On average the number of drum sets sold in Michigan each year is 96,537, which is seven times the average number of drum sets sold each year in Vermont. How many drum sets, on average, are sold each year in Vermont?

Answer:

The answer is Plane P

Step-by-step explanation:

The reason for the answer is because a closed, two-dimensional or flat figure is called a plane shape. Different plane shapes have different attributes, such as the numbers of sides or corners. A side is a straight line that makes part of the shape, and a corner is where two sides meet.

Answer:

C.

Step-by-step explanation:

Since the radius of the circle is 12 units, we can calculate the circumference.

2 * pi * r = 2 * pi * 12 = 24 * pi = 24pi.

The arc angle is 240 degrees, and the whole circle would be 360 degrees. So, we can set up an equation.

[tex]\frac{24\pi }{360} =\frac{x}{240}[/tex]

[tex]\frac{24\pi }{6} =\frac{x}{4}[/tex]

[tex]\frac{4\pi }{1} =\frac{x}{4}[/tex]

1 * x = 4 * 4 * pi

x = 16pi

So, your answer is C.

Hope this helps!

Answer:

(5/3 x - k)/c  =b

Step-by-step explanation:

x = 3 / 5 (cb+k)

Multiply each side by 5/3

5/3x =5/3* 3 / 5 (cb+k)

5/3x = (cb+k)

Subtract k

5/3 x - k = cb +k-k

5/3 x - k = cb

Divide by c

(5/3 x - k)/c  = cb/c

(5/3 x - k)/c  =b

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 8}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{4a + 10 = 2a + 26}[/tex]

Move 2a to left hand side and change it's sign

Similarly, move 10 to right hand side and change it's sign

⇒[tex] \sf{4a - 2a =26 - 10}[/tex]

Collect like terms

⇒[tex] \sf{2a = 26 - 10}[/tex]

Subtract 10 from 26

⇒[tex] \sf{2a = 16}[/tex]

Divide both sides of the equation by 2

⇒[tex] \sf{ \frac{2a}{2} = \frac{16}{2} }[/tex]

Calculate

⇒[tex] \sf{a = 8}[/tex]

Hope I helped!

Best regards!!

Answer:

The Brain

Step-by-step explanation:

It goes down 3 and moves to the right 2

so its -3/2 =- 1.5

you slope is -1.5❤✔ hope I helped!

Answer:

his weekly exercise time goal in minutes = 200 minutes

Step-by-step explanation:

Jerry has reached 39% of his weekly exercise time goal.

so far this week ,he has exercise for a total of 78 minutes this week.

39% of total = 78 minutes

100%= x

X=100*78/39

X=100*2

X= 200 minutes

his weekly exercise time goal in minutes = 200 minutes

Answer:

  multiplication

Step-by-step explanation:

The evaluation of ...

  13 -2·3 +4/4 +4

starts with the multiplication, because there are no exponents or parentheses.

  13 -6 +4/4 +4

Next is the division:

  13 -6 +1 +4

Finally, the addition and subtraction:

  7 +1 +4

  8 +4

 12

_____

We have assumed your x is not a variable, but is intended to indicate multiplication. We have also assumed that your "divided by" implies no particular grouping, so that the numerator is the first preceding number and only the first following number is in the denominator.

Answer:

4.5 divided by 0.5=9

9 times 5=45

45 feet

Step-by-step explanation:

Answer:

45 feet

Step-by-step explanation:

Set up a proportion:

[tex]\frac{0.5}{5}[/tex] = [tex]\frac{4.5}{x}[/tex]

Cross multiply:

0.5x = 22.5

x = 45

= 45 feet

Answer:

Had Picked

Step-by-step explanation:

Answer:

D) x + y ≤ -4

    3x + 2y ≤ -5

Step-by-step explanation:

Step(i):-

we will choose the system of inequalities

                                             x + y ≤ -4

                                            3x + 2y ≤ -5

                                          x + y = -4 ...(i)

                                         3x + 2y = -5..(ii)

Multiply equation (i) with '3'

                                    3x + 3y = -12

                                    3x  + 2 y = -5

                                   -      -           +

                                    0 +  y =    -7              

Step(ii):-                              

Substitute   y  = -7  in equation (i)

                        x + y = -4

                       x - 7 = -4

                         x = -4 + 7

                        x = 3

The solution of the given inequalities is ( 3, -7)

Answer:

32,768

Step-by-step explanation:

Remember to follow PEMDAS.

First, solve for the exponents for both terms:

[tex]4^6 = 4 * 4 * 4 * 4 * 4 * 4 = 4096[/tex]

[tex]2^3 = 2 * 2 * 2 = 8[/tex]

Multiply the two terms together:

[tex]4096 * 8 = 32768[/tex]

32,768 is your answer.

~

Answer:

  2

Step-by-step explanation:

The parallel line will have the same coefficients, but a constant suited to the given point:

  x + 3y = constant

That is, A=1, B=3, so B-A = 2.

___

The constant for the parallel line will be -1.

Answer:

No

Step-by-step explanation:

Assuming that the x- and y- axes are respectively horizontal and vertical, a vertical line has an undefined slope and cannot be diagonal.

Note that only a diagonal line can have a slope defined.

Step-by-step explanation:

Hey, there!!

Principal (p) = 4000

Time = 3/2= 1.5 yrs.

rate = 10%

Now, we have formula,

[tex]c.a = p \times {(1 + \frac{r}{100}) }^{t} [/tex]

Putting their values,

[tex]ca = 4000\times {(1 + \frac{10}{100} )}^{1.5} [/tex]

[tex]ca =4000 \times {(1 + 0.1)}^{1.5} [/tex]

[tex]ca = 4000 \times 1.153689[/tex]

Simplifying them we get,

C.A = 4614.75

Hope it helps...

Answer:

Step-by-step explanation:

From the given information:

the null hypothesis and the alternative hypothesis can be computed as follows:

[tex]\mathbf{H_o:}[/tex] The sample have a distribution that agrees with the distribution of state populations.

[tex]\mathbf{H_1:}[/tex] The sample have a distribution that does not agrees with the distribution of state populations.

The Chi-Square test statistics [tex]\mathbf{X^2 = \dfrac{(Observed \ value - Expected \ value )}{(Expected \ value ) ^2 }}[/tex]

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana.

The observed and the expected value can be computed as follows:

States           Observed           Expected                        [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

Washington     450             0.51 × 1000 = 510

Oregon            340              0.30 × 1000 = 300

Idaho                150               0.11  × 1000 = 110

Montana             60              0.08 × 1000 = 80

Total                 1000                                1000

For washington :

[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

[tex]X^2 = \dfrac{(450 -510)^2}{510}[/tex]

[tex]X^2 = \dfrac{3600}{510}[/tex]

[tex]X^{2}=[/tex] 7.06

For Oregon

[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

[tex]X^2 = \dfrac{(340- 300)^2}{300}[/tex]

[tex]X^2 = \dfrac{1600}{300}[/tex]

[tex]X^{2}=[/tex] 5.33

For Idaho

[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

[tex]X^2 = \dfrac{(150- 110)^2}{110}[/tex]

[tex]X^2 = \dfrac{1600}{110}[/tex]

[tex]X^2 =14.55[/tex]

For Montana

[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

[tex]X^2 = \dfrac{(60- 80)^2}{80}[/tex]

[tex]X^2 = \dfrac{400}{80}[/tex]

[tex]X^2 = 5[/tex].00

The Chi-square test statistics for the observed and the expected value can be computed as follows:

States           Observed           Expected                        [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]

Washington     450             0.51 × 1000 = 510                  7.06

Oregon            340              0.30 × 1000 = 300                5.33

Idaho                150               0.11  × 1000 = 110                 14.55

Montana             60              0.08 × 1000 = 80                  5.00

Total                 1000                                1000                 31.94

The Chi-square Statistics Test [tex]\mathbf{X^2 = 31.94}[/tex]

Degree of freedom = n -  1

Degree of freedom = 4 - 1

Degree of freedom = 3

At 0.05 level of significance, the critical value of :

[tex]X^2_{(df, \alpha) }=X^2_{(3, 0.05)[/tex] = 7.815

Decision Rule: To reject null hypothesis if the test statistics is greater than the critical value

Conclusion: We reject the null hypothesis since test statistics is greater than critical value, therefore, we conclude that there is sufficient information to say that the sample has a distribution that does not agrees with the distribution of state populations.

Step-by-step explanation:

1.

Point M is the bisector of AB

AM = 13...(given)

Therefore, AB = 2AM = 2* 13 = 26

2.

Ray MC is the bisector of AB

AM = 8...(given)

Therefore, AB = 2AM = 2* 8 = 16

3.

Line l is the bisector of angle AB.

BM = 26...(given)

Therefore, AB = 2BM = 2* 26 = 52

Answer:

a. 0.40198

b. 0.36049

c. 0.20046

Step-by-step explanation:

To solve for this we make use of the z score formula.

z-score formula is

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Compute the probability of a value between 75.0 and 90.0.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

Using the z score table to find the probability

P-value from Z-Table:

P(x = 75) = P(z = -0.35714)

= 0.36049

For x = 90

z = 90 - 80/14

z = 0.71429

Using the z score table to find the probability

P-value from Z-Table:

P(x = 90) = P(z = 0.71429)

= 0.76247

The probability of a value between 75.0 and 90.0 is:

75 < x < 90

= P( x = 90) - P(x = 75)

= 0.76247 - 0.36049

= 0.40198

Therefore, probability of a value between 75.0 and 90.0 is 0.40198

b. Compute the probability of a value of 75.0 or less.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

Using the z score table to find the probability

P-value from Z-Table:

P(x ≤ 75) = 0.36049

c. Compute the probability of a value between 55.0 and 70.0.

For x = 55

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 55 - 80/ 14

z = -1.78571

Using the z score table to find the probability

P-value from Z-Table:

P(x = 55) = P(z = -1.78571)

= 0.037073

For x = 70

z = 70 - 80/14

z = -0.71429

Using the z score table to find the probability

P-value from Z-Table:

P(x = 70) = P(z = -0.71429)

= 0.23753

The probability of a value between 55.0 and 70.0 is:

55 < x < 70

= P( x = 70) - P(x = 55)

= 0.23753 - 0.037073

= 0.200457

Approximately to 4 decimal place = 0.20046

Step-by-step explanation:

the answer for 6y+21+7=4y−20+5y is

y =16

Answer:

The area of the triangle is 24 [tex]\text{cm}^{2}[/tex].

Step-by-step explanation:

We are given that the length of the base of a right-angle triangle ABC is 6 cm and the length of the hypotenuse is 10 cm.

And we have to find the area of the triangle.

As we know that the area of the triangle is given by the following formula;

Area of the triangle =  [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]

Firstly, we will find the height (perpendicular) of the triangle ABC bu using the Pythagoras Theorem.

[tex]\text{Hypotenuse}^{2} =\text{Perpendicular}^{2} +\text{Base}^{2}[/tex]

[tex]\text{10}^{2} =\text{Perpendicular}^{2} +\text{6}^{2}[/tex]

[tex]100=\text{Perpendicular}^{2} +36[/tex]

[tex]\text{Perpendicular}^{2} =100-36[/tex]

[tex]\text{Perpendicular}^{2} =64[/tex]

[tex]\text{Perpendicular} =\sqrt{64}[/tex]  = 8 cm.

Now, the area of the triangle =  [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]

                                                =  [tex]\frac{1}{2}\times \text{6} \times \text{8}[/tex]

                                                =  24 [tex]\text{cm}^{2}[/tex]

Hence, the area of the triangle is 24 [tex]\text{cm}^{2}[/tex].

Answer:

The length of segment XZ is 15 units

Step-by-step explanation:

Given

[tex]XY = 5[/tex]

[tex]YZ = 10[/tex]

Required

Determine XZ

Assuming XY and YZ are on the same plane such that

[tex]XZ = XY + YZ[/tex]

Substitute values for XY and YZ

[tex]XZ = 5 + 10[/tex]

[tex]XZ = 15[/tex]

Hence, the length of segment XZ is 15 units

Answer:

The data is missing in the question, below is the complete question:

The number of credits being taken by a sample of 13​ full-time college students are listed below. Find the​ mean, median, and mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why. 9    9    12    12    9    10    8    8    8    8    8    8    11    Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The mean is nothing . ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a mean. Does the mean represent the center of the​ data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below​ and, if​necessary, fill in the answer box to complete your choice. A. The median is nothing . ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a median. Does the median represent the center of the​ data? A. The median represents the center. B. The median does not represent the center because it is the largest data value. C. The median does not represent the center because it is not a data value. D. The median does not represent the center because it is the smallest data value. E. The data set does not have a median. Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ mode(s) is/are nothing . ​(Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as​ needed.) B. The data set does not have a mode. Does​ (Do) the​ mode(s) represent the center of the​ data? A. The​ mode(s) represent(s) the center. B. The​ mode(s) does​ (do) not represent the center because it​ (they) is​ (are) not a data value. C. The​ mode(s) does​ (do) not represent the center because it​ (one) is the largest data value. D. The​ mode(s) does​ (do) not represent the center because it​(one) is the smallest data value. E. The data set does not have a mode.

Answer:

a.) mean = 9.23

ii) The mean represents the centre (A)

b) Median = 9

ii) The median represents the centre (A)

c) Mode = 8

ii)  The​ mode(s) does​ (do) not represent the center because it​(one) is the smallest data value. (D)

Step-by-step explanation:

Arranging the data in ascending order:

8 8 8 8 8 8 9 9 9 10 11 12 12

a) calculating for mean

[tex]\bar x = \frac{sum\ of\ data}{number\ of\ data}\\ \bar x = \frac{8+8+8+8+8+8+9+9+9+10+11+12+12}{13} \\\bar x =\frac{120}{13} \\\bar x = 9.23[/tex]

ii) does the mean represent the centre of the data?

The measure of central tendency/location is a statistical tool used to accurately depict values that are at the central location of the data set

Yes, the mean represents the centre of the data, because there are no outliers in the data set. Outliers are unusual values compared to the rest of the values in the dataset.

b) calculating the median (M)

[tex]M =( \frac{n\ +\ 1}{2})th\ term\\ \\where:\\n = number\ of\ data\ in\ the\ dataset = 13\\\\\therefore M = \frac{13+1}{2}\\ M = \frac{14}{2} \\M= 7th\ term[/tex]

The 7th term after arranging in ascending or descening order, is the median term

8 8 8 8 8 8 9 9 9 10 11 12 12

∴ Median = 9

ii) Yes, the Median represents the center of the data, because it litterally tells the data at the middle of the distribution  

c) The mode is the data with the highest number of occurrence in the dataset (highest frequency);  8 8 8 8 8 8 9 9 9 10 11 12 12

The data with the highest number of occurrence is 8, which occurred 6 times.

Mode = 8

ii) The mode does not represent the centre of the data because it is the smallest value in the dataset, hence it doesn't tell the value that is the middle term.

Answer:

15

Step-by-step explanation:

a^2 + b^2 = c^2

9=a

12-b

Plug in the numbers

Answer:

d) $146.15

Step-by-step explanation:

From the above Question, we are given the following values:

The annual dividend per share of a perpetual preferred stock = $9.50

The required return rate on this preferred stock = 6.5% = 0.06

The selling price of the stock = ??

The formula to calculate the Selling price of the stock =

Annual dividend per share / Required return rate

= $9.5/ 0.065

= $146.15384615

Approximately $146.15

Therefore, the price at which the stock should sell is $146.15.

Answer:

The  probability is  [tex]P(X < 20 ) = 0.68807[/tex]

Step-by-step explanation:

From the question we are told that

     The proportion of  total part-time workforce is  [tex]\r p = 0.221[/tex]

     The  sample  size is  n  =  80  

Generally the mean is mathematically represented as

         [tex]\mu = n* p[/tex]

          [tex]\mu = 0.221 * 80[/tex]

        [tex]\mu = 17.68[/tex]

The  proportion of not part - time   workforce

      [tex]q = 1- p[/tex]

=>   [tex]q = 1- 0.221[/tex]

=>   [tex]q = 0.779[/tex]

The  standard deviation is mathematically represented as

     [tex]\sigma = \sqrt{ 80 * 0.221 * 0.779 }[/tex]

     [tex]\sigma = 3.711[/tex]

Now  applying the normal approximation,

Then the  probability that fewer than 20 people from this sample were between the ages of 25 and 34 is mathematically represented as

     [tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ 20 - 17.68 }{ 3.711} )[/tex]

Applying  continuity correction

     [tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ (20-0.5 ) - 17.68 }{ 3.711} )[/tex]

       [tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ (20-0.5 ) - 17.68 }{ 3.711} )[/tex]

      [tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < 0.4904 )[/tex]

Generally

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

So  

    [tex]P(X < 20 ) = P( Z< 0.4904 )[/tex]

From the z-table  

        [tex]P( Z< 0.4904 ) = 0.68807[/tex]

The probability is  

         [tex]P(X < 20 ) = 0.68807[/tex]

Answer: y=x³+2 or f⁻¹(x)=x³+2

Step-by-step explanation:

To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.

[tex]y=\sqrt[3]{x-2}[/tex]                        [replace y with x and x with y]

[tex]x=\sqrt[3]{y-2}[/tex]                        [cube both sides to cancel out the cubed root]

[tex]x^3=y-2[/tex]                          [add both sides by 2]              

[tex]x^3+2=y[/tex]

Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.

Answer:

f^-1(x)=x^3+2

Step-by-step explanation:

The third column is optional/extra. It's to show which data values fit in what specific class limit interval.

===================================================

Explanation:

Imagine we had a bunch of cards. Each card will have a number that is from the data set {70, 88, 103, 64, ... etc}

The goal is to sort the cards into 7 boxes. The first box is labeled "60 through 66", the next is "67 through 73", etc.

The first box has 4 cards placed inside it because we have the values {64,65,60,60 } which fit the interval from 60 through 66. Therefore the frequency here is 4.

The next box has the cards labeled {70,69,71,72,70 } inside it. We have 5 cards here, so the frequency is 5.

This pattern is kept up until all of the cards have been sorted into the proper boxes.

What you'll end up with is what you see in the image below. It shows the table of class limits with their corresponding frequencies. I have added a third column to show which values go where, which is optional and likely something you wont put as your answer to the teacher. This third column is just something for you to help keep track of everything.

Answer:

Length of each pieces= 1/8 inch

Step-by-step explanation:

Length of metal rod= 51/64 inch

1/64 was cut from one end and 1/32 was cut from the other end

Total cut out= 1/64 + 1/32

Total cut out= (1+2)/64

Total cut out= 3/64 inch

Length remaining= 51/64-3/64

Length remaining= 48/64 inch

So the remaining length was cut into six pieces.

Length of each pieces= (48/64) * 1/6

Length of each pieces= 8/64

Length of each pieces= 1/8 inch

Answer:

Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].

Step-by-step explanation:

We have to find the equation of the line that passes through the points (8,0) and (-9,-9).

Let the two points be ([tex]x_1,y_1[/tex]) = (8, 0) and ([tex]x_2, y_2[/tex]) = (-9, -9).

Now, we will find the two-point slope using the above two points, i.e;

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          =  [tex]\frac{-9-0}{-9-8}[/tex]  =  [tex]\frac{9}{17}[/tex]

Now, the equation of the line using one of the point, let's say ([tex]x_1,y_1[/tex]) = (8, 0) is given by;

[tex]y - y_1 = \text{Slope} \times (x - x_1)[/tex]

[tex]y - 0 =\frac{9}{17} \times (x - 8)[/tex]

[tex]y =\frac{9x}{17} - \frac{72}{17}[/tex]

Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].

Complete Question

The mean height of women in a country (ages 20-29) is 64.4 inches. A random sample of 75 women in this age ground is selected. what is the probability that the mean height for the sample is greater than 65 inches? assume [tex]\sigma = 2.97[/tex]

Answer:

The value is  [tex]P(X > 65) = 0.039715[/tex]

Step-by-step explanation:

From question we are told that

  The mean is [tex]\mu = 64.4 \ inches[/tex]

  The  sample size is  [tex]n = 75[/tex]

The probability that the mean height for the sample is greater than 65 inches is mathematically represented as

     [tex]P(X > 65) = P[\frac{X - \mu }{ \sigma_{\= x} } > \frac{65 - 64.4 }{ \sigma_{\= x} } ][/tex]

Where  [tex]\sigma _{\= x }[/tex] is the standard error of mean which is evaluated as

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

=>   [tex]\sigma_{\= x } = \frac{2.97}{\sqrt{75} }[/tex]

=>    [tex]\sigma_{\= x } = 0.343[/tex]

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

       [tex]P(X > 65) = P[Z> \frac{65 - 64.4 }{0.342 } ][/tex]

So  

    [tex]P(X > 65) = P[Z >1.754 ][/tex]

From the z-table  the value of  

     [tex]P(X > 65) = P[Z >1.754 ] = 0.039715[/tex]

     [tex]P(X > 65) = 0.039715[/tex]

Answer:

The sample size is  [tex]n =419[/tex]

Step-by-step explanation:

From the question we are told that

    The population proportion is  [tex]p = 0.45[/tex]

     The  margin of error is  [tex]E = 0.04[/tex]

Given that the confidence level is  90%

  Then the level of significance can be mathematically represented as

          [tex]\alpha = 100 -90[/tex]

          [tex]\alpha = 10\%[/tex]

         [tex]\alpha = 0.10[/tex]

Next we obtain the level of significance from the normal distribution table the value is    

             [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

   Generally the sample size is mathematically represented as  

        [tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1- p )[/tex]

substituting values

         [tex]n = [ \frac{1.645 }{0.04} ]^2 * 0.45(1- 0.45 )[/tex]

        [tex]n =419[/tex]