The following data shows the grades that an 8th grade mathematics class received on a recent exam.

{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}

Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)

Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)

Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.

b) degrees of freedom.

Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.

Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.

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Complete Question

Since critical values of t vary by sample size, before using the t table we must first calculate:

a) the Z score.

b) degrees of freedom.

c) the population standard deviation.

d) the sample size.

The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.

To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:

1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.

By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.

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The Surface Area of wooden box is 432 inch².

We have,

length = 12 inch

width = 8 inch

Height = 6 inch

So, Surface Area of wooden box

= 2 (lw + wh + lh)

= 2 (96 + 48 + 72)

= 2 x 216

= 432 inch²

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substitute 140 for 'y', because 'y' is the amount of available cabinets (they need to be available in order for it to be installed).

you have;

140 = 8x + 40

solve for x from here

Answer:

Step-by-step explanation:

To find out how many weeks it will take to fill the high school's order, we need to solve the equation for the number of weeks (x). We can start by plugging in the given value of 104 for y since y represents the number of cabinets, and then solving for x:

y = 8x + 40

104 = 8x + 40

-40           -40

64 = 8x

x = 8

Therefore, it will take 8 weeks to produce enough cabinets to fill the high school's order.

Answer: 71

Step-by-step explanation: to get the answer you have to know that all the angles of a triangle have to add up to 180 so therefore you add the angles they gave you and then you minus them from 180 and you get 71

On solving the provided question we can say that equation  As a result, the expedition can go 476 kilometres before running out of fuel.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 equals 2, for instance.

To calculate how far the expedition can travel before running out of gas, apply the following formula:

Miles = (Gallons of gas) x (Miles per gallon)

Plugging in the given values, we get:

Miles = 28 gallons x 17 mpg

Miles = 476 miles

As a result, the expedition can go 476 kilometres before running out of fuel.

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Answer:

2(3h^2+2)

Step-by-step explanation:

Answer:

a = 10

b = 5

Step-by-step explanation:

A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.

The formula for the ratio of the sides is x : x√3 : 2x where:

From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:

If x√3 = 5√3, then x = 5. Therefore:

From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).

As the parabola is originating from the origin and opens at the y-axis, hence:

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The sum of the given polynomial  [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]is [tex]9x^{3} - 8x^{2}[/tex].

Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.

Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.

The following polynomial equation is [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

Polynomial addition is accomplished by combining 'like terms'.

As a result, sorting and adding

= [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

= [tex]7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}[/tex]

= [tex]9x^{3} - 8x^{2}[/tex]

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Complete question:

What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)

Answer:

life insurance is the most common type of employee benefit

This sample is likely to be biased because it only includes individuals who use the city's parks, which means it may not represent the entire population of voters who would be affected by a tax increase to improve the parks.

A sample is a subset or a smaller group of individuals or 17 that are selected from a larger population to represent the population.

The park commission's study of 500 park users is likely biassed because it only covers people who use the city's parks. This indicates that the sample does not accurately reflect the full electorate who would be impacted by a tax hike to fund park improvements.

Various people may hold various views regarding whether or not a tax increase is required to develop the parks. For instance, if they don't frequent the parks or have other priorities for their tax money, they might be less likely to approve a tax hike.

If the park commission only conducted surveys of people at specific times of day or in specific locations of the city, the sample may also be skewed. This could omit those who visit the parks at various hours or in various locations around the city.

In order to get accurate and valid results, it's crucial to utilise a representative sample that includes people from different demographic groups. A biased sample can produce results that are erroneous or misleading.

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Rodger's weekly unemployment amount will be $ 705.0225

Given that the total of the quarterly wages of two consecutive quarters and divided by 26.

The weekly unemployment is 65% of that amount.

Rodger made a total of $13,950.80.

Then he made a total of $14,250.10

Step 1:  the total of the quarterly wages of two consecutive quarters.

= $ 13,950.80 + $ 14,250.10

= $28,200.90

Now Divide the total  by 26

 = $28,200.90 / 26

 =  1,084.65

Then,  =   1,084.65 x 65%

 =  1,084.65 x 65/100

=   705.0225

Hence, Rodger's weekly unemployment amount is; $ 705.0225

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Answer: Split it in half to turn it into a triangle! The hypotenuse if the triangle will give you the diagonal length of the suitcase, because it’s a rectangle. Hope this helps :D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is attached below. There isn't much explanation for this. You just translate the word problem into a mathematical inequality.

On solving the provided question we can say that - 12.99(y - 9) + 2.75y = 100 , by solving, the expression  x = 11.2, y = 19

What is  linear equation?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

let x be the base ball cards.

and y be page card.

x + y = 9 -------------------1

12.99x + 2.75y = 100-------------------2

12.99(y - 9) + 2.75y = 100

by solving

x = 11.2

y = 19

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Answer: The 90% confidence interval for the population mean of the length of text messages is a range of values that is likely to contain the true population mean with a probability of 0.90 (or 90%). Based on the given information, we can calculate the confidence interval as follows:

Standard error of the mean (SE) = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and sqrt denotes the square root.

SE = 3 / sqrt(22) ≈ 0.639

Margin of error (ME) = t(α/2, df) × SE

where t(α/2, df) is the critical value from the t-distribution with df degrees of freedom, and α is the level of significance (1 - confidence level).

For a 90% confidence level and 21 degrees of freedom (df = n - 1), the critical value is approximately 1.717.

ME = 1.717 × 0.639 ≈ 1.098

The confidence interval can be calculated as:

CI = sample mean ± ME

= 31 ± 1.098

= (29.902, 32.098)

Therefore, we can say that we are 90% confident that the true population mean of the length of text messages falls between 29.902 and 32.098 characters. In other words, if we were to repeat the sampling process many times and construct a 90% confidence interval for each sample, we would expect 90% of the intervals to contain the true population mean. Additionally, we can interpret the margin of error as the maximum amount that the sample mean is expected to differ from the true population mean, with a probability of 90%.

Step-by-step explanation:

The probability that the weight of a randomly caught Pacific yellowfin tuna is less than 50 pounds is approximately 0.0668 or 6.68%.

The weights of the Pacific yellow fin tuna follow a normal distribution with a mean weight of 68 pounds and a standard deviation of 12 pounds. To find the probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds, we can follow these steps:

1. Calculate the z-score for the weight of 50 pounds using the formula:
z = (X - μ) / σ
where X is the weight, μ is the mean, and σ is the standard deviation.

2. Find the probability associated with the z-score using a z-table or calculator.

Let's calculate the z-score:
z = (50 - 68) / 12
z = -18 / 12
z = -1.5

Now, we can use a z-table or calculator to find the probability associated with the z-score of -1.5. The probability that a randomly caught Pacific yellow fin tuna weighs less than 50 pounds is approximately 0.0668, or 6.68%.

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The simplified rational expression for this problem is given as follows:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

The rational expression in the context of this problem is defined as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]

The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]

Applying the subtraction of perfect squares, the denominator is given as follows:

2² x 3 - 7 = 12.

The numerator is:

[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]

Thus the simplified expression is:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

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The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters

Area = length * width

Perimeter = 2(length + width)

Given the following:

Length of the rectangle = 5√7 + 2√3 meters

Width of the rectangle = 6√7 - 3√3 meters

a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)

10√7 + 4√3 + 12√7 - 6√3

22√7 - 2√3 meters

b. Area = (5√7 + 2√3)(6√7 - 3√3)

= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)

= 210 - 15√21 + 12√21 - 18

= 192 - 3√7

= 4√12 - 3√7 square meters

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The value of x in the right triangle below by using Pythagorean Theorem (H² = P² + B²) is 19.53

According to question; Perpendicular (P) = 16, Base (B) = 11.2 and Hypoteneus (H) = X

According to Pythagorean Theorem

H² = P² + B²

X² = 16² + 11.2²

X² = 256 + 125.44

X² = 381.44

X = 19.53

The Pythagorean Theorem, or, in standard algebraic notation, a² + b² = c², states that the total of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).

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The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value. Graph is in below figure.

The domain of a function is the set of all possible input values (also called the independent variable) for which the function is defined. In other words, it is the set of values that can be plugged into the function to produce a valid output value (also called the dependent variable).

The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value.

To graph this function, we can plot points by choosing values of x and computing the corresponding values of f(x). Since the domain of the function is [0, ∞), we will only consider non-negative values of x.

x f(x)

0 3

1 4

2 7

3 12

4 19

We can plot these points on a coordinate plane and connect them with a smooth curve to obtain the graph of the function:

Note that the graph is a parabola that opens upwards and passes through the point (0, 3).

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The correct answer is B.

N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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The correct answer is B.N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500

This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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Michelle’s equations that is true for all values of x is 6x + 15 = x + x + x + x + x + x + 15.

Michelle’s equations that is false for all values of x is 6x + 15 = 6(x + 15).

Another equivalent expression for 6x + 15 is 3(2x + 5).

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

Michelle’s equations can be written for all values of x as follows;

6x + 15 = x + x + x + x + x + x + 15.

However, Michelle’s equations is false for all values of x when it is written as 6(x + 15).

Another equivalent expression is given by;

6x + 15 = 3(2x + 5).

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Answer:

Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it distributes the 6 to both terms inside the parentheses and simplifies to the original expression. However, the equation 6x + 15 = x + x + x + x + x + x + 15 is false for all values of x. While it may be true for specific values of x, such as x = 1 or x = 2, it is not true for all values of x because the number of x terms changes depending on the value of x.

Part B: Another equivalent expression for 6x + 15 could be 3(2x + 5), which also simplifies to the original expression. This is because we can factor out a common factor of 3 from both terms and simplify to 3(2x + 5) = 6x + 15.

Step-by-step explanation:

If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.

Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.

From the problem, we know that one side of the swimming area is the beach, so we have:

L + W + L = 70

Simplifying this equation, we get:

2L + W = 70

To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:

W = 70 - 2L

Substituting this expression for W into the formula for the perimeter, we get:

P = L + W + L

= 2L + (70 - 2L)

= 70

So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.

Therefore, Kyle needs a minimum of 70 meters of rope.

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The surface area of the figure is derived to be equal to 656.4 square meters.

The top of the figure is a triangular prism, the bottom is a triangle, and the sides are 3 same size rectangles, so the surface area is calculated as follows:

area of one top triangle face = 1/2 × 12 m × 5 m = 30 m²

area of top triangular prism = 3 × 30 m² = 90 m².

area of bottom triangle = 1/2 × 12 m × 10.4 m = 62.4 m²

area of one rectangle side = 14 m × 12 m = 168 m²

area of the three rectangle sides = 3 × 168 m² = 504 m²

surface area of the figure = 90 m² + 62.4 m² + 504 m²

surface area of the figure = 656.4 m².

Therefore, the surface area of the figure is derived to be equal to 656.4 square meters.

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Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

a.

1. LCM of 2 & 5 is 10

2. [tex]\frac{15x}{10} =\frac{12}{10}[/tex]  -> 15x = 12

3. x = [tex]\frac{12}{15}[/tex] or [tex]\frac{4}{5}[/tex]

b.

1. LCM of 3 & 9 is 9

2. 2x - [tex]\frac{6}{9}[/tex] = [tex]\frac{4}{9}[/tex]  ->  2x = [tex]\frac{10}{9}[/tex]  ->  [tex]\frac{18}{9} x[/tex] = [tex]\frac{10}{9}[/tex]  ->  x = [tex]\frac{10}{9}[/tex] × [tex]\frac{9}{18}[/tex]  ->  x = [tex]\frac{10}{18}[/tex]  ->  x = [tex]\frac{5}{9}[/tex]

3. x = [tex]\frac{5}{9}[/tex]

An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.

When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.

This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.

Now, consider an inscribed angle that intercepts the same arc as the chord.

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.

Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.

Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.

Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.

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A statement that could be expressed as a percent : 'how many of the 100 yogurts in the refrigerator are strawberry'

The correct answer is an option(A)

We know that a part-to-whole ratio is nothing but a ratio that compares a part of a whole to another part of a whole.

And the percent is nothing but a part-to-whole ratio where the whole is 100.

Consider the case 'how many of the 100 yogurts in the refrigerator are strawberry.'

Let us assume that x represents the number of strawberry yogurts out of total 100 yogurts in the refrigerator'

So, a part-to-whole ratio would be x/100

We can observ ethat here whole = 100

So, we could express the number of strawberry yogurts as a percent.

The correct answer is an option(A)

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Answer: in2

Step-by-step explanation:

answerd

Answer:

Below

Step-by-step explanation:

To find the break-even point, we need to determine the point at which the total revenue equals the total cost. Let's call the number of shirts sold "x".

The total cost includes the initial costs of $1,500 and the cost per shirt of $3x, so the total cost is:

y = 1500 + 3x

The total revenue is the price per shirt of $10 multiplied by the number of shirts sold, so the total revenue is:

y = 10x

To find the break-even point, we need to set the total cost equal to the total revenue and solve for x:

1500 + 3x = 10x

Simplifying this equation, we get:

1500 = 7x

Dividing both sides by 7, we get:

x = 214.29

Therefore, Steve needs to sell 215 shirts to break even.So the correct system to find the break-even point is:

y = 1500 + 3x (total cost)

y = 10x (total revenue)