A dog named Bella has a rectangular bed that is 2 feet wide and 3 feet long. A larger dog, Kahuna, has a rectangular bed which is 5x feet wider and 8x feet longer than Bella's bed.


Which of the following equations could be used to determine the area of Kahuna's bed?

The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is 91%. Option A is the correct answer.

To calculate the coefficient of variation, first, we need to calculate the standard deviation and mean of the sample.

The mean of the sample is (3 + 5 + 12 + 3 + 2)/5 = 5.

To find the standard deviation, we first need to calculate the variance. The variance can be found by taking the sum of the squared differences between each data point and the mean, dividing by the sample size minus one, and then taking the square root.

The variance is ((3-5)² + (5-5)² + (12-5)² + (3-5)² + (2-5)²)/4 = 20.5.

The standard deviation is the square root of the variance, which is approximately 4.53.

Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100%.

Coefficient of variation = (4.53/5) x 100% = 90.6%.

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The question is -

A researcher has collected the following sample data. The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is?

a. 91%

b. 72.66%

c. 330%

d. 264%

Answer:

Step-by-step explanation:

Medium is 28

Mean is 29

Range is 11

Midrange is 29.5

2x² - 6у² is a difference of two squares since we can rewrite it as (x√2)² - (y√6)². Therefore, the answer is D.

A binomial expression is a polynomial with two terms. The terms can be added or subtracted from each other and may contain variables, coefficients, and exponents.

A common example of a binomial expression is (x+y). This binomial expression has two terms, x and y, which are added together. Another example is (2a - b), which has two terms, 2a and -b, which are subtracted from each other.

Binomial expressions are commonly used in algebra to express equations, formulas, and identities. They can be combined with other binomial expressions, constants, and variables to create more complex expressions. For example, (x+y)(x-y) is a binomial expression that represents the difference of two squares and can be simplified to x² - y².

Binomial expressions can also be raised to powers using the binomial theorem. This theorem provides a formula for expanding the power of a binomial expression, such as (x+y)^n or (a-b)^n, where n is a positive integer. The resulting expression will contain multiple terms, which can be simplified and rearranged using algebraic techniques.

The difference of two squares is a binomial expression in the form of a² - b², where a and b are terms. Using this definition, we can identify which of the given expressions is the difference of two squares:

A. 9g - 36h is not a difference of two squares since there are no squares involved.

B. 9a² - 4b⁶ is not a difference of two squares since both terms are squares, but they are not subtracted from each other.

C. 49m² + 81n² is not a difference of two squares since both terms are squares, but they are not subtracted from each other.

D. 2x² - 6у² is a difference of two squares since we can rewrite it as (x√2)² - (y√6)². Therefore, the answer is D.

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Therefore, the difference in mass between Earth and Venus is approximately 5.96513 x 10^24 kilograms.

The difference in mass between Earth and Venus is:

5.97 x 10^24 kg - 4.87 x 10^12 kg

To subtract these two values, we need to express them in the same scientific notation. Since 4.87 x 10^12 is much smaller than 5.97 x 10^24, we can express it in scientific notation with the same exponent as the mass of Earth:

4.87 x 10^12 kg = 0.00487 x 10^24 kg

Now we can subtract the two values:

5.97 x 10^24 kg - 0.00487 x 10^24 kg = 5.96513 x 10^24 kg

Therefore, the difference in mass between Earth and Venus is approximately 5.96513 x 10^24 kilograms.

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The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.

When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.

In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.

Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

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The equation of g(x) in parabola vertex form is g(x) = (x + 4)^2 + 3. Option (D) is the correct answer.

Since the vertex of the parabola is at (-4, 3), we can write the equation of the parabola in vertex form as:

g(x) = a(x + 4)^2 + 3

where "a" is a constant that determines the shape of the parabola. Since the parabola opens upward, "a" must be positive.

We also know that the parabola passes through the points (-6, 7) and (-2, 7). Substituting these values into the equation above, we get:

7 = a(-6 + 4)^2 + 3

7 = 4a + 3

4a = 4

a = 1

Substituting "a = 1" into the equation above, we get:

g(x) = (x + 4)^2 + 3

Therefore, the equation of g(x) in vertex form is g(x) = (x + 4)^2 + 3. Option (D) is the correct answer.

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Answer:  the solution for y in terms of x is y = (-1/4)x - 8.

Step-by-step explanation: In order to obtain a solution for y in the given equation of 4y = -x - 32, it is imperative to achieve the isolation of y on a singular side of the equation. To accomplish this task, it is possible to perform division on both sides of the equation by a factor of 4:

The given equation 4y/4 = (-x - 32)/4 can be expressed in an academic manner as follows: The given equation reveals that the quotient of 4y divided by 4 is equivalent to the quotient of the opposite of x added to negative 32, also divided by 4.

Upon performing simplification, the expression on the right-hand side yields:

The equation y = (-1/4)x - 8 can be expressed in an academic manner as follows: The dependent variable y is equivalent to the product of the constant (-1/4) and the independent variable x, with an additional decrement of eight.

16.) Mean average deviation= option C

17.) Range of a data set = option E.

18.) First quartile = opinion AB

19.) Second quartile = option B

20.) Third quartile = option A

21.) Interquartile range = option D

To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:

16.) Mean average deviation: The average deviation of data from the mean.

17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.

18.) First quartile: The median in the lower half.

19.) Second quartile: The median value in a data set.

20.) Third quartile: The median in the upper half.

21.) Interquartile range: The distance between the first and the third quartile.

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Answer: To find the length of the box using the partial quotient method, we divide the volume of the box by the product of its width and height:

Step 1: Divide the first digit of the dividend (5) by the divisor (7), and write the quotient (0) above the digit.

    0

  -----

7 |  5 0 4

Step 2: Multiply the divisor (7) by the quotient (0), and write the product (0) below the first digit of the dividend.

    0

  -----

7 |  5 0 4

      0

Step 3: Subtract the product (0) from the first digit of the dividend (5), and bring down the next digit (0) to the right of the difference.

    0

  -----

7 |  5 0 4

      0

    ---

      5 0

Step 4: Divide the first two digits of the new dividend (50) by the divisor (7), and write the quotient (7) above the second digit.

    0 7

  -----

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

Step 5: Multiply the divisor (7) by the quotient (7), and write the product (49) below the first two digits of the new dividend.

    0 7

  -----

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

      4 9

Step 6: Subtract the product (49) from the first two digits of the new dividend (50), and bring down the next digit (4) to the right of the difference.

    0 7

  -----

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

      4 9

    -----

        5 4

Step 7: Divide the first two digits of the new dividend (54) by the divisor (7), and write the quotient (7) above the second digit.

    0 7 7

  -------

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

      4 9

    -----

        5 4

Step 8: Multiply the divisor (7) by the quotient (7), and write the product (49) below the first two digits of the new dividend.

    0 7 7

  -------

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

      4 9

    -----

        5 4

      4 9

Step 9: Subtract the product (49) from the first two digits of the new dividend (54), and bring down the next digit (2) to the right of the difference.

    0 7 7

  -------

7 |  5 0 4

      0

    ---

      5 0

    - 4 9

    -----

        1 0

      4 9

    -----

        5 4

      4

Step-by-step explanation:

The circumference of the circle is approximately 54.1 yards.

Circumference is a term used to describe the distance around the edge of a circular object. It is a measurement of the total length of the circle's perimeter. The circumference of a circle is calculated by multiplying its diameter by the mathematical constant pi (π), which is approximately equal to 3.14.

The formula for calculating circumference is C=πd or C=2πr, where C represents the circumference, d represents the diameter, and r represents the radius of the circle. The diameter is the distance across the circle, passing through its center, while the radius is the distance from the center to the edge.

Circumference is a fundamental concept in geometry and is used to solve various real-world problems, such as calculating the distance traveled by a rotating wheel or finding the length of a wire needed to make a circular ring. Additionally, many physical phenomena, such as the movement of planets and the orbits of electrons, can be described using the concept of circumference.

The circumference of a circle with a radius of 8.6 yards can be found using the formula:

C = 2πr

where r is the radius and π is the mathematical constant approximately equal to 3.14.

Substituting the given value of the radius, we get:

C = 2 × 3.14 × 8.6

C = 54.088

Rounding this to the nearest tenth, we get:

C ≈ 54.1 yards

Therefore, the circumference of the circle is approximately 54.1 yards.

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The values of x and y of a curved ladder in feet given by the equation y=-1/20x^2+x are as follows in tabular form,

Values of x (in feet)                               Values of y (in feet)

0                                                               0

5                                                               3.75

10                                                              5

15                                                              3.75

20                                                             0

A curved ladder that children can climb on is modeled by the system of equations as,

y=-(1/20)x^2+x

where, x and y are measured in feet.

Putting x= 0 in the above equation y=-(1/20)x^2+x , we get,

y = - (1/20) (0^2) + (0) = 0

Putting x= 5 in the above equation y=-(1/20)x^2+x , we get,

y= - (1/20)(5^2)+(5) =  -5/4 + 5 = 15/4 = 3.75

Putting x= 10 in the above equation y=-(1/20)x^2+x , we get,

y= - (1/20)(10^2)+(10) =-5 +10 = 5

Putting x= 15 in the above equation y=-(1/20)x^2+x , we get,

y= - (1/20)(15^2)+(15)  = -45/4 +15= 3.75

Putting x= 20 in the above equation y=-(1/20)x^2+x , we get,

y= - (1/20)(20^2)+(20)  = -20 +20 = 0

Hence, when x= 0 feet, y = 0 feet ; x= 5 feet, y = 3.75 feet ; x = 10 feet, y = 5 feet ; x =15 feet , y =03.75 feet ;and x = 20feet, y = 0 feet from the solving the given equation.

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The median is the best measure of center because there are no outliers present.

In the given line plot, we have the following data points for the cost of used books in dollars:

1 at $2, 1 at $4, 3 at $3, 1 at $8, 2 at $6, 2 at $7, and 1 at $9.

To decide which measure of center is most appropriate, let's first understand the difference between the mean and the median.

Mean: The mean is the sum of all the data points divided by the number of data points. It is sensitive to outliers, which means that if there are extreme values in the data, the mean can be significantly affected.

Median: The median is the middle value of a dataset when the data points are arranged in ascending order. If there are an even number of data points, the median is the average of the two middle values. The median is less sensitive to outliers, making it a more robust measure of center when extreme values are present.

Now, let's examine the given data for any outliers. There doesn't seem to be any extreme values in the data; the costs are fairly close together. However, the data is slightly skewed to the right, which means there is a higher concentration of lower values.

In this case, the median would be a better measure of center because it is less sensitive to the skewed distribution.

To find the median, first, arrange the data in ascending order:

$2, $3, $3, $3, $4, $6, $6, $7, $7, $8, $9

There are 11 data points, so the middle value is the 6th data point:

Median = $6

Thus, the median is the most appropriate measure of center for this data, and the median cost of used books is $6.

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The probability that the pirate will encounter exactly 3 islands with treasure and none with traps while searching all 6 islands is approximately 0.240 or 24%.

Let's calculate the probability that the pirate will encounter exactly 3 islands with treasure and none with traps.

First, we need to consider the probabilities for each outcome on each island:

P(treasure) = 1/4

P(traps) = 1/12

P(neither treasure nor traps) = 2/3

Now, we want to find the probability of encountering 3 islands with treasure and none with traps out of 6 islands. This is a binomial probability problem, where n is the number of trials (6 islands) and k is the number of successful outcomes (3 islands with treasure). The probability of success (p) is the probability of finding treasure on an island (1/4), and the probability of failure (q) is the probability of not finding traps on an island (1 - 1/12 = 11/12).

The binomial probability formula is:

[tex]P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{n-k}[/tex]

where:

[tex]\binom{n}{k} = \frac{n!}{k! \cdot (n-k)!}[/tex]

Plugging in the values:

n = 6 (number of islands)

k = 3 (number of islands with treasure)

p = 1/4 (probability of finding treasure on an island)

q = 11/12 (probability of not finding traps on an island)

[tex]P(X = 3) = \binom{6}{3} \cdot \left(\frac{1}{4}\right)^3 \cdot \left(\frac{11}{12}\right)^3[/tex]

Calculating (6 choose 3):

[tex]\binom{6}{3} = \frac{6!}{3! \cdot (6-3)!} = 20[/tex]

Now, plug in the values:

[tex]P(X = 3) = \binom{6}{3} \cdot \left(\frac{1}{4}\right)^3 \cdot \left(\frac{11}{12}\right)^3 \approx 0.240[/tex]

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The complete question:

A pirate is searching for buried treasure on 6 islands. on each island, there is a 1/4 chance that the island has buried treasure and no traps, a 1/12 chance that the island has traps but no treasure, and a 2/3 chance that the island has neither traps nor treasure. what is the probability that while searching all 6 islands, the pirate will encounter exactly 3 islands with treasure, and none with traps?

Answer:

15π

Step-by-step explanation:

If it is in terms of pi, then it would be 15π.

If you want the full circumference, it would be 47.1.

Explanation:

15/2 = 7.5.

7.5*2 = 15.

15π = 47.1.

Hope this helped!

Answer:

1767.1

Step-by-step explanation:

circle = 4/3 x pie x r^3

Divid 15 by 2 to get radius

15/2=7.5

7.5^3 = 421.875

421.875 x pie = 1325.359401

1325.359401 x 4/3 = 1767.145868

1767.145868 Estimated = 1767.1

The total area of the space is given as 1729 sq ft.

We can make use of engineered wood because it fits the budget

A mathematical model is a representation of a real-world system, process, or phenomenon using mathematical concepts, equations, and symbols. The purpose of creating a mathematical model is to understand and analyze the behavior of the system under different conditions and to make predictions about its future behavior.

Mathematical models can be used in various fields, including physics, engineering, economics, biology, and social sciences. They can range in complexity from simple algebraic equations to sophisticated computer simulations and can incorporate various factors such as time, space, and multiple variables.

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All four zeros are real solutions in the polynomial equation.

What are polynomials in equations?

A polynomial is an expression that consists of one or more variables, coefficients, and non-negative integer exponents of the variables. An equation is a mathematical statement with an equal sign between two algebraic expressions with equal values. 

x⁴ – 41 x² = – 400

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

       x⁴ - 41x² + 400 = -400 + 400

     x⁴ - 41x² + 400 = 0

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

         x⁴ - 25x² - 16x²  + 400 = 0

Making it into two groups, we get

  (x⁴ - 25x²) + (-16x² + 400) = 0

Factoring out GCF of each group, we get

  x²(x² - 25) (x² - 16) = 0

(x² - 25) = x² - 5²  = (x - 5) (x + 5)

x² - 16 = x² - 4² = (x - 4)(x + 4)

(x - 5) (x + 5) (x - 4)(x + 4) = 0

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

x = -5, -4, 4 and 5.

All four zeros are real solutions.

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Answer:

 the first one: 5x3y2 - 2xy4 +xy

Step-by-step explanation:

hope it helps :)

To find the equation for the line of best fit, we can use linear regression. Based on the given data:

x: 2, 5, 7, 12, 16

y: 9, 10, 5, 3, 2

The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.

Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.

The result is:

Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)

So, the correct answer is:

A. y = -0.580x + 10.671

The compound inequality ​20 < 90 + x < 30 when solved has a solution of -70 < x < -60.

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

20 < 90 + x < 30

Subtracting 90 from all parts of the inequality, we get:

-70 < x < -60

Therefore, the solution to the compound inequality is: -70 < x < -60.

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Answer:

To find the density of the brick, we need to divide its mass by its volume:

density = mass / volume

Plugging in the values given in the problem, we get:

density = 2,022.75 g / 1,064.5 cm³

Simplifying the division, we get:

density = 1.8996 g/cm³

Rounding to the nearest tenth, we get:

density ≈ 1.9 g/cm³

Therefore, the density of the brick is approximately 1.9 grams per cubic centimeter (g/cm³).

The equation to model the cost of making different numbers of shirts is c = 7.50t - 750.

Y = mx + b, where x is the independent variable, m is the slope, and b is the y-intercept, is the slope-intercept form of a linear equation. The dependent variable's rate of change with respect to the independent variable is represented by the slope (m), and its value when the independent variable is zero is shown by the y-intercept (b).

This equation's form is helpful for charting linear functions since the slope and y-intercept provide information about the direction and steepness of the line as well as its point of intersection with the y-axis.

The linear equation is given by the formula:

y = mx + b

Here. m is the slope.

The value of m is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the points 100, 600) and (250, 1387.50) from the table:

m = (1387.50 - 600) / (250 - 100)

m = 7.50

Now, for the y-intercept b we have:

b = y - mx

Substituting the data point:

b = 600 - 7.50(100)

b = -750

Now the equation of the model is:

c = 7.50t - 750

Hence, the equation to model the cost of making different numbers of shirts is c = 7.50t - 750.

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The length of v, to the nearest 10th of a centimeter is 2.2.

To find the length of side v in triangle UVW, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Using this formula, we have,

v/sin(m∠V) = w/sin(m∠W)

We know that w = 1.4 cm and m∠W = 63°. To find sin(m∠W), we can use a calculator,

sin(63°) ≈ 0.89

Substituting the values we know into the formula, we get,

v/sin(m∠V) = 1.4/0.89

To solve for v, we need to find sin(m∠V). We know that the sum of the angles in a triangle is 180°, so we can find m∠V by subtracting the measures of the other two angles from 180°,

m∠V = 180° - m∠U - m∠W

m∠V = 180° - 29° - 63°

m∠V = 88°

Now, we can substitute the value of sin(m∠V) into the equation and solve for v,

v/ sin(88°) = 1.4/0.89

v ≈ 2.2 cm

Therefore, the length of side v in triangle UVW is approximately 2.2 cm to the nearest tenth of a centimeter.

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Answer:

1.6

Step-by-step explanation: This is answer on DeltaMath

Answer:

Step-by-step explanation:

it is -2

Answer: -2

Step-by-step explanation:

So this is asking for the cube root of -8.

This is the same as asking what is multiplied by itself 3 times to get -8.

-2 * -2 *-2 = -8

You can also use a calculator.

Another way to solve it is to write -8^(1/3).

Hope this helps!!!

As three dice are thrown together and the probability of any two of them being the same will be 5/12.

When a dice is thrown there are 6 possible outcomes. So, when three dice are thrown, the number of outcomes will be 6× 6× 6 = 216.

The probability of a number repeating = ₆C₂ = (6×5)/2 = 15

So each number will have possible 15 outcomes.

6 numbers will have 6 × 15 outcomes = 90 outcomes

So probability = Number of desired outcomes/ total number of outcomes  = 90 / 216 = 5/12

So the probability of any two number matches when three dices are thrown together will be 5/12.

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The number of envelopes left to address by Sani is at most 51 .

And Messages > 10 to have unlimited plan cheaper than paying for each messages.

At least numbers of envelopes Sani has = 68

Number of envelops he addressed = 17

Let x be the number of envelopes that Sani has left to address.

Then we have,

x ≤ 68 - 17

Simplifying this inequality, we get,

x ≤ 51

Sani has at most 51 envelopes left to address.

Cost per text message send or received by Nadine = $0.5

Cost pf unlimited number of text message send or received = $5

Let m be the number of messages Nadine sends or receives.

Then the cost of paying for each message is,

0.5m

The cost of the unlimited plan is $5.0.

The number of messages m such that,

5.0 ≤ 0.5m

Simplifying this inequality, we get,

⇒ 10 ≤ m

If Nadine sends or receives more than 10 messages, the unlimited plan is cheaper than paying for each message.

So the solution to the inequality is m > 10.

Therefore, number of message Sani left to address is at most 51 envelopes .

And to have unlimited plan cheaper than paying for each messages for Nadine is m > 10.

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Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

What is the rate of change?

The rate of change is the amount of change in the output (dependent variable) for a given change in the input (independent variable).

In this case, the input is the number of days ridden, and the output is the cost of transportation for a month.

For Function 1, the cost is $5.50 per day. Therefore, the rate of change is $5.50 per day.

For Function 2, the equation E = 8.25 + 1.50d represents the cost of transportation for a month, where d is the number of days ridden. The rate of change is the coefficient of d, which is $1.50 per day.

Hence, Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.

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The number of square feet of glass used for your windows is $129.09.

Glass is an amorphous, transparent material that is hard, brittle, and corrosion-resistant. It is composed of silica, soda ash, and other materials that when heated and cooled form a non-crystalline material. Glass is a non-conductor of electricity and heat, and is also highly resistant to chemicals. It is often used in windows and other applications where transparency is desired. Additionally, glass can be used in a variety of decorative and functional applications such as mirrors, tableware, kitchenware, and art.

$200 + 33x = 4490$
Subtract $200$ from both sides:
$33x = 4290$
Divide both sides by $33:
$x = 129.09
Therefore, the number of square feet of glass used for your windows is $129.09.

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Kaylee will have to pay $28 in interest.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

The interest Kaylee will have to pay is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the time period in years. Since Kaylee has to pay back the loan in 24 months, or 2 years, we can plug in the given values to get:

Interest = 700 x 0.02 x 2 = $28

Therefore, Kaylee will have to pay $28 in interest.

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Answer: 102 miles.

Step-by-step explanation:

You divide 17 by 5 and then multiply by 30.