. Determine the radius of a circle whose arc length measures meters and central angle measures radians. Round your answer to the nearest hundredth.

To find the number of ways to form a committee of 6 members with each class and major represented, we can consider each class and major separately.

Freshman Class:

There are 3 members in the freshman class: 1 engineer and 2 in CS. We need to choose 1 member from this class. Therefore, there are 3 options for the freshman representative.

Junior Class:

Similar to the freshman class, there are 3 members in the junior class: 1 engineer and 2 in CS. We need to choose 1 member from this class. Hence, there are 3 options for the junior representative.

Sophomore Class:

There are 3 members in the sophomore class: 2 engineers and 1 in CS. We need to choose 1 member from this class. Therefore, there are 3 options for the sophomore representative.

Senior Class:

Similarly, there are 3 members in the senior class: 2 engineers and 1 in CS. We need to choose 1 member from this class. Thus, there are 3 options for the senior representative.

Since we need to choose 6 members in total, we have 2 remaining spots to fill on the committee. From the remaining members, we can choose any 2 to fill these spots.

The number of ways to choose 2 members from the remaining 8 members (12 total members minus the 4 already selected) is given by the combination formula:

C(8, 2) = 8! / (2! * (8 - 2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28

Therefore, the number of ways to have a committee of 6 members with each class and major represented is:

3 (freshman) * 3 (junior) * 3 (sophomore) * 3 (senior) * 28 (remaining members) = 3^4 * 28 = 3,528 ways.

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Answer:

Step-by-step explanation:

4, you could pull out green, blue, red, or yellow

Answer:

14

Step-by-step explanation:

4 + 3 + 2 + 5 = 14

Answer: 14

The mechanical license rate for a previously recorded song used in a film, but not released on a soundtrack varies based on the terms of the licensing agreement. Typically, the rate is negotiated between the music publisher and the producer of the film.

The rate is usually a percentage of the revenue earned by the film or a flat fee per unit of distribution. The rate may also depend on the length of the song, the prominence of the song in the film, and the popularity of the song.

In general, it is recommended to consult with a music licensing professional or an entertainment attorney to negotiate the mechanical license rate for using a previously recorded song in a film.

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The player's batting average is 0.333.

The baseball player's batting average is found by dividing the number of hits by the number of times at bat. This number is then rounded to the nearest thousandth.

The question states that Cole Becker was at bat nine times with three hits.

To determine the player's batting average, divide the number of hits by the number of times at bat. A calculator can be used to compute this, and the result can be rounded to the nearest thousandth.

Batting Average = Number of hits/Number of times at bat

Batting Average = 3/9

Batting Average = 0.33333333...

Rounded to the nearest thousandth, the player's batting average is 0.333.

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Yes, the given transformation is found to be  linear.

To determine if a transformation is linear, we need to check two conditions: preservation of addition and preservation of scalar multiplication.

For the preservation of addition, let's consider two arbitrary vectors u and v in R^2.

The transformation Lwt translates each vector up by 3 units.

Therefore,

Lwt(u+v) = (u+v) + (3,3)

= (u + (3,3)) + (v + (3,3))

= Lwt(u) + Lwt(v).

For the preservation of scalar multiplication, let's consider an arbitrary vector u in R^2 and a scalar c. The transformation Lwt translates the vector u up by 3 units.

Therefore,

Lwt(cu) = cu + (3,3)

= c(u + (3,3))

= cLwt(u).

Since both conditions hold true, the transformation Lwt is linear.

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The question is that the number of particles of contamination per pound of material is modeled variable  by a Poisson random variable with a mean of 0.01 particle per pound.

This means that on average, there are 0.01 particles of contamination per pound of material.To study the raw materials for contamination, the number of particles per pound is observed and analyzed. This information helps determine the level of contamination in the raw materials and allows for appropriate actions to be taken if necessary.

By using a poisson random variable, it is possible to calculate the probability of a certain number of particles per pound occurring. This can help in assessing the likelihood of contamination and making informed decisions based on the observed data.In summary, raw materials are studied for contamination using a poisson random variable with a mean of 0.01 particle per pound. This allows for the analysis of the number of particles of contamination per pound and helps in assessing the level of contamination in the raw materials.

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No, not every five measurements of a quadrilateral can determine a quadrilateral uniquely. The choice of measurements depends on the properties of the quadrilateral.

For instance, the measurements for a parallelogram are different from the measurements for a trapezoid, and so on. Therefore, the five measurements must be selected based on the properties of the quadrilateral in question.

Let's see how five measurements can uniquely determine a quadrilateral?

A quadrilateral has 4 sides and 4 angles. The sum of the angles in a quadrilateral is 360°. Therefore, three of the angles can be measured. The fourth angle can be found by subtracting the sum of the other three angles from 360°. In other words, any three angles of a quadrilateral can determine the fourth angle. This gives us four measurements.

The fifth measurement can be any one of the following:

Diagonal length - A quadrilateral has two diagonals. The length of one diagonal can be measured to give us the fifth measurement. This is useful for quadrilaterals with perpendicular diagonals, such as a rhombus or a square.

Length of one side and two diagonals - This is useful for quadrilaterals with two diagonals that bisect each other at right angles, such as a kite.

Lengths of all four sides - This is useful for quadrilaterals with all four sides of equal length, such as a square or a rhombus.

Lengths of three sides and an angle - This is useful for quadrilaterals with two sides of equal length and two adjacent angles of equal measure, such as an isosceles trapezoid.

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Each one of the following is classified as:

7. -15 = Integer

8. 5/4 = rational number

9. 0.48 = Rational number

10. 32 = Whole number

To classify each of the given numbers, let's understand the definitions of whole numbers, integers, and rational numbers:

1. Whole numbers: These are non-negative numbers that do not include fractions or decimals. Examples of whole numbers are 0, 1, 2, 3, etc.

2. Integers: These include both positive and negative whole numbers, as well as zero. Examples of integers are -3, -2, -1, 0, 1, 2, 3, etc.

3. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include integers as well as fractions. Examples of rational numbers are -2/3, 1/4, 0.5, 2, etc.

Now, let's classify each of the given numbers:

7. -15: This is an integer because it is a negative whole number.

8. 5/4: This is a rational number because it can be expressed as a fraction, where the numerator and denominator are both integers.

9. 0.48: This is a rational number because it can be expressed as a fraction. We can write it as 48/100, which can be simplified to 12/25.

10. 32: This is a whole number because it is a positive whole number.

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The z-score associated with a raw score of 68 is 1.8.

Given mean = 50 and standard deviation = 10.

Z-score is also known as standard score gives us an idea of how far a data point is from the mean. It indicates how many standard deviations an element is from the mean. Hence, Z-Score is measured in terms of standard deviation from the mean.

The formula for calculating the z-score is given as

z = (X - μ) / σ

where X is the raw score, μ is the mean and σ is the standard deviation.

In this case, the raw score is X = 68.

Substituting the given values in the formula, we get

z = (68 - 50) / 10

z = 18 / 10

z = 1.8

Therefore, the z-score associated with a raw score of 68 is 1.8.

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The expression -x² + 13x - 12 can be factored as (x + 1)(-x + 12).

To factor the expression -x² + 13x - 12, we can use the factoring method. First, we look for two numbers that multiply to give -12 and add up to 13. In this case, the numbers are 12 and -1.

Now, we can rewrite the expression as follows:

-x² + 12x - x + 13x - 12

Next, we group the terms:

(-x² + 12x) + (-x + 13x) - 12

Now, we can factor out common terms from each group:

x(-x + 12) + 1(-x + 12) - 12

Notice that we have a common binomial factor, (-x + 12), so we can factor it out:

(x + 1)(-x + 12)

Therefore, the expression -x² + 13x - 12 can be factored as (x + 1)(-x + 12).

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The statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

To make the statement true, we need to replace the underlined term. The correct term should be "midsegment" instead of "perpendicular distance between the bases."

The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases and its length is equal to the average of the lengths of the bases.

Here's a step-by-step explanation:

1. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

2. The bases of a trapezoid are the parallel sides.

3. The midsegment of a trapezoid connects the midpoints of the non-parallel sides.

4. The midsegment is parallel to the bases and its length is equal to the average of the lengths of the bases.

5. Therefore, the statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

6. To make it true, we should replace "perpendicular distance between the bases" with "midsegment".

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Answer:

4.58 litres per hour

Step-by-step explanation:

To find the rate of water flow, we need to divide the amount of water that passed through the sponge by the time it took:

In this case, the amount of water that passed through the sponge is 110 litres and the time it took is 24 hours. So we can calculate the rate of water flow as:

Simplifying this, we get:

Therefore, the rate of water flow is 4.58 litres per hour.

________________________________________________________

According to the given statement the number of sides in the polygon is: n = 12. So, the polygon has 12 sides.

To find the number of sides in a regular polygon, we can use the formula:
Sum of interior angles = (n-2) × 180 degrees,
where n represents the number of sides in the polygon.
Given that the sum of the interior angles is 1800 degrees, we can substitute this value into the formula:
      1800 = (n-2) × 180.
To solve for n, we can divide both sides of the equation by 180:
      1800 / 180 = n - 2.
Simplifying the equation gives:
       10 = n - 2.
To isolate n, we can add 2 to both sides:
       10 + 2 = n.
Therefore, the number of sides in the polygon is: n = 12.
So, the polygon has 12 sides.

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Los Angeles, California, has an average daily temperature between 70 degrees F and 80 degrees F throughout most of the year. There's very little rainfall except for during a rainy season beginning in the fall. This describes the city's climate.

The climate in Los Angeles can be characterized as a Mediterranean climate. This type of climate is typically found in areas close to the ocean, with dry summers and mild, wet winters. The average daily temperature range of 70-80 degrees F indicates the warm and mild nature of the climate.

The limited rainfall throughout most of the year suggests a dry climate, with the exception of the rainy season in the fall. This seasonal pattern is common in Mediterranean climates, where the majority of rainfall occurs during the cooler months.

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The midpoint of the line segment is (-4, 0).

To find the midpoint of a line segment starting from the origin (0, 0) and ending at (-8, 0), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) of a line segment with endpoints (x1, y1) and (x2, y2) are given by:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

In this case, the coordinates of the origin are (0, 0) and the coordinates of the endpoint are (-8, 0). Plugging these values into the midpoint formula, we get:

x = (0 + (-8)) / 2 = -8 / 2 = -4

y = (0 + 0) / 2 = 0 / 2 = 0

Therefore, the midpoint of the line segment is (-4, 0). Option b) (–4, 0) is the correct answer.

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Sample ranges do not necessarily target the value of the population range and may not make good estimators of population ranges due to sampling variability.

Different samples from the same population can yield varying results, with extreme values that may not be representative of the entire population. Consequently, the sample range can differ significantly from the population range, leading to inaccurate estimations.

To obtain more reliable estimates, statistical methods that account for sampling variability, such as confidence intervals and hypothesis tests, are commonly employed to provide a range of plausible values for the population range based on the sample data.

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The ratio of computers to households is 21:25 given that the ratio of computers to households can be calculated.

In the survey of 5000 households, 4200 had at least one computer.

To find the ratio of computers to households, we divide the number of computers by the number of households.

The calculation is done by dividing the number of computers by the number of households.

By that way, the ratio of computers to households can be calculated.

So the ratio is 4200 computers divided by 5000 households.

Simplifying the ratio gives us 42:50, which can be further simplified to 21:25.

Therefore, the ratio of computers to households is 21:25.

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The proof of the Supplement Theorem can be stated as follows: If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.

The Supplement Theorem states that if two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.

To prove this theorem, we can use the following steps:

Let's assume we have two angles, angle A and angle B, which are both supplementary to angle C.

By definition, supplementary angles add up to 180 degrees.

So, we can express this as:

angle A + angle C = 180 degrees (equation 1)

angle B + angle C = 180 degrees (equation 2)

We want to prove that angle A is congruent to angle B, so we need to show that angle A = angle B.

To do that, we can subtract equation 2 from equation 1:

(angle A + angle C) - (angle B + angle C) = 180 degrees - 180 degrees

angle A - angle B = 0 degrees

angle A = angle B

Hence, we have shown that if two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.

Therefore, the Supplement Theorem is proven.

This proof relies on the fact that if two expressions are equal to the same value, subtracting one from the other will result in zero.

In this case, subtracting the two equations shows that the difference between angle A and angle B is zero, implying that they are congruent.

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By considering the elements in set A, Thomas can gain insights into the diversity of experiences and preferences within his family when it comes to living arrangements after high school.

Set A represents the number of different places where nine of Thomas' family members have lived after high school. The set A consists of unique values that indicate the number of locations each family member has lived in. Each element of set A represents a specific count, reflecting the diversity in the experiences of Thomas' family members regarding their living arrangements after high school.

Set A is a collection of values that represent the number of different places where each family member has lived after high school. The elements of set A could include values such as 0, 1, 2, 3, and so on, depending on the range of experiences within Thomas' family.

For instance, if one family member has only lived in their hometown after high school, their corresponding element in set A would be 1. On the other hand, if another family member has lived in three different cities, their element in set A would be 3.

By considering the elements in set A, Thomas can gain insights into the diversity of experiences and preferences within his family when it comes to living arrangements after high school. The set A provides a comprehensive overview of the number of different places each family member has chosen to reside in, allowing Thomas to explore various perspectives and make informed decisions about his own future living choices.

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This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, the exact decimal or simplified fraction solution is [tex]\frac{7}{20}[/tex].

To solve the expression [tex]\frac{79}{40}[/tex] - 162.5%, we first need to convert the percentage to a decimal.
To convert a percentage to a decimal, we divide it by 100.

So, 162.5% becomes [tex]\frac{162.5}{100}[/tex] = 1.625.
Now, we can rewrite the expression as [tex]\frac{79}{40}[/tex] - 1.625.
To subtract fractions, we need a common denominator.

In this case, the least common multiple (LCM) of 40 and 1 is 40.

So, we need to rewrite both fractions with the denominator of 40.
For the first fraction, [tex]\frac{79}{40}[/tex], we can multiply both the numerator and denominator by 1 to keep it the same.
For the second fraction, 1.625, we can multiply both the numerator and denominator by 40 to get [tex]\frac{65}{40}[/tex]
Now we can subtract the fractions:

[tex]\frac{79}{40} - \frac{65}{40} = \frac{79-65}{40}[/tex]

= [tex]\frac{14}{40}[/tex]
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[tex]\frac{79}{40} - 162.5\%[/tex] is equal to [tex]\frac{7}{20}[/tex] or [tex]0.35[/tex] as a decimal. To solve the expression [tex]\frac{79}{40}-162.5\%[/tex], we have to follow some step.

Steps to solve the expression:

1. Convert the percentage to a decimal: [tex]162.5\% = \frac{162.5}{100} = 1.625[/tex]

2. Now, we have [tex]\frac{79}{40}-1.625[/tex].

3. In order to subtract fractions, we need a common denominator. The least common denominator (LCD) for 40 and 1 is 40.

4. Rewrite the fractions with the common denominator:

    [tex]\frac{79}{40}-1.625 =\frac{79}{40}- (1.625 * \frac{40}{40})[/tex]

                     [tex]= \frac{79}{40}  - \frac{65}{40}[/tex]

5. Subtract the fractions:

    [tex]\frac{79}{40} - \frac{65}{40} = \frac{79-65}{40}[/tex]
                    [tex]= \frac{14}{40} [/tex]

6. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:

    [tex] \frac{14}{40} = \frac{(\frac{14}{2})}{(\frac{40}{2})}[/tex]

        [tex]= \frac{7}{20}[/tex]

Therefore, the simplified answer to [tex]\frac{79}{40}-162.5\%[/tex] is [tex]\frac{7}{20}[/tex] or [tex]0.35[/tex] as a decimal.

In conclusion, [tex]\frac{79}{40}-162.5\%[/tex] is equal to [tex]\frac{7}{20}[/tex] or [tex]0.35[/tex] as a decimal.

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Familiar language can provide a starting point for understanding statistical concepts, it is crucial to delve deeper into the specific definitions and principles of statistics to gain a more accurate and comprehensive understanding. This involves learning the technical vocabulary and concepts that are unique to the field of statistics.

The use of everyday language, such as the words "normal," "confidence," and "random," can provide some initial familiarity and context when describing statistical concepts. These familiar words can serve as entry points for understanding the concepts being discussed. However, it is important to note that the meaning of these words in everyday language might not align precisely with their specific definitions in statistics.

For example, when we say "I had a pretty normal day," we are generally referring to a typical or ordinary day. In statistics, the term "normal" has a specific meaning when describing a normal distribution, which is a bell-shaped probability distribution. While the everyday use of the word "normal" might evoke a sense of familiarity, it does not fully capture the technical aspects and characteristics of a normal distribution.

Similarly, when we say "I have little confidence in our ability to win today," we are expressing doubt or uncertainty. In statistics, confidence refers to the level of certainty we have in the results obtained from a sample or an estimate. However, the everyday use of the word "confidence" might not fully convey the technical definition of statistical confidence, which involves intervals and probabilities.

Likewise, the term "random" is often used in everyday language to describe something unexpected or without a specific pattern. In statistics, randomness refers to a process or outcome that cannot be predicted with certainty. While the everyday use of the word "random" may share some common aspects with its statistical definition, it does not capture the precise mathematical properties and implications of randomness in statistical analysis.

Therefore, while familiar language can provide a starting point for understanding statistical concepts, it is crucial to delve deeper into the specific definitions and principles of statistics to gain a more accurate and comprehensive understanding. This involves learning the technical vocabulary and concepts that are unique to the field of statistics.

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Answer:

The use of familiar words like "normal," "confidence," and "random" in everyday language can provide a starting point for understanding statistical concepts. These words aid in bridging the gap between everyday experiences and statistical concepts. It's crucial to understand that these terms' technical definitions in statistics may not correspond to how they are commonly used. It is required to delve into the particular definitions, assumptions, and mathematical underpinnings connected with these phrases in order to have a thorough comprehension of statistical ideas. While the use of common language might be a good place to start, accurate understanding and application require a deeper investigation of statistical principles.

The student can buy the most of her favorite soft drink at store A, where she can purchase a maximum of 15 bottles within her budget.

To determine which store the student can buy the most of her favorite soft drink for no more than $20, let's compare the options at store A and store B.

At store A, the price of a 2-liter bottle is $1.29 (plus a 10-cent deposit).
To find out how many bottles the student can buy for $20, we divide $20 by the cost per bottle:

$20 / ($1.29 + $0.10) = 15.50 bottles.
However, since we cannot buy a fraction of a bottle, the student can only buy a maximum of 15 bottles.

At store B, the price of a 12-pack of 12 fl oz cans is $2.99 (plus a 5-cent deposit per can).
To find out how many 12-packs the student can buy for $20, we divide $20 by the cost per 12-pack: $20 / ($2.99 + ($0.05 * 12)) = 6.49 12-packs.
Again, since we cannot buy a fraction of a 12-pack, the student can only buy a maximum of 6 12-packs.

Therefore, the student can buy the most of her favorite soft drink at store A, where she can purchase a maximum of 15 bottles within her budget.

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The statement "approximately 3.24 billion gallons of water flow over Niagara Falls daily" describes a continuous relationship.

In a continuous relationship, the variable (in this case, the amount of water flowing) can take on any value within a certain range. In contrast, a discrete relationship involves distinct, separate values.

In this case, the amount of water flowing can vary continuously and is not limited to specific, separate values. Therefore, the relationship between the amount of water flowing over Niagara Falls daily and the given value is continuous.

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The result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.

To find the result when the number 31 is increased by 8%, we can calculate 8% of 31 and add it to 31.

8% of 31 can be found by multiplying 31 by 0.08:

8% of 31 = 31 * 0.08 = 2.48

Now, we add this result to 31:

31 + 2.48 = 33.48

Rounding this answer to the nearest tenth, we get:

33.5

Therefore, the result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.

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The probability that both jurors selected are female is 1/6. To calculate the probability that both jurors selected are female,.

We need to determine the number of favorable outcomes (two female jurors selected) divided by the total number of possible outcomes.

In this scenario, there are two female alternate jurors available out of a total of four alternates. Since we need to select two jurors, we can use combinations to calculate the number of possible outcomes.

The number of possible outcomes is given by selecting 2 jurors out of 4, which can be calculated as:

C(4, 2) = 4! / (2! * (4-2)!) = 6

Therefore, there are 6 possible outcomes.

Out of these possible outcomes, we are interested in the favorable outcome where both selected jurors are female. Since there are two female alternate jurors available, we can calculate the number of favorable outcomes by selecting 2 female jurors out of 2, which is:

C(2, 2) = 2! / (2! * (2-2)!) = 1

Therefore, there is 1 favorable outcome.

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Number of possible outcomes

= 1 / 6

= 1/6

Thus, the probability that both jurors selected are female is 1/6.

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The area is 28 square feet.

The formula to find the area of a trapezoid is (base1 + base2) * height / 2. In this case, the base lengths are 6 feet and 8 feet, and the height is 4 feet. So, we can substitute these values into the formula.

Using the formula, we get:
Area = (6 + 8) * 4 / 2
      = 14 * 4 / 2
      = 56 / 2
      = 28 square feet

Therefore, the area of the trapezoidal tabletop is 28 square feet.

A trapezoid is a quadrilateral with one pair of parallel sides. The bases of a trapezoid are the parallel sides, and the height is the perpendicular distance between the bases. To find the area of a trapezoid, we multiply the sum of the bases by the height, and then divide by 2.

In this case, the sum of the bases is 6 + 8 = 14. Multiplying 14 by the height of 4 gives us 56. Dividing 56 by 2 gives us the final answer of 28 square feet.

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The solution to the equation is s = 12.

To solve the equation 9 + s = 21, we need to isolate the variable "s" on one side of the equation.

First, we can start by subtracting 9 from both sides of the equation to get rid of the constant term on the left side. This gives us:

s = 21 - 9

Simplifying the right side, we have:

s = 12

So the main answer to the equation is s = 12.

Start with the equation 9 + s = 21.

To isolate the variable "s", subtract 9 from both sides of the equation.

9 + s - 9 = 21 - 9

This simplifies to:

s = 12

Therefore, the solution to the equation is s = 12.

In conclusion, to solve the equation 9 + s = 21, we subtracted 9 from both sides of the equation to isolate the variable "s". The answer to the equation is s = 12.

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The graph will show a linear relationship, where the distance increases steadily as time increases.

To complete the table and graph, we need to determine the relationship between distance and time based on the given information.

Given:

Time taken = 5 minutes

Distance travelled = 13 kilometers

Since the distance is proportional to the time taken, we can set up a proportion to find the constant of proportionality:

Distance / Time = Constant

Let's calculate the constant of proportionality:

13 kilometers / 5 minutes = 2.6 kilometers/minute

Now, we can complete the table and graph:

| Time (minutes) | Distance (kilometers) |

|---------------|----------------------|

| 5              | 13                     |

| 10             | 26                    |

| 15             | 39                    |

| 20            | 52                    |

| 25            | 65                    |

To graph the data, we can plot the points (5, 13), (10, 26), (15, 39), (20, 52), and (25, 65) on a coordinate plane with time on the x-axis and distance on the y-axis. Connect the points with a straight line to represent the constant speed of the train.

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The new average salary for the twenty employees is [tex]$83,000[/tex]per year.Hence, the answer is 83,000.

Let's begin by calculating the initial salary of the twenty employees:

Average salary of 20 [tex]employees = $48,000[/tex] per year

Therefore, the total initial salary of the twenty employees = Average salary x [tex]Total number of employees= $48,000 x 20= $960,000[/tex] Now, ten of the employees get a[tex]$22,000[/tex] per year raise.

This means that their new salary will be [tex]$48,000 + $22,000 = $70,000[/tex]

Therefore, the new total salary of these ten employees = [tex]$70,000 x 10 = $700,000[/tex] To calculate the new average salary for all twenty employees, we need to add the new total salary to the total initial salary and then divide by the total number of employees.

New total salary of twenty employees =[tex]$960,000 + $700,000= $1,660,000[/tex] New average salary of twenty employees = New total salary / Total number of employees= [tex]$1,660,000 / 20= $83,000,[/tex]

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The dimensions of the rectangular window are 42 inches by 1.6 times 42 inches, which is 67.2 inches.

To find the dimensions of the rectangular window, we can set up an equation using the given ratio and area. Let's call the shorter side of the window x.
According to the ratio, the longer side of the window would be 1.6x.
The area of a rectangle is calculated by multiplying the length by the width.

So, we can set up the equation:
x * 1.6x = 2822.4
Simplifying this equation,

we get:
1.6x² = 2822.4
Dividing both sides of the equation by 1.6, we have:
x² = 1764
Taking the square root of both sides, we find:
x = 42
Therefore, the dimensions of the rectangular window are 42 inches

by 1.6 times 42 inches,

which is 67.2 inches.

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The dimensions of the window are approximately 67.2 inches for the length and 42 inches for the width.

The ratio of the lengths of the sides of the rectangular window is 1.6 to 1.

Let's represent the length as 1.6x and the width as x.

The area of the window is given as 2822.4 in².

To find the dimensions of the window,

we can use the formula for the area of a rectangle:

area = length × width.

Substituting the given values, we have:

2822.4 = (1.6x)(x)

To solve this equation, we can multiply 1.6x by x, giving us:

2822.4 = 1.6x²

Now, let's solve for x by dividing both sides of the equation by 1.6:

x² = 2822.4 / 1.6

x² = 1764

Taking the square root of both sides, we find:

x = √1764

x = 42

Now that we have the value of x, we can find the length and width of the window.

The length is 1.6 times the width, so:

Length = 1.6x = 1.6 * 42 = 67.2

Width = x = 42

Therefore, the dimensions of the window are approximately 67.2 inches for the length and 42 inches for the width.

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