The box plot represents the scores on quizzes in a history class.

A box plot uses a number line from 69 to 87 with tick marks every one-half unit. The box extends from 75 to 82 on the number line. A line in the box is at 79. The lines outside the box end at 70 and 84. The graph is titled History Quizzes, and the line is labeled Scores on Quizzes.

What value does 75% of the data lie below? Find the value.

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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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

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!!!

Answer:

x > 12

Step-by-step explanation:

3x + 18 > 54

To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.

We define the actual score, theoretical score, and explain how to calculate the percent success on an exam.
Actual score:

The actual score refers to the number of points a student has earned on an exam.

It represents the student's performance on the test, taking into account the correct and incorrect answers.
Theoretical score:

The theoretical score is the maximum number of points a student can earn on an exam.

This represents a perfect performance, where the student answers all questions correctly.
Calculating percent success:

To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
a. Divide the actual score by the theoretical score: (actual score) / (theoretical score)
b. Multiply the result by 100: (result from step a) * 100
c. The final value is the percent success.

For example, if a student has an actual score of 80 and the theoretical score is 100, the percent success would be calculated as follows:
a. 80 / 100 = 0.8
b. 0.8 * 100 = 80
c. The percent success is 80%.

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The slope of the second line is also positive, as it is parallel to the first line which has a positive slope.

Slope is a measure of how steep a line is, and is defined as the ratio of the change in the y-coordinate (vertical change) to the change in the x-coordinate (horizontal change) between any two points on the line. It represents the rate at which the line is rising or falling as it moves from left to right. Slope can be positive, negative, or zero. A positive slope indicates that the line is increasing as it moves from left to right, a negative slope indicates that the line is decreasing as it moves from left to right, and a zero slope indicates that the line is horizontal.

Here,

When two lines are parallel, they have the same slope. In this case, the first line has a positive slope of "a," which means that it is increasing as it moves from left to right. Since the second line is parallel to the first line, it will also have the same slope as the first line. Therefore, the slope of the second line will also be positive, indicating that it is increasing as it moves from left to right.

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Answer:

 the first one: 5x3y2 - 2xy4 +xy

Step-by-step explanation:

hope it helps :)

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 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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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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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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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.

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).

Answer:

Step-by-step explanation:

Medium is 28

Mean is 29

Range is 11

Midrange is 29.5

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%

The value of the missing angles are:

w = 109°

x = 39°

y = 141°

z = 109°

In geometry, we know that the sum of angles on a straight line is 180 degrees. Thus:

w = 180 - 71

w = 109°

We know that alternate angles are formed when two parallel lines are cut by a transversal. Thus:

x = 39°

y = 180 - 39

y = 141°

Similarly:

z = 180 - 71

z = 109°

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Answer: 102 miles.

Step-by-step explanation:

You divide 17 by 5 and then multiply by 30.

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 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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The expected winning is $2.

To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.

There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.

Here are all the possible outcomes with the number of heads in each outcome:

The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)

For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.

Using this formula, we can calculate the probability and expected winning for each outcome:

To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:

(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2

Therefore, the expected winning is $2.

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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:

f -1

Step-by-step explanation:

the inverse of a function (f) is denoted by f -1 and exsists only when f is both one to one and onto function.

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:

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 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

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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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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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 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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