consider a hypothesis test of the claim that eating an apple every day reduces the likelihood of developing a cold. identify the type i and type ii errors for this test. a type i error is accepting that there was a significant relationship between eating an apple every day and developing a cold. a type ii error is accepting that there was not a signficant relationship between eating an apple every day and developing a cold. a type i error is stating that the likelihood of eating an apple every day is reduced by developing a cold. a type ii error is stating that the likelihood of eating an apple every day is not effect by the development of a cold. a type i error is concluding that eating an apple every day reduces the likelihood of developing a cold, when in reality, eating an apple every day has no effect on the likelihood of developing a cold. a type ii error is concluding that eating an apple every day has no effect on the likelihood of developing a cold, when in reality, eating an apple every day actually reduces the likelihood of developing a cold. a type i error is concluding that eating an apple every day has no effect on the likelihood of developing a cold, when in reality, eating an apple every day reduces the likelihood of developing a cold. a type ii error is concluding that eating an apple every day effectively reduces the likelihood of developing a cold, when in reality, eating an apple every day does not effect the likelihood of developing a cold.

The zeroes of the function as required to be determined in the task content are; 0, 2, -4, 4.

It follows from the task content that the zeroes of the given function; f(x) = -5x (x - 2) (x² - 16) is to be determined.

To determine the zeroes; we have;

-5x = 0; x = 0

x - 2 = 0; x = 2

x² - 16 = 0; x² = 16; x = ± 4.

Ultimately, the zeroes of the function are; 0, 2, -4, 4.

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Answer:

75%

Step-by-step explanation:

We Know

Mandy collected 80 stamps last year.

Collected 140 stamps this year.
What was the percentage increase in her stamp collection?

We Take

(140 ÷ 80) x 100 = 175%

Then We Take

175 - 100 = 75%

So, the stamp collection increase by 75%

The null hypothesis states that the average age of community college students is equal to 24.6 years. The alternative hypothesis states that the average age of community college students is not equal to 24.6 years.

In other words, the null hypothesis assumes that the given average age is accurate, and the alternative hypothesis suggests that the given average age is either higher or lower than 24.6 years. These hypotheses can be tested through statistical analysis to determine if there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. This analysis can provide insights into the characteristics of the community college student population and inform decisions related to education policy and programs.

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The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.

Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.

The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:

TR = PQ - ST = 60 - 24 = 36 inches

The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:

UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches

So, the dimensions of section B are 36 inches by 48 inches.

Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.

The area of rectangle B is the product of its length and breadth, which is:

Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches

The area of rectangle WVTX is the product of its length and breadth, which is:

Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches

The area of rectangle PQRS is the product of its length and breadth, which is:

Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches

Therefore, the area of the piece of sheet metal after both sections are cut and removed is:

Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX

= 8640 - (1728 + 576)

= 8640 - 2304

= 6336 square inches

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Answer:

Area of the semi-circle:

(1/2)π(2^2) = 2π = 6.28 square centimeters

Area of the triangle:

(1/2)(4)(5.7) = 11.4 square centimeters

Total area:

6.28 + 11.4 = 17.68 square centimeters

Answer:

If not choose all that apply, technological process will shift the PPC right (outwards)

Step-by-step explanation:

The production possibilities curve represents the maximum amount of goods and services that a country can produce with its limited resources. It is a graphical representation of the trade-offs a country must make between producing one good or service over another. Any factor that can increase production will shift the curve outward, indicating an increase in the maximum amount of goods and services that can be produced.

An increase in the production of investment goods will shift the curve outward because it will increase the amount of capital goods that can be used to produce other goods and services. Investment goods are items like machinery, equipment, and infrastructure that are used to produce other goods and services. By increasing the production of investment goods, a country can increase its productive capacity, allowing it to produce more goods and services in the future.

An increase in the production of consumer goods will not shift the curve outward because it does not increase the country's productive capacity. Consumer goods are items that are consumed immediately, like food, clothing, and electronics. While an increase in the production of consumer goods can lead to short-term economic growth, it will not increase the country's long-term productive capacity.

Technological progress, on the other hand, will shift the production possibilities curve outward. Technological progress refers to advancements in technology that increase productivity, reduce costs, and improve efficiency. By adopting new technologies, a country can produce more goods and services with its existing resources, allowing it to shift its production possibilities curve outward.

In conclusion, an increase in the production of investment goods and technological progress will shift the production possibilities curve outward, while an increase in the production of consumer goods will not.

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The correct answer is B. For a 95% confidence level, the z* value should be calculated using qnorm(0.975).

The proposed solution to construct a 95% confidence interval for the population proportion has several errors. Let's review each of them in detail:

A. phat was already provided, so dividing that value by the sample size is incorrect:

This is incorrect because phat represents the sample proportion, which is the point estimate of the population proportion. The sample proportion alone is not enough to estimate the variability of the sample proportion, which is required to construct a confidence interval. Therefore, we need to divide phat by the sample size to obtain the standard error of the sample proportion.

B. For a 95% confidence level, the z* is calculated by qnorm(0.95):

This is incorrect because a 95% confidence level corresponds to a 1.96 standard error for a two-tailed test, not a 1.645 standard error. Therefore, we need to use qnorm(0.975) or qnorm(1 - 0.025) to find the z* value.

C. You cannot use "phat" in an R Studio command. The decimal must be written:

This is incorrect because "phat" is a valid R Studio command that represents the sample proportion. However, it is important to define this variable beforehand to avoid any errors.

D. You cannot have negative values as one of the limits on your interval. This should be made positive:

This is correct. A confidence interval cannot have negative values as limits since proportions must be between 0 and 1. Therefore, we need to take the absolute value of the lower limit.

E. The proposed solution is correct:

This is incorrect, as discussed above. The correct solution should use the formula:

phat +/- z* * sqrt(phat*(1-phat)/n)

where phat = 0.43, n = 200, and z* is the critical value of the standard normal distribution corresponding to a 95% confidence level, which is approximately 1.96. Therefore, the correct 95% confidence interval is:

0.43 +/- 1.96 * sqrt(0.43*(1-0.43)/200) = (0.369, 0.491).

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Answer:The answer is $911.68.

Step-by-step explanation:

Answer:

we will need 20 glass panels to cover the walls of the greenhouse with 5' x 4' glass panels.

Step-by-step explanation:

First, let's calculate the total wall area:

2 walls (10' x 8') = 160 sq. ft.

2 walls (15' x 8') = 240 sq. ft.

Total wall area = 400 sq. ft.

Next, let's calculate the total floor area:

15' x 5' = 75 sq. ft. (total floor area)

75 sq. ft. / 2 = 37.5 sq. ft. (floor area for tomatoes)

To cover the walls with glass panels, we need to divide the total wall area by the area of each glass panel:

Glass panel area = 5' x 4' = 20 sq. ft.

400 sq. ft. (total wall area) / 20 sq. ft. (area of each glass panel) = 20 glass panels

Therefore, we will need 20 glass panels to cover the walls of the greenhouse with 5' x 4' glass panels.

The number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.

To find the number of different simple random samples of size 4 that can be obtained from a population whose size is 48, we can use the combination formula. The combination formula is written as:

C(n, k) = n! / (k!(n-k)!)

where n is the population size (48), k is the sample size (4), and ! denotes a factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).

So, in this case:

C(48, 4) = 48! / (4!(48-4)!)

C(48, 4) = 48! / (4!44!)

C(48, 4) = (48 × 47 × 46 × 45) / (4 × 3 × 2 × 1)

C(48, 4) = 194580

Therefore, the number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.

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The PMT or monthly contribution is pegged at $764.57

Individuals employ a financial tactic known as a retirement plan to accumulate and invest funds, which will enable them to have access to revenue during their retirement period.

The aim of this approach is to certitude that these individuals possess ample income to maintain their standard of living and fulfil any additional monetary requirements once they terminate employment.

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Step-by-step explanation:

Area of a triangle = 1/2 base leg  * height

                area =  1/2 * 9 * 6 = 27 cm^2

Answer: 27 cm²

Step-by-step explanation:

     To find the area of the base of this right triangular prism we can use the area formula for a triangle. Make sure you are using the correct base (b) and height (H) in the formula that apply to the base triangle.

Given:

   A = [tex]\frac{bH}{2}[/tex]

Substitute known values:

   A = [tex]\frac{(9\;cm)(6\;cm)}{2}[/tex]

Multiply:

   A = [tex]\frac{54\;cm^2}{2}[/tex]

Divide:

   A = 27 cm²

The use of regression modeling in retail analytics can help businesses make data-driven decisions that ultimately lead to increased profits and growth.

Based on the information given, it seems that the large sports supplier is interested in predicting the annual revenue of a particular store based on various factors, such as population, promotion expenditure, and distance from the city center. This is a common approach in retail analytics, where regression models are often used to predict sales or revenue based on different variables.

By constructing a regression model, the sports supplier can gain valuable insights into which factors are most strongly associated with revenue, and how they can optimize their operations to increase sales. For example, they may find that stores located closer to the city center tend to have higher revenue, or that increased promotion expenditure leads to a greater increase in revenue in smaller towns.

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The range for the scores is 1.0 (from 9.9 to 8.9). The range is the difference between the highest and lowest numbers in a set of numbers. In this case, the highest score is 9.9 and the lowest score is 8.9, so the range is 1.0.

In mathematics, the range of a function can refer to one of two similar terms:

the common area of ​​the function

The image of the function

Given two groups X and Y, the binary relation f between X and Y is a (exact) function (X to Y), if there is a y in Y for every x in X, so f is associated with y. The sets X and Y are called the area of ​​f and the common domain, respectively.

The range is a measure of dispersion in a set of numbers. To find the range, you need to subtract the lowest score from the highest score. In this case, the scores for the Olympic gymnast are: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8.

First, identify the highest and lowest scores:
Highest score: 9.9
Lowest score: 8.9

Next, subtract the lowest score from the highest score:
Range = 9.9 - 8.9

The range for the scores is 1.0 (9.9 to 8.9).

Your answer: 1.0 (9.9 to 8.9)

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Math is not relevant to the research question as it is not directly related to smartphone ownership. Verbal, Credits, Year, Exercise, Sleep, Veg, and Cell are also not relevant to the research question as they do not provide information on smartphone ownership or the proportion of smartphone owners at a specific university. The relevant variable in this research question is smartphone ownership.

The relevant variable in this research question is smartphone ownership. This variable is quantitative as it involves measuring the proportion of smartphone owners at a specific university. The proportion of smartphone owners can be expressed as a percentage or a decimal value, which are both quantitative measurements.

Categorical variables are not relevant to this research question as they do not provide information on the proportion of smartphone owners. Categorical variables involve categorizing data into groups or categories, such as gender or race, which are not directly related to smartphone ownership.

In summary, the only relevant variable in this research question is smartphone ownership, which is a quantitative variable.

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The upper bound should be entered in cell A29 and the lower bound in cell A30.

Assuming the data is in cells A1 to A15, the Excel functions to calculate the required statistics are:

Mean (average) waiting time:

= AVERAGE(A1:A15)

Result: This will return the average waiting time of the 15 customer phone calls.

Median waiting time:

= MEDIAN(A1:A15)

Result: This will return the median waiting time of the 15 customer phone calls.

Standard deviation of waiting time:

= STDEV(A1:A15)

Result: This will return the standard deviation of the waiting time of the 15 customer phone calls.

95% Confidence Interval of the mean waiting time:

Lower bound: = AVERAGE(A1:A15) - (T.INV(0.05,14)*STDEV(A1:A15)/SQRT(15))

Upper bound: = AVERAGE(A1:A15) + (T.INV(0.05,14)*STDEV(A1:A15)/SQRT(15))

Result: This will return the lower and upper bounds of the 95% confidence interval of the mean waiting time of the 15 customer phone calls.

The upper bound should be entered in cell A29 and the lower bound in cell A30.

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The probability that the batch gets rejected is 0.445 or 44.5%.

The probability that the batch gets rejected can be calculated using the binomial distribution. Let's define the following terms:

n = number of samples tested = 13
p = proportion of defective doses in the batch = 10/203
q = proportion of good doses in the batch = 1 - p

Now we can calculate the probability of finding k defective doses in a sample of size n as:
P(k defective doses)[tex]= (n choose k)(p^k)q^{(n-k)}[/tex]

To calculate the probability that the batch gets rejected, we need to find the probability of finding at least one defective dose in the sample:

P(rejecting the batch) = P(1 or more defective doses) = 1 - P(0 defective doses)

P(0 defective doses) [tex]= (13 choose 0)(p^0)q^{13}= q^{13} = (\frac{193}{203})^{13}[/tex]

P(rejecting the batch) = [tex]1 - (\frac{193}{203})^{13} =[/tex]=0.445 or 44.5%

Therefore, the probability that the batch gets rejected is 0.445 or 44.5%.

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In part (d), we had to calculate the probability of choosing 4 out of the 18 remaining students because we know that Bob is not chosen.

The probability that Billy is among the 5 selected students is given by the number of ways Billy can be selected out of 20 students, divided by the total number of ways to select 5 students out of 20:

P(Billy is selected) = 1/ C(20,5) = 1/15504

b. The probability that both Billy and Bob are chosen among the 5 students is given by the number of ways both Billy and Bob can be selected out of 20 students, divided by the total number of ways to select 5 students out of 20:

P(Billy and Bob are selected) = C(2,2) * C(18,3) / C(20,5) = 816/15504 = 0.0526

c. The probability that Bob or Billy is chosen among the 5 students is given by the sum of the probabilities of Billy being chosen and Bob being chosen, minus the probability of both Billy and Bob being chosen (to avoid double-counting):

P(Bob or Billy is selected) = P(Billy is selected) + P(Bob is selected) - P(Billy and Bob are selected)

= 1/ C(20,5) + 1/ C(20,5) - 816/15504

= 2/15504 + 2/15504 - 816/15504

= 168/15504 = 0.0108

d. The probability that Bob is not chosen and Billy is chosen among the 5 students is given by the number of ways to choose 4 students out of the 18 remaining students, multiplied by the number of ways to choose Billy from those 4 students, divided by the total number of ways to choose 5 students out of 20:

P(Bob is not chosen and Billy is chosen) = C(18,4) * C(1,1) / C(20,5) = 3060/15504 = 0.1971

Explanation: In order to calculate the probabilities, we used the formula for the probability of a combination, which is the number of favorable outcomes divided by the total number of possible outcomes. In part (c), we had to subtract the probability of both Billy and Bob being chosen to avoid double-counting. In part (d), we had to calculate the probability of choosing 4 out of the 18 remaining students because we know that Bob is not chosen.

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Answer:

  (c)  They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

Step-by-step explanation:

You want to know the relation between the lines ...

These equations can be put into standard form by removing the common factor from the coefficients:

We see that the equations give the same line. That is ...

  (c)  They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

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The arrow would hit the ground after 2.25 seconds.

The height from which this arrow was shot is 18 feet.

Based on the information provided, we can logically deduce that the height (h) in feet, of this arrow above the​ ground is related to time by the following quadratic function:

h(t) = (1 + 2t)(18 - 8t)

Generally speaking, the height of this arrow would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = (1 + 2t)(18 - 8t)

(18 - 8t) = 0

8t = 18

By dividing both sides of the equation by 8, we have:

Time, t = 18/8

Time, t = 2.25 seconds.

Next, we would determine the height from which this arrow was shot by substituting time (t) with zero;

h(0) = (1 + 2(0))(18 - 8(0))

h(0) = 1(18)

h(0) = 18 feet.

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Complete Question:

The height in feet of an arrow is modeled by the equation h(t) = (1+2t)(18-8t),

where t is seconds after the arrow is shot.

a. When does the arrow hit the ground? Explain or show your reasoning.

b. From what height is the arrow shot? Explain or show your reasoning.

the 95% confidence interval for the mean prediction accuracy of nonpsychology students is (0.60 - 1.77, 0.60 + 1.77), which is approximately equal to (−1.17, 2.37).

To calculate the 95% confidence interval for the mean prediction accuracy of nonpsychology students, we can use the following formula:

CI = X  ± t(α/2, df) × (SE)

where:
- X  is the sample mean (0.60 in this case)
- t(α/2, df) is the t-value for the given level of significance (α), degrees of freedom (df) and two-tailed test. For a 95% confidence interval with df = n - 1 = 14, the t-value is 2.145
- SE is the estimated standard error of the mean (2.696 in this case)

Substituting the given values into the formula, we get:

CI = 0.60 ± 2.145 × (2.696/√15)

Simplifying the expression, we get:

CI = 0.60 ± 1.77

Therefore, the 95% confidence interval for the mean prediction accuracy of nonpsychology students is (0.60 - 1.77, 0.60 + 1.77), which is approximately equal to (−1.17, 2.37).

Note that the confidence interval includes the population mean of 75%, which suggests that the psychologist's prediction is correct - nonpsychology students are likely to do worse than psychology students at predicting the outcomes of psychology experiments. However, the confidence interval is quite wide, indicating that there is considerable uncertainty in our estimate of the mean accuracy for nonpsychology students based on this small sample size.

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Answer:

Ya

Step-by-step explanation:

Yes, the maximum likelihood estimator (MLE) of the standard deviation (sigma) in a normal distribution is an unbiased estimator. This means that on average, the MLE will provide an estimate of the true standard deviation that is equal to the true value. However, it's important to note that the MLE is not always the most efficient estimator, meaning that there may be other estimators that have lower variance and are therefore more precise.

Yes, the Maximum Likelihood Estimator (MLE) of σ (the standard deviation) is an unbiased estimator for a random sample from a normal distribution with mean 0 and standard deviation 10. The reason is that the MLE of σ is based on the sample variance, which is an unbiased estimator of the population variance. Since the population variance is σ^2, the MLE of σ is also an unbiased estimator of σ.

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The area of the circle is approximately 55.39 square inches.

The circumference of the circle is approximately 26.38 inches.

The area of a circle = πr²

The circumference of the circle = 2πr

Where, r is the radius of the circle, which is half of the diameter of the circle.

Therefore, we have:

radius (r) = 8.4/2 = 4.2 inches

π = 3.14

Thus:

The area of the circle = πr² = 3.14 * 4.2²

Area ≈ 55.39 square inches [nearest hundredth]

The circumference of the circle = 2πr = 2 * 3.14 * 4.2

Circumference ≈ 26.38 inches.

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Answer:

-------------------------------

Volume of cylinder formula:

We are given values:

Substitute and calculate the volume:

Answer: 36 quarts

Step-by-step explanation:

pretty much just do 9 * 4 qts

hope this helped!!

Answer: Parker has 36 Quarts of water.

We are given the following:

We are asked to find:

This question strictly revolves the around the conversion of units. In other words, in order to answer this question, we must know how many quarts are in a gallon.

Fortunately, we know that 4 quarts = 1 gallon.

Since Parker possesses 9 gallons of water, we would do [tex]4*9=36[/tex]. Arriving us at our answer of 36 quarts of water.

Parker has 36 quarts of water.

Answer:

Step-by-step explanation:

To find the optimal ticket price that will maximize revenue, we need to determine the price point where the increase in revenue from selling each ticket at a higher price is greater than the decrease in revenue from selling fewer tickets due to the higher price.

Let's start by calculating the current revenue generated at the current ticket price of $6.00:

Current revenue = 1800 x $6.00 = $10,800

Now, we need to determine the effect of increasing ticket prices by $0.50 on the number of tickets sold:

For each $0.50 increase in ticket price, 100 fewer people will attend. So, for a $0.50 increase, the new ticket price will be $6.50, and the number of attendees will be:

1800 - 100 = 1700

For a $1.00 increase, the new ticket price will be $7.00, and the number of attendees will be:

1700 - 100 = 1600

And so on.

We can create a table to calculate the revenue at different price points:

Ticket Price Number of Tickets Sold Revenue

$6.00                 1800                                $10,800

$6.50                 1700                                $11,050

$7.00                 1600                          $11,200

$7.50                 1500                                $11,250

$8.00                  1400                          $11,200

$8.50                  1300                          $11,050

$9.00                  1200                          $10,800

As we can see from the table, the optimal ticket price that will maximize revenue is $7.50, where the revenue is $11,250. Beyond this point, the decrease in attendance outweighs the increase in ticket price, resulting in a decrease in revenue.

Therefore, the owner should increase the ticket price to $7.50 to maximize revenue.

The matrices [T]β and [T]γ, which represent a linear transformation T with respect to ordered bases β and γ in vector space V, are similar.

To prove that [T]β and [T]γ are similar, we need to show that there exists an invertible matrix P such that [T]γ = P⁻¹ [T]β P.

Since β and γ are ordered bases of V, there exists an invertible change of basis matrix Q such that γ = βQ.

Then, we can write [T]γ = [T]βQ(Q⁻¹) = P⁻¹[T]β P where P = Q^(-1).

Therefore, [T]β and [T]γ are similar, and the matrix P is the change of basis matrix from β to γ.

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The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.

Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:

p = 0.716

Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Substituting in the values of n and p, we get:

σ = sqrt(9 * 0.716 * (1 - 0.716))

σ = 1.168

Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

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H0: p1 = p2 (the proportions are equal)

Ha: p2 > p1 (the proportion in Population 2 exceeds that in Population 1)

Hypothesis testing involves making a statement about a population parameter (such as a mean or a proportion) based on a sample of data. The statement is made in the form of two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).

The null hypothesis is the default assumption that there is no significant difference between the two populations being compared. In this case, the null hypothesis would be that the proportion found in Population 2 is not significantly different from the proportion found in Population 1.

The alternative hypothesis is the statement we are trying to support with our evidence. In this case, the alternative hypothesis would be that the proportion found in Population 2 exceeds the proportion found in Population 1.

So, in step 1 of hypothesis testing, we would state the null and alternative hypotheses as follows:

H0: p1 = p2 (the proportions are equal)

Ha: p2 > p1 (the proportion in Population 2 exceeds that in Population 1)

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Means that we are 90% confident that the true proportion of masks with lenses that pop out at 250° is between 7.6% and 32.4%.

We can use the formula for a confidence interval for a proportion:

CI = p ± z*sqrt(p(1-p)/n)

where:

p = sample proportion = 11/55 = 0.2

z = the z-score for a 90% confidence level, which is 1.645

n = sample size = 55

Plugging in the values, we get:

CI = 0.2 ± 1.645*sqrt(0.2(1-0.2)/55)

CI = 0.2 ± 0.124

Therefore, the 90% confidence interval for the true proportion of masks of this type whose lenses would pop out at 250° is (0.076, 0.324). This means that we are 90% confident that the true proportion of masks with lenses that pop out at 250° is between 7.6% and 32.4%.

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The value of x is equal to 17.

In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the triangle BHY is equal to the measure of angle x (∠NYB);

m∠BHY + m∠HBY = m∠NYB

(2x + 7)° + (8x - 18)° = (4x + 91)°

10x - 11 = 4x + 91

10x - 4x = 91 + 11

6x = 102

x = 102/6

x = 17.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.