Use the photo below to help me with this problem

Use The Photo Below To Help Me With This Problem

Answers

Answer 1

The domain and the range of the function are given as follows:

Domain: (-6, 1].Range: [-2, 4).

What are the domain and range of a function?

The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.

The values of x of the function are from an open circle at x = -6 to a closed circle at x = 1, hence the domain is given as follows:

(-6, 1].

The minimum value of the function is y = -2, while the maximum value is an open circle at y = 4, hence the range of the function is given as follows:

[-2, 4).

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Related Questions

What is the coordinate of R

Answers

Answer:

if you go into your reading lessone on one of the sentences in page 2 or 4 there is the answer hope this helped

Step-by-step explanation:

please help me IXL have to achieve a smart score of 80 part 1

Answers

The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

What is a linear equation

A linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

given the slope m = -3/5 and y intercept b = 6, we can write the equation as;

y = (-3/5)x + 6

y = -3x/5 + 6.

Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

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after a snowstorm city workers removed an estimated 10000 cubic yards of snow from the downtown area if this snow were apread in an even layer ocer the entire rectangular football field shown below about how many yards deep would the layer of snow be

Answers

The 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

To determine how many yards deep the layer of snow would be if spread evenly over the rectangular football field, we need to know the volume of the snow and the area of the football field.

First, let's find the area of the football field. Assuming standard dimensions for a football field, we have:

Length = 120 yards

Width = 53.3 yards

Area = Length x Width

Area = 120 yards x 53.3 yards

Area = 6,396 square yards

Now, let's find the volume of the snow. We are given that 10,000 cubic yards of snow were removed from the downtown area, so the volume is:

Volume = 10,000 cubic yards

Finally, to find the depth of the layer of snow, we can divide the volume of the snow by the area of the football field:

Depth = Volume / Area

Depth = 10,000 cubic yards / 6,396 square yards

Depth ≈ 1.56 yards

Therefore, if the 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

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Two similar solids have edges of 4 feet in 24 feet if the smaller saw that has a volume of 16 ft.³ find the volume of the other solid?

Answers

Answer: 3,456

Step-by-step explanation:

B. Solve:
1. If there are 13 yellow balls and 25 brown balls in a jar, what is the probability that Jaide will pick out a brown ball from the jar?
2. From a pack of 52 cards, a card is drawn at random. What is the probability of getting a king?

Answers

Answer:

Step-by-step:

1.The probability of picking a brown ball can be calculated as:

Probability of picking a brown ball = Number of brown balls / Total number of balls

Number of brown balls = 25

Total number of balls = 13 + 25 = 38

Probability of picking a brown ball = 25/38

Probability of picking a brown ball is approximately 0.658 or 65.8%

Therefore, the probability of Jaide picking a brown ball from the jar is approximately 0.658 or 65.8%.

2.There are four kings in a pack of 52 cards (one king for each suit). Therefore, the probability of drawing a king from a pack of 52 cards can be calculated as:

Probability of drawing a king = Number of kings / Total number of cards

Number of kings = 4

Total number of cards = 52

Probability of drawing a king = 4/52

Probability of drawing a king is approximately 0.077 or 7.7%

Therefore, the probability of getting a king when drawing a card at random from a pack of 52 cards is approximately 0.077 or 7.7%.

a quality control inspector wants to test whether the average weight of product on the line has varied from the specified value of 16 ounces. he takes a simple random sample of 100 products and obtains a mean of 16.3 and a standard deviation of 2.5. what are the hypotheses of this test?

Answers

Answer: The hypotheses of this test are:

Null hypothesis: The average weight of the product on the line is equal to the specified value of 16 ounces.

Alternative hypothesis: The average weight of the product on the line is different from the specified value of 16 ounces.

Step-by-step explanation:

a probability distribution of the claim sizes for an auto insurance policy is given in the table below: claim size 20 30 40 50 60 70 80 probability 0.10 0.10 0.10 0.20 0.15 0.10 0.25 what percentage of the claims are within one standard deviation of the mean claim size?

Answers

55% of the claims are within one standard deviation of the mean claim size.

To find the percentage of claims that are within one standard deviation of the mean claim size, we first need to calculate the mean and standard deviation of the distribution.

The mean claim size is:

u = (20 × 0.10) + (30 × 0.10) + (40 × 0.10) + (50 × 0.20) + (60 × 0.15) + (70 × 0.10) + (80 × 0.25) = 54

The variance can be calculated as follows:

s^2 = [[tex](20-54)^{2}[/tex] × 0.10] + [[tex](30-54)^{2}[/tex] × 0.10] + [[tex](40-54)^{2}[/tex] × 0.10] + [[tex](50-54)^{2}[/tex] × 0.20] + [[tex](60-54)^{2}[/tex] × 0.15] + [[tex](70-54)^{2}[/tex] × 0.10] + [[tex](80-54)^{2}[/tex] × 0.25] = 340

The standard deviation is the square root of the variance:

s = √340 ≈ 18.44

To find the percentage of claims that are within one standard deviation of the mean claim size, we need to find the range of claim sizes that fall within the interval (u - s, u + s).

(u - s) = 54 - 18.44 = 35.56

(u + s) = 54 + 18.44 = 72.44

We can see from the table that the claim sizes 40, 50, 60, and 70 fall within this range, and their probabilities add up to:

0.10 + 0.20 + 0.15 + 0.10 = 0.55

Therefore, 55 percentage of the claims are within one standard deviation of the mean claim size.

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The radius of a circle is 9 inches. What is the area of the circle to the nearest tenth? Question 2 options: 28.3 square inches 56.5 square inches 224.8 square inches 254.3 square inches

Answers

The area of the circle rounded of to the nearest tenth having radius 9 inches is 254.3 square inches.

Hence option d is the correct answer.

The radius of a circle is, say r = 9 inches

The formula of calculating area of a circle is,

Area = πr² (square units)

= π(9)² square inches

= 81π square inches

Let us take π= 3.14 (approximated up to two decimal places).

Thus, area of the circle = 81(3.14) square inches = 254.34 square inches

Rounding of a number is a process of approximating the original number to some decimal points resulting the original number to shorten up for more explicit representation.

Rounding of a number to its nearest tenth gives the original number to round of to one decimal place.

Here Area =  254.34 square inches is rounded of to the nearest tenth is 254.3 square  inches, since the digit after the first decimal place of the original number is lesser than 5 then we round down the number by decreasing the previous place value digit by 1.

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4. The usual 110-V household alternating current varies from -155 V
to 155 V with a frequency of 60 cycles/ sec (frequency is the
reciprocal of period). Assume the current starts at rest and then
rises.

Make a sketch of the curve.

Write an equation to describe the curve:_

Determine the value of y when t = 1/90 sec.:_

Approximate the value of t when y = 100 for the first time:_

Answers

Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

Find the missing measures in a circle in a square

Answers

The measure of the missing angle in the cyclic quadrilateral is 104°

Circle Geometry: Calculating the measure of the inscribed angle

From the question, we are to determine the measure of the inscribed angle in the given diagram

In the given diagram, we have a cyclic quadrilateral.

From one of the circle theorems, we known that

The sum of the opposite angles of cyclic quadrilateral are supplementary. That is they sum up to 180 degrees.

Let the unknown angle measure be x,

Then,

We can write that

x + 76°  = 180°

x = 180° - 76°

x = 104°

Hence, the missing angle measure is 104°

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1/4 exponent 4 equal to in fraction form

Answers

Answer:

(1/256)

Step-by-step explanation:

[tex](\frac{1}{4})^{4} = \frac{1^{4} }{4^{4} } = \frac{1}{256}[/tex]

Using laws of exponents I distributed the exponent to the fraction and solved.

ΔDEF ∼ ΔABC. What is the sequence of transformations that maps ΔABC to ΔDEF?

Answers

The sequence of transformation that maps ΔABC to ΔDEF is a rotation of 90° about the origin and a translation 2-units down.

What is rotation?

An thing rotates when it moves about its own axis. This can be used to describe the rotation of natural items like wheels and gears as well as the rotation of celestial bodies like planets and stars. A fundamental idea in physics, rotation is used to describe a variety of motions.

What is translation?

The act of shifting an object from one point to another without altering its size, shape, or orientation is referred to as translation. The coordinates of each point in the object are adjusted by a set amount to achieve this. In geometry and computer graphics, translation is a type of transformation that is frequently used to reposition objects on a two-dimensional plane or in three-dimensional space. In physics, the term "translation" can also refer to an object moving straight ahead without rotating or deforming.

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Developers determine the specifics of how to build a system in the _____ phase.
a. analysis
b. design
c. implementation
d. testing

Answers

Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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i need help with this math hw

Answers

The situation that represents a proportional relationship is " Renting a movie for $5 per day"

What is proportion relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent.

For example, A student reads 5 novels per 2days is a statement that shows the relationship between the Novels read and the number of days. This means that 10 novels will be read in 4 days.

In general a proportion relationship should obey,

change in y/ change in x= constant. The constant is the slope.

Therefore the statement that best explain a proportional relationship is " Renting a movie for $5 per day"

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If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, take away 1 and multiply the result by 3."

Answers

Using x as the unknown number, the algebraic expression for the given situation would be:

3(x - 1)

Answer:

"I think of a number, take away 1 and multiply the result by 3" can be written algebraically as:

3(x - 1)

where x is the unknown number that is being thought of.

We subtract 1 from x because the problem asks to "take away 1", and then we multiply the result by 3 because the problem asks to "multiply the result by 3".

So the expression 3(x - 1) represents the result of thinking of a number, taking away 1, and multiplying the result by 3.

Find the area of the shaded region for each composite figure.

Answers

The area of the shaded region is 192 m².

We have,

(g)

The shaded region.

= Area of the rectangle - Area of the triangle

So,

Length = 16 m

Width = 18 m

Area of the rectangle.

= 16 x 18

= 288 m²

And,

Base² + 16² = 20²

Base² = 400 - 256

Base = √144 = 12

So,

Area of the triangle.

= 1/2 x base x height

= 1/2 x 12 x 16

= 96

Now,

The shaded region.

= Area of the rectangle - Area of the triangle

= 288 - 96

= 192 m²

Thus,

The area of the shaded region is 192 m².

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help! as soon as possible

Answers

The quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

Explain about the features of kite:

A quadrilateral known as a kite has four sides that may be grouped into two adjacent pairs of equal-length sides, and the diagonals cross each other at right angles. The quadrilateral is a polygon with four sides.

Kite's two diagonals meet at a right angle to form its properties.A kite's primary diagonal is symmetrical.The diagonal's primary opposed angles are equal.A set of congruent triangles having a common base can be thought of as the kite.The kite is split into two isosceles triangles by the shorter diagonal.

Thus, the quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

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Using the calculus rule, how could the following derivative be rewritten as 2 partial derivatives?(dx/dz) at constant y

Answers

Using the calculus rule, we can rewrite the total derivative (dx/dz) at constant y as the sum of two partial derivatives.

The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y

Apply the chain rule
The chain rule in calculus allows us to find the derivative of a function with respect to another variable, by considering how the intermediate variables change.

In this case, we want to find (dx/dz) at constant y.

The chain rule states:
(dx/dz) = (dx/dy)*(dy/dz) + (dx/dz) at constant y
Identify the partial derivatives:
Since we want to rewrite (dx/dz) as a sum of two partial derivatives, we will keep the terms (dx/dy) and (dy/dz) as partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Final answer
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y.

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Approximate the square root to the nearest integer.
√23​

Answers

The square root of the number 23 is 5 after using the division method the answer is 25.

What is a number?

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 23 which is a real number and positive number.

As we know we can find the square root of a positive numbers only, the square root of a negative number cannot exist

The square root of the number 23 = [tex]\sqrt{23}[/tex]

The sign √ is a radical sign.

After using the division method:

[tex]\sqrt{23} = 4.7958[/tex]

After reducing the number up to two decimal places:

[tex]= 4.79[/tex]

Rounding the above number to the whole:

[tex]= 4.79 \thickapprox 5[/tex]

[tex]5\times5 = 25[/tex]

Thus, the square root of the number 23 is 5 after using the division method the answer is 25.

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which of the following statements is true? group of answer choices in general, it is no more difficult to solve an integer programming model than a linear programming one. all of these answers. an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

Answers

The true statement is that An integer programming solution can be better than the linear programming solution to the same problem. So, option(b) is right one.

In integer linear programming is harder than linear programming, because the branch-and–bound method requires many iterations of the simplex method, integer programming problems, So, option(a) is false one.

It usually takes longer than linear programming problems of the same size.Integer programming is a mathematical method that produces numerical solutions to linear programming problems.In integer programming, obtained integer solutions that should be neither feasible nor optimal. So, option(c) is also false.

Hence, required answer is option(b).

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Complete question :

which of the following statements is true? group of answer choices

a) in general, it is no more difficult to solve an integer programming model than a linear programming one.

b) an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily.

c) provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

d) all of these answers

In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.

pls help i well give brllant

Answers

The scale factor was used for each dilation are-

Part a: For ΔABC - scale factor = 2Part b: For ΔDEF - scale factor = 1/2Part c: For ΔGHJ - scale factor = 1/3Part d: For ΔKML - scale factor = 3Explain about the dilation:

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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Chloe had 74 pennies and then lost 10. Now she wants to buy a treat that costs 5 eighths of the pennies she has left. How many pennies does the treat cost?

Answers

The cost of the treat would be 40 pennies.

In mathematics, an expression is a combination of symbols (such as numbers, variables, and operations) that represents a value.

Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables. They can also include functions, exponents, and other mathematical concepts.

Chloe started with 74 pennies and lost 10, so she has 74 - 10 = 64 pennies left. The treat costs 5/8 of her remaining pennies,

Calculate the cost by multiplying 5/8 by 64:

(5/8) x 64 = 40

Therefore, the treat costs 40 pennies.

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Provide a detailed example. How lessons from Micah chapter 2 can be pacifically apply toward our lives today.

Answers

One lesson that we can learn from Micah chapter 2 is the importance of treating others with fairness and compassion. This includes being mindful of the ways in which our actions may impact those around us, particularly those who are less privileged than ourselves. We should strive to use our resources and influence in a way that benefits the greater good, rather than solely focusing on our own self-interest.

The lessons from Micah chapter 2 can be applied to our lives today in a peaceful and meaningful way. By treating others with fairness and compassion, acknowledging our mistakes and striving to become better people, and holding onto hope and faith in difficult times, we can live out the prophetic vision of a just and peaceful society that Micah envisioned.

Enter the surface area of the figure

Answers

The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.

How to find the area ?

We can use the formula for the surface area of a cone:

Surface Area = πr² + πr√(r² + h²)

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:

Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)

Surface Area = π(20.25) + π(4.5)√(436.25)

Surface Area = 353.43 millimeters²

Therefore, the surface area of the cone is approximately 353.43 square millimeters.

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marvin is trying to get to his friend's house. he walks 4 blocks north to the park, then turns right and walks 3 blocks. finally he turns right and walks 4 blocks. how far from his starting point does he wind up?

Answers

Answer: Marvin walks a total of 4 + 3 + 4 = 11 blocks.

To find how far he is from his starting point, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the 4 blocks north and 3 blocks east form the legs of a right triangle, and the distance Marvin is from his starting point is the hypotenuse.

So we can calculate it as follows:

distance = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

Therefore, Marvin is 5 blocks from his starting point.

Step-by-step explanation:

Question 3

A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.

5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20

A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.

Which measure of variability should the charity use to accurately represent the data? Explain your answer.

The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.

Question 4

The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.

circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent

Which of the following conclusions can we draw from the circle graph?

Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.

Question 5

The line plot displays the number of roses purchased per day at a grocery store.

A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.

Which of the following is the best measure of variability for the data, and what is its value?

The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.

Answers

The correct answer is: The IQR of 13 is the most accurate to use, since the data is skewed. (Option B).

The correct answer is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents. (Option A).

The correct answer is: The IQR is the best measure of variability, and it equals 6.

How to Solve the Problem?

1. Since the data is skewed, it is not appropriate to use the range as a measure of variability. The range is sensitive to extreme values and can be misleading in skewed data. The interquartile range (IQR) is a better measure of variability for skewed data since it is not affected by extreme values. Therefore, the charity should use the IQR of 13 as the measure of variability for this data.

2. From the circle graph, we can draw the following conclusion:

Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. 42% of 400 is 168 residents.

3. The line plot shows that the data is discrete and not continuous. Also, the data is not normally distributed and is skewed. Therefore, the range is not an appropriate measure of variability. The interquartile range (IQR) is a better measure of variability for skewed data. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.

From the plot, we can see that Q1 is 2 and Q3 is 8. Therefore, the IQR is 8 - 2 = 6.

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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!

Answers

The measure of the angle LAF is 4°

Explain the term angle

An angle is a geometric figure formed by two rays that share a common endpoint called a vertex. The rays are usually referred to as the sides of the angle. Angles are measured in degrees or radians and are used in various fields, including mathematics, physics, and engineering, to describe and calculate shapes and movements.

According to the given information

Here we have:

mYL + mSF = 360°

We also know that mYS = 48 degrees and mLF = 160 degrees. Since arc YS and arc LF are on the same circle, they must add up to 360 degrees. Therefore:

mYS + mLF + mYSF = 360°

Substituting the given values, we have:

48 + 160 + mYSF = 360°

Simplifying and solving for mYSF, we get:

mYSF = 152°

Now we can find the measure of the central angle LSF that intercepts arc LF by subtracting mYSF from the measure of the arc LF:

mLF - mYSF = 160 - 152 = 8°

Finally, we can find the measure of angle LAF by dividing the central angle LSF in half, since angle LAF is an inscribed angle that intercepts arc LF:

mLAF = 1/2 * mLSF = 1/2 * 8 = 4°

Therefore, m/LAF = 4 °

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What function is inverse of the exponential function y=(1. 5)^x

Answers

Answer:

[tex]y = {1.5}^{x} [/tex]

[tex] ln(y) = ln( {1.5}^{x} ) [/tex]

[tex] ln(y) = x ln(1.5) [/tex]

[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]

[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]

Suppose that Leni and Thom are lawyers and each has a taxable income of $230,000. They can't decide if they should be married in December or in January. If they marry in December, then they are considered married for the entire tax year and could file a joint return. If they get married in January of the next year, they would file a separate return each as a single taxpayer. Examine Schedules X and Y-1. Which filing status would yield the lower tax? If so, by how much? is there really a marriage penalty?

Answers

Getting married in December and filing a joint return would result in a lower tax liability by: $65,917.

Based on the given tax schedules, if Leni and Thom get married in December and file a joint return, their total tax liability would be:

$4,220 for the first $19,900 of taxable income

$20,227 for the remaining $210,100 of taxable income ($230,000 - $19,900)

Total tax liability: $24,447

If they get married in January of the next year and file separate returns, each as a single taxpayer, their total tax liability would be:

Leni's tax liability: $45,182

Thom's tax liability: $45,182

Total tax liability: $90,364

Therefore, getting married in December and filing a joint return would result in a lower tax liability by: $90,364 - $24,447 = $65,917.

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The rain gauge after a week showed that there were ten inches of rain. Every day the rain evaporated four inches but two more inches of rain was added. By what day was the rain gauge free of water?

A. day 11

B. day 10

C. day 8

D. day 7

Answers

Therefore, it takes four days for the rain gauge to be free of water. The answer is option D, day 7.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation usually contains one or more variables, which are symbols that represent unknown or varying quantities. The values of the variables that satisfy the equation are called the solutions of the equation.

Here,

Let's start by finding out how much water is left in the gauge after one day of evaporation and addition. If the rain gauge had 10 inches of water at the start of the week, then after one day:

4 inches of water would have evaporated, leaving 10 - 4 = 6 inches of water.

2 more inches of rain would have fallen, bringing the total to 6 + 2 = 8 inches of water.

So after one day, the rain gauge has 8 inches of water.

Now we need to repeat this process until there is no water left in the gauge.

After the second day:

4 more inches of water would have evaporated, leaving 8 - 4 = 4 inches of water.

2 more inches of rain would have fallen, bringing the total to 4 + 2 = 6 inches of water.

After the third day:

4 more inches of water would have evaporated, leaving 6 - 4 = 2 inches of water.

2 more inches of rain would have fallen, bringing the total to 2 + 2 = 4 inches of water.

After the fourth day:

4 more inches of water would have evaporated, leaving 4 - 4 = 0 inches of water.

2 more inches of rain would have fallen, but it would not have filled the gauge since it was already empty.

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