X) = 8-4[/tex]

        [tex]Var (X) = 6[/tex]

The standard deviation is mathematically evaluated as

       [tex]\sigma = \sqrt{Var(x)}[/tex]

      [tex]\sigma = \sqrt{4}[/tex]

      [tex]\sigma = 2[/tex]

Answer:

Option C is the correct option

Step-by-step explanation:

[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{x}{3x - 1} \times \frac{2x}{x - 2} [/tex]

Multiply the fractions

[tex] \frac{2 {x}^{2} }{(3x - 1)(x - 2)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} }{3x(x - 2) - 1(x - 2)} [/tex]

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 6x - x + 2 } [/tex]

Collect like terms

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]

Hope this helps...

Best regards!!

Answer: 14384 ways

Step-by-step explanation:

With 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.

The marble arrangements are: (7,0,0,0) in 4!/3! = 4 ways, (6,1,0,0) in 4!/2! = 12 ways, (5,2,0,0) in 4!/2! = 12 ways, (5,1,1,0) in 4!/2! = 12 ways, (4,3,0,0) in 4!/2! = 12 ways, (4,2,1,0) in 4! = 24 ways, (4,1,1,1) in 4!/3! = 4 ways, (3,3,1,0) in 4!/2! = 12 ways, (3,2,2,0) in 4!/2! = 12 ways, (3,2,1,1) in 4!/2! = 12 ways, (2,2,2,1) in 4!/3! = 4 ways.

Total of ways = 4+12+12+12+12+24+4+12+12+12+4 = 120 as previously determined above for identical marbles and distinct jars.

Taking into account distinct colored marbles, the number of ways of marble distribution into 4 jars becomes as follows:

For (7,0,0,0) = 4*(7!/7!) =4. For (6,1,0,0) = 12*[7!/(6!)(1!)] = 84. For (5,2,0,0) =

12*[7!/(5!)(2!)] = 252. For (5,1,1,0) = 12*[7!/(5!)(1!)(1!)] = 504. For (4,3,0,0) =

12*[7!/(4!)(3!)] = 420. for (4,2,1,0) = 24*[7!/(4!)(2!)(1!)] = 2,520. For (4,1,1,1) =

4*7!/(4!)(1!)(1!)(1!)] = 840. For (3,3,1,0) = 12*]7!/(3!)(3!)(1!) = 1,680. For (3,2,20) = 12*]7!/(3!)(2!)(2!) = 2,520. For (3,2,1,1) = 12*]7!/(3!)(2!)(1!)(1!) = 5,040. For (2,2,2,1) = 4*]7!/(2!)(2!)(2!)(1!) = 2,520.

Total of ways as requested for distinct colored marbles and distinct jars = 4+84+252+504+420+2,520+840+1,680+2,520+5,040+2,520 = 14,384.

Answer:

true

Step-by-step explanation:

Answer:

The likelihood is [tex]P(X < 25.2) = 0.91668[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 24.7 \ years[/tex]

      The standard deviation is  [tex]\sigma = 2.8 \ years[/tex]

      The sample size is [tex]n = 60 \ men[/tex]

       The  consider random value is  x =  25.2  years

Given that mean age is normally distributed, the likelihood that the age when they were first married is less than x is mathematically represented as

          [tex]P(X < x) = P( \frac{X - \mu }{\sigma_{\= x }} < \frac{x - \mu }{\sigma_{\= x }} )[/tex]

Generally  [tex]\frac{X - \mu }{ \sigma_{\= x}} = Z (The \ standardized \ value \ of \ X )[/tex]

So

      [tex]P(X < x) = P(Z< \frac{x - \mu }{\sigma_{\= x }} )[/tex]

Where [tex]\sigma_{\= x }[/tex] is the standard error of the sample mean which mathematically evaluated as

       [tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

      [tex]\sigma_{\= x } = \frac{ 2.8 }{\sqrt{ 60 } }[/tex]

      [tex]\sigma_{\= x } = 0.3615[/tex]

So  

     [tex]P(X < 25.2) = P(Z< \frac{ 25.2 - 24.7 }{0.3615} )[/tex]

     [tex]P(X < 25.2) = P(Z< 1.3831 )[/tex]

From z-table the value for  P(Z<    1.3831  ) is [tex]P(Z < 1.3831 ) = 0.91668[/tex]

  So

        [tex]P(X < 25.2) = 0.91668[/tex]

The answer is 3,240

Explanation:

To calculate the total income tax, it is necessary to calculate what is the 15% of 8000, and 17% for the remaining money, which is 12.000 (20,000 - 8,000= 12,000). Considering the statement specifies the 15% is paid for the first 8,000 and from this, the 17% is paid. Now to know the percentages you can use a simple rule of three, by considering 8000 and 12000 as the 100%. The process is shown below:

1. Write the values

[tex]8000 = 100[/tex]

[tex]x = 15[/tex] (the percentage you want to know)

2. Use cross multiplication

[tex]x =\frac{8000 x 15 }{100}[/tex]

[tex]x = 1200[/tex]

This means for the first 8000 the money Rafael needs to pay is 1,200

Now, let's repeat the process for the remaining money (12,000)

[tex]12000 = 100\\\\[/tex]

[tex]x = 17[/tex]

[tex]x = \frac{12000 x 17}{100}[/tex]

[tex]x = 2040[/tex]

Finally, add the two values [tex]1200 + 2040 = 3240[/tex]

Answer:

1.

a. 20 m²: barn door is 5m x 4m

b. 468 m²:surface area of barn

i. left and right barn walls: 2(15 x 7) = 210

ii. back wall: 7 x 8 = 56

iii. front wall: (7 x 8) - 20* = 36

*20 for the barn door

iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16

*I split the triangle into 2 smaller triangles

v. sides of roof: 2(5 x 15) = 150

2.

a. 15 m²: silo door is 3m x 5m

b.  244.18 m²: surface area of silo

i. SA(silo)=2πrh+2πr²

ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²

iii. SA(silo) = 259.18

iv. SA(silo - door) = 259.18 - 15

v. SA(silo - door) = 244.18

3.

a. 712.18 m²: total surface area painted red

i. add both surface areas: 468 + 244.18 = 712.18 m²

hope this helps :)

Complete Question:

Which statement about the following equation is true?

[tex]2x^2-9x+2 = -1[/tex]

A) The discriminant is less than 0, so there are two real roots

B) The discriminant is less than 0, so there are two complex roots

C) The discriminant is greater than 0, so there are two real roots

D) The discriminant is greater than 0, so there are two complex roots

Answer:

C) The discriminant is greater than 0, so there are two real roots

Step-by-step explanation:

The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes

[tex]2x^2 - 9x + 3 = 0[/tex]

For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]

If the discriminant D is greater than 0, the roots are real and different

If the discriminant D is equal to 0, the roots are real and equal

If the discriminant D is less than 0, the roots are imaginary

For the quadratic equation under consideration, a = 2, b = -9, c = 3

Let us calculate the discriminant D

D = (-9)² - 4(2)(3)

D = 81 - 24

D = 57

Since the Discriminant D is greater than 0, the roots are real and different.

Answer:

Step-by-step explanation:

C) The discriminant is greater than 0, so there are two real roots

Answer:

1 ): 3x-2y=-1,-x+2y=3 (1,2)

2): 4x-3y=-1 , -3x+4y=6       (2,3)

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

Step-by-step explanation:

4x-3y=-1

-3x+4y=6  ( multiply first by 3 and second equation by 4)

12x-9y=-3

-12x+16y=24 subtract

7y=21

y=21/7=3

x=2, y=3 (2,3)

3x-2y=-1

-x+2y=3

solve by addition/elimination ( same as other equation):

multiply second equation by 3

3x-2y=-1

-3x+6y=9

4y=8

y=2

x=1

3x+6y=6, 2x+4y=-4 ( no solution)

-3x+6y=-3, 5x-10y=5 infinite

Answer: 7299, 7301

Step-by-step explanation:

x + x + 2= 14,600

2x = 14,598

x = 7,299

Therefore, the office numbers are 7299 and 7301

Answer:

Limits for B scores

( 79,2 ; 92 )

Step-by-step explanation:

The interval we are looking for is between 6 % and 59%

p₁  = 6 %     p₁ = 0,06

As this point is at the right tail of the bell we better look for

p = 1- 0,06     p = 0,94

In z-table z score for 0,94062  is:    z₁ = 1,56      ( 0,94062 ≈ 0,94 )

Doing the same to find z₂ score for 59%  or 0,59

In z-table again

p =  0,59      

z₂ = 0,023

Now we know

1,56 * σ  = x₁ - 79

1,56*8,4 + 79 = x₁

x₁  =  92,10        or  x₁ = 92

And

0,023*8,4 + 79  = x₂

x₂ = 79,19         or    x₂ = 79,2

Answer:

D (The last choice)

Step-by-step explanation:

We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.

Answer:

A perfect square

Answer:

square

Step-by-step explanation:

An example of a perfect square is 9.

9 squared is 3.

Answer:

Step-by-step explanation:

There is no algebraic way to solve such an equation. It can be simplified to ...

  [tex]-2x-6=-2^x-6\\\\2x-2^x=0\qquad\text{add $2x+6$}[/tex]

This has solutions at x=1 and x=2 as shown in the attached graph.

__

The second attachment shows the functions graphed on the same graph.

Answer:

C

Step-by-step explanation:

A modified box plot does not include the outliers in the whiskers, instead they are points outside of the whiskers

5,25,33,34,34,37,37,40,42,45,45,46,46,49,73

This data has 2 outliers 5 and 73 so we have 2 choices for a modified box plot D or D

The lowest value outside of the outliers is 25 , so C would be the logical choice

D has the lower end of the whisker too close to the outlier

Answer:

Answer:

The  probability is  [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

B =business

J=jumbo

Or =ordinary

From the question we are told that  

     The proportion of the passenger on business in the ordinary jet  is [tex]P(B| Or) = 0.25[/tex]

     The proportion of the passenger on business in the jumbo jet  is  [tex]P(B|J) = 0.30[/tex]

     The  proportion of the passenger on jumbo jets is  [tex]P(j) = 0.40[/tex]

      The   proportion of the passenger on ordinary jets is evaluated as

         [tex]1 - P(J) = 1- 0.40 = 0.60[/tex]

According to  Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as

        [tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]

substituting values

         [tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]

         [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

__

The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

[tex]csc (\theta)=\frac{33}{55}[/tex]

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:

[tex]sin(\theta)=\frac{55}{33}[/tex]

3) So, remembering operations with fractions then the cosecant is:

[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]

[tex]csc (\theta)=\frac{33}{55}[/tex]

Answer:

The zeros are x=-3,-2,1

end behavior is one up one down

Step-by-step explanation:

The zeros are x=-3,-2,1

The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.

Answer:

7/9

Step-by-step explanation:

P(blue or odd) = P(blue) + P(odd) − P(blue and odd)

P(blue or odd) = 4/9 + 5/9 − 2/9

P(blue or odd) = 7/9

Alternatively:

P(blue or odd) = 1 − P(not blue and not odd)

P(blue or odd) = 1 − 2/9

P(blue or odd) = 7/9

Answer:

If [tex]r >> h[/tex], the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

[tex]A = \pi \cdot r^{2} + 2\pi\cdot s[/tex]

Where:

[tex]r[/tex] - Base radius of the cone, measured in inches.

[tex]s[/tex] - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

[tex]s = \sqrt{r^{2}+h^{2}}[/tex]

Where [tex]h[/tex] is the altitude of the cone, measured in inches. If [tex]r >> h[/tex], then:

[tex]s \approx r[/tex]

And:

[tex]A = \pi\cdot r^{2} +2\pi\cdot r[/tex]

Given that [tex]A = 1885.7143\,in^{2}[/tex], the following second-order polynomial is obtained:

[tex]\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0[/tex]

Roots can be found by the Quadratic Formula:

[tex]r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}[/tex]

[tex]r_{1,2} \approx -1\,in \pm 24.521\,in[/tex]

[tex]r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in[/tex]

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

Answer: Experimental probability.

Step-by-step explanation:

This starts as "based on past experience."

So we can suppose that this estimation is obtained by looking at the mean of the number of guests on the past N weekday evenings. (With N a large number, as larger is N, more data points we have, and a better estimation can be made)

Then, this would be an experimental probability, because it is obtained by repeating an experiment (counting the number of guests on weekday evenings) and using that information to make an estimation.

Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        [tex]28.37< L\ 30.63[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n = 59[/tex]

    The mean score is  [tex]\= x = 29.5[/tex]

     The standard deviation [tex]\sigma = 5.2[/tex]

Generally the standard deviation of mean is mathematically represented as

                [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]

             [tex]\sigma _{\= x} = 0.677[/tex]

The degree of freedom is mathematically represented as

          [tex]df = n - 1[/tex]

substituting values

        [tex]df = 59 -1[/tex]

        [tex]df = 58[/tex]

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         [tex]\alpha = 100 -95[/tex]

        [tex]\alpha =[/tex]5%

        [tex]\alpha = 0.05[/tex]

Now the critical value at  this significance level and degree of freedom is

       [tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      [tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]

substituting value

      [tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]

       [tex]28.37< L\ 30.63[/tex]