find the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5,8,20,12,7,5

If the question states that and are in direct proportion, it means that the relationship between them follows the pattern of direct proportionality. Hence, the answer is (a) in direct proportion.

When two quantities, and , are in direct proportion, it means that as one quantity increases or decreases, the other quantity also increases or decreases proportionally. In other words, there is a constant ratio between the two quantities.

Mathematically, we can express direct proportionality as:

= k

where is the first quantity, is the second quantity, and is the constant of proportionality.

If the relationship between and is described as direct proportion, it implies that the value of remains constant for different values of .

On the other hand, if the relationship between and is described as inverse proportion, it means that the product of and remains constant for different values of .

Therefore, if two quantities, and , are in direct proportion, then they are in direct proportion.

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the value of f is 70, g is 50 and h is 30. So, correct option is

c

We know that sum of all angles of a triangle is 180°.

So, h + 20 + 130 = 180

h + 150 = 180

h = 180 - 150

h = 30

We know that straight line make an angle of 180°

130 + g = 180

g = 180 - 130

g = 50

g + f + 60 = 180

50 + f + 60 = 180

f + 110 = 180

f = 180 - 110

f = 70

Therefore, the value of f is 70, g is 50 and h is 30. So, correct option is

c

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Given question is incomplete, the complete question is below

Find the values of angles h, f, and g

The equation representing the number of candy bars Khalil has sold can be written as n(t) = 20 + 6(t/8), where n(t) is the number of candy bars sold and t represents the number of hours since the initial sale of 20 bars.

Initially, Khalil sold 20 candy bars. After that, he sold an additional 6 bars every 8 hours. To represent this situation with an equation, we can use the function n(t), where n is the number of candy bars sold and t is the number of hours since the initial sale.

Since Khalil sold 20 candy bars initially, we start with that as the base value. Then, for every 8 hours that pass, he sells an additional 6 bars. We can represent this using the equation n(t) = 20 + 6(t/8), where t/8 represents the number of 8-hour intervals that have passed since the initial sale.

By substituting different values of t into the equation, we can calculate the number of candy bars Khalil has sold at different points in time. For example, if t = 8, it means 8 hours have passed since the initial sale, and Khalil would have sold 20 + 6(8/8) = 26 candy bars.

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To find out how long it will take to travel a distance of 12 km at an average rate of 5 m/s, we can use the formula for speed:

Speed = Distance / Time

Rearranging the formula to solve for time, we have:

Time = Distance / Speed

Substituting the values, we have:

Time = 12 km / 5 m/s

To perform the calculation, we need to convert the distance to meters since the speed is given in meters per second. There are 1000 meters in 1 kilometer, so 12 km is equal to 12,000 meters.

Now, we can substitute the values into the formula:

Time = 12,000 meters / 5 m/s

Dividing 12,000 by 5, we get:

Time = 2400 seconds

Therefore, it will take approximately 2400 seconds to travel a distance of 12 km at an average rate of 5 m/s.

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The required Olivia has read approximately 75.26% of the pages, and  Olivia has not read approximately 24.74% of the pages.

Part A:

To represent the proportion for the percent of pages that Olivia has read, we can use the equation:

(Number of pages read) / (Total number of pages) = (Percent of pages read) / 100

Given:

Book 1: 40 pages out of 40 pages

Book 2: 60 pages out of 85 pages

Book 3: 43 pages out of 65 pages

Total number of pages read = 40 + 60 + 43 = 143 pages

Total number of pages = 40 + 85 + 65 = 190 pages

Plugging in these values into the proportion, we get:

143 / 190 = (Percent of pages read) / 100

To find the percent of pages read, we can solve for (Percent of pages read):

(Percent of pages read) = (143 / 190) * 100

(Percent of pages read) ≈ 75.26%

Therefore, Olivia has read approximately 75.26% of the pages.

Part B:

To find the percentage of pages that Olivia has not read, we can subtract the percentage of pages read from 100%.

Percentage of pages not read = 100% - (Percent of pages read)

Percentage of pages not read = 100% - 75.26%

Percentage of pages not read ≈ 24.74%

Therefore, Olivia has not read approximately 24.74% of the pages.

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The area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

To find the area of triangle OBC in terms of r and θ, we can utilize the formula for the area of a triangle: Area = (1/2) * base * height. In this case, the base of the triangle is the side BC, which has a length equal to r, and the height is the perpendicular distance from point O to side BC.

Considering that point O is the origin (0,0) and point B is located on the positive x-axis, the distance from the origin to the line BC is equal to the radius r. Thus, the height of the triangle is r.

To find the angle θ between the positive x-axis and the line BC, we can use trigonometry. Since the line BC forms an angle of θ with the positive x-axis, the perpendicular from point B to the x-axis creates a right triangle. Therefore, sin(θ) can be determined by dividing the height of the triangle (r) by the hypotenuse (also r), resulting in sin(θ) = r/r = 1.

Substituting the values into the formula for the area of a triangle, we have Area = (1/2) * r * r * 1 = (1/2) * r^2.

Therefore, the area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

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Two cyclists meet at the library and then go for a bike ride. The distance each person has traveled from her home at x hours from the start of the ride is linear, as shown.

Let's assume that cyclist A and B start at a distance x and y, respectively, from the library. Further, let's assume that cyclist A starts at t = 0. Then, the distance from the library for cyclist A at t hours after the start of the ride is represented by x + rt. The distance from the library for cyclist B at t hours after the start of the ride is represented by y + st.As the question says, the distance each person has traveled from her home at x hours from the start of the ride is linear. Thus, we can write their distances from the library as:dA(x) = x + rtdB(x) = y + st, where dA and dB represent the distance covered by cyclists A and B respectively.Now, if we want to find out the distance between the two cyclists at x hours after the start of the ride, we can use the following formula:distance between the two cyclists = dB(x) - dA(x)= (y + st) - (x + rt) = (y - x) + (s - r)tSince s and r are constants, the expression (y - x) + (s - r)t is linear with respect to t. Hence, the statement "The distance between the two cyclists is a linear function of x" must be true.

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We find: z = x Therefore, the value of z, the side length of the bottom square, is equal to the side length of the top square.

Let's assume the side length of the top square is x. Since the right triangle is formed by joining the squares at their vertices, the hypotenuse of the triangle is the diagonal of the top square.

In a square, the length of the diagonal is equal to the side length multiplied by the square root of 2. Therefore, the hypotenuse of the right triangle is x * √2.

The two legs of the right triangle are the side lengths of the squares adjacent to the hypotenuse. In this case, one leg is z, the side length of the bottom square.

Using the Pythagorean theorem, we have the equation:

z^2 + z^2 = (x * √2)^2

Simplifying the equation, we get:

2z^2 = 2x^2

Dividing both sides by 2, we have:

z^2 = x^2

Taking the square root of both sides, we find:

z = x

Therefore, the value of z, the side length of the bottom square, is equal to the side length of the top square.

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At the water slides, there are a total of 37 temporary employees and 37 permanent employees. To determine the percentage of employees who are temporary,  50% of the employees at the water slides are temporary employees.

The total number of employees at the water slides is the sum of temporary and permanent employees: 37 temporary + 37 permanent = 74 employees.
To find the percentage of temporary employees, we divide the number of temporary employees by the total number of employees and multiply by 100:
Percentage of temporary employees = (Number of temporary employees / Total number of employees) * 100
Plugging in the values:
Percentage of temporary employees = (37 / 74) * 100
Calculating this expression gives us:
Percentage of temporary employees = 0.5 * 100 = 50%
Therefore, 50% of the employees at the water slides are temporary employees.

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The quadratic equation (x - 3)^2 = 5 can be rearranged into the standard form x^2 - 6x + 4 = 0. We need to find the values of x that satisfy this equation.

To find the values of x that make the quadratic equation (x - 3)^2 = 5 true, we can rearrange it into the standard form:

(x - 3)^2 - 5 = 0.

Expanding the square, we get:

x^2 - 6x + 9 - 5 = 0,

x^2 - 6x + 4 = 0.

Now, we have a quadratic equation in the form ax^2 + bx + c = 0, with a = 1, b = -6, and c = 4. To solve this equation, we can use factoring, completing the square, or the quadratic formula.

In this case, we can try factoring:

(x - 2)(x - 2) = 0,

(x - 2)^2 = 0.

Taking the square root of both sides:

x - 2 = 0,

x = 2.

So, the only value of x that satisfies the equation is x = 2.

Therefore, the solution to the quadratic equation (x - 3)^2 = 5 is x = 2.

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To subtract 1/4 from 11/24, you need to find a common denominator for both fractions. The least common multiple (LCM) of 4 and 24 is 24. Convert 1/4 to an equivalent fraction with a denominator of 24 by multiplying the numerator and denominator by 6. This gives you 6/24. Now, subtract 6/24 from 11/24, which equals 5/24. Therefore, 11/24 - 1/4 simplifies to 5/24.

To subtract fractions, you need to have a common denominator. In this case, the denominators are 24 and 4. To find a common denominator, you can use the least common multiple (LCM) of the two denominators.

The LCM of 4 and 24 is 24. To convert 1/4 to an Summary:

To subtract 1/4 from 11/24, you need to find a common denominator for both fractions. The least common multiple (LCM) of 4 and 24 is 24. Convert 1/4 to an equivalent fraction with a denominator of 24 by multiplying the numerator and denominator by 6. This gives you 6/24. Now, subtract 6/24 from 11/24, which equals 5/24. Therefore, 11/24 - 1/4 simplifies to 5/24.

To subtract fractions, you need to have a common denominator. In this case, the denominators are 24 and 4. To find a common denominator, you can use the least common multiple (LCM) of the two denominators.

The LCM of 4 and 24 is 24. To convert 1/4 to an equivalent fraction with a denominator of 24, you can multiply the numerator and denominator by 6. This gives you (1 * 6) / (4 * 6) = 6/24.

Now that both fractions have a common denominator of 24, you can subtract them:

11/24 - 6/24 = (11 - 6) / 24 = 5/24.

Therefore, 11/24 - 1/4 simplifies to 5/24. with a denominator of 24, you can multiply the numerator and denominator by 6. This gives you (1 * 6) / (4 * 6) = 6/24.

Now that both fractions have a common denominator of 24, you can subtract them:

11/24 - 6/24 = (11 - 6) / 24 = 5/24.

Therefore, 11/24 - 1/4 simplifies to 5/24.

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The blimp will be directly overhead of Ethan in 9.94 minutes.

To determine how long it will take for the blimp to be directly overhead of Ethan, we can use the information about the blimp's altitude and speed.

First, let's find the horizontal distance covered by the blimp in the time it takes to be directly overhead. Since the blimp is moving at a speed of 15 mph, we need to convert this to feet per minute:

15 mph * (5280 ft / 1 mile) * (1 hour / 60 minutes) = 1320 ft/minute

So, the blimp is moving at a rate of 1320 feet per minute horizontally.

Now, let's calculate the vertical distance the blimp needs to cover to be directly overhead of Ethan. This is equal to the altitude of the blimp, which is given as 1150 feet.

Since Ethan is looking up at an angle of 5 degrees, we can use trigonometry to find the horizontal distance covered by the blimp when it reaches the altitude of 1150 feet.

tan(5 degrees) = vertical distance / horizontal distance

We want to solve for the horizontal distance, so rearranging the equation:

horizontal distance = vertical distance / tan(5 degrees)

horizontal distance = 1150 ft / tan(5 degrees)

Using a calculator, we find:

horizontal distance ≈ 13129.01 ft

Now, we can determine the time it takes for the blimp to cover this horizontal distance at a rate of 1320 feet per minute:

time = horizontal distance / rate

time = 13129.01 ft / 1320 ft/minute

Calculating this, we get:

time ≈ 9.94 minutes

Therefore, the blimp will be directly overhead of Ethan in approximately 9.94 minutes.

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Myron received $43.20.

We have,

To determine how much Myron received, we need to find the proportion of the job he completed compared to the total work done by all three workers.

First, let's calculate the total number of days worked by all three workers:

Total days worked = Josiah's days + Nathaniel's days + Walden's days

Total days worked = 7 + 5 + 3

Total days worked = 15

Next, we'll calculate the proportion of the job that Myron completed:

Myron's proportion = Myron's days / Total days worked

Myron's proportion = 3 / 15

Myron's proportion = 1/5

Finally, we'll determine how much Myron received:

Myron's payment = Myron's proportion x Total payment

Myron's payment = (1/5) x $216.00

Myron's payment = $43.20

Therefore,

Myron received $43.20.

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The point where you end after moving is (4, 5)

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

Start = (-3, 5)

Direction: 1 unit left and 8 units right

using the above as a guide, we have the following:

New point = (-3, 5) + (-1 + 8, 0)

So, we have

New point = (-3 - 1 + 8, 5 + 0)

Evaluate

New point = (4, 5)

Hence, the point where you end is (4, 5)

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The system of inequalities that represents the constraints of the situation, where g represents the hours worked at the gas station and r represents the hours worked at the restaurant, is:

g ≥ 8

r > 6

g + r ≤ 18

To represent the constraints of the situation in the form of a system of inequalities, we can use the given information. Let's break down the given conditions:

The student works a minimum of 8 hours each week at the gas station: This can be represented by the inequality g ≥ 8.

The student works more than 6 hours each week at the restaurant: This can be represented by the inequality r > 6.

The student works a maximum of 18 hours each week at both jobs combined: This implies that the sum of hours worked at the gas station (g) and the hours worked at the restaurant (r) should not exceed 18. This can be represented by the inequality g + r ≤ 18.

Combining these inequalities, the system that represents the constraints of the situation is:

g ≥ 8

r > 6

g + r ≤ 18

Therefore, the system of inequalities that represents the constraints of the situation, where g represents the hours worked at the gas station and r represents the hours worked at the restaurant, is:

g ≥ 8

r > 6

g + r ≤ 18

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Neither Cheyenne nor Sebastian got the correct answer when subtracting the given polynomial.

Subtracting polynomials requires careful attention to terms and their coefficients. If both Cheyenne and Sebastian arrived at incorrect answers, it indicates a mistake in their subtraction process. To determine if either of them got the correct answer, we need to compare their solutions with the correct solution. Without the specific polynomial provided, we cannot provide a detailed analysis. However, we can consider some common errors that might occur during polynomial subtraction.

One possible error is neglecting to distribute the subtraction sign to all terms of the polynomial being subtracted. This mistake can result in incorrect coefficients and signs of terms in the final answer. Another common error is misaligning the terms when subtracting, which leads to incorrect cancellations and additions. It's also possible that both Cheyenne and Sebastian made different mistakes, resulting in distinct incorrect answers.

In conclusion, without the specific polynomial and the calculations performed by Cheyenne and Sebastian, it is challenging to determine the exact nature of their errors. However, since they both arrived at incorrect answers, it suggests that they made mistakes during the subtraction process, such as neglecting to distribute the subtraction sign or misaligning the terms.

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One scenario where the steps for conflict resolution can be applied is in a workplace setting. Let's consider a personal experience where I encountered a conflict with a colleague.

In my previous job, I was working on a project with a coworker, let's call her Sarah. We had different approaches and ideas on how to tackle a critical aspect of the project, leading to a conflict.

The steps for conflict resolution can be followed in this scenario. First, I recognized the need to address the conflict promptly to avoid further issues. I approached Sarah to discuss our differences openly and respectfully, emphasizing the importance of finding a mutually beneficial solution.

Next, we both actively listened to each other's perspectives, allowing each person to express their ideas and concerns without interruption. This step helped us understand each other's viewpoints and underlying motivations.

After listening, we focused on finding a compromise that integrated aspects of both our ideas. We brainstormed potential solutions and considered the feasibility and impact of each option on the project.

Finally, we selected the most suitable solution that met our project's goals and aligned with our team's resources and constraints. We implemented the chosen solution and regularly evaluated its effectiveness, ensuring that the conflict resolution process had a lasting positive impact on our working relationship.

Through the application of the conflict resolution steps, we were able to resolve our differences, strengthen our collaboration, and successfully complete the project together.

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The latitude of Independence Hall in Philadelphia is given as 39.948859°. Therefore, the latitude of Independence Hall can be expressed as 39° 56' 55.9"

To convert the given latitude into degrees, minutes, and seconds, we follow the conversion rules.

First, we take the whole number part of the latitude, which represents the degrees. In this case, the degrees are 39.

To find the minutes, we multiply the decimal part of the latitude by 60 since 1° is equivalent to 60 minutes. Thus, 0.948859 * 60 = 56.93154.

Next, we take the whole number part of the minutes, which is 56, to represent the minutes.

To find the seconds, we multiply the decimal part of the minutes by 60 since 1' is equivalent to 60 seconds. Thus, 0.93154 * 60 = 55.8924. Rounding this to the nearest tenth, we get 55.9.

Therefore, the latitude of Independence Hall can be expressed as 39° 56' 55.9", where the whole number part represents the degrees, the next whole number part represents the minutes, and the rounded decimal part represents the seconds.

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The ratios of the number of boys to girls in ninth grade (4:5) and the number of apples to pears sold at the farmers market (12:15) are equivalent because we were able to convert 4:5 into 12:15 by multiplying both terms by 3.

Ratios equivalent:

When two ratios have the same value, they are equivalent ratios. To verify that two ratios are equivalent, you may cross-multiply and reduce the resulting fractions. In the ninth grade, there are 4 boys for every 5 girls. 4:5 is the ratio of boys to girls. Similarly, 12 apples are sold for every 15 pears at the farmers' market. 12:15 is the ratio of apples to pears, and we need to decide whether this ratio is equivalent to 4:5 or not.Let's convert the ratio 4:5 to its equivalent ratio 12:15 by multiplying both terms by 3, which gives us 12:15. Since 12:15 is the same as 12:15, the two ratios are equivalent.

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Amy compared the fractions 4/2 and 5/8 by converting each fraction into a whole number.

To compare fractions, Amy converted each fraction into an equivalent form with a common denominator of 1. For 4/2, she multiplied both the numerator and denominator by 2 to get 8/4. Then, she simplified it to 2/1, since both the numerator and denominator are divisible by 4. Similarly, for 5/8, she multiplied both the numerator and denominator by 8 to get 40/64. Amy then simplified it to 5/8 by dividing both the numerator and denominator by their greatest common divisor, which is 8.

Comparing the two fractions, Amy found that 2/1 is greater than 5/8. This means that 4/2 is greater than 5/8 when comparing the fractions as whole numbers. It is important to note that comparing fractions by converting them to whole numbers may not always provide an accurate comparison. Other methods, such as finding a common denominator and comparing the fractions directly, are more reliable.

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There is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.

The coefficient of variation (CV) is a measure of relative dispersion, which compares the standard deviation to the mean of a dataset. A higher CV indicates greater dispersion relative to the mean, while a lower CV indicates less dispersion.

If the distribution of GPA has a higher coefficient of variation compared to the distribution of age, it means that there is more dispersion relative to the mean in the GPA distribution. This suggests that there is greater variation or diversity in GPA scores among the students compared to their ages. In contrast, if the distribution of GPA had a lower coefficient of variation compared to the distribution of age, it would indicate less dispersion relative to the mean in the GPA distribution, implying less variation or more uniformity in GPA scores.

Therefore, we can interpret that there is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.

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The unit price of the pecans is $0.815 per ounce (rounded to three decimal places).

To calculate the unit price, we divide the total cost of the item by the quantity purchased. In this case, Averi bought a 6-ounce can of pecans for $4.89.

To find the unit price, we divide the total cost ($4.89) by the quantity purchased (6 ounces):

Unit price = Total cost / Quantity purchased

= $4.89 / 6 ounces

To simplify the unit price, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4.89 and 6 is 3.

Dividing both the numerator and denominator by 3, we get: Unit price = ($4.89 / 3) / (6 ounces / 3)

= $1.63 / 2 ounces

Therefore, the unit price of the pecans is $0.815 per ounce (rounded to three decimal places). This means that Averi paid approximately $0.815 for each ounce of pecans she purchased.

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It is advisable to consult local government authorities or financial experts for accurate information regarding a particular jurisdiction's practices.

Other local government entities within the same jurisdiction.

This typically occurs when multiple municipalities or local government agencies collaborate on a project or service that requires financing.

In such cases, they may jointly issue debt instruments to raise the necessary funds.

A common example of shared municipal debt is the issuance of bonds. Bonds are debt securities that governments issue to borrow money from investors.

When multiple municipalities or local government entities collaborate on a project, they may issue bonds collectively to finance it.

These bonds are often referred to as "jointly issued" or "shared" bonds.

The shared bonds may be backed by a cooperative agreement or an intergovernmental agreement between the participating entities.

The agreement outlines the responsibilities, rights, and obligations of each entity in relation to the debt.

It may specify the allocation of debt service payments, the sharing of repayment responsibilities, and other relevant terms.

By sharing the debt burden, the participating municipalities or local government entities can pool their resources and secure better financing terms.

This can include obtaining lower interest rates due to the collective credit strength of the participating entities.

It is important to note that the specifics of overlapping municipal debt can vary depending on the legal and administrative framework of each jurisdiction.

The governance structure, local laws, and regulations may influence how shared municipal debt is structured and managed.

Therefore, it is advisable to consult local government authorities or financial experts for accurate information regarding a particular jurisdiction's practices.

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The sequence that best represents the relationship between DNA and the traits of an organism is: DNA base sequence -> Amino acid sequence -> Protein function -> Protein shape -> Trait.

1. DNA base sequence: The DNA molecule contains genetic information in the form of a sequence of nucleotide bases (adenine, thymine, cytosine, and guanine). This sequence acts as a template for protein synthesis.

2. Amino acid sequence: The DNA base sequence is transcribed into mRNA, which is then translated into a sequence of amino acids. The sequence of amino acids determines the primary structure of a protein.

3. Protein function: The specific sequence of amino acids in a protein determines its function. Proteins perform various roles in cells, such as enzymatic activity, structural support, and signaling.

4. Protein shape: The sequence of amino acids determines the folding and three-dimensional structure of a protein. The shape of a protein is crucial for its proper function.

5. Trait: Proteins play a fundamental role in the expression of traits. Traits are characteristics of an organism that result from the combined effects of various proteins and their functions.

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Jessica will pay $119.15 for her phone after applying the 15% off coupon and the $50 discount.To calculate the final price that Jessica will pay for her phone, we need to consider the 15% off coupon and the $50 discount.

First, let's calculate the discount amount based on the 15% off coupon. We can find this by multiplying the original price ($199) by 15% (or 0.15):

Discount amount from coupon = $199 * 0.15 = $29.85

Next, we need to subtract the $50 discount offered by the store:

Discount amount from store = $50

Now, we can calculate the final price Jessica will pay by subtracting the total discount amount from the original price:

Final price = $199 - ($29.85 + $50) = $199 - $79.85 = $119.15

Therefore, Jessica will pay $119.15 for her phone after applying the 15% off coupon and the $50 discount.

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The entrance measures 6 feet wide and 8 feet long, and the hallway is 3 feet wide and 14 feet long. We need to calculate the area of both and then multiply by $2.40. We can do that as follows:

Entrance area = 6 feet x 8 feet

= 48 square feet

Hallway area = 3 feet x 14 feet

= 42 square feet

Total area = 48 + 42

= 90 square feet

The cost of the carpet, we can multiply the total area by the cost per square foot: $2.40/square foot x 90 square feet = $216.00

It will cost Zac $216.00 to carpet the entrance and hallway of his house if he selects the carpet that sells for $2.40 a square foot.

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To meet the demand and minimize total costs, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings.

By producing this quantity, the company can meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while using the minimum number of pineapples and minimizing costs.

To determine the optimal production quantity, we need to consider the requirements for each product and the costs associated with production.

Since each pint of pineapple juice requires 2 pineapples and each can of pineapple rings requires 1 pineapple, the total number of pineapples needed for both products is 39,600 (36,000 pints + 3,600 cans).

Given that the company anticipates using at least 72,000 pineapples, this quantity is sufficient to meet the demand.

Next, we consider the costs. Each pint of pineapple juice costs 16¢ to produce, while each can of pineapple rings costs 40¢ to produce. To minimize costs, the company should produce the product with the lower cost per unit.

In this case, producing pineapple juice is more cost-effective as it costs 16¢ per pint compared to 40¢ per can of pineapple rings. Therefore, Fancy Pineapple should produce 18,000 pints of pineapple juice to meet the demand.

In summary, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings to meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while minimizing costs.

This production quantity ensures the optimal use of pineapples and takes into account the lower production cost per unit for pineapple juice compared to pineapple rings.

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The difference between the median of the data, including the possible outlier, and excluding the possible outlier is 9.

Given that

The number of lattes sold daily for two coffee shops is shown in the table: Lattes 55 52 56 48 57 45 41 Based on the data.

We have to determine

What is the difference between the median of the data, including the possible outlier, and excluding the possible outlier?

According to the question

The number of lattes sold daily for two coffee shops is shown in the table: 55 52 56 48 57 20 45 41  Lattes Based on the data.

The data set with the outlier is 55 52 56 48 57 20 45 41; Meaning the median falls in between 48 and 57, which is 52.5

Then the data set without the outlier is  55 52 56 48 57 20 45 41;  Making the median here 52.5

Therefore, the difference between the median of the data, including the possible outlier, and excluding the possible outlier is = 57 - 48 = 9

Hence, The difference between the median of the data, including the possible outlier, and excluding the possible outlier is 9.

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Equation x + 2 = 3y, which represents a relation between acute angles x,y in a right triangle. To find values, we need more information.With such information, we could apply trigonometric functions.

The equation x + 2 = 3y relates the angles of a right triangle, but it is not sufficient to determine the specific values of x and y. The relationship between the acute angles in a right triangle is given by the trigonometric ratios, such as sine, cosine, or tangent. However, without any additional information or equations, we cannot solve for the exact values of x and y.

To determine the values of x and y, we would need either the lengths of the sides of the right triangle or additional equations or relationships between the angles. With such information, we could apply trigonometric functions or use geometric properties of right triangles to find the values of x and y.

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It would take Arnob approximately 4.12 minutes to catch up to Kathleen.

We need to find out the time it would take Arnob to catch up to Kathleen, given their speeds. Since we know their speeds, we can set up a proportion with the distance they are apart and their speeds. The proportion would be as follows:Distance Arnob travels = Distance Kathleen travels - Distance Arnob travels Arnob's speed = Kathleen's speed. Distance Arnob travels = Distance Kathleen travels - Distance Arnob travels Arnob's speed = Kathleen's speedTherefore, using the distance formula:Distance = Rate x TimeD = RTWhere:D is the distanceR is the rateT is the timeIn this scenario, Arnob and Kathleen are moving towards each other, meaning the distance between them is getting shorter. We can add their speeds together to find the rate at which the distance between them is getting shorter. Rate = Arnob's speed + Kathleen's speed = 9 + 8 = 17Since we know the rate at which the distance between them is getting shorter, we can use the formula to find the time it would take for Arnob to catch up to Kathleen. Let's call this time "t".D = RTDistance = Distance between Arnob and Kathleen = 75 - 5 = 70R = Rate at which the distance is getting shorter = 17T = Time it would take for Arnob to catch up to KathleenTherefore,70 = 17tSolving for t:t = 70/17 ≈ 4.12 minutes

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