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## The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1 Create a dot plot to represent the data. What can you conclude about the dot plot of the data set? Check all that apply. The range of the number line should be 0 to 7 to represent the frequency. Four families said they ate out twice the previous week. One family said they ate out 5 times the previous week. The data set is symmetrical. The median best represents the data set.

The correct options are:

• Four families said they ate out twice the previous week.
• One family said they ate out 5 times the previous week.
• The median best represents the data set.

Step-by-step explanation:

We are given a data set as:

4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1

On arranging this data set in the frequency table we get:

Number of times they went for dinner    Number of families

0                                                          2

1                                                           3

2                                                          4

3                                                           1

4                                                           2

5                                                           1

6                                                            1

• Hence, the range of the number line is between 0 to 6.
• Also there are 4 dots above 2.

Hence,  Four families said they ate out twice the previous week.

• Also there is one dot above 5.

Hence,  One family said they ate out 5 times the previous week.

• The data set is not symmetrical since the median is 2 and the data points to the left and to the right do not have symmetry.

Hence, the data set is not symmetrical.

• Also we know that the median of the data is the central tendency of the data and always best represents the data.

Hence, The median best represents the data set.

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## To determine the pH of a solution using a pH indicator, you need a? A. Color key B. neutral Solution C. Range of acids and bases

To determine the pH of a solution using a pH indicator, you need a? A. Color key B. neutral Solution C. Range of acids and bases

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## Joshua wants to buy some land in Wyoming to start a free range chicken ranch. He wants the land to have a length 500 feet greater than the width, so the chickens have room to run. If the area of the land needs to be 1,742,400 square feet, what must the length be? Round answer to the nearest whole foot.

Joshua wants to buy some land in Wyoming to start a free range chicken ranch. He wants the land to have a length 500 feet greater than the width, so the chickens have room to run. If the area of the land needs to be 1,742,400 square feet, what must the length be? Round answer to the nearest whole foot.

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## The range for the given domain of the function is .

The domain of a function is the numbers on the x coordinate that the function can be. The range is the same, but for the y axis. So for the function you gave, if the domain is all numbers between -1 and 3, you plug in those numbers.

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## Which articulations allow for greatest range of motion?

Which articulations allow for greatest range of motion?

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## Two groups of students were asked how many hours they spent reading each day. The table below shows the numbers for each group: Group A 1 2 1 1 3 3 2 2 3 Group B 3 2 3 2 2 2 1 1 2 Based on the table, which of the following is true? The interquartile range for Group A students is 0.5 less than the interquartile range for Group B students. The interquartile range for Group A students is equal to the interquartile range for Group B students. The interquartile range for Group A employees is 0.5 more than to the interquartile range for Group B students. The interquartile range for Group A employees is 1 more than the interquartile range for Group B students.

Solution:

Data represented as number of hours spent in studying by Group A Students:

1,2,1,1,3,3,2,2,3

Arranging it in ascending order: 1,1,1 ,2, 2, 2, 3, 3, 3,

As number of terms is odd, The median will be middle value of observation.Which is 2.

The Data arranged in ascending order are , (1,1,1,2),2(2,3,3,3).

Median of (1,1,1,2) = =1

Median of (2,3,3,3)==3

=Interquartile Range ==3-1=2

For Data Set 2,

The Data for group B students are:  3   2 3 2 2 2 1 1 2

Arranging in ascending order: 1,1,2,2,2,2,2,3,3

total number of observation = 9

Median = 2

Arranging the data as : (1,1,2,2) 2,(2,2,3,3)

Median of (1,1,2,2)= Number of observation is 4 which is even , so Median= =

Median of (2,2,3,3)=

S=Interquartile Range = =

Interquartile range for Group A Students =Interquartile range for Group B students + 1

Option (D) The interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.

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## Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation:Which city should Dominick visit, and why? He should visit Orlando. It has a greater IQR. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. He should visit Tampa Bay. The highest temperature occurred there. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.

Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation:Which city should Dominick visit, and why? He should visit Orlando. It has a greater IQR. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. He should visit Tampa Bay. The highest temperature occurred there. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.

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## The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range but not the domain of the transformed function is the same as that of the parent function. The domain but not the range of the transformed function is the same as that of the parent function.

D. The domain but not the range of the transformed function is the same as that of the parent function.

Step-by-step explanation:

We are given,

The function is reflected across x-axis, which gives .

And then the function is translated to the right by 6 units, which gives .

Thus, the transformed function is

So, from the graph shown below, we get,

Domain of both the functions f(x) and g(x) is set of all real numbers.

Range of f(x) is .

But, Range of g(x) is .

Hence, the correct option is,

D. The domain but not the range of the transformed function is the same as that of the parent function.

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## Choose the values that are in the range….

now… that fraction, becomes undefined if the denominator becomes 0

when does that happen?  well, it happens when sin(y) becomes 0, when is that?, notice your Unit Circle, that happens at 0, π, 2π, 3π and so on

now, on those angles, sin(y) is 0, and the rational of the cotangent, becomes undefined, so, therefore, those angles are NOT valid values for the angle, and outside the range.

now, just check for those, everyone else should be in the range.

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## What is the range of the function f(x) = – 1/3 |x − 1| − 2? all real numbers all real numbers less than or equal to −2 all real numbers less than or equal to 1 all real numbers greater than or equal to −2

What is the range of the function f(x) = – 1/3 |x − 1| − 2? all real numbers all real numbers less than or equal to −2 all real numbers less than or equal to 1 all real numbers greater than or equal to −2

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## From the table below, determine whether the data shows an exponential function. Explain why or why not. (x) -5, -4, -3, -2 (y) 0.5, 2, 8, 32 A) Yes; the domain values are at regular intervals and the range values have a common factor 8. B) Yes; the domain values are at regular intervals and the range values have a common factor 4. C) No; the domain values are not at regular intervals. D) No; the domain values are at regular intervals and the range values have a common factor 4. Please help, and please give me an explanation on the answer you choose because I need to make corrections. Please.

Option B-  Yes; the domain values are at regular intervals and the range values have a common factor 4.

Step-by-step explanation:

Given : The data

(x) -5,   -4,  -3,   -2

(y) 0.5,  2,   8,   32

To find : The data shows an exponential function or not

Solution :

The general form of an exponential form is

To check whether the data give the exponential function we form equation with the help of two points and verify the other two points .

Let x= -5 and y=0.5

……[1]

Let x= -4 and y=2

………[2]

Equate LHS because RHS is equal in equation [1] and [2]

Put back in [2]

.

a=512 and b=4

Exponential function –

To verify this function put

1) x=-3

The point satisfied.

2) x=-2

The point satisfied.

Therefore, The given data is an exponential function

The domain values are at regular intervals and the range values have a common factor 4 because b=4 and the change happen but value of b remain same.

Hence, Option B is correct.

Yes; the domain values are at regular intervals and the range values have a common factor 4.

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## (20 pts) What is the range of the relation? Coordinate grid with labeled points at (negative one, negative two), (negative four, negative three), (negative two, zero), (two, two) A. {–4, 4} B. {–4, –2, –1, 0, –2} C. {–3, –2, 0, 2} D. {–4, –2,–1, 2}

(20 pts) What is the range of the relation? Coordinate grid with labeled points at (negative one, negative two), (negative four, negative three), (negative two, zero), (two, two) A. {–4, 4} B. {–4, –2, –1, 0, –2} C. {–3, –2, 0, 2} D. {–4, –2,–1, 2}

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## Which of the following is not true about the distribution of species? a. A species’ native range does not include areas where it was introduced by humans. b. Some species have a range they inhabit only for breeding. c. Seasonal ranges include areas where species are found for part of the year. d. All the organisms in an ecosystem share distribution patterns.

d. All the organisms in an ecosystem share distribution patterns.

Explanation:

Native range is what is known in biology as the areas where a species is naturally found, not places were humans introduced them, species have some range only for breeding, for example some frogs only go into the rapids for breeding, and not for living or hunting, and seasonal ranges are areas where the species are found for a part of the year, for example the butterflies that migrate south to Mexico on the coldest months of the year and then come back to the United States for the warm summer, the only one that is not true is that all the organisms in an ecosystem share distribution patterns.

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## What is an example of how you can be proactive about your personal health and wellness? Know your family health history and use reliable resources to research any family illnesses, because this will help you understand risks and available treatments Schedule regular doctor appointments, because getting checked by the doctor ensures that you will not get sick or contract communicable diseases Get extra sleep on days you don’t exercise, because this will help you keep your body composition in a healthy range and avoid changes in weight Use vitamins and performance-enhancing supplements, because they increase energy levels and help build muscles to keep your body physically fit Question 4(Multiple Choice Worth 1 points)

Your answer is: Know your family health history and use reliable resources to research any family.illnesses because this will help you understand risks and available treatments. By process of deduction, doctor’s appointments cannot perfectly ensure a lack of sickness, increasing sleep has studies that suggest it actually increases chances of weight gain, and performance-enhancing supplements are actually harmful if you don’t need them. Good Luck!

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## The domain of the function is given. Find the range. f(x) = 2x – 1

The domain of the function is given. Find the range. f(x) = 2x – 1

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## Given the range of the function, find the corresponding domain. f(x) = 4x – 1 Range: {3, 7, 11, 15}

The range is the output value or the y value.
You would work backwards to find the domain.

f(x) = 4x – 1                              f(x) = 4x – 1
3 = 4x – 1                                    7 = 4x – 1
4 = 4x                                            8 = 4x
divide both sides by 4              divide both sides by 4
x = 1                                              x = 2

f(x) = 4x – 1                                  f(x) = 4x – 1
11 = 4x – 1                                      15 = 4x – 1
12 = 4x                                              16 = 4x
divide both sides by 4                  divide both sides by 4
x = 3                                                    x = 4
Domain { 1, 2, 3, 4}

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## Analyze the characteristics of exponential and logarithmic functions. Make sure you talk about domain and range. Compare them to other functions.

Analyze the characteristics of exponential and logarithmic functions. Make sure you talk about domain and range. Compare them to other functions.

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## PLEASE HELP!!!!!! The Jonas school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student. School Low High Range Mean Median IRQ σ High School M 128 180 62 141 160 55.5 41.5 High School N 131 180 49 159 154 48.5 36.5 High School P 140 180 40 153 165 32.5 31.5 Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.

High School P has the most consistent attendance among its students.

School N should be awarded for the highest average attendance.

Step-by-step explanation:

Consider the provided information.

Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically.

Standard deviation (σ) is a measure of how a data set is spread out.

If the standard deviation is low, this implies that the information tends to be near to the set mean, whereas a high standard deviation implies that the information points are spread across a wider spectrum of values.

Therefore, for more consistency we need to look for the low standard deviation.

From the provided table we can see that the school P has low standard deviation (σ) i.e 31.5

Hence, High School P has the most consistent attendance among its students.

Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.

The formula for mean is:

Mean is the same as average.

The sum of mean or average will be larger if each students contributes more attendance.

For highest average attendance the school with higher mean should be awarded.

Hence, School N should be awarded for the highest average attendance.

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## Determine the range of the function in the table below. x f(x) -11 50 -13 63 10 -51 21 -72 {-11, -13, 10, 21} {(-11, 50), (-13, 63), (10, -51), (21, -72)} {50, 63, -51, -72} {(50, -11), (63, -13), (-51, 10), (-72, 21)}

Determine the range of the function in the table below. x f(x) -11 50 -13 63 10 -51 21 -72 {-11, -13, 10, 21} {(-11, 50), (-13, 63), (10, -51), (21, -72)} {50, 63, -51, -72} {(50, -11), (63, -13), (-51, 10), (-72, 21)}

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## A machine that provides both constant speed and maximum resistance throughout the full range of motion provides what type of muscular contraction?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## The table below shows data from a survey about the amount of time high school students spent reading and the amount of time spent watching videos each week (without reading): Reading Video 5 1 5 4 7 7 7 10 7 12 12 15 12 15 12 18 14 21 15 26 Which response best describes outliers in these data sets? A) Neither data set has suspected outliers. B) The range of data is too small to identify outliers. C) Video has a suspected outlier in the 26-hour value. D) Due to the narrow range of reading compared to video, the video values of 18, 21, and 26 are all possible outliers.

Arranging the data in ascending order

1, 4,5,5,7,7,7,7, 10,12,12,12,12,14,15,15,15,18,21,26

There are 20 data values in data set.

Mean of data set

Since there are , even number of data values in the data set,

So, Median

First Quartile and third Quartile can be calculated directly ,using the concept of even and odd number of Observations in the data set.

Mode> 12

Since data values is negatively skewed, Mean < Median <Mode.

To calculate Outlier

Interquartile Range (IQR)

Also,

No, value exceeds 27, nor any value is less than -5.

So, there are no outliers in Data set, which has 20 values.

Option A:  Neither data set has suspected outliers.

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## What is the range of f(x)=log0.6x

Solution:

Data represented as number of hours spent in studying by Group A Students:

1,2,1,1,3,3,2,2,3

Arranging it in ascending order: 1,1,1 ,2, 2, 2, 3, 3, 3,

As number of terms is odd, The median will be middle value of observation.Which is 2.

The Data arranged in ascending order are , (1,1,1,2),2(2,3,3,3).

Median of (1,1,1,2) = =1

Median of (2,3,3,3)==3

=Interquartile Range ==3-1=2

For Data Set 2,

The Data for group B students are:  3   2 3 2 2 2 1 1 2

Arranging in ascending order: 1,1,2,2,2,2,2,3,3

total number of observation = 9

Median = 2

Arranging the data as : (1,1,2,2) 2,(2,2,3,3)

Median of (1,1,2,2)= Number of observation is 4 which is even , so Median= =

Median of (2,2,3,3)=

S=Interquartile Range = =

Interquartile range for Group A Students =Interquartile range for Group B students + 1

Option (D) The interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.

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## Match the range of the function f(x) = x2 + 2x − 1 to its domain. Tiles 2 -2 3 -3 Pairs 2 14 7 -1

Number of copy machines must be made to minimize the unit cost=160.

Step-by-step explanation:

We are given that the unit cost function C ( the cost in dollars to make each copy machine)

Then the unit cost function is given by

We have to find the number of copy machines for  minimize the unit  cost

Differentiate with respect to x

Then we get

……(equation I)

To find the value of x then we susbtitute is equal to zero

By using division property of equality

Again differentiate the equation I with respect to x then we get

Hence, the unit cost is minimize for x=160

Therefore, the number of copy machines must be made to minimize the unit cost =160

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Number of cans donated the first week = 132
Number of cans donated the second week = 146
Number of cans donated the third week = c, where c is some positive number

Add up the three values (132, 146, and c) to get 132+146+c. I’m choosing not to simplify because each answer choice hasn’t simplified either.

The expression of 132+146+c represents the total amount of cans donated for weeks 1 through 3. We want “at least 325 cans”, so that means the expression is 325 or larger. That translates to this inequality

The “greater than or equal to” sign indicates we want that sum to be 325 or larger.

Now we solve for c

So the amount of cans donated for week three needs to be 47 or larger. If you collect exactly 47 cans for week three, then you meet the goal of 325 total cans. If you collect more than 47 cans for week three, then you exceed the goal of 325 total cans.

————————————

In summary we have the inequality

which solves to

Meaning that the answer is choice D

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## The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?

Answer: The answer is (C) Patricia is not correct because both 3 – 4i  and -11+√2i  must be roots.

Step-by-step explanation:  Given that  (-11-√2i) , (3 + 4i), and 10 are the roots of the polynomial function f(x) that Patricia is studying.

We know that the complex roots of a polynomial function always occur in pairs. That is, if (a + bi) is a root of a function, then (a – bi) will also be a root (one is the complex conjugate of the other).

The complex conjugate of (3 + 4i) is (3 – 4i) and the complex conjugate of (-11 – √2i) is (11 + √2i).

Therefore,  (3 – 4i) and (-11 + √2i) both are the roots of f(x).

Hence, since we have 5 roots, so the degree of the polynomial function f(x) cannot be 4.

Since Patricia concludes that the degree of f(x) is 4, so she is not correct because both (3 – 4i)  and (-11+√2i)  must be roots.

Thus, option (C) is correct.