Forty-eight female students participated in a math fair. This represents 60% of the total students that participated. How many students participated in the math fair? I need to get it right I don’t want to fail

Answer:

36/5 as a decimal is 7.2

Step-by-step explanation:

In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".

When we calculated 36 divided by 5, we found that 36/5 in decimal form is:

36 ÷ 5 = 7.2

Therefore, the decimal form of 36/5 is 7.2

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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The distribution of candy colors in both years is not uniform. The hypothesis tests indicate that there are unequal amounts of each color represented in each year.

To test whether the distribution of candy colors is uniform in each year, we can use the chi-square goodness-of-fit test. The null hypothesis for each year's test would state that the distribution of colors is uniform (i.e., equal amounts of each color). The alternative hypothesis would be that the distribution is not uniform.

For last year's bag, we can calculate the expected frequencies for each color by dividing the total number of candies (296, excluding abnormal packages) by the number of colors (5). The expected frequency for each color would be 296/5 = 59.2. We can then calculate the chi-square statistic by summing the squared differences between the observed frequencies and the expected frequencies, divided by the expected frequencies. This gives us the test statistic.

Performing the chi-square goodness-of-fit test for last year's data, we compare the calculated chi-square value with the critical chi-square value at a given significance level (e.g., α = 0.05 with 4 degrees of freedom for 5 colors). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis, indicating that the distribution of colors is not uniform.

Similarly, we can perform the chi-square goodness-of-fit test for this year's bag, using the observed frequencies and expected frequencies based on the total number of candies (292, excluding abnormal packages) and the number of colors (5).

For the third hypothesis test comparing the two bags, we can use the chi-square test of independence. The null hypothesis would state that the distribution of colors in both years is the same. The alternative hypothesis would be that the distribution differs between the two years.

Performing the chi-square test of independence, we compare the calculated chi-square value with the critical chi-square value at a given significance level (e.g., α = 0.05 with 16 degrees of freedom for 5 colors in each year). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis, indicating that the distributions of colors in the two years are different.

In conclusion, the hypothesis tests indicate that the distribution of candy colors is not uniform in both years. The abnormal packages found in last year's bag and the differences in observed frequencies compared to expected frequencies suggest an unequal representation of colors. The chi-square tests can help determine the significance of these differences.

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The number of trees the farmer should harvest for the maximum harvest is given by A = 39

Given data ,

To maximize her harvest, the farmer needs to find the optimal number of trees to plant per acre. Let's denote the number of trees planted per acre as "x".

If she plants 70 trees per acre, each tree will yield 30 bushels of fruit.

For each additional tree planted per acre, the yield of each tree will decrease by 4 bushels.

Based on this, the yield of each tree can be modeled by the equation: 30 - 4(x - 70)

So the total yield per acre (T) can be represented as:

T = x(30 - 4(x - 70))

On differentiating T with respect to x , we get

T = x(30 - 4(x - 70))

T = 30x - 4x^2 + 280x

dT/dx = 30 - 8x + 280

Setting dT/dx equal to 0 and solving for x:

30 - 8x + 280 = 0

8x = 310

x = 310/8

x = 38.75

Therefore , the value of A is 39

Hence , the optimal number of trees to plant per acre to maximize the harvest is 39

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In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.

THE MATCHING LAW

Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.

After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.

Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.

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Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion.

(a)

\(\frac{PQ}{AB}\) = \(\frac{RS}{CD}\) ( substitute values )

\(\frac{PQ}{6}\) = \(\frac{12}{8}\) ( cross- multiply )

8 × PQ = 72 ( divide both sides by 8 )

PQ = 9 cm

(b)

\(\frac{AD}{PS}\) = \(\frac{CD}{RS}\) ( substitute values )

\(\frac{AD}{10.5}\) = \(\frac{8}{12}\) ( cross- multiply )

12 × AD = 84 ( divide both sides by 12 )

AD = 7 cm

(c)

given 2 similar figures with ratio of sides = a : b , then

ratio of areas = a² : b²

here ratio of sides CD : RS = 8 : 12 = 2 : 3

then ratio of areas = 2² : 3² = 4 : 9

let the area of PQRS be x , then using proportion

\(\frac{4}{48}\) = \(\frac{9}{x}\) ( cross- multiply )

4x = 432 ( divide both sides by 4 )

x = 108

then area of PQRS = 108 cm²

Answer:

C. Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines.

The two equations are in slope intercept form which is y = mx + b where m is the slope and b is the y-intercept.

In the first equation (y = -2x + 3), -2 is the slope since it is the coefficient. "b" is 3 since it is the constant of the equation.

In the second equation (y = -4x -1), -4 is the slope is the coefficient, and the y-intercept is -1 since it is the constant.

To solve the equations graphically, graph them and find the point where they intersect.

Step-by-step explanation:brainlist

Answer: C

Step-by-step explanation:

Answer:

I hope it is correct.. :)

Answer:

T6 = 1 944

Step-by-step explanation:

Tn = a\(r^{n-1}\)

T6 = \(8(3)^{6-1}\)

T6 = 1 944

Answer:

$102

Step-by-step explanation:

Reset Scarlet bought a coat originally priced at $120. She got a 15% discount. How much did she pay for the coat?

1. Convert the discount percentage to a decimal:

15/100 = 0.15

2. Multiply the original price by the decimal:

120*0.15 = $18

This is the discount they got.

3. Now, subtract the discounted value from the original price:

120 - 18 = $102

This means that they paid $102 for the coat.

Hope this helps!

Answer:

$102

Step-by-step explanation:

15% of 120

= 15/100×120

0.15×120=$18

therefore, 15% of 120 equal 18

discount= $18

Amount she paid= 120-18= $102

There is sufficient evidence to suggest that there is a relationship between the type of automobile owned and the gender of the individual.

1. The sample size is large enough such that

np1≥10, np2≥10, n(1−p1)≥10, and n(1−p2)≥10,

2. The samples are independent.

3. Since |z| = 3.82 > 1.645, we reject the null hypothesis.

Automobile Ownership

A study was conducted to find out whether there is a relationship between the type of automobile owned and the gender of the individual. The data are shown below:

Luxury Large Midsize Small

Men 10 17 19 24

Women 40 33 29 28

At a=0.10, the relationship between the type of automobile owned and the gender of the individual can be determined by using the critical value method with tables.In order to conduct a hypothesis test for the equality of two population proportions, we must first check if the following conditions are met or not:

1. The sample size is large enough such that

np1≥10, np2≥10, n(1−p1)≥10, and n(1−p2)≥10,

where n1 and n2 are the sample sizes, p1 and p2 are the sample proportions, and

n=n1+n2 is the total sample size.

2. The samples are independent.

3. Both populations are at least ten times larger than their respective sample sizes.Let p1 be the proportion of men who own luxury cars. Let p2 be the proportion of women who own luxury cars. Then the null hypothesis is given by,

H0: p1 = p2The alternative hypothesis is given by,

Ha: p1 ≠ p2

The level of significance is given by,

α = 0.10

Since it is a two-tailed test, the critical values of z are given by,

zα/2 = ±1.645

The test statistic is given by,

z = (p1 - p2) / √((p^(1-p^2)) * ((1/n1) + (1/n2)))

Here,

p = (x1 + x2) / (n1 + n2)

= (10 + 40) / (10 + 17 + 19 + 24 + 40 + 33 + 29 + 28)

= 50 / 200 = 0.25

Replacing the values in the formula, we get,

z = (0.10 - 0.40) / √((0.25*(1-0.25)) * ((1/94) + (1/130)))

z = -3.82

Since |z| = 3.82 > 1.645, we reject the null hypothesis.

Hence, there is sufficient evidence to suggest that there is a relationship between the type of automobile owned and the gender of the individual.
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The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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Answer:

The fossil is 0.254 meters long.

Step-by-step explanation:

254 millimeters is equal to 25.4 centimeters, which is equal to 0.254 meters.

Answer:

3(2x + 3) = 5(x + 1)

Step-by-step explanation:

lets call the number X

Answer:

3*(2n+5) = n-5

Step-by-step explanation:

Step 1. Let n be the number.

Step 2. Let 2n+5 be the sum of twice a number and five

Step 3. Let 3(2n+5) be three times the sum of twice a number and five

Step 4 Let n-5 be five less than the number.

Step 5. Then using Steps 3 and 4, we have 3%282n%2B5%29=n-5 since three times the sum of twice a number and five is equal to five less than the number.

Step 6. Solving the equation in Step 5 yields the following steps

If the person has same neighbor to the left and right , Seating is considered same. By using circular permutation, the answer is 2.

A conceivable order or arrangement for a group of items, especially one among several alternatives.

The formula for permutation is:

\(P(n,r)= \frac {n!}{(n-r)!}\) (Permutation)

\(P(n)=(n-1)!\) (Circular permutation)

Total number of people=5

Since the orientation with same neighbor to left and right is considered same. We consider 3 people as 1 which represent a person with neighbors.

Total people used in circular permutation=3

P(3)= (3-1)!

=2!

=2.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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The cups of sugar needed is 2.5 cups.

The cups of flour needed is 3.75 cups

The cups of butter needed is 1.25 cups.

Given the information in the question, the ratio of sugar to flour to butter is 1 : 1.5 : 0.5

Cups of sugar needed = (ratio representing sugar / sum of ratios) x total number of cups

Sum of ratios = 1 + 1.5 + 0.5 = 3

Cups of sugar needed = (1 / 3) x 7.5 = 2.5 cups

Cups of flour needed = (ratio representing flour / sum of ratios) x total number of cups

Cups of flour needed = (1.5 / 3) x 7.5 = 3.75 cups

Cups of butter needed = (ratio representing butter / sum of ratios) x total number of cups

Cups of butter needed = (0.5 / 3) x 7.5 = 1.25 cups

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150 meters of wire is required to enclose the land 5 times.

To find the length of wire required to enclose the equilateral triangle plot of land, we need to calculate the perimeter of the triangle.

An equilateral triangle has all sides of equal length. Let's assume the length of each side of the triangle is "s".

The area of an equilateral triangle is given by the formula:

Area = (√3 / 4) * s²

Given that the area is 43.3 sq m, we can set up the equation:

43.3 = (√3 / 4) * s²

To find the length of each side, we solve for "s":

s² = (43.3 * 4) / √3

s = 9.999

Rounding to integer

s = 10 m

Now, to find the perimeter of the triangle, we multiply the length of one side by 3

Perimeter = 3s

Perimeter = 3 * 10

Perimeter = 20

Since the wire needs to enclose the land 5 times, we multiply the perimeter by 5

Total wire required = 5 * Perimeter

Total wire required ≈ 5 * 30

Total wire required ≈ 150 meters

Therefore, 150 meters of wire is required to enclose the land 5 times.

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Answer:

42%

Step-by-step explanation:

462÷1100×100=42%

Answer:

42 %

Step-by-step explanation:

to find percentage we have to multiply the number by 100

so , 462/1100×100

= 42%

To obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years, we can use the formula; P-hat = Number of adults who have donated blood / Total number of adults surveyed Substituting the values we have.

P-hat = 419 / 2298= 0.182 (rounded to three decimal places) Therefore, the point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years is 0.182.B) The requirements for constructing a confidence interval about P are satisfied if; np ≥ 10 and nq ≥ 10where p and q are the sample proportions, and n is the sample size. Substituting the values from the question ;

np = 2298(0.182) = 418.836

nq = 2298(0.818)

= 1879.164 Since np ≥ 10 and nq ≥ 10, the requirements for constructing a confidence interval about P are satisfied.

It was a definite and specific offer that could be accepted by anyone who met the requirements. It is an example of a unilateral offer since it was an open offer, anyone who agreed to the terms of the contract could have accepted it. Furthermore, it was a clear and unambiguous offer since it did not require any more clarification. Shawna and Beatrice, by virtue of their status as the offerees, had the option of accepting or rejecting the offer. The acceptance must meet the requirements of a valid contract. The acceptance must be communicated clearly and immediately. In addition, the acceptance must conform to the offer's terms. In Hyde v Wrench (1840), the court held that an acceptance must be unconditional and absolute and that if the acceptance is not in line with the terms of the offer, it is a counteroffer that terminates the original offer. Since Shawna and Beatrice had not yet responded to the offer, there was no acceptance of the contract. Therefore, there was no legal agreement between the parties as a contract must have both an offer and an acceptance in order to be considered valid.

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Answer: The unit value of a cubic centimeter (cm^3) is the same as the metric measurement of a milliliter (mL).

This is because 1 milliliter is equal to 1 cubic centimeter. In other words, if you have a cube that measures 1 centimeter on each side, its volume would be 1 cubic centimeter, which would also be equivalent to 1 milliliter of volume.

This relationship between cm^3 and mL is commonly used in scientific and medical measurements involving liquids and gases.

The unit value of a cubic centimeter (cc) is equivalent to one milliliter (mL) in the metric system. Both cubic centimeters and milliliters are used to measure volume, and their conversion is straightforward: 1 cc = 1 mL.

The metric system uses base units such as meters, liters, and grams, and applies prefixes like kilo-, centi-, and milli- to indicate larger or smaller units of measurement.
Cubic centimeters are often used to measure the volume of solid objects or the capacity of containers, while milliliters are more commonly used to measure the volume of liquids. However, both units represent the same volume and can be used interchangeably.
It is important to understand the difference between volume measurements and other metric measurements, such as length or mass. For instance, meters are used to measure length or distance, and grams are used to measure mass or weight. These units cannot be directly converted to cubic centimeters or milliliters, as they represent different physical properties.
In summary, a cubic centimeter (cc) is a unit of volume in the metric system that is equivalent to one milliliter (mL). Both units can be used to measure volume, and they have a simple conversion of 1 cc = 1 mL. Understanding the relationship between these units and other metric measurements is essential for accurately quantifying and comparing different physical properties.

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The probability that no two members of the family are assigned to the same station is 2/9.

From the information given, the probability that all three family members are assigned to the same station will be:

= 3 × (1/3) ³

= 1/9

Now, the probability that at most two family members are allocate to the same station will be:

= 1 - 1/9

= 8/9.

The total number of outcomes for the experiment is 3^3 = 27.

The number of outcomes in which no two members of the family are assigned to the same station is 3! = 6.

Therefore, the probability that no two members of the family are assigned to the same station is 6/27 = 2/9.

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Answer: \(\frac{2}{25}\) is the solution.

Step-by-step explanation;

Apply the property of fractions. Multiply the numerator with the numerator (1*2) and then the denominator with the denominator (5*5). This will give you: \(\frac{2}{25}\).

No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) \(n_{1}\)=628, \(p_{1}\)=7%, sample 2( 30 years old)\(n_{2}\)=2309, \(p_{2}\)=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

\(H_{0}:\)π1-π2=0

\(H_{1}:\)π1-π2≠0

α=0.05

Difference between proportions \(p_{1}-p_{2} =-0.04\)

\(p_{d}=0.07-0.11=-0.04\)

The pooled proportion needed to calculate standard error is:

\(p=(X_{1} -X_{2} )/(n_{1} +n_{2} )\)

=(44+254)/(628+2309)

=0.10146

The estimated standard error of difference between means is computed using the formula:

\(S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }\)

=\(\sqrt{0.101*0.899/628+0.101*0.899/2309}\)

=\(\sqrt{0.000143+0.00003}\)

=\(\sqrt{0.000173}\)

=0.01315

Z= Pd-(π1-π2)/\(S_{p_{1} -p_{2} }\)

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

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Question is incomplete as it also includes:

Significance level of 5%.

Answer:

32

Step-by-step explanation:

(a)The value of radians θ= π/2 or approximately 1.57 radians.(b) degrees θ= 90°.

Given vectors

u = ⟨2, 2⟩,

v = ⟨4, −4⟩.

We need to find the angle θ between them in radians and degrees.

The formula for finding the angle between two vectors is given by

θ = cos⁻¹(u·v/|u||v|),

where· represents the dot product of the two vectors and || represents the magnitude of the vector.

Let's begin by finding the dot product of the two vectors u and v.

u·v = 2(4) + 2(−4)

= 0

Now, let's find the magnitude of the vectors.

u = √(2² + 2²)

= √8

= 2√2

v = √(4² + (−4)²)

= √32

= 4√2

Putting these values in the formula, we get

θ = cos⁻¹(0/2√2 × 4√2)

= cos⁻¹(0/16)

= cos⁻¹(0)

= π/2 radians

Therefore, the angle θ between the vectors u and v in radians is π/2, which is approximately equal to 1.57 radians.

To convert radians to degrees, we need to multiply by 180/π.

θ = (π/2) × (180/π)

= 90°

Therefore, the angle θ between the vectors u and v in degrees is 90°.

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Combination is the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects, where order of selection is not important.

The formula for combination is given by:

C = N! / n!(N - n)!

where N is the set of objects

and n is the number of objects to be selected from N

example: If the order doesn't matter, how many ways can 3 girls be selected from a group of 5 girls?

C = N! / n!(N - n)!

where N = 5 and n = 3

C = 5! / 3!(5 - 3)!

C = 120/(6)(2)

C = 10

Hence, there are 10 ways to select 3 girls from a group of 5 girls.

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Answer:

y = 2x + 2

Step-by-step explanation:

y = mx+c

m = slope

c =y -intercept

Therefore, the required equation is:

y = 2x + c

Putting the point (0,4) in it as it lies on a line, we get:

4 = 2 + c

Therefore:

c = 2

So, y = 2x + 2

Brainlist pls!

The equation of a line that passes through the point (0,4) and has a gradient of 2 is y = 2x + 4

The equation of a line in point-slope form is expressed as:

y = y1 = m(x-x1)

Given the following

Slope m = 2

(x1, y1) = (0, 4)

Substitute

y - 4 = 2(x- 0)

y -4 = 2x

y = 2x + 4

Hence the equation of a line that passes through the point (0,4) and has a gradient of 2 is y = 2x + 4

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It is true, that the most level of confidence used in creating confidence intervals is 90%.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

We have given,

Given n = 93, u =24, x' = 23, α=5.5

z = x'- u / α(/√n) = 1.645

Hence the answer choice is true.

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