Line segment FG begins at (-9,-5) and ends at (8,-5). The segment is translated right 10 units and down 7 units to form line segment F’G’. Enter the distance, in units, of line segment F’G’.

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

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 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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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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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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The requried number of students that study both language and French is 20 and 145 respectively.

From the information given, we know that:
The total number of students is 225.
80 students study Arabic only.

125 students study French (which includes some who also study Arabic).

To find the number of students who study both subjects, we can subtract the number of students who study Arabic only from the total number of students who study French:
= 225 - 80 -125

= 20

Now the number of students who study French is given as:

= 20 + 125
= 145

Thus, the requried number of students that study both language and French are 20 and 145 respectively.

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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 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 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 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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Answer:

C

Step-by-step explanation:

7.3<7.4<72.14<91.34<723.99

Answer:

Angle A° is less than 90°

Angle B° is less than 90°

Step-by-step explanation:

Angle A° = Angle B° = 45°

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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$36.75 is the price of chicken feed.

Given that,

A farmer is purchasing feed for his chickens. Before tax, a large bag of chicken feed costs $35. The farmer wants to know the total price, including the 5% sales tax.

To find tax:

5/100 * 35

*5% basically means 5 out of 100%.

The Tax is $1.75.

Then, to find the price of chicken feed, we add the tax with $35.

So...

1.75 + 35

=36.75

Answer:

$36.75

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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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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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Answer:

(0, -3) and (3, -5)

Step-by-step explanation:

To graph the line of the equation f(x) = -2/3x - 3, we can choose any two points on the line. One way to do this is to find the y-intercept and another point using the slope of the line.

1. To find the y-intercept, let x = 0 and solve for y:

f(0) = -2/3(0) - 3 = -3

So the y-intercept is (0, -3).

2. To find another point, we can use the slope of the line, which is -2/3. We can start from the y-intercept (0, -3) and move down 2 units (since the slope is negative) and to the right 3 units (since the denominator of the slope is 3) to get another point on the line:

(3, -5)

So the two points we can use to graph the line are (0, -3) and (3, -5).

The figure is composed of a rectangle and a triangle, therefore, the area is calculated as: 96 square inches.

Area of the triangle = 48 square inches.

The composite figure is composed of a triangle and a rectangle. Therefore, we have:

Area = area of triangle + area of rectangle

Area of rectangle = length * width = 12 * 4 = 48 square inches.

Area of the triangle = 1/2 * base * height = 1/2 * 12 * 8 = 48 square inches.

The area of the composite figure = 48 + 48

= 96 square inches.

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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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The maximum value of the function on the closed interval is 11

Given  the function

f(x) = 2x + 5, with interval [-10, 3].

First need to find the critical points of the function within the interval and compare their values. The critical points occur when the derivative of the function is equal to zero or undefined.

first order derivative of f(x):

f'(x) = 2 ≠ 0 (no critical points)

Since the interval is bounded, the maximum value of the function occurs at either one of the endpoints or at a critical point outside the interval.

At x = -10,

f(-10) = 2(-10) + 5 = -15

At x = 3,

f(3) = 2(3) + 5 = 11

Therefore, the maximum value of f(x) on the closed interval [-10, 3] is 11, which occurs at x = 3.

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If the function's f(x) = |x|, graph is shifted right by 3 units, and vertically stretched by a factor of "4", then function which best describes the transformed-function is 4|x-3|.

Let the transformed function be : g(x); The transformed function g(x) is obtained by applying two transformations to the original function f(x) = |x|.

The "first-transformation" is to make a "horizontal-shift" (right-shift) of 3 units. This means that the entire graph of the function is shifted to the right by 3 units, so, function becomes |x-3|.

The "second-trans-formation" is to stretch the graph vertically by a factor of 4. This means that the entire graph of the function is stretched vertically,

Now, the function becomes, g(x) = 4|x-3|.

Therefore, the transformed function is 4|x-3|.

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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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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 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

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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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.

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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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 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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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