suppose you wish to compare the average class size of mathematics classes to the average class size of english classes in your high school. which is the most appropriate technique for gathering the needed data.

Answer:

In the numerator:

2x^2 + 3x - 20 = (2x - 5)(x + 4)

- no asymptotes

- x-intercept is at x = 2.5 (since there is a hole at x = -4)

- y-intercept is at y = -5

Answer:

Cylinder problem:

28.26 = 3.14(r^2)(9)

28.26 = 28.26(r^2), so r = 1 cm

Trapezoid problem:

Since we have similar trapezoids, the side lengths of WXYZ are each 5 times the side lengths of ABCD.

60/12 = 5, so b = 5 × 10 = 50 inches

Answer:

Step-by-step explanation:

The diameter of each bead is 1.5 millimeters, which means the radius of each bead is 0.75 millimeters (since radius = diameter/2).

The volume of a sphere is given by the formula V = (4/3)πr^3.

Substituting the radius of each bead into the formula, we get:

V = (4/3)π(0.75)^3 ≈ 1.7671 cubic millimeters

To find the total volume of the 360 beads used to create the border of the picture frame, we can simply multiply the volume of one bead by the total number of beads:

Total volume = 360 × 1.7671 ≈ 635.76 cubic millimeters

Therefore, the approximate total volume of the beads that form the border of the picture frame is about 635.76 cubic millimeters.

Answer:

6x^2+16x+8

Step-by-step explanation:

it is handwritten in the photo

Histograms are primarily used to demonstrate how often data values fall into certain ranges. So, option 3 is correct.

Histograms are graphical representations of a dataset's distribution, with the data separated into intervals or "bins" and the frequency of values falling into each bin represented as bars.

Histograms can be used to find the trends and the specific information in the data for the help of data analyst. They are especially useful for huge datasets when the distribution of values from a simple list may be difficult to understand. Although histogram could be used for more than two data types and but this is not there natural purpose. Hence option option 3 is correct choice.

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Complete question - A data analyst creates a histogram to share in a presentation. what are histograms used to demonstrate?

1. how two or more values contrast and compare

2. how much each part of something makes up the whole

3. how often data values fall into certain ranges

4. how data has changed over time.

Option B To find the z-score corresponding to an observation of 470, we use the formula: z = (x - μ) / σ

where x is the observation, μ is the mean, and σ is the standard deviation. Substituting the values given in the question, we get: z = (470 - 570) / 10.1489.

z = -9.84, Therefore, the z-score corresponding to an observation of 470 is -0.97, which is option B.

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. Sal Khan invented it.

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Answer:

  y = -6x +3

Step-by-step explanation:

You want the slope-intercept equation matching the given graph.

The line on the graph crosses the y-axis at the marked point (0, 3). Another point is marked at (1, -3), which is 1 unit right and 6 units down.

The first point tells you the y-intercept (b) is +3.

The second point tells you the slope (m) is rise/run = -6/1 = -6.

Then the point-slope equation is ...

  y = mx + b

  y = -6x +3

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Integrating and evaluating the function gives f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x and f(2) = -8

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

∫ 1/3x³ - 2x² + 3x - 5 dx

The rule of integration is

x^n = x^(n + 1)/(n + 1)

using the above as a guide, we have the following:

∫ 1/3x³ - 2x² + 3x - 5 dx = 1/12x⁴ - 2/3x³ + 3/2x² - 5x

So, we have

f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x

Next, we are to calculate f(2)

This means that x = 2

So, we have

f(2) = 1/12(2)⁴ - 2/3(2)³ + 3/2(2)² - 5(2)

Evaluate

f(2) = -8

Hence, the value of f(2) is -8

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The calculated probability that the job is offered to a man is 0.455

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

There are 5 men and 6 women interviewed for a job.

This means that

Men = 5

Women = 6

The probability that the job is offered to a man is

P = men/Total

So, we ave

P = 5/11

Evaluate

P = 0.455

Hence, the probability is 0.455

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The axis of symmetry for the given object and image is added as an attachment

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

The object and the image

By definition, the axis of symmetry is any line that divides a shape and its image into symmetrical parts i.e. into identical shapes and sizes

In this case, the axis of symmetry would be a vertical line that divides both triangles in to identical figures

Using the above definition as a guide, we can draw the axis of symmetry for the object and image & then label it AB

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To find the interval(s) over which the function -3x^2+12 is decreasing, we need to find the critical points of the function and test the sign of the derivative on either side of these points.

The derivative of the function -3x^2+12 is -6x.

Setting the derivative equal to zero to find the critical points:

-6x = 0

x = 0

Testing the sign of the derivative on either side of x = 0:

-6x is negative for x > 0, meaning the function is decreasing on the interval (0, infinity).

-6x is positive for x < 0, meaning the function is increasing on the interval (-infinity, 0).

Therefore, the interval over which the function -3x^2+12 is decreasing is (0, infinity).

The statement is true. In order to generate a sample size using XL data analyst software, you must first estimate the population proportion (p) and specify your allowable margin of error.

Estimating p involves making an educated guess about the proportion of the population that possesses a certain characteristic or meets a certain criteria. This estimation can be based on prior research, historical data, or your own observations. It is important to note that your estimation of p will affect the size of your sample, with a larger sample size needed for smaller values of p.

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the width of the reproduced piece is 2.78 inches.

Now, we first need to find the original area of the painting.

Since, The original area is,

= 29 inches x 25 inches

= 725 square inches

Now. we know that the reproduction has 1/9 of the original area, which means that the area of the reproduction is:

= 725 square inches / 9

= 80.56 square inches

Hence, for the width of the reproduced piece, we need to find the width of a rectangle whose area is 80.56 square inches, given that the height is 29 inches which remains constant in the reproduction.

Hence, We can use the formula for the area of a rectangle,

Area = length x width

In this case, we know the area is, 80.56 square inches)

and the length is, 29 inches

Thus, we can solve for the width:

80.56 square inches = 29 inches x width

width = 2.78 inches

Thus, the width of the reproduced piece is 2.78 inches.

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Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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There are 210 ways we can give 4 different prizes to any 4 of 10 people if no person receives more than 1 prize.

To calculate the number of ways we can do this, we can use the formula for combinations. The formula for the number of ways to choose r objects from a set of n objects is:

ⁿCₓ = n! / x!(n-x)!

where n! represents the factorial of n, which is the product of all positive integers up to n.

5! = 5 x 4 x 3 x 2 x 1 = 120.

In this problem, we want to choose 4 people from a set of 10, so we can use the formula:

¹⁰C₄ = 10! / 4!(10-4)!

Simplifying this expression, we get:

¹⁰C₄ = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

¹⁰C₄ = 210

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Answer:

Angle A° is less than 90°

Angle B° is less than 90°

Step-by-step explanation:

Angle A° = Angle B° = 45°

In statistics, a series of random events in which the probability of a given event is determined only by its predecessors is known as a "chain". This concept is attributed to the Russian mathematician Andrey Markov, and such chains are commonly referred to as Markov chains.

Markov chains have important applications in many areas of science and engineering, including physics, economics, genetics, and computer science. They are used to model a wide range of phenomena, including the behavior of financial markets, the spread of diseases, the performance of computer networks, and the evolution of populations.The basic idea behind a Markov chain is that the future state of the system depends only on the current state, and not on any previous states. The probability of transitioning from one state to another is determined by a transition matrix, which specifies the probabilities of moving from one state to another in a single time step.

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It's crucial to take a collaborative approach and involve employees in the change process as much as possible.

In the unfreezing stage, it is important to gather information and input from various stakeholders in order to influence change effectively. Therefore, asking the VP and analyst questions such as "What do you think are the areas that need improvement in our current system?" or "How do you think changing the system would benefit our organization?" can provide valuable insight into the motivation for change.

Surveying a sample set of employees at each location to ask their opinions on the current system and whether they think changes are necessary is also a good approach. This can help to identify common pain points and gauge the level of employee buy-in for potential changes. It's important to also consider other factors such as the cost and feasibility of implementing changes, as well as potential risks and benefits.

Mandating change without proper analysis and buy-in from employees may lead to resistance and resentment. Ultimately, the decision to change or not should be based on a thorough assessment of the situation, including feedback from stakeholders and the potential impact on the organization.

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If the 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9, the two numbers are 63 and 48.

Let x and y be the two numbers. Then we have two equations based on the given information:

2/3(x+y) = 74 ... (1)

3/5(x-y) = 9 ... (2)

To solve for x and y, we can start by isolating one variable in terms of the other from one of the equations. For example, from equation (1), we have:

x + y = (3/2) * 74

x + y = 111

Next, we can substitute this value of (x + y) into equation (2) and solve for the other variable:

3/5(x - y) = 9

x - y = 15

Now we have two equations with two variables:

x + y = 111

x - y = 15

Solving for x and y by adding the two equations gives:

2x = 126

x = 63

Substituting this value of x into either equation gives:

y = 48

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Complete question is:

The 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9. Find the two numbers.

The area formed by the water pattern of a sprinkler that can spray out 14 feet in any direction is about 615.44 square feet.

Explain the term area.

Area is the measure of the size of a two-dimensional surface or region, usually measured in square units. It is the amount of space enclosed by a flat shape or the surface of an object. The area of a shape can be calculated using formulas based on its dimensions and geometry.

According to the given information

The formula for calculating the area of a circle is A = πr² where A is the area and r is the radius of the circle. In this case, r = 14 feet and π = 3.14 so A = 3.14 x (14)² = 615.44 square feet

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The area and perimeter of the shape are 370mm² and 90mm respectively.

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

Perimeter is the addition of the sides of the shape.

Therefore, the perimeter of the shape = 15+15+30+30 = 30+60 = 90mm

The area of the shape = area of the whole shape - area of the cut out

area of the whole shape = l×w

= 30×15 = 450mm²

area of the cut out =l×w

8× 10 = 80mm²

area of the shape = 450-80

= 370mm²

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The variable which is being forecasted is referred as option A: endogenous variable.

A variable in a statistical or economic model that is explained by or determined by other variables inside the model is known as an endogenous variable. In other words, the endogenous variable's value depends on the values of other model variables.

Exogenous variables are often thought of as external or independent factors that may have an impact on endogenous variable values but are not directly impacted by them. A variable that is used to predict or explain the values of another variable, also known as the dependent variable, is known as an explanatory variable.

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Correct question:

The variable which is being forecasted is referred as:

endogenous variable

independent variable

explanatory variable

exogenous variable

Answer:

Step-by-step explanation:

Use pythagorean   the hypotenuse is always across from th right angle and is the longest in a right triangle

34² = 16² + x²

1156 = 256 + x²                bring 256 over to other side by subtracting

900 = x²                take square root of both sides to solve for x

x = 30

Answer:

Step-by-step explanation:

In the given figure,

34 is Hypotenuse i.e the largest side

16 is perpendicular

b = Base

Using Pythagoras theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

(34)² = (16)² + (b)²

1156 = 256 + b²

1156 - 256 = b²

900 = b²

b = √900

b = 30

Therefore, Value of b is 30.

The length of each piece of wood is 0.725 feet.

We are given that the Length= 3.5feet

Now,

This is a word problem that can be solved by using algebra and arithmetic.

Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:

4x + 0.6 = 3.5

This is the equation that could be used to determine the length of each piece of wood.

Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.

Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:

4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725

Therefore, by the algebra the answer will be 0.725 feet.

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The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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13 is the y-intercept, which is the initial number of space.

6 is the slope, which means the number of spaces is increasing by 6.

x represent number of rolls.

40 the minimum number of spaces required to win the game.

The fewest number of rolls it would take Li to win the game is 0.054 rolls.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Li's current situation, we have the following inequality:

13 ÷ 6x ≥ 40

13/6x ≥ 40

13 ≥ 240x

x ≤ 0.054

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The values of each number using power 10 is shown below.

1. 79 x 10

= 790

2. 15 x 100

= 1500

3. 22 x 1,000

= 22,000

4. 15 x 1000

= 15,000

5. 83 x 102

= 8,466

6. 23 x 10²

= 2300

7. 72 x 10²

= 7200

8. 4 x 10²

= 400

9. 75 x 10²

= 7500

10. 55 x 10²

= 5500

11. 81 x 10³

= 81,000

12. 3 x 10³

= 3000

13. 85 x 10³

= 85, 000

14. 98 x [tex]10^{-1[/tex]

= 9.8

15. 86 x [tex]10^{-3[/tex]

= 0.086

16. 65 x [tex]10^{-2[/tex]

= 0.65

17. 19 x 10³

= 19,000

18. 3.49 x [tex]10^{9[/tex]

= 349,000,000,000

19. 2.79 x [tex]10^{8[/tex]

= 27,900,000,000

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The correct statements regarding a translation are given as follows:

A : The sides of the image and pre-image are congruent.

G: each point has moved the same number of units.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The side lengths are not changed, hence the image and the pre-image are congruent. The angle measures are also not changed, hence the image and the pre-image are similar, and the shapes also remain constant.

For a translation, the movements have to be:

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Answer:

C

Step-by-step explanation:

7.3<7.4<72.14<91.34<723.99

The equation of the line in slope - intercept form, given the two points, would be D. y = - 10 / 3 x - 2 / 3.

First, write out the points on the graph to be ( -2, 6 ) and ( 1, - 4 ) .

The slope would be:

=  (change in y) / (change in x)

=  (-4) - 6  / 1 - (-2)

= - 10 / 3

Use a point to find the y - intercept in the form:

y = mx + b

6 = - 10 / 3 ( - 2 ) + b

b = - (2/3)

The equation then is :

y = - 10 / 3 x - 2 / 3

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