Select the correct answer.
What are the x-intercepts of this function?
g(x) = -0.25x2 – 0.25x + 5
O
(-20,0) and (-4,0)
(4,0) and (20,0)
(5,0) and (-4,0)
(-5,0) and (4,0)

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

Answer:

1. [tex] P(x) [/tex] ÷ [tex] Q(x) [/tex]---> [tex] \frac{-3x + 2}{3(3x - 1)} [/tex]

2. [tex] P(x) + Q(x) [/tex]---> [tex]\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}[/tex]

3.  [tex] P(x) - Q(x) [/tex]---> [tex] \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} [/tex]

4. [tex] P(x)*Q(x) [/tex] --> [tex] \frac{12}{(3x - 1)(-3x + 2)} [/tex]

Step-by-step explanation:

Given that:

1. [tex] P(x) = \frac{2}{3x - 1} [/tex]

[tex] Q(x) = \frac{6}{-3x + 2} [/tex]

Thus,

[tex] P(x) [/tex] ÷ [tex] Q(x) [/tex] = [tex] \frac{2}{3x - 1} [/tex] ÷ [tex] \frac{6}{-3x + 2} [/tex]

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

[tex] \frac{2}{3x - 1}*\frac{-3x + 2}{6} [/tex]

[tex] \frac{2(-3x + 2)}{6(3x - 1)} [/tex]

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

2. [tex] P(x) + Q(x) [/tex] = [tex] \frac{2}{3x - 1} + \frac{6}{-3x + 2} [/tex]

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

[tex] \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{12x - 2}{(3x - 1)(-3x + 2)} [/tex]

[tex] = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} [/tex]

3. [tex] P(x) - Q(x) [/tex] = [tex] \frac{2}{3x - 1} - \frac{6}{-3x + 2} [/tex]

[tex] \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} [/tex]

[tex] \frac{-24x + 10}{(3x - 1)(-3x + 2)} [/tex]

[tex] = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} [/tex]

4. [tex] P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} [/tex]

[tex] P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} [/tex]

[tex] P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} [/tex]

Composite functions involve combining multiple functions to form a new function

The functions are given as:

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

[tex]Q(x) = \frac{6}{-3x + 2}[/tex]

[tex]P(x) \div Q(x)[/tex] is calculated as follows:

[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}[/tex]

Express as a product

[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}[/tex]

Divide 2 by 6

[tex]P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}[/tex]

Multiply

[tex]P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}[/tex]

Hence, the value of [tex]P(x) \div Q(x)[/tex] is [tex]\frac{-3x + 2}{3(3x - 1)}[/tex]

P(x) + Q(x) is calculated as follows:

[tex]P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}[/tex]

Take LCM

[tex]P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]

Open brackets

[tex]P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}[/tex]

Collect like terms

[tex]P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}[/tex]

[tex]P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}[/tex]

Factor out 2

[tex]P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) + Q(x) is [tex]\frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]

P(x) - Q(x) is calculated as follows:

[tex]P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}[/tex]

Take LCM

[tex]P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]

Open brackets

[tex]P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}[/tex]

Collect like terms

[tex]P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}[/tex]

[tex]P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}[/tex]

Factor out -2

[tex]P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) - Q(x) is [tex]\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]

P(x) * Q(x) is calculated as follows:

[tex]P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}[/tex]

Multiply

[tex]P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}[/tex]

Hence, the value of P(x) * Q(x) is [tex]\frac{12}{(3x - 1)(-3x + 2)}[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

Answer:

25 magazines for $70. (For why, read explanation)

Step-by-step explanation:

We can find the unit price of each of these deals by dividing the cost and the quantity.

[tex]\frac{45}{15}[/tex] = 3, so the first deal is $3 per magazine.

[tex]\frac{70}{25}[/tex] = 2.8, so the second deal is $2.80 per magazine.

Therefore, 25 magazines for $70 is a better deal.

Hope this helped!

Answer:

301.44

Step-by-step explanation:

V=π r² h

V=π (4)² (12)

V= 603.19

divide by 2 to find half full: ≈ 301

301.44

Answer:

(67/10)x + 9 (answer [2])

Step-by-step explanation:

3(7/5x + 4) - 2(3/2 - 5/4x). after the indicated multiplication has been carried out, is:

(21/5)x + 12 - 3 + (5/2)x

Combining like terms, we get (4.2 + 2.5)x + 9, or

6.7x + 9, or (67/10)x + 9 (answer [2])

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 speed of the jet is 347 mph and the  speed of the wind is 18 mph.

Step-by-step explanation:

We have the following:

x = the speed of the jet in still air.

y = the speed of the wind

we know that the speed is equal to:

v = d / t

therefore the distance would be:

d = v * t

if we replace with the information of the exercise we have:

3 * (x + y) = 1095

3 * (x - y) = 987

we must solve this system of equations, add both equations and we are left:

3 * x + 3 * y = 1095

3 * x - 3 * y = 987

3 * x + 3 * y + 3 * x - 3 * y = 1095 + 987

6 * x = 2082

x = 2082/6 = 347

now to calculate y, we replace:

3 * (347 + y) = 1095

1041 + 3 * y = 1095

3 * y = 1095 - 1041

y = 54/3 = 18

The speed of the jet is 347 mph and the  speed of the wind is 18 mph.

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:

-4x + 4

Step-by-step explanation:

4x - 2( 4x - 2 )

→ Expand out 2 ( 4x - 2 )

2 ( 4x - 2 ) = 8x - 4

→ Substitute the expanded bracket back into the expression

4x - (8x - 4)

→ Collect the 'x' values

-4x + 4

Answer:

think its 3a 3.83838

Step-by-step explanation:

Answer:

-23/11

Step-by-step explanation:

Answer:

C. x = 2

Step-by-step explanation:

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

Since you have square roots, you need to separate the square roots and square both sides.

[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]

Now that one square root is on each side of the equal sign, we square both sides.

[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]

[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]

Now we isolate the square root and square both sides again.

[tex] 7x - 42 = -14\sqrt{2x} [/tex]

Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.

[tex] x - 6 = -2\sqrt{2x} [/tex]

Square both sides.

[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]

[tex] x^2 - 12x + 36 = 4(2x) [/tex]

[tex] x^2 - 20x + 36 = 0 [/tex]

We need to try to factor the left side.

-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.

[tex] (x - 2)(x - 18) = 0 [/tex]

[tex] x = 2 [/tex]   or   [tex] x = 18 [/tex]

Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.

Test x = 2:

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]

[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]

[tex] 5 + 2 = 7 [/tex]

[tex] 5 = 5 [/tex]

We have a true equation, so x = 2 is a true solution of the original equation.

Now we test x = 18.

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]

[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]

[tex] \sqrt{169} + 6 = 7 [/tex]

[tex] 13 + 6 = 7 [/tex]

[tex] 19 = 7 [/tex]

Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.

Answer: C. x = 2

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:

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:

x=(2+ √-32)/2 or x=(2- √-32)/2

Step-by-step explanation:

x^2 - 2x = -9

x^2 - 2x + 9 =0

x = 2± (√(-2)^2 - 4*1*9)/2*1

Use the quadratic formula in the expression using a=1, b= -2, c=9

x = 2±√4-36 /2

x = 2+√4-36 or x = 2 - √4 - 32 /2

x = (2+√-32) /2 or x=( 2 - √-32 )/2

The solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.

The given quadratic equation is x²-2x=-9.

Quadratic formula is the simplest way to find the roots of a quadratic equation.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

By comparing x²-2x+9=0 with ax² + bx + c = 0, we get a=1, b=-2 and c=9

Substitute a=1, b=-2 and c=9 in the quadratic formula, we get

x = [2±√(-2)²-4×1×9)]/2×1

= [2±√4-36]/2

= (2±i5.7)/2

x = (2+i5.7)/2 or (2-i5.7)/2

Therefore, the solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.

To learn more about the quadratic formula visit:

https://brainly.com/question/11540485.

#SPJ5

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 :)

Answer:

x4+7x+3

Step-by-step explanation:

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.

________________________Alike______________________

→ Both of the lines are proportional meaning they go through the origin.

→ Both of the lines have a positive slope meaning the slope goes towards the top right corner.

__________________________________________________

_____________________Difference_____________________

→ The 2 lines have different slopes, the first one has a slope of 1/3x whereas the 2nd one has a slope of 3x.

→ The points that create the lines are totally different, no two points are the same.

__________________________________________________

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:

https://brainly.com/question/10758924

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:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

Dot paper helps to understand and bring in the big picture in perspective drawing.

Step-by-step explanation:

Dot paper helps to understand patterns and features of the big picture. It helps to understand patterns at various intervals. Drawing with perspective helps to understand the big idea. Perspective reveals your point of view and helps gravitate your idea of the spatial onto paper. You can express linear perspectives.

You can use your principles of perspective drawing to create a perception of your world and your world view through your art.

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]

Answer:

Step-by-step explanation:

Given,

a = 4

y = -6

Now,

[tex] - a + 3y[/tex]

Plug the values

[tex] = - 4 + 3 \times ( - 6)[/tex]

Multiply the numbers

[tex] = - 4 + ( - 18)[/tex]

When there is a (+) in front of an expression in parentheses, the expression remains the same.

[tex] = - 4 - 18[/tex]

Calculate

[tex] = - 22[/tex]

Hope this helps..

Best regards!!

Answer:

14

Step-by-step explanation:

-4 + 3(6)

-4+18

14

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:

[tex]5.625\pi[/tex] m³.

Step-by-step explanation:

The volume of a cylinder is found by calculating pi * r^2 * h.

In this case, h = 2.5, and r = 1.5.

pi * 1.5^2 * 2.5

= pi * 2.25 * 2.5

= pi * 5.625

So, the exact volume of the cylinder is [tex]5.625\pi[/tex] m³.

Hope this helps!

Answer: Volume of Cylinder: [tex]\pi r^{2} *h[/tex]

               5.625π  m.

Step-by-step explanation:

[tex]\pi r^{2} *h[/tex]   Cylinder Area Formula

[tex]\pi *1.5^{2} *2.5[/tex]   Substitution

[tex]\pi * 2.25 *2.5[/tex]   Exponent

[tex]\pi *5.625[/tex]   Multiply

[tex]5.625\pi[/tex] Answer