Rewrite 84 + 36 in the form
a(b+c)
where a is the greatest common factor of 84 and 36

According to operations in maths, -8 - 12 is solved by adding the two numbers together and maintaining the negative sign, which will give us: -20.

Operations in mathematics are often guided by these rule listed below:

minus + plus = minus

minus + minus = minus

minus × minus = plus

minus × plus = minus

Thus, if we are given the expression, -8 - 12, applying the second rule stated above, we will have:

-8 - 12 = -20

This means we are adding two negative numbers together, which will give us the negative value of their sums.

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The solution of the given problem of function comes out to be Option C,  t ≥ 0, which is the proper domain for the specified function

Each subject will include a range of problems on the final exam covering both real and fictitious locations as well as the formation of numerical factors. a diagram illustrating the connections between various components that work together to produce the same outcome. A service is made up of several individual components that work together to produce unique outcomes for each input.

Here,

In order to represent the height of the ball above the ground after t seconds, the function

=>  h(t) = -3t² + 9t + 12

has the correct domain of C. t ≥ 0.

Reason: Since time (t) here refers to the duration in seconds since the ball was thrown, it cannot be negative.

Therefore, t values greater than or equal to 0 should be the only values allowed in the function's domain.

Option C,  t ≥ 0, is the proper domain for the specified function and accurately represents this limitation.

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The range of the function graphed above include the following: D. -∞ ≤ y ≤ 2.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = {-∞, 2} or -∞ ≤ y ≤ 2.

Domain = {-1, ∞} or -1 < x < ∞.

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The statement that is true about having a salaried job is "The employee is paid the same amount each week regardless of the number of hours worked." So, correct option is B.

Salaried jobs typically offer a set salary for a specified period, such as weekly, bi-weekly, or monthly, regardless of the number of hours worked. This is in contrast to hourly jobs where an employee is paid based on the number of hours worked.

Salaried employees often have a contract that specifies their salary and may include additional benefits, such as health insurance, paid vacation days, or retirement plans.

The amount of the salary is often negotiated during the hiring process and may be based on factors such as the employee's experience, education, and qualifications.

While salaried employees are expected to work a certain number of hours per week, the salary remains the same regardless of whether the employee works more or less than the expected hours.

So, correct option is B.

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Answer:

y - 2 = 2(x + 3)

Step-by-step explanation:

the equation of a line in point- slope form is

y = b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (2, 12 )

m = [tex]\frac{12-2}{2-(-3)}[/tex] = [tex]\frac{10}{2+3}[/tex] = [tex]\frac{10}{5}[/tex] = 2

using (a, b ) = (- 3, 2 ) , then

y - 2 = 2(x - (- 3) ) , that is

y - 2 = 2(x + 3)

For given triangle,  Length of XY and YZ is equal to 7√2.

What is a triangle's definition?

A triangle has three straight sides and three angles. It is one of the basic shapes in geometry and has many properties and applications in mathematics and everyday life. The sum of the interior angles of a triangle is always 180 degrees, and there are different types of triangles depending on their side lengths and angle measures and it includes 6 types of triangles.

Now,

If one of the angles of a right triangle is 90 degrees and another angle is 45 degrees, then the third angle must also be 45 degrees. This means that the triangle is a 45-45-90 triangle, which has a special property that the two legs are congruent and the hypotenuse is the square root of 2 times the square length of each leg.

In this case, the hypotenuse is given as 14, so we can set up the following equation:

14 = √2x²

where x is the length of each leg of the triangle. To solve for x, we can square both sides of the equation:

14² = 2x²

196 = 2x²

x² = 98

x = 7√2

So, each leg of the triangle has a length of 7√2, and the hypotenuse has a length of 14.

Hence,

             Length of XY and YZ is equal to 7√2.

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To express 1/4 as an equivalent fraction with a different denominator, we need to find a common multiple of 4 and the desired denominator.

Let's say we want to express 1/4 as an equivalent fraction with a denominator of 12. To do this, we can multiply both the numerator and denominator of 1/4 by 3, which gives us:

1/4 x 3/3 = 3/12

So 1/4 is equivalent to 3/12 when the denominator is 12.

In general, to express a fraction a/b as an equivalent fraction with a different denominator c, we can multiply both the numerator and denominator by the same value that makes b equal to c.

This is because when we multiply both the numerator and denominator by the same value, we are essentially multiplying the fraction by 1, which does not change its value.

For example, to express 2/5 as an equivalent fraction with a denominator of 15, we can multiply both the numerator and denominator by 3, which gives us:

2/5 x 3/3 = 6/15

Therefore, 2/5 is equivalent to 6/15 when the denominator is 15.

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1.35% is the percentage change in the population of the city that grew from the years 2010 to 2020.

The population of the city = 89,000

Percentage in the growth of people from 2010 to 2015 = 6.8%

Percentage in the decline of people from  2015 to 2020 = 4.9%

The formula to calculate the percentage change is:

percentage change = (new value - old value) / old value x 100%

To calculate the population of the city after the growth of 6.8%

Population in 2015 = 89,000 x (1 + 6.8/100)

Population in 2015 = 95,012

To calculate the population of the city after the decline of 4.9%

Population in 2020 = 95,012 x (1 - 4.9/100)

Population in 2020 = 90,199.88

Population in 2020 = 90,200

The total change in the percentage of growth of population in the city is:

percentage change = (new population - old population) / old value * 100%

percentage change = (90,200 - 89,000) / 89,000 x 100%

percentage change = 1,200 / 89,000 x 100%

percentage change = 1.35%

Therefore, we can conclude that the population in the city grew by 1.35% from 2010 to 2020.

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The image of the point (0, 3) after dilation by a scale factor of 2 centered at the origin is (0, 6).

Dilation is a transformation in which a figure is enlarged or reduced by a scale factor.

We are to find the image of (0,3) after a dilation by a scale factor of 2 centered at the origin.

The scale factor is 2, which means the figure will be enlarged.

To find the image of (0, 3) after dilation, we multiply its x-coordinate and y-coordinate by 2.

Hence;

(0, 3)

Multiply the coordinates by 2.

(0 × 2, 3 × 2)

= (0, 6)

Therefore, the image after dilation is (0, 6).

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Answer:

the answer is c(t)=x2 +3

Step-by-step explanation:

because if u insert every x value in x place u will get the 2nd coordinate or y value so it is the correct equation

The expected value of X is 7, and the standard deviation of X is 2.42 respectively.

The average of X's potential values is the expected value of X. We must first determine the sum of all potential x values multiplied by each value's associated probability before we can determine the expected value.

Calculate the expected value of X

Expected value = (2×(1/36)) + (3×(2/36)) + (4×(3/36)) + (5×(4/36)) + (6×(5/36)) + (7×(6/36)) + (8×(5/36)) + (9×(4/36)) + (10×(3/36)) + (11×(2/36)) + (12×(1/36))

Expected value = 7

Calculate the variance of X

Variance = (2-7)2×(1/36) + (3-7)2×(2/36) + (4-7)2×(3/36) + (5-7)2×(4/36) + (6-7)2×(5/36) + (7-7)2×(6/36) + (8-7)2×(5/36) + (9-7)2×(4/36) + (10-7)2×(3/36) + (11-7)2×(2/36) + (12-7)2×(1/36)

Variance = 5.83

Calculate the standard deviation of X

Standard deviation = √(variance)

Standard deviation = 2.42

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Complete Question:

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

x             P(x)

2            1/36

3            2/36

4            3/36

5            4/36

6            5/36

7            6/36

8            5/36

9            4/36

10           3/36

11            2/36

12            1/36

Determine the expected value and standard deviation of X.

Answer:

3568 or 3567

Step-by-step explanation:

42820 divided by 12

Analysis of variance can be used to determine differences in test scores of more than two groups. It is true.

What is variance?

Apart from the measurement of statistics range and interquartile range, variance is a measure of dispersion that takes into account the spread of all data points in a data set. It is the measure of dispersion which has the most often utility, along with the standard deviation, which is nothing but the square root of the variance.

An analysis of variance (ANOVA) is called an analysis tool in statistics which separates an observed aggregate  variability which is found inside a two part data set.

As ANOVA is the extension of of t-tests and z-tests so a one way ANOVA can be used for three or more groups of data  in the purpose to gain information about the relationship in between dependent and independent variable.

So ANOVA can be used to determine differences in test scores of more than two groups.

Hence, the statement is true.

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Rewriting 11,000,000 as a power of 10 using scientific notation is: 1.1 * 10⁷

A number is written in scientific notation whenever a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 * 10^8.

Now, we want to write the number 11000000 as a power of 10. Using the concept of scientific notation, we have:

11000000 = 1.1 * 10⁷

That is the final expression of the given number as a power of 10

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Zip line B's total length requires 301 feet of cable using the distance between trees and change in height.

To determine the length of cable needed, we need to calculate the horizontal and vertical distances between the trees, and then apply the constraints.

Let's start by labeling the trees and their distances:

Tree 1: 120 ft from Tree 2, 150 ft from Tree 3

Tree 2: 140 ft from Tree 3

Zip line B is the longest, so calculate the length of cable needed for that option.

Horizontal distance: Tree 2 to Tree 3 is 140 ft.

Vertical distance: The starting platform needs to be 16 ft above the ground, and the harness hangs down 4 ft below the cable, plus an additional 3 ft for the rider's legs. So the total height difference is 16 + 4 + 3 = 23 ft.

Using the slope constraint, we want a vertical change of 6 to 8 feet for every 100 feet of horizontal change. For a horizontal distance of 140 ft, we want a vertical change of:

(6/100) x 140 = 8.4 ft

(8/100) x 140 = 11.2 ft

So the zip line needs to have a vertical drop of between 8.4 and 11.2 ft.

Using the slack constraint, we need to add 5% slack to the length of the cable:

140 ft x 1.05 = 147 ft

Adding 7 ft of extra cable at each end, the total length of cable needed is:

140 ft + 147 ft + 7 ft + 7 ft = 301 ft

Therefore, the total length of cable needed for Zip line B is 301 ft.

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Complete question:

Designing a Zip Line You and your friend Latisha work at the community center. You will be counselors at a summer camp for middle school students. The camp director has asked you and Latisha to design a zip line for students to ride while at camp. A zip line is a cable stretched between two points at different heights with an attached pulley and harness to carry a rider. Gravity moves the rider down the cable. The zip line will be secured to two trees. The camp has a level field with three suitable trees to choose from. All three trees are on level ground. • Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. • Tree 1 is 150 feet from Tree 3. Tree 2 Tree 3 Tree 1 120 ft 140 ft acer Tree 1 is 120 feet from Tree 2. • Tree 2 is 140 feet from Tree 3. Tree 1 is 150 feet from Tree 3. - Tree 2 Tree 3 Tree 1 120 ft 140 ft 150 ft There are three possible zip line locations: Zip line A between Tree 1 and Tree 2, Zip line B between Tree 2 and Tree 3, or Zip line C between Tree 1 and Tree 3. acer Tree 2 Tree 1 Tree 3 Zip line A Zip line 8 Zip linec A professional company will be hired to install the zip line. They will build platforms at the two trees used for starting and ending the zip line. The starting platform will require the cable to start at a height 16 feet above the ground You and Latisha researched how to build a zip line. There are four basic constraints for your design. • Slope Constraint: The slope of the zip line should be 6 to 8 feet of vertical change for every 100 feet of horizontal change. • Slack Constraint: The zip line should have a 5% slack in it. acer • Harness Constraint: The cable must be high enough that the rider, while buckled into the harnese dnes not touch the ground. • The harness hangs down 4 feet below the cable. • An additional 3 feet must be used to allow for a rider's legs to hang down below the harness. • Brake Constraint: A brake must be placed on the cable to ensure the rider does not hit the tree. A bungee cord connects the brake to an anchor in the ground. . The length of the bungee cord is 24 feet. • The bungee cord stretches to a maximum of 175% of its original length. Harness Constraint Brake Constraint Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor acer Rider 4 ft Rider Brake 3 ft Harness Bungee cord Brake anchor Your task is to choose which zip line to build, Zip line A, Zip line B, or Zip line C, and to design this zip line within the given constraints. acer The camp director is ready to purchase the cable. Use the distance between the trees and the change in height of the cable to determine the length of cable needed. Be sure to include: • the required 5% slack in the line, and • 7 extra feet of cable at each end to wrap around each tree. Enter the total length, in feet, of cable needed.

Approximately 39% of coin tosses resulted in tails

Probability is the likelihood or possibility of an event. For example, the probability of tossing a coin  is ½ because there is 1 way to get heads and the total number of possible outcomes is 2 (heads or tails).

Since the coin landed  heads 31 times in 51 tosses, it must be 51 - 31 = 20 times.

We can use the following formula to figure out the percentage of conversions that result in leads.

percentage of tails = (number of tails / total number of spins) x 100

Let's paste the values ​​we have:

percentage of heads = (20/51) x 100

percentage of heads = 0.39215686274 x 100

percentage of tails = 39.215686274

Rounding to the nearest percentage, we get:  tail rate ≈ 39%  

Thus, approximately 39% of  coin tosses resulted in tails

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The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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The equation of the parabola in vertex form is y = (1/4)x² - 6.

To write the equation of the parabola in vertex form, we use the formula:

y = a(x-h)² + k

Where (h,k) is the vertex and "a" is a constant that determines the shape of the parabola.

Given that;

The vertex is (0,-6)

Hence:

h = 0 and k = -6.

We can substitute these values into the formula to get:

y = a(x-h)² + k

y = a(x - 0)² - 6

y = ax² - 6

Now we need to find the value of "a". We are also given that the parabola passes through the point (-6,3).

x = -6 and y = 3

We can substitute this point into the equation to get:

y = a(x - h)² + k

3 = a( - 6)² - 6

3 = 36a - 6

9 = 36a

a = 1/4

Now we know the value of "a", we can substitute it back into the equation we derived earlier:

y = ax² - 6

y = (1/4)x² - 6

Therefore, the equation in vertex form is y = y = (1/4)x² - 6.

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Answer:

s < [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

8s + 8 < s + 9

7s + 8 < 9

7s < 1

s < [tex]\frac{1}{7}[/tex]

Answer:

You just need to create an expression with the variables then add them together to get the total income: 7e + 13n

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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The vertical component of the initial velocity will basically decide where the vertices will be. that is how the initial velocity is related to the vertex of the parabola.

A parabola is a symmetrical curve that is formed by the intersection of a plane and a cone, where the plane is parallel to one of the cone's generating lines. The shape of a parabola is similar to that of a U-shaped curve, but with a sharper curve near the bottom of the U.

The parabola has several important properties, including a focus and a directrix. The focus is a point on the axis of symmetry of the parabola that is equidistant from every point on the curve. The directrix is a line that is perpendicular to the axis of symmetry and is equidistant from every point on the curve.

The equation of a parabola in standard form is y = ax² + bx + c, where "a" determines the direction and shape of the parabola, "b" determines the horizontal shift of the parabola, and "c" determines the vertical shift of the parabola.

The initial velocity will have two component basically, a horizontal component and a vertical component. The vertical component will decide how high the object will go, or in other words the vertical component of the velocity will decide the position of the vertex of the parabolis path which the object is going to follow.

When the vertical component of the velocity becomes 0, the object will be at it's maximum height (i.e the object will be at the vertex of the parabola)

The vertical component of the initial velocity will basically decide where the verties will be. that is how the initial velocity is related to the vertex of the parabola.

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1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer: 3:1

Step-by-step explanation:

a. The length of one side of the cube  shape x ≈ 3.633 ft

b. The length of one side of the cube  shape is roughly 3.633 feet.

c. The case has a more noteworthy surface region than the block by roughly 10.325 square feet.

Let x be the length of one side of the cube. Since the cube has equal length, width, and height, its volume is  = x^3.

The volume of the box  = (4 feet 5 in) * (3 feet 2 in) * (4 feet 3 in),

which can be converted to feet as Volume of box =

(4 + 5/12) * (3 + 2/12) * (4 + 3/12) = 4.3135 * 3.1667 * 4.25 =

55.0448 cubic feet.

Since the cube has the same volume as the box, we can set Volume of cube = Volume of box and

solve for x:

[tex]x^3 = 55.0448\\x = (55.0448)^{1/3}\\[/tex]

x ≈ 3.633 ft

b. The length of one side of the cube is approximately 3.633 feet.

c. We must determine the surface area of each to compare the cube's and box's surfaces. A cube with side length x has the surface area given by

Surface area of cube = [tex]6x^2[/tex], and

Surface area of a box = 2lw + 2lh + 2wh is the formula for the surface area of a box with the dimensions l, w, and h. Based on the box's dimensions, we have:

Surface area of cube = [tex]6(3.633)^2[/tex] ≈ 79.342 sq. feet

Surface area of box = 2(4.4167 * 3.25) + 2(4.4167 * 4.25) + 2(3.25 * 4.25) ≈ 89.667 sq. feet

By about 10.325 square feet, the surface area of the box is greater than that of the cube.

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Answer:

5

Step-by-step explanation:

6.5 / x = 1.3

multiply by x on each side to cancel it out

6.5 = 1.3x

/1.3   /1.3

x = 5

1.3 x 5 = 6.5

Answer:

So, the possible width of the banner would be 9 feet or less, since we have assumed a maximum total trim of 50 feet. If the width exceeds 9 feet, the total trim required would exceed the available trim of 50 feet. Therefore, the possible widths of the banner are 9 feet or less.

Step-by-step explanation:

Given:

Length of the banner (L) = 16 feet

Total trim available (T) = 50 feet

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Width)

In this case, the perimeter of the banner would be equal to the total trim available, since the trim goes all the way around the banner.

So, we can set up the equation as follows:

2 * (L + w) = T

Plugging in the given values:

2 * (16 + w) = 50

Simplifying the equation:

32 + 2w = 50

2w = 50 - 32

2w = 18

w = 18 / 2

w = 9

The cash collection from customers which adds the change in accounts receivable to the sales for the year 2014 is $749,000. Option C is the correct answer.

To determine the cash collected from customers during 2014, we need to find out the change in accounts receivable from the beginning to the end of the year.

The change in accounts receivable is calculated as follows:

Change in accounts receivable = Accounts receivable, December 31, 2014 - Accounts receivable, December 31, 2013

= $63,000 - $67,000

= -$4,000

The negative sign indicates a decrease in accounts receivable, meaning that cash was collected from customers.

Now, to find the cash collected from customers, we need to add the change in accounts receivable to the sales for the year:

Cash collected from customers = Sales - Change in accounts receivable

= $745,000 - (-$4,000)

= $749,000

Therefore, the answer is C. $749,000.

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The question is -

Mallick Corp. reported the following information for 2013 and 2014.

Accounts receivable, December 31, 2013, $ 67,000

Accounts receivable, December 31, 2014, 63,000

Sales (all on credit) -- 2014 745,000

How much cash was collected from customers in 2014?

A. $741,000

B. $745,000

C. $749,000

D. $753,000