A line passes through the points (–
3,–
18) and (3,18). Write its equation in slope-intercept form

The properties of exponents

1. [tex](64)^{1/2}[/tex] = √(64) = 8

2.  [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]

3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]

The properties of exponents can be used to simplify and rewrite expressions involving powers and roots. The most common properties are:

Product of powers: [tex]a^m[/tex] * aⁿ = [tex]a^{m+n}[/tex]

Quotient of powers: [tex]a^m[/tex]/ aⁿ = [tex]a^{m-n}[/tex]

Power of a power: [tex](a^m)^n[/tex] = [tex]a^{mn}[/tex]

Power of a product: [tex](ab)^m[/tex] = [tex]a^m[/tex] * [tex]b^m[/tex]

Power of a quotient: [tex](a/b)^m[/tex] = [tex]a^m[/tex]/ [tex]b^m[/tex]

Using these properties, we can rewrite the given equations as follows:

1. [tex](64)^{1/2}[/tex] = √(64) = 8

The square root of 64 is 8. The power of 1/2 represents the square root.

2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]

The power of 3/2 represents the square root of the square. We can use the product of powers property to combine the m and n terms under the same square root.

3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]

We can use the power of a product property to square the 5ab term, and then simplify by combining the like terms.

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Answer:

There is a cylinder with a height of 6 centimeters and a radius of r1, which has a volume of 302 cubic centimeters. It's fascinating to see how the volume of different shapes can vary based on their dimensions.

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When x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.

Differential,

To find the differential dy, we use the formula:

dy = f'(x) * dx

where f'(x) is the derivative of the function y = tan(5x + 5) with respect to x.

Taking the derivative, we get: f'(x) = sec^2(5x + 5) * 5 Plugging in x = 3, we get: f'(3) = sec^2(20) * 5

Now we can find the differential dy for dx = 0.4 and dx = 0.8:

When dx = 0.4: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.4 dy ≈ 4.056

When dx = 0.8: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.8 dy ≈ 8.113

Therefore, when x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.

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Her total earnings increase by $21.25 for every hour she works, since her hourly wage is constant.

The relationship between Natalie's earnings and the number of hours she works can be represented by a linear equation in the form y = mx + b, where y is her total earnings, x is the number of hours she works, m is her hourly wage, and b is her initial earnings (or y-intercept).

To find the hourly wage, we can divide her total earnings by the number of hours she works:

hourly wage (m) = total earnings / number of hours worked

m = 85 / 4 = 21.25

So, Natalie's hourly wage is $21.25.

Now, we can use this information to create a table that shows the relationship between the number of hours she works and her total earnings:

| Hours worked (x) | Total earnings (y) |
|------------------|-------------------|
|       1          |       21.25       |
|       2          |       42.50       |
|       3          |       63.75       |
|       4          |       85.00       |

As you can see, her total earnings increase by $21.25 for every hour she works, since her hourly wage is constant. Therefore, the correct table that represents the relationship between the number of hours she works and her total earnings is the one shown above.

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There are approximately 5500 dimes in the jar. A) 5.5 x 103 dimes.

To determine the number of dimes in the jar, we can divide the total mass of the dimes by the mass of each dime.

Total mass of dimes = 1.265 x 10 grams

Mass of each dime = 2.3 grams

Let "x" be the number of dimes in the jar. Then, we can set up the following equation:

x(2.3 grams) = 1.265 x 10 grams

Simplifying this equation, we get:

x = 1.265 x 10 / 2.3

x ≈ 5500

It is important to that this calculation assumes that all dimes have the same mass, and that there are no other objects in the jar.

the actual number of dimes may vary slightly due to measurement error or variability in the mass of each dime.

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Answer:

  b. g(t) = 1.5 sin (π t) +3.5

Step-by-step explanation:

You want to choose the function that has the given graph.

At t = 0, the graph shows a value of 3.5. The sine of 0 is 0, so this eliminates choice A.

At t = 1/2, the graph shows a value of 5. The values given by the different formulas are ...

  b. g(1/2) = 1.5·sin(π/2) +3.5 = 5 . . . . . matches the graph

  c. h(1/2) = 1.5·sin(π) + 3.5 = 3.5 . . . . no match

  d. h(1/2) = 1.5·sin(π/4) +3.5 = 0.75√2 +3.5 . . . . no match

__

Additional comment

The horizontal distance for one period of the graph (from peak to peak, for example) is T = 2 seconds. If the sine function is sin(ωt), then the value of ω is ...

  ω = 2π/T = 2π/2 = π

This tells you the function g(t) = 1.5·sin(πt)+3.5 is the correct choice.

Peter will need 60 square inches of gold paper to cover the entire square pyramid for his History class.

You need to find the total surface area of the square pyramid that Peter creates for his History class to determine how much gold paper he will need. This can be done as follows.

1: Identify the given information.

Base area: 20 square inches

Triangle area: 10 square inches

2: Determine the number of triangles in a square pyramid.

A square pyramid has 4 triangular faces.

3: Calculate the total area of the triangular faces.

Multiply the area of one triangle by the number of triangles: 10 square inches x 4 = 40 square inches.

4: Calculate the total surface area of the pyramid.

Add the base area and the total area of the triangular faces: 20 square inches (base) + 40 square inches (triangles) = 60 square inches.

Hence, the gold paper to cover the entire square pyramid is 60 square inches.

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Therefore, the correct sequence of transformations is:

Dilation by a scale factor of 2, centered at the origin.

Translation of 7 units to the left.

This is equivalent to option D.

To move AABC onto ADEF, we need to perform a sequence of transformations that will map each point of AABC onto the corresponding point of ADEF. Let's first label the vertices of AABC and ADEF as shown:

We can see that A and D have the same coordinates, so we only need to map B, C, and A' to E, F, and D', respectively.

Option A suggests a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis. This transformation will map B to E, but it will also map C to C' which is not the same as F. Moreover, A' will be mapped to a point that is reflected over the y-axis and does not coincide with D. Therefore, option A is not the correct answer.

Option B suggests a translation of 7 units to the right, followed by a dilation by a scale factor of 2 centered at the origin. This transformation will not map B to E, but it will map A' to D', and C to a point that is 7 units to the right of F. Therefore, option B is not the correct answer either.

Option C suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the right. This transformation will map A' to D', and B to a point that is 7 units to the right of E. However, it will also map C to a point that is 7 units to the right of F, which is not the same as F. Therefore, option C is not the correct answer.

Option D suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the left. This transformation will map B to E, and A' to D', but it will also map C to a point that is 7 units to the left of F. However, if we reflect the resulting figure over the y-axis, we obtain the desired result.

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Astha's account was greater than the amount of money in Henry's account is:

5700 + 100x > 75x

Let's start by finding the total amount of money deposited by Astha and Henry after x weeks.

Astha deposited $100 into her account each week for x weeks, so the total amount she deposited is 100x.

Similarly, Henry deposited $75 into his account each week for x weeks, so the total amount he deposited is 75x.

To find the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account, we need to compare the total amount of money each of them deposited.

Astha started with $5,700 and deposited $100 each week for x weeks, so the total amount of money in her account after x weeks is:

5700 + 100x

Henry started with zero dollars and deposited $75 each week for x weeks, so the total amount of money in his account after x weeks is

75x

Therefore, the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account is:

5700 + 100x > 75x

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Drawing a number line is a useful way to visualize the relationship between tons and pounds and can help make conversions easier to understand.

If we were to draw a number line that shows the relationship between tons and pounds, we would start with the fact that one ton is equivalent to 2000 pounds. We would then draw tick marks on the number line for every whole number from 0 to 10, with each tick mark representing 100 pounds. So, the tick mark at 0 would represent 0 pounds, the tick mark at 1 would represent 100 pounds, the tick mark at 2 would represent 200 pounds, and so on. The tick mark at 20 would represent 2000 pounds, or one ton.

We could then continue the number line past 20 to show larger quantities of tons and pounds, with each additional tick mark representing another ton (2000 pounds). For example, the tick mark at 30 would represent 3000 pounds, or 1.5 tons, the tick mark at 40 would represent 4000 pounds, or 2 tons, and so on.

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The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.

The null hypothesis (H₀) states,

That there is no significant difference between the population means of the experimental group and the control group.

The alternative hypothesis (H₁) states that there is a significant difference between the two means.

State the hypotheses as,

H₀: μ₁ - μ₂ = 0 (there is no difference in means)

H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)

where μ₁ is the population mean of the experimental group

And μ₂ is the population mean of the control group.

The test statistic,

Use the t-test formula,

t = (x - μ) / (s / sqrt(n))

where x is the sample mean = 102

μ is the hypothesized population mean = 100

s is the sample standard deviation =88

n is the sample size= 10

Plugging in the values, we get,

t = (102 - 100) / (88 / sqrt(10))

 = 0.45

Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of  88, a mean of 100, and with a sample size of 10.  

a. State the null and the alternative hypotheses.

b. Compute the test statistic for sample mean 102.

Answer:

31

Step-by-step explanation:

1. Replace the variables with numbers

8(5)-(9)

2.Conduct order of operations

8(5)-9           -->     40-9    ---> 31

Answer:

31

Explanation:

Trust

The possible total number of boys and girls in the class is 21, and

the answer is b).

Let's denote the number of girls in the class as 'g' and the number of

boys as 'b'.

We know that all students in the class study either French or German,

but not both.

Therefore, the total number of students in the class is equal to the sum

of the number of students who study French and the number of students

who study German

From the given information, we can write the following equations:

        study German

Substituting this into the first equation, we get:

Substituting this into the first equation, we get:

Therefore, the total number of students in the class must be a multiple

of 3.

Let's try the answer choices:

a) 15 students (total number of students is not a multiple of 3)

b) 21 students (total number of students is a multiple of 3 and the

number of girls is a multiple of 3, so this is a possible solution)

c) 24 students (total number of students is a multiple of 3 and the

number of girls is not a multiple of 3)

d) 30 students (total number of students is a multiple of 3 but the

number of girls is not a multiple of 3)

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The number of pints of paint that the club will need is given as follows:

2 pints of paint.

Before obtaining the amount of paint, we must obtain the surface area of the figure.

The figure in this problem is composed as follows:

Hence the surface area is given as follows:

S = 19 x 8 + 19 x 6 + 2 x 0.5 x 6 x 8

S = 314 in².

If one pint of paint covers 200 square inches, hence the number of pints is given as follows:

314/200 = 2 -> rounded up, as there is not a decimal amount of pints, and one pint is not enough.

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Answer:

Step-by-step explanation:

Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.

Answer:

1) I think the graph is suggesting that a higher level of skill, or degree, will ultimately help you get a better job easier and faster.

2) With a skill level of five, you can become a sales worker or labourer. It is a low percentage of people with a skill level five to become community and personal service workers.

Thanks for reading! Always work toward your dreams! :)

the area of the circle on the paper is approximately 0.8 square inches.

To find the area of the circle traced on the paper, we'll use the formula for the area of a circle, which is A = πr², where A is the area, π is approximately 3.14, and r is the radius.

The diameter of the quarter is about 1 inch, so the radius is half of that, which is 0.5 inches. Now, plug the radius into the formula:

A = 3.14 × (0.5)²
A = 3.14 × 0.25
A ≈ 0.785

Therefore, the area of the circle on the paper is approximately 0.8 square inches when rounded to the nearest tenth.

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The volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.

The volume of a sphere is given by the formula:

V = (4/3)πr³

where r is the radius of the sphere.

If the diameter of the globe is reduced by half, then the new diameter would be 9 inches, and the new radius would be half of that, or 4.5 inches.

The new volume would be:

V' = (4/3)π(4.5)³

= (4/3)×3.14×(91.125)

= 381.51 cubic inches

Therefore, the volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.

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The value of c is 0.4 and  the corresponding horizontal distance travelled by the ball is 4 meters.

We are given the projectile equation:

y = -1/8x² + x + c

To find the value of c, we can use the fact that the maximum height attained by the ball is 2.4 meters. The maximum height occurs at the vertex of the parabola, which is given by:

x = -b/2a

where a = -1/8 and b = 1.

Therefore,

x = -(1)/(2*(-1/8)) = 4

So, the corresponding horizontal distance travelled by the ball is 4 meters.

Now, we can use the maximum height attained by the ball to solve for c.

y = -1/8x² + x + c

Substituting x = 4 and y = 2.4, we get:

2.4 = -1/8(4)² + 4 + c

2.4 = -1/8(16) + 4 + c

2.4 = -2 + 4 + c

c = 0.4

Therefore, the value of c is 0.4.

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The length of MQ and QN is 10 and 15 respectively and verify that MQ: QN = 2:3

The coordinate of M = (-12,-5)

The coordinate of N = (8,10)

n = 2 , m = 3

By using the section formula coordinate of Q =( [tex]\frac{mx_{1} + nx_{2} }{m+n }[/tex] , [tex]\frac{my_{1} + ny_{2} }{m+n}[/tex])

Coordinate of Q = ([tex]\frac{(-12)3 + 8(2)}{3+2}[/tex] , [tex]\frac{10(2) + 3(-5)}{2+3}[/tex])

Coordinate of Q = ( -4, 1)

Now using the distance formula

MQ = [tex]\sqrt{ (x_{2}- x_{1} )^{2} +(y_{2} -y_{1} )^{2}[/tex]

MQ = [tex]\sqrt{(-4+12)^{2}+(1+5)^{2} }[/tex]

MQ = √100

MQ = 10

Similarly,

QN = [tex]\sqrt{(8+4)^{2}+(10-1)^{2} }[/tex]

QN =  [tex]\sqrt{225}[/tex]

QN = 15

MQ:QN = 10:15

MA :QN = 2:3

Hence it is verified that MQ: QN = 2:3

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The range of the equation y = x² + 2x -5 where -3 ≤ x ≤ 3 is [-3,10]

The function is y = x² + 2x -5

Domain of x is [-3,3]

By putting the value of x = -3

y = (-3)² + 2(-3) - 5

y = 9 - 6 -5

y = -2

Minimum possible value is -2

And by putting the value of x = 3

y = 3² + 2(3) -5

y = 9 + 6 -5

y = 10

Maximum possible value is 10

The value of y ranges between -2 ≤ y ≤ 10

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The question is incomplete the complete question is :

If y =  = x² + 2x -5 for  -3 ≤ x ≤ 3  then what will be the range of y ?

The volume of one smaller box is 1 cubic foot.

The volume of one smaller box is calculated by raising the length of its sides to the power of 3, so the volume of one smaller box is:

Volume (smaller box) = (1 foot)³ = 1 cubic foot

The number of smaller boxes that fit into a shipping container is obtained by multiplying the number of boxes that fit along each dimension, so the number of smaller boxes that fit into a shipping container is:

Number of smaller boxes = 20 boxes (width) × 40 boxes (length) × 20 boxes (height) = 16,000 boxes

To calculate the volume of the large shipping container, we need to multiply the length, width, and height of the container. Since each dimension is given in terms of the number of boxes it can hold, we need to multiply each dimension by the length of one smaller box (1 foot) to obtain the dimensions in feet. Therefore, the volume of the large shipping container is:

Volume of the large shipping container = 20 boxes (width) × 1 foot (length of one smaller box) × 40 boxes (length) × 1 foot (length of one smaller box) × 20 boxes (height) × 1 foot (length of one smaller box) = 16,000 cubic feet

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By using Pythagoras' theorem, triangle 3 and 4 is a right triangle, and others are not.

What is the triangle?

A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees.

What is right-angled triangle?

A right-angled triangle is one with one of its interior angles equal to 90 degrees, or any angle is a right angle.

According to the given information:

The Pythagorean theorem states that " In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides"

Let's check fig (3)

[tex]15^{2} =12^{2} +9^{2}[/tex]

225 = 144 + 81

225 = 225

both sides are equal, Therefore it is a right-angled triangle.

Let's check fig (4)

[tex]48.5^{2}=39^{2}+32.5^{2}[/tex]

2352.25 = 1521 + 1056.25

2352.25 ≠ 2577.25

Both sides are not equal, Therefore it is not a right-angled triangle.

Let's check fig (5)

[tex]11^{2}=9^{2}+\sqrt{115} ^{2}[/tex]

121 = 81 + 115

121 ≠ 196

Both sides are not equal, Therefore it is not a right-angled triangle.

Let's check fig (6)

[tex]16^{2} = 10^{2} + (2\sqrt{39}) ^{2}[/tex]

256 = 100 + 156

256 = 256

both sides are equal, Therefore it is a right-angled triangle.

Hence figure 3 and 6 is right angle triangle, others are not.

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To determine the person who made the best kick, you could use an equation that relates distance, speed, and height: distance = speed × time.

To determine the person with the best kick, it is vital that a correlation be drawn between the distance and height. In the absence of information about time, the person with the farthest distance and longest height can be determined as the person with the best kick.

So, to get the result without having the complete data, you can compare the height to determine the individual with the farthest distance and highest kick.

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The range of the number of bottled waters that approximately 68. 2% of the students drink is between 131 and 175 bottled waters per day.

The range of the number of bottled waters that approximately 68.2% of the students drink can be calculated using the empirical rule, also known as the 68-95-99.7 rule.

According to this rule, for a normal distribution:

Approximately 68.2% of the data falls within one standard deviation of the mean

Approximately 95.4% of the data falls within two standard deviations of the mean

Approximately 99.7% of the data falls within three standard deviations of the mean

falls within a certain number of standard deviations from the mean

Since we are interested in the range of values that approximately 68.2% of the students drink, we can start by calculating one standard deviation from the mean:

One standard deviation = mean ± standard deviation

= 153 ± 22

= 131 to 175

This answer is based on the empirical rule, which is a useful tool for understanding the spread of data in a normal distribution. It tells us that for a normal distribution, a certain percentage of the data

Therefore, approximately 68.2% of the students drink between 131 and 175 bottled waters per day.

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A) Internal goods in mathematics include problem-solving skills, logical thinking, analytical reasoning, and a deep understanding of mathematical concepts.

B) Coercive power, on the other hand, might manifest when individuals impose their methods or beliefs on others, potentially stifling creativity and discouraging alternative perspectives.
C) Teachers affirm their students' dignity as creative human beings in the ways they do mathematics by creating a safe space, encourage exploration and expression, value the learning process, celebrate creativity and originality in problem-solving

A) When you share these goods with others, they multiply in the sense that others also develop these skills, fostering collaboration, and generating new ideas, ultimately contributing to the overall progress in the field of mathematics.
B) Creative power in mathematical settings can be seen when individuals or teams come up with innovative solutions to problems, develop new theories, or find unique ways to apply mathematics to real-world situations.
C) Teachers can affirm their students' dignity as creative human beings in the ways they do mathematics by:
1. Encouraging students to explore multiple solution methods and strategies, allowing them to find the approach that best suits their thinking style.
2. Valuing each student's input, ideas, and questions, creating a safe and supportive environment for them to express their thoughts.
3. Challenging students with open-ended problems that require creativity and critical thinking, emphasizing the importance of understanding concepts over rote memorization.
4. Recognizing and celebrating each student's unique strengths and contributions to the learning process, promoting a growth mindset and a sense of accomplishment.

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Analysis whether the biases were present in the survey or not .

The different types of biases are:

Nonresponse bias

Under coverage

Poorly worded

Given,

Biases in survey .

When it comes to surveys, there are several factors that can influence a person's decision to participate, such as the timing and location of the survey, the perceived relevance of the questions and incentives offered for participation. In some cases, people may opt-out of participating in a survey due to privacy concerns, lack of interest or distrust of the organization conducting the survey.

In terms of biases, survey designers should be careful of different types of biases that can affect the results, such as sampling bias, selection bias and response bias.

For example, if a survey is only given to certain demographics, the results may not be representative of the target audience.

Similarly, if the survey questions are worded in a leading or biased way, it can influence a person's response and skew the results.

It is important for survey designers to be aware of these biases and take steps to minimize their impact. This can include using random sampling techniques to ensure a representative sample, testing survey questions with focus groups to ensure they are clear and unbiased, and providing clear and transparent information about the purpose and use of the survey data. By taking these steps, survey designers can create surveys that produce accurate and reliable results.

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Answer:

[tex]\frac{-5}{34}[/tex]

Step-by-step explanation:

[tex]\frac{5}{12} * \frac{-6}{17}[/tex]  = [tex]\frac{-30}{204}[/tex]

We can simplify.

[tex]\frac{-15}{102}[/tex]  ⇒ Divided both by 2

[tex]\frac{-5}{34}[/tex]  ⇒  Divided both by 3

[tex]\frac{-5}{34}[/tex] is the final answer

There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

Let's denote the number of $2 coins as x, the number of $1 coins as y, and the number of quarters as z.

We need to find all the possible combinations of x, y, and z that satisfy the equation:

2x + y + 0.25z = 2.50

Here's the corrected organized list of combinations:

(1, 0, 2) → $2 + $1 + $0 = $2.50

(0, 2, 2) → $0 + $2 + $0.50 = $2.50

(0, 1, 6) → $0 + $1 + $1.50 = $2.50

(0, 0, 10) → $0 + $0 + $2.50 = $2.50

There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

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