Consider the following probability distribution for a random variable :3, 4, 5, 6, 7
P(): 0.15, 0.10, 0.20, 0.25, 0.30
What is P(≤5.5)?

The probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.

The probability is a metric for determining how likely an event is to occur. It assesses the event's certainty. P(E) = Number of Favorable Outcomes / Number of Total Outcomes is the probability formula.

To calculate the probability of a Type I error, we first need to specify the null and alternative hypotheses.

Null hypothesis: The true mean weight of cereal in the boxes is equal to or greater than 520 grams.

Alternative hypothesis: The true mean weight of cereal in the boxes is less than 520 grams.

Let's denote the true mean weight of cereal in the boxes as μ. Under the null hypothesis, we have μ ≥ 520.

We can use the fact that the distribution of fills is normal with a known standard deviation of 3 grams to find the sampling distribution of the sample mean weight of cereal in a sample of size 3. Since we are sampling without replacement, we need to use the formula for a finite population:

Standard error of the sample mean = standard deviation / sqrt(sample size) * sqrt(N-n/N-1)

where N is the population size (the total number of boxes filled), n is the sample size (3 in this case), and N-1 is the degrees of freedom.

We know that the population mean is μ and the population standard deviation is 3 grams. We also know that the machine is set to put 523 grams in each box, so N (the population size) is equal to 515 / 523 times the number of boxes filled. Let's assume that the machine fills 10,000 boxes per day, so N = 9,856.

Plugging in the values, we get:

Standard error of the sample mean = 3 / √(3) * √(9,856-3/9,855) = 1.539 grams

Next, we need to find the critical value of the sample mean weight that separates the rejection region (when we reject the null hypothesis) from the acceptance region (when we fail to reject the null hypothesis).

Since the alternative hypothesis is one-tailed (we are only interested in the left tail), we can use a one-tailed t-test with a significance level of 0.05. The degrees of freedom is n-1 = 2.

Using a t-table or a calculator, we find the critical value to be -2.353.

Finally, we can calculate the probability of a Type I error as follows:

Probability of Type I error = P(reject null | null is true)

= P(sample mean < critical value | μ ≥ 520)

= P(z < (critical value - μ) / standard error of the sample mean | μ ≥ 520)

= P(z < (-2.353 - 520) / 1.539 | μ ≥ 520)

= P(z < -9.747 | μ ≥ 520)

= extremely small (close to 0)

Therefore, the probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.

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The can that will provide the largest volume is Can C, with a volume of 36π cubic inches.

To determine which can will provide the largest volume, we need to use the formula for the volume of a cylinder, which is V = πr^2h (where V is volume, r is radius, and h is height).

Using the formula, we can calculate the volumes of each can as follows:

- Can A: V = π(2)^2(6) = 24π cubic inches
- Can B: V = π(2.5)^2(5) = 31.25π cubic inches
- Can C: V = π(3)^2(4) = 36π cubic inches
- Can D: V = π(3.2)^2(3) = 30.528π cubic inches

Therefore, the can that will provide the largest volume is Can C, with a volume of 36π cubic inches.

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The mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

To determine the value of mean that will ensure that 98% of 6 oz cups will not overflow, we can use the following steps:

Calculate the z-score corresponding to the desired percentile (98%):

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 98th percentile is approximately 2.33.

Convert the given cup size (6 oz) to a z-score using the formula:

z = (x - μ) / σ

where x is the given cup size, μ is the mean fill in ounces, and σ is the standard deviation in ounces. Solving for μ, we get:

μ = x - z × σ

= 6 - 2.33 × 0.4

= 5.068

Therefore, the mean fill in ounces should be set at 5.068 to ensure that 98% of 6 oz cups will not overflow.

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Population growth rate is determined by the difference between the birth rate and the death rate, and the net migration rate.

This statement is incorrect. The rate of growth of a population cannot be calculated by simply measuring and subtracting a rate. Population growth rate is determined by the difference between the birth rate and the death rate, and the net migration rate.

To calculate the population growth rate, you need to use the following formula:

Population Growth Rate = (Birth Rate - Death Rate) + Net Migration Rate

The birth rate is the number of live births per 1000 people in a given population in a given year, and the death rate is the number of deaths per 1000 people in the same population and year. The net migration rate is the difference between the number of people immigrating to a country and the number of people emigrating from the same country.

By plugging in the values for the birth rate, death rate, and net migration rate, you can calculate the population growth rate.

A positive value indicates a population increase, while a negative value indicates a population decrease.

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Answer:

approximately 200.96 square inches.

Step-by-step explanation:

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Since the diameter of the pizza is 16 inches, the radius is half of the diameter, or 8 inches. Thus, the area of the top of the pizza is:

A = π(8)^2

A = 64π

Therefore, the area of the top of the pizza is 64π square inches. If you want a numerical approximation, you can use 3.14 as an approximation for π and calculate:

A ≈ 64(3.14)

A ≈ 200.96

So the area of the top of the pizza is approximately 200.96 square inches.

Answer:

about 201 sq.inches

Step-by-step explanation:

have a good day :)

Answer:

Answer is :

x=45.5

y=129.5

Sorry for bad handwriting

Answer:

x + 2x + 4 + y = 270, so 3x + y = 266

x + y + 5 = 180, so x + y = 175

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

2x = 91

x = 40.5, y = 134.5

The price of the headphones after the discount is $14.95

Madison bought headphones for $65

She used a coupon code of 30% discount

= (1-30/100)× (1 +10/100)

= (1-0.3) × (1 + 0.1)

= 0.7 × 1.1

= 0.77 × 65

= 50.05

The price after discount is

= 65-50.05

= $14.95

Hence the price after discount is $14.95

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The solution of the given differential equation is y(t) = [tex]e^{t}[/tex] cos(t) - sin(t) -t[tex]e^{t}[/tex]sin(t).

To solve the differential equation y'' - 2y'y = et, we will take the Laplace transform of both sides of the equation.

L{y'' - 2y'y} = L{et}

Using the linearity of the Laplace transform and the fact that

L{y''} = s²Y(s) - sy(0) - y'(0) and L{y'} = sY(s) - y(0), we get

s²Y(s) - sy(0) - y'(0) - 2[sY(s) - y(0)]Y(s) = 1/(s-1)

Substituting y(0) = 0 and y'(0) = 3, we get

s²Y(s) - 3s - 2sY²(s) = 1/(s-1)

Simplifying the equation and solving for Y(s), we get

Y(s) = [3s - 1 + 2/(s-1)]/[s² - 2sY(s)]

Multiplying both sides by (s² - 2sY(s)) and rearranging, we get

s²Y(s)² - 3sY(s) + 1 = 2Y(s)/(s-1)

Multiplying both sides by (s-1), we get

s²Y(s)² - 3sY(s) + (s-1) = 2Y(s)

Substituting Y(s) = U(s)/s, we get

sU(s)² - 3U(s) + (s-1) = 2U(s)

Simplifying and solving for U(s), we get

U(s) = (s-1)/(s² - 2s + 2)

To find the inverse Laplace transform of U(s), we will complete the square in the denominator of U(s)

s² - 2s + 2 = (s-1)² + 1

Using partial fraction decomposition, we can write

U(s) = [(s-1)/((s-1)²+1)] - [1/((s-1)²+1)]

Taking the inverse Laplace transform of both terms using Laplace transform table, we get

u(t) = [tex]e^{t}[/tex] cos(t) - sin(t)

Finally, taking the Laplace inverse of Y(s), we get

y(t) = L⁻¹{U(s)/s} = L⁻¹{[(s⁻¹)/((s⁻¹)²+1)]/s} - L⁻¹{[1/((s⁻¹)²+1)]/s}

Using the derivative property of the Laplace transform, we can simplify the second term as

L⁻¹{[1/((s⁻¹)²+1)]/s} = d/dt[L⁻¹{1/((s⁻¹)²+1)}] = d/dt[[tex]e^{t}[/tex] sin(t)]

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As we have proved that the formula F = A(F/A, i, n) = A[((1+i)ⁿ - 1)/i] and it  shows that the future value of an annuity can be calculated by multiplying the annuity payment by the sum of a geometric series with a common ratio.

Let's assume that the annuity has n payments, and each payment is denoted by A. The future value of the first payment is A(1+i)ⁿ-1. This is because the first payment will earn interest for n periods, which is represented by (1+i)ⁿ, and then we subtract the original payment A because it was not earning interest. Similarly, the future value of the second payment will be A(1+i)ⁿ-2, and so on.

Therefore, the total future value of the annuity will be the sum of all the future values of each payment. We can express this as:

F = A(1+i)ⁿ-1 + A(1+i)ⁿ-2 + ... + A(1+i)⁰

Now, let's try to simplify this expression. We can factor out A to get:

F = A[(1+i)ⁿ-1 + (1+i)ⁿ-2 + ... + (1+i)⁰]

Notice that the expression inside the brackets is a geometric series with a common ratio of (1+i)⁻¹ and n terms. We can use the formula for the sum of a geometric series to simplify this expression further. This formula is:

S = a(1-rⁿ)/(1-r)

where a is the first term, r is the common ratio, and n is the number of terms.

In our case, the first term is (1+i)ⁿ-1, the common ratio is (1+i)⁻¹, and there are n terms. Therefore, we can substitute these values into the formula to get:

S = (1+i)ⁿ-1[(1+i)⁻ⁿ - 1]/[(1+i)⁻¹ - 1]

Simplifying this expression gives:

S = [(1+i)ⁿ - 1]/i

Now, substituting this value of S into the expression we obtained earlier for F, we get:

F = A[(1+i)ⁿ-1 + (1+i)ⁿ-2 + ... + (1+i)⁰]

= A[(1+i)ⁿ - 1]/i

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Complete Question:

Given (F/P, i, N) = P(1+i)ⁿ, and (P/F, i, N) = F/(1+i)ⁿ, prove the following formula

F =  A(F/A, i , n)  = A [((1+i)ⁿ - 1) / i]

Influential scores, indicated by large residuals, have a significant impact on the regression line when removed from the data. These points, characterized by extreme x or y-values, can alter the slope and intercept of the regression line, emphasizing their importance in regression analysis.

The correct statements about influential scores are i and ii.

i. Influential scores have large residuals because they have a strong effect on the regression line. This means that if we remove an influential score from the data, it will significantly change the slope and intercept of the regression line.

ii. Removal of an influential score sharply affects the regression line because influential scores have a large impact on the regression line. If we remove an influential score, it will significantly change the slope and intercept of the regression line.

iii. This statement is not true. An x-value that is an outlier in the x-variable may be indicative of a point being influential, but a y-value that is an outlier in the y-variable can also be indicative of a point being influential.

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The probability of rolling a 9 is 1/9, or approximately 0.111.

To find the probability of rolling a 9 with a pair of standard, six-sided dice, we need to count the number of ways we can get a sum of 9 and divide it by the total number of possible outcomes.

There are four ways to get a sum of 9:

rolling a 3 on the first die and a 6 on the second die

rolling a 4 on the first die and a 5 on the second die

rolling a 5 on the first die and a 4 on the second die

rolling a 6 on the first die and a 3 on the second die

Each die has six possible outcomes, so there are 6 x 6 = 36 possible outcomes in total.

Therefore, the probability of rolling a 9 is 4/36 = 1/9, or approximately 0.111.

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The error interval for the number n as an inequality is 3.85 ≤ n ≤ 3.89

From the question, we have the following parameters that can be used in our computation:

A number is rounded 2 decimal places the result is 3.87

Represent the number with n

So, we have

n = 3.87 i.e. 3.86 to 3.88

To write the error interval of n, we do the following:

Calculate the difference between the intervals

difference = 3.88 - 3.86

difference = 0.02

Divide by 2

difference/2 = 0.01

So, we have

Error interval: 3.86 - 0.01 ≤ n ≤ 3.88 = 0.01

Evaluate

3.85 ≤ n ≤ 3.89

Hence, the error interval for the number n is 3.85 ≤ n ≤ 3.89

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There is not sufficient evidence to conclude that the average calorie content of chocolate chip cookies is greater than 110 calories at the 0.01 level of significance.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.

We will use a one-sample t-test to test the hypothesis.

Null hypothesis: The mean calorie content of chocolate chip cookies is 110 calories.

Alternative hypothesis: The mean calorie content of chocolate chip cookies is greater than 110 calories.

We will use a significance level of α = 0.01.

We first calculate the sample mean and sample standard deviation:

[tex]$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = \frac{1780}{15} = 118.67$[/tex]

[tex]$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2} = \sqrt{\frac{1}{14} \sum_{i=1}^{n} (x_i - 118.67)^2} = 26.899$[/tex]

The test statistic is calculated as:

[tex]$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} = \frac{118.67 - 110}{26.899/\sqrt{15}} = 1.84$[/tex]

Using a t-distribution table with 14 degrees of freedom and a one-tailed test at the 0.01 level, the critical value is 2.977.

Since the test statistic (1.84) is less than the critical value (2.977), we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to conclude that the average calorie content of chocolate chip cookies is greater than 110 calories at the 0.01 level of significance.

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Answer:

about 10 times

Step-by-step explanation:

60 times 1/6 (probability ) = 60/6 or 10

The indefinite integral of ∫(−6x⁶−4x⁵ + 5x −3)dx is -6x⁷/7 - 2x⁶/3 + 5x²/2 + 3x.

The solution of the  indefinite integral of ∫(−6x⁶−4x⁵ + 5x −3)dx, is calculated as follows;

Using the power rule, we can integrate each term of the given expression as follows:

∫(−6x⁶−4x⁵ + 5x −3)dx

= -6∫x⁶ dx - 4∫x⁵ dx + 5∫x¹ dx - 3∫dx

= -6(x⁷/7) - 4(x⁶/6) + 5(x²/2) - 3x

= -6x⁷/7 - 2x⁶/3 + 5x²/2 + 3x

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The length c of the triangle is 12.3 units.

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given.

c² = a²  + b²  -2ab cosC

where a, b and c are the lengths and A, B and C are the angles

Using the formula:

c² = a²  + b²  -2ab cosC

c² = 18²  + 13² - (2×18×13 × cos43)

c² = 150.73

c = √150.73

c = 12.3 units

Therefore, the length of c is 12.3 units.

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The mode, on the other hand, would not be a useful measure in this case, as it represents the most commonly occurring salary value.

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

For the salary of players on a professional baseball team, I would be more interested in looking at the mean.

The reason for this is that salaries of professional baseball players are typically not evenly distributed, with a few highly paid players at the top end and many players with lower salaries. The mean salary would provide an average value that takes into account the full range of salaries on the team, including the highly paid players.

The median salary would also be a reasonable measure to use in this case, as it represents the middle value of the distribution when the salaries are arranged in order from lowest to highest. However, it may not be as informative as the mean in capturing the full range of salaries and the distribution of highly paid players.

The mode, on the other hand, would not be a useful measure in this case, as it represents the most commonly occurring salary value, and it is unlikely that there would be many identical salaries among the players.

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Complete question is

For the following type of data set, would you be more interested in looking at the mean, median, or mode? state your reasoning.

The salary of players on a professional baseball team.

Let X = number of red Skittles in a fun size Skittles package. Then X is a random variable, which means its value is uncertain and subject to chance.

The possible values of X range from 0 (if there are no red Skittles in the package) to the total number of Skittles in the package (if all Skittles are red). The probability distribution of X describes the likelihood of each possible value occurring.

The terms you've mentioned relate to the number of red Skittles in a fun size package. In this context, X represents a discrete random variable, as it can take on a finite number of distinct values (i.e., the possible counts of red Skittles in each package).

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the mean  decrease and the standard deviation  increase.

To find the new mean and standard deviation, we need to remove the score of 30 from the original set of ten test scores and recalculate the mean and standard deviation based on the remaining nine scores.

First, we can find the sum of the original set of ten test scores:

10 * 50 = 500

Then, we can subtract the score of 30:

500 - 30 = 470

Now we can find the new mean based on the remaining nine scores:

470 / 9 = 52.22

Next, we can find the sum of the squared deviations from the new mean:

(52.22 - 50)^2 + ... + (52.22 - x)^2

where x is the score of the remaining student.

Since we don't know the value of x, we can't calculate the exact value of the standard deviation for the new set of nine scores. However, we do know that the standard deviation is a measure of how spread out the scores are, and removing a score that is below the mean (such as the score of 30) will tend to make the scores less spread out. Therefore, we can conclude that the standard deviation of the new set of nine scores would likely decrease.

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Travis ate 1/12 of the whole cake the next day

A fraction represents a part of a whole. In this case, the whole cake represents the whole, and the part that was eaten represents the fraction. When we say that 3/4 of the cake was eaten, it means that out of the whole cake, 3/4 or three-fourths of the cake was consumed.

Travis ate 1/3 of the remaining cake the next day.

This means that after 3/4 of the cake was eaten, there was 1/4 of the cake remaining. Travis ate 1/3 of that remaining 1/4 of the cake, which can be written as

=> 1/3 x 1/4.

To simplify this fraction, we multiply the numerators (1 x 1) and the denominators (3 x 4), giving us 1/12.

We can write this fraction as a percentage, which is 8.33%. To summarize, fractions are used to represent parts of a whole, and in this case, Travis ate 1/12 or 8.33% of the whole cake the next day.

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There are 1440 possible seating arrangements for eight people with X and Y sitting next to each other around the table.

To find the number of possible seating arrangements for eight people with X and Y sitting next to each other, follow these steps:

1. Treat X and Y as a single unit since they are seated next to each other. This means we now have 7 "units" to arrange (6 individual people and 1 unit of X and Y together).

2. Determine the number of arrangements for these 7 units around the table. Since the chairs don't matter and right and left are different, we use the formula for circular permutations: (n-1)! = (7-1)! = 6! = 720 possible arrangements.

3. Within the X and Y unit, there are 2 possible arrangements: X can be on the left of Y or on the right. So, we need to multiply the number of arrangements by the arrangements within the X and Y unit: 720 * 2 = 1440.

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Frequency analysis is not useful for understanding the relationships among multiple variables.

Frequency analysis is a statistical technique that involves counting the frequency of each value or category within a dataset. It is useful for analyzing categorical and continuous variables and determining the degree of item nonresponse. It can also help in locating outliers, as the frequencies of unusual values can be easily identified.

However, frequency analysis alone cannot provide insights into the relationships among multiple variables, as it only focuses on the distribution of individual variables. To understand the relationships among variables, more advanced statistical techniques such as correlation analysis or regression analysis need to be employed.

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Answer:

The number 1 can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer. This is only possible because 1 is a RATIONAL number.

Step-by-step explanation:

if it helped u please mark me a brainliest :-))

The THEORETICAL probability of choosing a vowel is 3/8 and the experimental probability is 36/75

From the question, we have the following parameters that can be used in our computation:

In the letters of the word, we have

Vowels = 3

Letters = 8

By calculation, the theoretical probability of choosing a vowel is

Theoretical probability = Vowels/Letters

So, we have

Theoretical probability = 3/8

Based on the experiment, we have

Vowels = 15+9+12 = 36

Letters = 8+15+7+5+20+20 = 75

So, we have

Experimental probability = 36/75

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We can expect to observe 14 complete interference fringes within the central diffraction peak.

The act of bending light around corners such that it spreads out and illuminates regions where a shadow is anticipated is known as diffraction of light. In general, since both occur simultaneously, it is challenging to distinguish between diffraction and interference.

The number of complete interference fringes within the central diffraction peak depends on the specific experimental setup, such as the distance between the slits and the screen, the distance between the slits, and the wavelength of the light being used.

However, we can use the following equation to calculate the number of interference fringes within the central diffraction peak:

N = (2d/a)(L/λ)

where N is the number of interference fringes, d is the distance between the slits, a is the width of the slits, L is the distance between the slits and the screen, and λ is the wavelength of the light being used.

Assuming that we have a double-slit setup and the distance between the slits and the screen is much larger than the slit width, we can simplify the equation to:

N = 2d/a

Given that d/a = 7, we can substitute this value into the equation to get:

N = 2(7) = 14

Therefore, we can expect to observe 14 complete interference fringes within the central diffraction peak.

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for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

For a two-tailed test at a 12.66% significance level, we need to find the critical value of z.

Step 1: Determine the significance level for each tail.
Since this is a two-tailed test, we need to divide the overall significance level (12.66%) by 2. This gives us 6.33% (or 0.0633 in decimal form) in each tail.

Step 2: Find the z-score associated with the given significance level.
To find the critical value of z, you can use a z-table or an online calculator. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

Using a z-table or calculator, you'll find that the z-score is approximately ±1.53.

So, for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53.

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Two numbers that each have exactly 16 factors two of which are 8 and 12 are 120 and 168

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Total number of factors of 120 = 16

Pairs of factors = (1, 120) (2,60) (3,40) (4,30) (5,24) (6,20) (8,15) (10,12)

Total Pairs of factor = 8

Hence the number of total factors = 16

Factors of 168 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168

Total number of factors of 168 = 16

Pairs of factors = (1, 168) (2,84) (3,56) (4,42) (6,28) (7,24) (8,21) (12,14)

Total Pairs of factor = 8

Hence the number of total factors = 16

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The "best-example" which shows the "safety-issue" related to large "manufacturing-business" is (b) broken machinery and flammable chemical containers are left sitting in "parking-lot".

The leaving of broken machinery and flammable chemical containers in the "parking-lot" poses a dangerous "safety-hazard" to both the employees and the surrounding community.

The broken machinery can cause accidents, while the flammable chemical containers can potentially leak or catch fire, leading to explosions and other dangerous situations. Therefore, it is crucial for the business to properly dispose of such hazardous waste and maintain a safe working environment.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Which example best shows a safety issue related to a large manufacturing business?

(a) The machines at the business are found to waste energy and cause excess costs.

(b) Broken machinery and flammable chemical containers are left sitting in the parking lot.

(c) Poverty has forced the neighborhood surrounding a business to become deserted.

(d) The flu season has caused a high rate of absent employees at the business.

The order would be DE < FD < EF. To order the sides of triangle ΔDEF from shortest to longest, you need to compare the lengths of the sides.

1. Determine the lengths of sides DE, EF, and FD.
2. Compare the lengths to find the shortest side.
3. Identify the next shortest side.
4. The remaining side will be the longest.

Once you have the side lengths, simply arrange them in ascending order (from shortest to longest) to answer your question. For example, if DE is 3 units, EF is 5 units, and FD is 4 units, the order would be DE < FD < EF.
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Answer:

x = 73°

Step-by-step explanation:

the inscribed angle x is half the measure of the central angle, that is

x = [tex]\frac{1}{2}[/tex] × 146° = 73°