A piece of paper is to display ~150~ 150 space, 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?.

Answers

Answer 1

The paper's smallest dimensions are height=8.660in and width=17.321in.

What are dimensions?

In physics and mathematics, the dimension of space is the smallest set of coordinates needed to specify any point within a mathematical space.

A line has a dimension of one because only one coordinate is needed to specify a point on a line, such as a point at 5 on a number.

So, we have:

Area = 150in²

Side margin = 1 in

Top and Bottom Margin = 2 in

To obtain the smallest dimensions, calculate as follows:

The printed material's area is:

Area = l*w

A1 = h*w

A1 should be changed to 150:

150 = h*w

h = 150/w

The complete paper's topic is:

Area = l*w

A2 = (w+2+2)*(H+1+1)

A2 = (w+4)*(H+2)

For H, substitute 150/W:

A2 = (w+4)*(150/w+2)

A2 = w(150/w+2) + 4(150/w+2)

A2 = 150 + 2w + 600w + 8

A2 = 2w = 600/w + 8 + 150

A2 = 2w = 600/w + 158

Calculate a difference with regard to w and set the outcome to 0:

A'2 = 2-600/w²+0

A'2 = 2-600/w²

0 = 2 - 600/w²

2 = 600/w²

2*w² = 600

w² = 600/2

w² = 300

w = 17.321

Remember that:

h = 150/w

h = 150/17.321

h = 8.660

Therefore, the paper's smallest dimensions are height=8.660in and width=17.321in.

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Related Questions

what is the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind? (answer: 40)

Answers

The probability that a deck to guarantee that you have 4 of a kind is 40.

Probability:

In math probability refers the possibility of event.

Given,

Here we need to find the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind.

As we know that the total number of cards in the deck is 52.

So, the number of ways of choosing 4 cards from a pack of 52 playing cards is calculated as,

=> ⁵²C₄ = 52!/4!48!

=> ⁵²C₄ = 270725

Similarly, the number of ways of choosing 4 cards of same suit

=> ¹³C₄ = 13!/4!9!

=> ¹³C₄ = 715

So, the number of ways of choosing 4 cards of different suit is calculated as,

=> 715/17 = 40

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A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience salary 0 $40,000 1 $42,150 2 $44,260 3 $46,785 4 $48,820 5 $51,126 use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (round your answer to the nearest dollar. ) $52,900 $53,340 $53,914 $55,573.

Answers

The wage for a worker with 7 years of experience may be calculated using the equation for the line of best fit as follows: D. $55,573.

A line of best fit is what?

A trend line, also known as a line of best fit, is a statistical (analytical) technique that is used with a scatter plot to ascertain whether or not there is any link (correlation) between a set of data.

In this case, the pay would be placed on the y-axis of the scatter plot and the employee's years of experience would be put on the x-axis.

What is the equation of best fit?

A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. To comprehend the idea of how to roughly approximate the equation of a line of best fit and make predictions, we will look at two examples that show a scatter plot with a line of best fit.

We may rationally and logically conclude that the equation for the line of best fit is given by: by carefully examining the scatter plot that models the data in the provided table (see attachment).

y = 2233.3x + 39940

The wage for an employee with seven years of experience would thus be predicted using the equation for the line of best fit as follows:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Tell whether 20/8 and 28/9 form a proportion.

Answers

The two given fractions  [tex]\frac{20}{8}[/tex] and [tex]\frac{28}{9}[/tex] do not form a proportion.

How to find fractions that are in the same proportion?

Proportion shows that two fractions are equivalent or equal.

The given fractions are  [tex]\frac{20}{8}[/tex] and [tex]\frac{28}{9}[/tex]

Proportions are expressed in the form a:b::c:d

Where a and b represent antecedent and consequent respectively

This implies that a:b::c:d ⇒ [tex]\frac{20}{8}[/tex] : [tex]\frac{28}{9}[/tex]

The values  [tex]\frac{20}{8}[/tex] = [tex]\frac{28}{9}[/tex]

Since (20x9) is not equal to (8x28)

Multiplying the two sides to get

180=224.  This is a wrong representation.

Therefore the two fractions do not show a proportion

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Parvinder wants to save $500 for a trip. Which inequality shows the least amount she must save each month for 6 months to accomplish this?

Answers

Answer: $84 i think

 

Step-by-step explanation:

Drag the tiles to the correct boxes to complete the pairs.

Answers

The correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

What is simplified expression?

Writing a similar expression devoid of similar terms is what is meant by the expression "simplify." In other words, we will rewrite the expression using the fewest number of terms.

Consider, the given expressions

(1)  (6r + 7) + (13 + 7r)

Simplifying this,

6r + 7 + 13 + 7r

13r + 20

(2) (13 - 3/2r) - (1 - r)

Simplifying this,

13 - 3/2r - 1 + r

12 - 1/2r

(3) (-8 - r) + (2r - 4)

Simplifying this,

-8 - r + 2r - 4

-12 + r

(4) (7r - 3/2) - (2/3 + 6r)

Simplifying this,

7r - 3/2 - 2/3 - 6r

r - 13/6

Hence, the correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

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Complete question:

Complete question is attached below,

a hand of 13 cards is dealt at random from a bridge deck of 52 cards. find the probability that the hand contains 4 queens. (round your answer to four decimal places.)

Answers

The probability of the hand containing 4 queens when picked at random is 0.0026.

We can solve the given question easily using probability,  permutations, and combinations.

 We can pick any card other than the queen in the following number of ways = ⁴⁸C₉  (i)

The queen card can be picked in the following number of ways

= ⁴C₄= 1 (ii)

The total number of ways to choose 13 cards is = ⁵²C₁₃  (iii)

Using the values of (i), (ii), and (iii), we get -

Probability = (⁴⁸C₉ * 1) /  ⁵²C₁₃

= [tex]\frac{48!/9!(48-9)! *1 }{52!/13!(52-13)! }[/tex]

= 1677106640 * 1 / 635013559600

= 0.00264

If this is rounded to four decimal places, we get = 0.0026.

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PLEASE HURRY! I WILL GIVE BRAINLIEST TO THE PERSON WHO GIVES THE RIGHT ANSWER! DO NOT SPAM OR I WILL REPORT!
2300 dollars is placed in an account with an annual interest rate of 5.5%. To the nearest tenth of a year, how long will it take for the account value to reach 4300 dollars?

Answers

Answer:

I think 6.2 years

Step-by-step explanation:

I THINK OK

a statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. the 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. suppose the distribution of the population of number of pushups that can be done is approximately normal. what is the standard error of the mean?

Answers

Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).

Given that,

One day, a teacher of statistics randomly selected 10 pupils' names from a hat and instructed them to complete as many pushups as they could before class began. The 10 students who were chosen at random performed an average of 15 pushups, with a standard deviation of 9. Assume that the population's distribution of the maximum number of pushups is roughly normal.

We have to find what is the standard error of the mean.

We know that,

For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.

The sample mean is of 15 is x=15 .

The sample standard deviation is of 9 is s=9.

The sample size is of 10 is n=10.

First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.

Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622

The margin of error is of:

M=ts/n

Then:

M=2.2622(9/√10)

M=6

The confidence interval is:

x±M

x-M=15-6=9

x+M=15+6=21

Therefore, Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).

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The mathematical way to describe an interaction is: O A difference in differences A A caveat O A qualified main effect O A patterned pattern

Answers

The mathematical way to describe an interaction is: A difference in differences.

What is an interaction?

In statistics, an interaction may appear when analyzing the relationship between three or more variables, and defines a situation in which the effect of one causal variable on an outcome forms on the state of a second causal variable.

Interactions are often considered in the context of regression analyses or factorial experiments. An interaction happens when an independent variable has a different effect on the outcome depending on the values of another independent variable.

To find an interaction, we need a factorial design, in which the two (or more) independent variables are crossed with one another, so there are reflections at every combination of levels of the two independent variables.

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a business major needs 3 humanities courses to graduate. they can be selected from 29 courses offered. how many ways can the 3 courses be selected?

Answers

The number of ways 3 courses can be selected is 3654.

How to calculate combination?

The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n denotes the total number of items and r denotes the number of things being chosen at a time.The sum of all positive integers that are greater than zero and less than your number is known as a factorial. An exclamation point is written after the number to represent a factorial.

Total no. of courses available = 29

Courses needed to graduate = 3

No of ways these courses can be selected:

= ²⁹C₃

= 29!/ [(29-3)! - 3!]

= 29! / 26! 3!

= 29 * 28 * 27 * 26!/ 26! 3*2

= 29* 14* 9

=3654

So, the number of ways 3 courses can be selected is 3654.

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I am a number with 3 tens and 23 ones. What number am I

Answers

Answer:

Is it 53?

Step-by-step explanation:

3 tens means 30, and adding 23 ones would be 53

An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?​

Answers

Answer:

Step-by-step explanation:

consider the following binomial experiment: a survey shows 53% of households in centercity own a dvd player. in a random sample of 22 households in this city, what is the probability that exactly 17 households own a dvd player? a) 0.0121 b) 0.0124 c) 0.0120 d) 0.0123 e) 0.0126 f) none of the above.

Answers

The probability that exactly 17 households own a DVD player is b) 0.0124

How to calculate the probability?

P = probability of own DVD player = 53% = 0.53

n = sample of households = 22

x = number of households own a DVD player = 17

Since it is binomial experiment, we use binomial probability formula to calculate the probability.

P(X) = [tex]^{n}C_{x}\times P^{x}\times (1-P)^{n-x}[/tex]

With combination formula as below,

[tex]^nC_x[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]

P(X) = [tex]^{22}C_{17}\times 0.53^{17}\times (1-0.53)^{22-17}[/tex]

= [tex]\frac{22!}{17!(22-17)!}\times 0.53^{17}\times 0.47^{5}[/tex]

= 26334 × 0.0000205 × 0.0229345

= 0.0123811

= 0.0124

Thus, the probability is 0.0124 for 17 households own DVD player.

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Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare

Answers

The social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                            = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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Divide.
8 ÷ 1/9
Enter your answer in the box.​

Answers

Answer:

0.8888888..... repeating

Step-by-step explanation:

Answer:

72/1

Step-by-step explanation:

multiply 8 and 9/1

PLS HELPP Which algebraic expression is equivalent to 3(2x – 7)

Answers

Answer:

6x-21

Step-by-step explanation:

6x*3 - 7*3

Answer is 6x -21

Step by step

This expression can be simplified using distribution

3 (2x -7)

Multiply the number outside the brackets by the numbers inside the brackets

6x - 21

Without graphing or plugging in any values, enter a point that lies on y – 5 = 2(x + 9).

Answers

For the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, the equation of the line is

y – 5 = 2(x + 9)

Compare the equation with the standard equation as

y-y₁=m(x-x₁)

y – 5 = 2(x + 9).

y-5=2(x-(-9)

Where x₁ and y₁ are the points on which the line lies.

Thus, for the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

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What is the correct way to do 2x+24+x=150

Answers

Answer:

Step-by-step explanation:

for this one you need to solve for x and x=42

Answer:

Step-by-step explanation:

Divide both sides by 2. Divide 24 by 2 to get 12.

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Use the elimination method to get rid of one of the variables.

Find the value of one variable.

Find the value of the remaining variables using substitution.

Clearly state the final answer.

Check your answer by substituting both values into either of the original equations.

Factor each polynomial

Answers

Answer:

(x + 7)(x² - 8)

Step-by-step explanation:

x³ + 7x² - 8x - 56 =

let's put the total multiplier x² out of brackets

x²(x + 7) - 8x - 56 =

let's put the total multiplier -8 out of brackets

x²(x + 7) - 8(x + 7) =

let's put the total multiplier (x + 7) out of brackets

(x + 7)(x² - 8)

by what number do we multiply the initial enrollment to get the enrollment one decade later given a 30 % increase

Answers

The final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

Describe the term percentage of the number?A value or ratio that might be stated as a fraction over 100 is thought to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its total and then multiply it by 100. The proportion ultimately refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

For the stated question-

Let initial enrollment = 100.

After one decade, the enrollment added 30% of the initial.

Thus,

= 100 + 30% of 100

= 100 + 130

= 130

Thus, the final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

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A researcher is interested in whether using your finger to follow the words you are reading changes reading speed. He has students complete a reading speed test, first without using their fingers to follow the words and then again while using their fingers to follow the words. The researcher randomly selects a sample of 56 students who, at the beginning of the study, scored an average of 256 words per minute on the reading speed test. In the trial where they used their fingers while they read, the students scored an average of 6 words per minute higher. The standard deviation of the difference scores was 29. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of MD is normal. He uses a repeated-measures t test to test that the mean difference is zero, and he describes the results as follows: In the trial where they used their fingers while they read, the reading speed among students is not significantly different than when they do not use their fingers while they read, t(55) = 1.55, p = 0.127. If the researcher had used a repeated-measures ANOVA to test that the mean reading speed is the same before and after using their fingers while they read, he would describe the results as follows (fill in all missing values): In the trial where they used their fingers while they read, the reading speed among students is different than when they do not use their fingers while they read, F()=, p = 0.127.

Answers

The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

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please help me i need it bad

Answers

Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ \\ \\ \angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

a bowling team has 6 members. how many ways can the captain of the team arrange the bowlers for a game

Answers

The number of ways in which captain of the team arrange the 6 bowlers for a game is 720.

Explain the term arrangement?Generally speaking, an arrangement among objects is just a collection of them. A combination (ordering is disregarded) or permutation is used to determine the number possible "arrangements" of the components (order is significant). An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets were arranged in a linear or sequential order.

For the stated question-

Total members in bowling team = 6.

Number of ways to arrange them = 6!

Number of ways = 6 x 5 x 4 x 3 x 2 x 1

Number of ways = 720

Thus, the number of ways in which captain of the team arrange the 6 bowlers for a game is 720.

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10c - cd + d^3 (if c = -6 and d= 2)

Answers

The required simplified solution of the given expression is -40.

Given that,
To determine the simplified solution of the given expression 10c - cd + d³ at c = -6 and d = 2.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 10c - cd + d³

Substitute the values,
= -60 + 12 + 8
= -40

Thus, the required simplified solution of the given expression is -40.

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6. a survey shows that 360 out of 500 females and 600 out of 800 males enjoy a game show. based on this evidence, would you argue that the ratio of female and male viewers who enjoy the game show differs? use a 5% level of significance

Answers

It is concluded that the ratio of female and male viewers who enjoy the game shows the difference.

Explain the meaning of the term ratio of the number?When two or maybe more numbers are compared, the ratio shows how big one is in relation to the other. The dividend or quantity being divided is referred to as the antecedent, and also the divisor or quantity that also is dividing is referred to as the consequent. A ratio analyzes numbers by division.

According to the survey-

360 out of 500 females enjoy the game.

Thus,

Ratio female = number of females who enjoy/ total number of females.

Ratio female = 360/500

Ratio female = 0.72

Now, 600 out of 800 males enjoy a game show.

Ratio male = number of males who enjoy/ total number of males.

Ratio male = 600/800

Ratio male = 0.75

Thus, Ratio female ≠ Ratio male

Therefore, it is concluded that the ratio of female and male viewers who enjoy the game shows the difference.

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Çok acil arkadaşlar lütfen

Answers

Answer:

Step-by-step explanation:

what

Expand 2 ( c − 2 )

Answers

Answer:

[tex]\boxed{\tt 2c-4}[/tex]

Step-by-step explanation:

[tex]\tt 2\left(c-2\right)[/tex]

Apply the distributive property:-

[tex]\tt 2\left(c-2\right)=2c-2\times \:2[/tex]

[tex]\bf 2\times\:2=4[/tex]

[tex]\tt 2c-4[/tex]

___________________

Hope this helps!

Have a great day!

Write an equation for the nth term of the arithmetic seqeuence. Then find a10. 12,1,112,2,.

Answers

An equation for the nth term of the arithmetic sequence: an =  n - 6.

ad 10th term a10 = 4.

Define the term arithmetic sequence?A sequence of a form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.A common difference of the sequence is d, and the number an is the first term.

The formula for the nth term of the

an = a + (n -1)d

In which,

a = initial termd = common differencen = total number of terms

The arithmetic sequence is given as-

−5,−4,−3,−2, ...

Then, the equation will be

d = a2 - a1

d = -4 - (-5) = 1

an = a + (n -1)d

an = -5 + n - 1

Put n = 10 in the equation.

a10 = 10 - 6

a10 = 4

Thus, the 10th term of the sequence is 4.

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The correct question is-

Write an equation for the nth term of the arithmetic sequence. Then find a10.

−5,−4,−3,−2, ...

The hypotenuse of a right triangle measures 15 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

The value of the other leg of the right angled triangle is found as 4√14 cm.

Explain the term Pythagorean theorem?In a right-angled triangle, every square of a hypotenuse side is equal to total sum of the squares of the remaining two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

For the given question, the values for the right angled triangle are-

Hypotenuse (H)  - 15 cm

Side (B) = 1 cm

Let the other side be (P).

Then,

H² = P² + B²

P²  = H² - B²

Put the values-

P²  = 15² - 1²

P²  = 225 - 1

P²  = 224

P = 4√14

Thus, the value of the other leg of the right angled triangle is found as 4√14 cm.

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A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to at least three decimal places.

Answers

The true proportion of adults is in the interval 0.4026< P< 0.4594.

Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.

Data provided:

selected (x) = 329

Total(n) = 763

Sample proportion (p') = x/n

                                       = 329/ 763

                                       = 0.431

Critical z-value = 1.59

margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]

                             = 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]

                             = 1.59 × 0.0179

                             = 0.0284

88% confidence interval is:

(p' ± E) = ( 0.431 ± 0.0284)

          = 0.4594 and 0.4026

Therefore the estimate is 0.4026< P< 0.4594.

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