Zhang walks in a straight line from the trail head at (0,0). He travels at an average rate of 3 mi/h in the direction 30° west of north. What are the coordinates of Zhang's location, relative to the trail head, after 4 hours?

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The explanation of how to convert a general form equation to a standard form equation is given below:

Let's first look at how to convert a general form equation to a standard form equation. Given a general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Complete the square for both x and y:

a. Divide the coefficients D and E by 2, and square the results. Let's call these values Cx and Cy:

Cx = (D/2)^2

Cy = (E/2)^2

b. Add and subtract Cx and Cy on both sides of the equation:

x^2 + Dx + Cx + y^2 + Ey + Cy = -F + Cx + Cy

Rearrange the equation to form the standard form equation:

a. Group the x and y terms and rewrite as perfect squares:

(x + D/2)^2 + (y + E/2)^2 = -F + Cx + Cy

b. Now, compare this to the standard form equation:

(x - h)^2 + (y - k)^2 = r^2

c. Identify the values of h, k, and r:

h = -D/2

k = -E/2

r^2 = -F + Cx + Cy

Now let's see how to convert a standard form equation to a general form equation. Given a standard form equation:

(x - h)^2 + (y - k)^2 = r^2

Expand the squares:

(x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2

Rearrange the equation to form the general form equation:

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

Compare this to the general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Identify the values of D, E, and F:

D = -2h

E = -2k

F = h^2 + k^2 - r^2

Now you can convert equations between the general form and the standard form. If you're missing some variables in the general form equation, just treat them as zero and proceed with the same steps.

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Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

The total cost of renting a small car with insurance is:

$465 = $25x + $21x

Simplifying and solving for x, we get:

$465 = $46x

x = 10.11

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

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Therefore, the simplified expression is (c).-5.05u - 6.

To simplify an expression, you typically want to combine like terms and perform any necessary operations in the correct order. Here are the steps you can follow:

Identify any like terms in the expression. Like terms are terms that have the same variables raised to the same powers.

Combine the coefficients of like terms. If there are no like terms, leave the expression as is.

Simplify any operations in the expression, such as multiplication, division, addition, or subtraction, according to the order of operations.

Check if the expression can be simplified further. If it can, repeat steps 1-3 until the expression cannot be simplified further.

Here's an example of how to simplify the expression. [tex]3x + 2x^2 - 5x - x^2[/tex]:

Identify like terms: 3x and -5x are like terms, as are [tex]2x^2[/tex] and [tex]-x^2[/tex].

Combine the coefficients of like terms: [tex]3x - 5x = -2x[/tex], and [tex]2x^2 - x^2[/tex]= x^2. So, the expression becomes:

[tex]-2x + x^2[/tex]

The expression is already simplified in terms of like terms, so there are no further operations to perform.

The expression cannot be simplified further, so the final answer is [tex]-2x + x^2.[/tex]

(3.65u − 11) − (−5 + 8.7u) can be simplified as follows:

First, distribute the negative sign in the second parenthesis:

[tex](3.65u -11) + (5 -8.7u)[/tex]

Next, combine like terms:

[tex]3.65u - 8.7u - 11 + 5[/tex]

Simplify:

[tex]-5.05u - 6[/tex]

Therefore, the simplified expression is -5.05u - 6.

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the complete question: Simplify the expression.

(3.65u − 11) − (−5 + 8.7u)

(a).12.35u + (−6)

(b). −5.05u + (−16)

(c). −5.05u + (−6)

(d).12.35u + (−16)

The equation (x + 6)^2 + (y + 4)^2 = 36 is in the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle, and r is the radius of the circle. Comparing this with the given equation, we see that the center of the circle is (-6, -4), and the radius of the circle is 6.

Therefore, the signal is located at the point (-6, -4), which is the center of the circle. This is the point from which the radio signal is transmitted.

The range of the signal is the distance from the center of the circle to any point on the circumference of the circle, which is equal to the radius of the circle.

In this case, the radius is 6, which means that the range of the signal is 6 units in all directions from the center. This means that any receiver within 6 units of the center can pick up the radio signal transmitted from this source.

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1) The name of the shape is rectangle

2) The name of the shape is trapezoid

3) The name of the shape is rhombus

4) The name of the shape is rectangle

From the question, we are to state the most specific name for each of the given figures

1.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

2.

We have a quadrilateral

Only a pair of opposite sides are parallel

The name of the shape is trapezoid

3.

We have a quadrilateral

Opposite sides are parallel and equal

All sides are equal

None of the angle is a right angle

The name of the shape is rhombus

4.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

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If 75 kids of the 90 kids were girls. The ratio of boys to girls is 1:5.

If there were 75 girls out of 90 kids in total, then the number of boys can be found by subtracting 75 from 90:

The Number of boys = 90 - 75 = 15

Therefore, the ratio of boys to girls is:

The Number of boys : The Number of girls

15 : 75

To simplify this ratio, we can divide both sides by 15 (which is the greatest common factor of 15 and 75):

15 ÷ 15 : 75 ÷ 15

1 : 5

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Answer: 3 additional men are needed to reduce the work by 1 hour.

Step-by-step explanation: There is a relationship between working men and the hours needed to complete the work, both are inversely proportional to each other.

Let, x represent the number of men required to complete the work in :

5-1 = 4 hours

then,

4x = 5 * 12 = 60

Hence,

x = 60/4 = 15

There are 12 men, who are working currently on the job and 15 men are required to complete the work in 1 hour less time.

Then,

15 - 12 = 3

3 additional men are required to reduce work by 1 hour.

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The goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly. The statement is True.

The basic purpose of data analysis is to obtain meaningful insights and information from data by examining it. While knowing how information progresses is an important part of this process, the ultimate goal is to get a better knowledge of the data itself, as well as any patterns or correlations that may exist within it.

The process of troubleshooting and problem-solving is more directly tied to determining why information is not flowing properly. This may entail examining the data to discover any abnormalities, mistakes, or inconsistencies that may be interfering with information flow. Once these concerns have been recognized, efforts may be made to fix them and enhance information flow.

Therefore, the statement is true, the goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly.

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TRUE. In the data analysis step, the focus is on examining and evaluating data to identify patterns, trends, and insights. The goal is to pinpoint any issues or inefficiencies in the way information flows and to determine the root cause of these problems.

By analyzing the data, organizations can gain a better understanding of their processes and identify areas for improvement.
 In the data analysis step, the goal is to examine and understand the current flow of information. This involves analyzing the data to identify patterns, trends, and any potential issues. By pinpointing the reasons why the information is not flowing properly, you can then work towards implementing solutions to improve the efficiency and effectiveness of the data management process.

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Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

The total area of the figure with of the semicircle and triangle is 12.27 sq. ft.

Half of a circle is known as a semicircle, and the diameter of the circle is equal to the length of the semicircle's straight edge. A sector of a circle is a section of a circle that is bounded by an arc, two radii, and both. A semicircle is always half of a circle and has a constant central angle of 180 degrees, but a sector can be any part of a circle and has a central angle that can vary from 0 to 360 degrees. This is the major distinction between the two.

Given, the diameter of the semicircle is 3 ft, so its radius is 1.5 ft.

Now, area of the semicircle is given as:

A = 1/2 * pi * (1.5)² = 1.77 sq ft

The area of the triangle is:

A = 1/2 * 3 ft * 7 ft = 10.5 sq ft

Adding the areas we have the total area of the figure:

1.77 sq ft + 10.5 sq ft = 12.27 sq ft

Hence, the total area of the figure is 12.27 sq. ft.

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In a standard additions method workup the information from the linear regression that is most closely related to the unknown concentration is this:  the intercept of the linear regression line.

In the standard additions method workup, the information that is most closely related to the unknown concentration is the intercept of the linear regression line.

The reason why this is the case is that the intercept represents the y-value of the regression line where the line crosses the y-axis. This y-axis is the value of the dependent variable when the independent variable or concentration is zero. So, by solving for the intercept, we can determine the concentration of the unknown sample.

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Here are the given expressions and their respective variables and coefficients:

12s + 4t | Variables: s, t | Coefficients: 12, 4

46rs + 10x | Variables: r, s, x | Coefficients: 46, 10

12q + 14x | Variables: q, x | Coefficients: 12, 14

10x + 10y | Variables: x, y | Coefficients: 10, 10

17rs + 32x | Variables: r, s, x | Coefficients: 17, 32

5x + 7y - 12z | Variables: x, y, z | Coefficients: 5, 7, -12

36ab + 70m | Variables: a, b, m | Coefficients: 36, 70

3r + 19a + 10m | Variables: r, a, m | Coefficients: 3, 19, 10

7k + 16m | Variables: k, m | Coefficients: 7, 16

8r + 5s | Variables: r, s | Coefficients: 8, 5

9h + 120m | Variables: h, m | Coefficients: 9, 120

12k + m | Variables: k, m | Coefficients: 12, 1

7g + 15h + w | Variables: g, h, w | Coefficients: 7, 15, 1

4c - 8d + 12f | Variables: c, d, f | Coefficients: 4, -8, 12

6t + 17r - 35j | Variables: t, r, j | Coefficients: 6, 17, -35

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The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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Answer:

[tex]36x^{3}a+45xa^{2}=9xa(4x^{2} +5a)[/tex]

Step-by-step explanation:

You can factor out both 9, x, and a, as all the terms can be divided by 9xa.

Hope this helped!

The scientist used 0.786 liters of the liquid for the experiment.

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in a different unit of measurement.

To convert between different units of measurement, we need to use conversion factors, which relate to the two units.

In this case, the conversion factor is 1 liter = 1000 milliliters, which allows us to convert from milliliters to liters by dividing by 1000.

Here we have

A scientist used 786 millimeters  

To convert milliliters to liters, we need to divide by 1000 since there are 1000 milliliters in one liter.

So, to convert 786 milliliters to liters, we divide by 1000:

786 milliliters ÷ 1000 = 0.786 liters

Therefore,

The scientist used 0.786 liters of the liquid for the experiment.

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Complete Question:

A scientist used 786 milliliters of a liquid for an experiment. How many liters of the liquid did the scientist use for this experiment?

Therefore, the value of x that makes the equation true is x = 2/3.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It typically consists of variables, constants, and mathematical operators (such as addition, subtraction, multiplication, and division) that are used to describe a relationship between two or more quantities. Equations are often used in various fields of mathematics, science, engineering, and economics to model real-world phenomena and solve problems.

The equation is:

[tex]x + 4 = 4x + 2[/tex]

We need to find the value of x that makes this equation true.

First, we can simplify the equation by subtracting x from both sides:

[tex]4 = 3x + 2[/tex]

Next, we can simplify further by subtracting 2 from both sides:

[tex]2 = 3x[/tex]

Finally, we can solve for x by dividing both sides by 3:

[tex]x = 2/3[/tex]

Therefore, the value of x that makes the equation true is x = 2/3.

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The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

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The answer of the given question based on the graph is , option (b)  the function of the given graph could be f(x) = (x+2)(x − 2)³ (x-5)².

A function is a relationship between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output.

A function is typically represented symbolically by an equation that describes how the output depends on the input. For example, the function f(x) = 2x + 3 represents a relationship between the input x and the output 2x + 3, which is obtained by multiplying x by 2 and then adding 3.

The given graph has three x-intercepts at x=-2, x=2, and x=5. It also has a local minimum at x=4, where the function crosses the x-axis.

From the information given, we can see that f(x) has factors of (x+2), (x-2), and (x-5) raised to some power, which account for the x-intercepts.

We also know that the function changes sign at x=4, which means there must be a factor of (x-4) or (4-x) in the function.

Based on this information, we can eliminate options (a) and (d) since they do not include a factor of (x-4) or (4-x).

Option (c) includes an additional factor of (x-4), which would account for the sign change at x=4, but it has the same power on (x+2) as on (x-2), which is not consistent with the graph. Therefore, we can eliminate option (c).

This leaves us with option (b), which has the correct factors and powers to account for the x-intercepts and the sign change at x=4. Therefore, the function of the given graph could be f(x) = (x+2)(x − 2)³ (x-5)².

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The relative frequency of the given students surveyed and prefer to go to Cook Middle School and Energy Flow is equal to 0.4 or 40%.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow

= (Number of students go to Cook Middle School and prefer Energy Flow) /( total number of students surveyed)

From the given table,

The number of students who go to Cook Middle School and prefer Energy Flow is  equal to 20.

The total number of students surveyed is equal to 50.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow is,

= 20/50

= 0.4

Therefore, the relative frequency of all students surveyed going to the Cook Middle School and prefer Energy Flow is equal to 0.4 or 40%.

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The above question is incomplete, the complete question is :

Some students at Cook Middle School and Elm Middle School participated in a survey. They were asked which sports drink they prefer: Gym Juice or Energy Flow. The two-way table shows the results.

                       Gym Juice        Energy Flow   Total

Cook                   15                     20                    35

Elm                       5                     10                     15

Total                    20                     30                     50

What is the relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow?

According to the information, the surface area of the first prism is 795 cm², sencond prism is 843 in², and the cylinder is 3775.87 mm²

To find the surface area of two triangular prisms, we need to add the surface area of each prism. We can use the formula we found in the previous question to calculate the surface area of each triangular prism:

Surface area of first triangular prism = 2(0.5 x base x height) + perimeter x height

where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.

In this case, the first triangular face has a base of 9 cm, a height of 16 cm, and a perimeter of (9+15+12)=36 cm. Therefore, the area of each triangular face is:

0.5 x 9 cm x 16 cm = 72 cm²

The rectangular faces have dimensions of 9 cm x 15 cm, 15 cm x 16 cm, and 9 cm x 16 cm. Therefore, the area of each rectangular face is:

9 cm x 15 cm = 135 cm²

15 cm x 16 cm = 240 cm²

9 cm x 16 cm = 144 cm²

The total surface area of the first triangular prism is:

2(72 cm²) + (135 cm² + 240 cm² + 144 cm²) = 795 cm²

Similarly, for the second triangular prism, we have:

Surface area of second triangular prism = 2(0.5 x base x height) + perimeter x height

where base is the width of the triangular face, height is the height of the triangular face, and perimeter is the sum of the lengths of the three sides of the triangular face.

In this case, the second triangular face has a base of 8 in, a height of 15 in, and a perimeter of (8+15+20)=43 in. Therefore, the area of each triangular face is:

0.5 x 8 in x 15 in = 60 in²

The rectangular faces have dimensions of 8 in x 21 in, 15 in x 21 in, and 8 in x 15 in. Therefore, the area of each rectangular face is:

8 in x 21 in = 168 in²

15 in x 21 in = 315 in²

8 in x 15 in = 120 in²

The total surface area of the second triangular prism is:

2(60 in²) + (168 in² + 315 in² + 120 in²) = 843 in²

Therefore, the surface area of two triangular prisms is:

795 cm² + 843 in² = 795 cm² + (843 in² x 6.452 cm²/in²) ≈ 5508 cm²

For the cylinder, we can use the formula we found in the previous question to calculate the surface area:

Surface area of cylinder = 2πr² + 2πrh

where r is the radius of the circular face, h is the height of the cylinder.

In this case, the radius is 14 mm and the height is 29 mm. Therefore, the surface area of the cylinder is:

2π(14 mm)² + 2π(14 mm)(29 mm) = 2π(14 mm)(43 mm) ≈ 3775.87 mm²

Therefore, the surface area of two triangular prisms and a cylinder is approximately:

5508 cm² + 3775.87 mm² = 5508 cm² + (3775.87 mm² x 0.01 m²/mm²) ≈ 5885.47 cm²

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Answer: A possible thesis statement for this art piece could be:

Through his painting "Pont du Gard" (1787), Hubert Robert showcases his mastery of perspective and architectural detail, capturing the grandeur and beauty of the ancient Roman aqueduct and highlighting the interplay between nature and human engineering in the landscape.

Step-by-step explanation:

the sample space of two-digit numbers using the digits 9, 4, 5, and 8 consists of 16 possible outcomes, and we can list all these outcomes in a table as shown above.

How to solve the question?

To create a sample space of two-digit numbers using the digits 9, 4, 5, and 8, we need to consider all possible combinations of these digits. We can list all possible outcomes in a table where each digit represents a column and each combination represents a row.

The first digit can be any of the four digits, and the second digit can also be any of the four digits, including the same digit as the first. Therefore, the total number of outcomes is 4 x 4 = 16.

Here is the sample space of two-digit numbers using the digits 9, 4, 5, and 8:

         9    4   5     8

9 99 94 95 98

4 49 44 45 48

5 59 54 55 58

8 89 84 85 88

As shown in the table, the first digit can be any of the four digits, and the second digit can also be any of the four digits. For example, the first row shows that the possible two-digit numbers starting with 9 are 99, 94, 95, and 98. Similarly, the second row shows that the possible two-digit numbers starting with 4 are 49, 44, 45, and 48, and so on.

In conclusion, the sample space of two-digit numbers using the digits 9, 4, 5, and 8 consists of 16 possible outcomes, and we can list all these outcomes in a table as shown above.

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The probability of a bulb lasting between 547 and 580 hours is approximately 0.0392

To solve this problem, we first need to standardize the values using the formula

z = (x - μ) / σ

where

x is the value we want to find the probability for,

μ is the mean, and

σ is the standard deviation.

In this case, we want to find the probability that a bulb will last between 547 and 580 hours, so we need to find the z-scores for these values.

z1 = (547 - 530) / sqrt(625) = 1.72

z2 = (580 - 530) / sqrt(625) = 2.8

Next, we use a standard normal distribution table or calculator to find the probabilities for each z-score. For example, using a calculator, we can find that

P(z1 < Z < z2) = P(1.72 < Z < 2.8) ≈ 0.0392

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Answer:

Step-by-step explanation:

Here you go:

64 = 512x - 4

64 + 4 = 512x - 4 + 4

68 = 512x

Hope this helps

Three trigonometric ratios are Sin C=21/29,Cos C=20/29, Tan C=21/20.

Trigonometric ratios, also known as trigonometric functions, are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

In the given triangle;

AB=21

BC=20

AC=29

Calculating trigonometric ratios;

Sin C=Perpendicular/Hypotenuse

=AB/AC

=21/29

Cos C=Base/Hypotenuse

=BC/AC

=20/29

Tan C=Perpendicular/Base

=AB/BC

=21/20.

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The value of C of is 49/4

Completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. In other words, completing the square places a perfect square trinomial inside of a quadratic expression.

10k²+7k+C , to find the value of c that will make the expression a perfect square we divide b by 2 and Square it.

Since b = 7

therefore c =( b/2)²

c = (7/2)² = 49/4

therefore the value of C is 49/4.

The expression can now be written as;

10k²+7k +49/4

and it can be simplified as;

40k²+28k +49

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The expression that represents the total price of buying g pounds of grapes, b pounds of bananas, and p pounds of pears is Total cost = $2.19g + $0.59b + $1.49p

In this case, we need to use the given prices per pound of each fruit to calculate the total cost of purchasing a certain amount of each fruit. We can do this by multiplying the price per pound by the number of pounds of each fruit we want to buy, and then adding up these values.

So, to create the expression, we can start by using the given prices to calculate the cost of each fruit:

Grapes: $2.19/pound

Bananas: $0.59/pound

Pears: $1.49/pound

Next, we can use the variables g, b, and p to represent the number of pounds of each fruit we want to buy. We then multiply each price by its respective variable to get the cost of each type of fruit:

Cost of grapes: $2.19/g x g = $2.19g

Cost of bananas: $0.59/b x b = $0.59b

Cost of pears: $1.49/p x p = $1.49p

Finally, we can add up the costs of all three types of fruit to get the total cost:

Total cost = $2.19g + $0.59b + $1.49p

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Answer: D

Step-by-step explanation:

Zach won because 3 16/24 is less than 3 15/24. Then, 3.666666 is less than 3.625