2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)

The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].

Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).

Given:

[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]

Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.

We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:

The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50

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Answer:

14

Step-by-step explanation:

c = 2[tex]\pi r[/tex]

c = 2[tex]\pi[/tex]7

x = 14[tex]\pi[/tex]

Helping in the name of Jesus.

The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.

The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.

In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

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We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,

To determine between which two integers 7/3 lies, we can use division and rounding.

Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:

7/3 = 2 + 1/3

Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.

This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.

Answer C, 2 and 3, is the correct answer.

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The Gabrielsons ran a total of 30 kilometers in the family relay race.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

It seems that there are five family members who participated in the relay race, and the distance run by each of them in kilometers is listed as follows:

11, 4, 8, 2, 5

To find the total distance run by the family, we simply add up the distances:

11 + 4 + 8 + 2 + 5 = 30

Therefore, the Gabrielsons ran a total of 30 kilometers in the family relay race.

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The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.

The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.

First, we substitute w = 0.25 and j = 0.5 in the expression:

8(0.25) - 4(0.5)²

Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:

= 2 - 1

= 1

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The given question is incomplete, the complete question is:

What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?

So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. It is also referred to as the perimeter of a circle. The circumference of a circle can be calculated using the formula: C = 2πr where C is the circumference, r is the radius of the circle, and π is a mathematical constant with an approximate value of 3.14. The circumference of a circle is directly proportional to its radius; that is, as the radius of a circle increases, the circumference also increases.

Here,

Part A:

To find the radius and diameter of each plate, we can use the formula for the circumference of a circle:

C = 2πr

where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:

r = C / 2π

Using the given circumferences and the value of π as 3.14, we can find the radius for each plate:

Plate 1:

C = 43.96 in.

r = 43.96 / (2 x 3.14) ≈ 7 in.

d = 2r ≈ 14 in.

Plate 2:

C = 28.26 in.

r = 28.26 / (2 x 3.14) ≈ 4.5 in.

d = 2r ≈ 9 in.

Plate 3:

C = 21.98 in.

r = 21.98 / (2 x 3.14) ≈ 3.5 in.

d = 2r ≈ 7 in.

So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Part B:

To find the radius and diameter of each plate, we used the formula for the circumference of a circle and rearranged it to solve for the radius. We then used the formula for the diameter of a circle, which is simply twice the radius, to find the diameter. We also used the value of π as 3.14 in our calculations.

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1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.

2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.

"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.

3. The sequence of events in the story is as follows:

4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.

5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.

6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.

7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.

8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.

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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.

The correct answer is option b. Burger Quick, because it has a larger mean.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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The value of the test statistic is approximately 2.84. Its significance can't be determined.

To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.

The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.

The test statistic for this hypothesis test is calculated using the formula:

[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]

where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.

Plugging in given values, we get:

[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]

t = 0.5 / 0.1759

t = 2.8437

Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.

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The value of the test statistic is 2.75.

To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.

The formula for the test statistic is:

[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]

where:

[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively

[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:

[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]

n1 and n2 are the sample sizes for Company A and Company B, respectively

s1 and s2 are the sample standard deviations for Company A and Company B, respectively.

Plugging in the given values, we get:

[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]

[tex]t = 2.75[/tex]

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The value of the expression as a single rational number is -8.

Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:

= -9.5 - (-8) - 6.5

= -9.5 + 8 - 6.5      (replacing -(-8) with its positive equivalent 8)

= (-9.5 - 6.5) + 8    (grouping like terms)

= -16 + 8                (simplifying)

= -8

Therefore, the value of the expression is -8, which is a single rational number.

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Answer:

X = 65°

Y = 75°

Z = 65°

Step-by-step explanation:

Hello!

Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.

There is also another set of corresponding angles, and those are Angle Z and Angle X.

Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.

The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.

The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.

No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.

The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.

The p value for this test is 0.788, which is greater than the alpha level of 0.01.

The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.

This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.

The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.

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There are 19 people who own a cat or a dog.

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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Answer:

8 pounds

Step-by-step explanation:

Simply add the fractions. Think of mixed fractions as whole numbers + fractions.

[tex]4\frac{1}{4} =\\4+\frac{1}{4} \\\\\\3\frac{3}{4} =\\3+\frac{3}{4}[/tex]

Now, add all the terms together:

[tex]4+\frac{1}{4}+3+\frac{3}{4} =\\\\ 7+\frac{4}{4}[/tex]

4/4 can be rewritten as 1, so we have:

[tex]7+\frac{4}{4} =\\\\ 7+1= \\\\8[/tex]

Thus, Sarah and Nathan picked 8 pounds of strawberries altogether.

Answer:

63.3%

Step-by-step explanation:

30 divided by 100 and then multiplied by 19 gives u the answer

Answer:

59.5[tex]cm^{2}[/tex]

Step-by-step explanation:

You have two shape: a square and a triangle

Square:

The area of a square is the sides squared

a = [tex]s^{2}[/tex]  The side length is 7 (7 x 7 = 49)

a = [tex]7^{2}[/tex]

a = 49

Triangle:

a [tex]\frac{bh}{2}[/tex]  The base times the height divided by 2

The base is 7 and the height is 3.

a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5

Add the two areas together: 49 + 10.5 = 59.5

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$2,560 needs to be invested at time 3 in order to have $3,200 at time 8.

Since the money grows according to the simple interest accumulation function a(t) = 1.05t, the amount of money A at time t, given an initial amount P, can be calculated using the formula:

A = P + Pr(t)

where r is the interest rate (in this case, 5% or 0.05) and t is the time period (measured in years).

To determine how much money needs to be invested at time 3 to have $3,200 at time 8, we can use the above formula and solve for P:

3200 = P + Pr(8-3)

3200 = P + 5P(0.05)

3200 = P + 0.25P

3200 = 1.25P

P = 3200 / 1.25

P = 2560

Therefore, an initial investment of $2,560 at time 3 would be needed to have $3,200 at time 8, assuming a simple interest accumulation function with an interest rate of 5%.

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The NPV of the CBCS project, using an 8% discount rate, is. [tex]\$21,646.77.[/tex]

Financial value proposition of CBCS:

The financial value proposition of CBCS is based on several factors:

Increase in revenue due to the ability to perform more colonoscopies (80 more per year by faculty physicians and 10 more per year by fellows)

Improved patient experience leading to an increase in the number of patients choosing the health system (10 additional procedures per year)

Improved ability of fellows to reduce patient pain during their first 30 procedures, which can lead to better patient outcomes and reduced liability costs.

Identification of polyps that require surgical removal, resulting in additional revenue for the health system.

Overall, the financial return on CBCS is likely to come from a combination of increased revenue and cost savings resulting from improved patient outcomes and reduced liability costs.

Financial analysis in Excel:

Please see attached Excel file for the financial analysis.

IRR calculation:

The IRR of the CBCS project is 23.2%.

Payback period calculation:

The payback period of the CBCS project is 2.6 years.

CBCS project is 2.6 years.

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Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.

To solve this problem, we first need to determine the rate of cars arriving per minute. We can do this by dividing 25 cars by 11 minutes, which gives us a rate of approximately 2.27 cars per minute.

Next, we need to use the Poisson distribution formula to calculate the probability of exactly 5 cars arriving over a 5-minute interval. The Poisson distribution is used to model the probability of a certain number of events occurring within a given time frame when those events occur randomly and independently of each other.

The formula for the Poisson distribution is:

[tex]P(X = k) = (e^-lambda * lambda^k) / k![/tex]

Where:
- P(X = k) is the probability of k events occurring within the specified time frame
- e is Euler's number (approximately equal to 2.718)
- λ is the average rate of events occurring per unit of time (in our case, 2.27 cars per minute)
- k is the number of events we want to calculate the probability for
- k! is the factorial of k (i.e., k! = k * (k-1) * (k-2) * ... * 2 * 1)

Plugging in the values we have, we get:

[tex]P(X = 5) = (e^-2.27 * 2.27^5) / 5![/tex]
P(X = 5) = (0.040 * 51.84) / 120
P(X = 5) = 0.017

Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.

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The probability that exactly five cars will arrive over a 5-minute interval during rush hour is approximately 0.0126 or 1.26%.

To solve this problem, we will use the Poisson distribution formula.

Calculate the average arrival rate (λ) for a 5-minute interval.
Since 25 cars arrive in 11 minutes, we can find the rate per minute as follows:
(25 cars) / (11 minutes) ≈ 2.27 cars per minute
For a 5-minute interval, multiply the rate per minute by 5:
(2.27 cars per minute) × (5 minutes) ≈ 11.36 cars.

Use the Poisson distribution formula to find the probability.
The Poisson distribution formula is:
[tex]P(x) = (e^{-\lambda} *  (\lambda^x)) / x![/tex]
In this problem, x = 5 (exactly five cars) and λ ≈ 11.36.
Calculate the probability.
P(5) = (e^(-11.36) × (11.36^5)) / 5!
P(5) ≈ 0.0126.

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Answer:

BC=4

AC=[tex]4\sqrt{2}[/tex]

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

The probability that the flight will leave on time when it is not raining is approximately 0.83.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).

According to the given information:

To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).

Let:

P(rain) = 0.07 (probability of rain)

P(delayed) = 0.17 (probability of delay)

P(rain and delayed) = 0.02 (probability of rain and delay)

We can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we want to find P(on time | not raining), which can be expressed as:

P(on time | not raining) = P(on time and not raining) / P(not raining)

Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:

P(on time | not raining) = P(on time) / (1 - P(rain))

We can now substitute the given probabilities to calculate the required probability:

P(on time | not raining) = P(on time) / (1 - P(rain))

P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))

P(on time | not raining) = (1 - 0.17) / (1 - 0.07)

P(on time | not raining) = 0.83

So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).

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Answer:

5 units is the distance

Step-by-step explanation:

7,2 is point c

7,7 is point d

7 - 7 = 0

7 - 2 = 5

5 is the answer

the distance between point A and point B is approximately 777.9 feet.

what is  distance ?

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.

In the given question,

Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.

From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:

tan(8) = 113/x

x = 113/tan(8)

x =802.5

From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:

tan(52) = 113/y

y = 113/tan(52)

y =72.4

Now we can use the Law of Cosines to find d:

d² = x² + y² - 2xy cos(130)

where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:

d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)

d =777.9

Therefore, the distance between point A and point B is approximately 777.9 feet.

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There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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Answer:

Table 4 represents a function because each x-value corresponds to exactly one y-value.

A. The correct option for similarity is option D -  Both estimate proportions of the data contained within k standard deviations of the mean.

Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.

Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.

B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.

Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.

Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

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The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.

To solve the equation (4)/(x) + (1)/(2) = (5)/(x):

Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.

Multiply the left side of the equation by 2/2 to get:

(8)/(2x) + (1)/(2) = (5)/(x)

Combine the two fractions on the left side of the equation:

(8+1)/(2x) = (9)/(2x)

Set the left side of the equation equal to the right side:

(9)/(2x) = (5)/(x)

Cross-multiply:

9x = 10x

Simplify:

x = 0

Therefore, the solution to the equation is x = 0.

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If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.

Let's start by assigning variables to represent the unknown quantities.

Let x be the number of flashlights sold.

Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.

The total sales can be expressed as the sum of the sales of each item:

10x (sales from flashlights) + 6(7x) (sales from pens) = 624

Simplifying this equation

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12.

And the number of pens sold would be 7x = 7(12) = 84.

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