For each graph below, state whether it represents function_ Graph Graph 2 Graph 3 Function? Yes No Graph 4 Yes No Graph 5 No Yes Graph Function? Yes Yes

Answers

Answer 1

Graphs 1,5 are functions while graphs 2,3,4,6 are not functions.

A graph represents a function if it has one and only one y value or no y value for each x. If the graph has multiple y values for any x, then it is not a graph of a function.

We can check if the following graphs are functions or not by using the vertical line test.

In the vertical line test, we draw a vertical line across the function and if that line touches two points on the graph means the graph is not a function as per the definition of the function.

Let us apply this to the following graphs -

1. Graph 1-  If we draw a vertical line and drag it from left to right, we see that no two points line on the same line. So, graph 1 is a function.

2. Graph 2 - If we draw a vertical line and drag it from left to right, we see that the line crosse two points on each number. So, graph 2 is clearly not a function.

3. Graph 3 - Here too, if a vertical line is drawn and dragged from left to right, we cross two points on every number. So, graph 3 is also not a function.

4. Graph 4 -  If we draw a vertical line and drag it from left to right, we see that at some places the line crosse two points on each number. So, graph 4  too, is not a function.

5. Graph 5 - If we draw a vertical line and drag it from left to right, we see that no two points line on the same line. So, graph 5 is a function.

6. Graph 6 - Here also, if a vertical line is drawn and dragged from left to right, we cross two points on point -1. So, graph 6 is also not a function.

Hence, we can conclude that - Graph 1,5 are functions while graphs 2,3,4,6 are not functions.

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The complete question is -

For each graph below, state whether it represents a function or not.

1. Graph 1

2. Graph 2

3. Graph 3

4. Graph 4

5. Graph 5

6. Graph 6

For Each Graph Below, State Whether It Represents Function_ Graph Graph 2 Graph 3 Function? Yes No Graph

Related Questions

Erica recorded the number of sales she made during each of the first 4 months when
she began her new career. Erica plotted the data on a coordinate grid, and she noted
that the data correlate to an exponential equation, as shown.
What is the domain of the function shown in the graph?

Answers

The domain for the given graph is obtained as {1, 2, 3, 4}.

What is a function?

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

From the graph of the given exponential function,

The set of ordered pairs can be written as follows,

{(1, 10), (2, 20), (3, 40), (4, 80)}

Since the domain is the set of first elements for a given pair of ordered set.

The domain is given as {1, 2, 3, 4}.

Hence, the domain obtained from the given graph is {1, 2, 3, 4}.

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The graph missing in the question is attached here.

a rowing team rowed miles while going with the current in the same amount of time as it took to row miles going against the current. the rate of the current was miles per hour. find the rate of the rowing team in still water.

Answers

The rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

Given that,

In the same time it took to row 25 miles against the current, a rowing team was able to row 50 miles while travelling with it. 2 miles per hour was the current's speed.

We have to calculate the rowing team's speed in still water.

We know that,

Let rowing rate in still water = r

And current rate = c = 2 mph

Rowing with the current means the overall speed is r + c = r + 2

Rowing against the current means the overall speed is r - c = r - 2

Distance = Rate × Time

50 = (r+2) × t  ----->equation(1)  

25 = (r-2) × t  ----->equation(2)

By solving

Divide equation(1) by equation(2)

50/25 = (r+2) × t / (r-2) × t

2=r+2/r-2

2(r-2)=r+2

2r-4=r+2

2r-r=2+4

r=6mph

Substitute in equation(1)

50 = (r+2) × t

50=(6+2)×t

50=8t

t=50/8

t=6.25 hrs

t= 6 hours 15 minutes

Therefore, the rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

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The Girl Scouts sponsor a Movie Night each year. In the first year, there were 26 participants. In the fourth year, there were 89 participants. Write an equation in slope-intercept form modeling this situation where y, number of participants, is a function of x, number of years. How many participants are predicted for the 6th year?

Answers

The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

Slope-intercept form:

The slope-intercept form is One of the most common ways to describe a line's equation. The general form of a slope-intercept form is given by

                                y = mx + c

Where m is the slope and c is the y-intercept  

And the formula for Slope is given by

             Slope (m) = (y₂ - y₁)/ (x₂ - x₁)

Here we have

Number of participants in 1st year = 26

Number of participants in 4th year = 89

Take number of years as x - coordinate

Number of participants as y - coordinate

As we know for 1 year, number of participants is 26

=>  The pair of coordinates = (1, 26)

For 4th year, number of participants is 89  

=>  The pair of coordinates = (4, 89)

Now we will find the slope-intercept form for the situation

using the coordinates (1, 26) (4, 89)

As we know slope m = (y₂ - y₁)/(x₂- x₁)  

Slope m = (89 - 26)/(4 - 1) = 63/3 = 21      

As we know slope intercept form, y = mx + c  

=> y = 21x + c --- (1)

As per the situation, Line (1) will pass through (1, 26)  

=> 26 = 21(1) + c  

=> c = 26 - 21

=> c = 5

=>  y = 21x + 5

Therefore,

The required Slope-intercept form is y = 21x + 5

To find the number of participants in the 6th year, take x = 6

=> y = 21(6) + 5

=> y = 126 + 5

=> y = 131

Therefore,

The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

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solving systems by substation
x-4y=15
3x-12y=12

Answers

Answer:

There is no solution

Step-by-step explanation:

x - 4y = 15

3x -12y = 12

Times the first equation by -3

-3x +12y = -45

3x - 12y = 12

0 = -33

This is untrue; 0 is not equal to -33

So, there is no solution for this system.

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What is 2 divided by 3? Explain the steps pleas.

Answers

The value of 2 divided by 3 is 0.67

How to evaluate the quotient expression?

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

2 divided by 3

To start with, we need to represent the expression properly as a quotient

So, we have the following representation

2 divided by 3 = 2/3

Evaluate the quotient expression using a calculator

This gives

2 divided by 3 = 0.67

Hence, the solution to 2 divided by 3 is 0.67

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Write a linear function with the given values : f(0)=3, f(1)=5

Answers

The linear function that has f(0) = 3 and f(1) = 5 will be f(x) = 5x.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The function is a linear function which is given as,

f(x) = mx + c

The value of the function at x = 0 is 3, then we have

f(0) = m × 0 + c

3 = c

Then the equation is given as,

g(x) = mx

The value of the function at x = 1 is 5, then we have

f(1) = m × 1

5 = m

The linear function that has f(0) = 3 and f(1) = 5 will be f(x) = 5x.

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The midpoint of a line with the endpoints (-2, 0) and (-6, 8) is:
(4,4).
(-4,4).
(-4,-4)
(4,-4).

Answers

Answer:

(-4,4)

Midpoint= (x2 + x1 /2, y2+y1 /2)

Step-by-step explanation:

the coordinates of the midpoint between points A and B are

((xa + xb)/2, (ya + yb)/2)

in our case

((-2 + -6)/2, (0 + 8)/2) = (-8/2, 8/2) = (-4, 4)

elizabeth's family went to nyc for their vacation. at the gift shop on liberty island, valerie bought three t-shirts and four keychains for $134, and jennifer bought four t-shirts and five key chains for $175. find the price of each item.

Answers

Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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a survey was taken of a random sampling of residents of new york city and los angeles to compare how many of them own a car. a 4-column table with 3 rows. the first column has no label with entries l a residents, n y c residents, total. the second column is labeled own a car with entries 3,251; 1,478, 4,729. the third column is labeled do not own a car with entries 869; 6,182; 7,051. the fourth column is labeled total with entries 4,120; 7,660; 11,780. which statement about the two-way frequency table is true?

Answers

The true statement is;

There is a greater percentage of Los Angeles residents who own a car than New York City residents who do

Given,

Following is the presentation of the values:

The number of residents in Los Angeles own a car = 3251

The number of residents in New York City  own a car = 1478

Total residents who own a car = 4729

Los Angeles  residents who do not own a car = 869

New York City residents who do not own a car = 6182

Total residents who do not own a car = 7051

Total Los Angeles residents sampled = 4120

Total New York City residents sampled = 7660

Total residents of both cities sampled = 11780

Here,

Percentage of Los Angeles residents who own a car = (3251/4120)×100 = 78.9%

Percentage of New York City residents who own a car = (1478/7660)×100 = 19.3%

Then,

The total number of people in the poll who own a car = 4729

Therefore,

The correct option is that there is a greater percentage of Los Angeles residents who own a car than New York City residents who do.

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Answer: B

Step-by-step explanation:

Locate points A and B in the coordinate plane below. Use the Pythagorean Theorem to find the straight-line distance from each point to the origin.

Which point is close to the origin and by how much?

the options for the first one is "A" or "B" and the options for the second one is " more than" or "less than". (please ignore my chosen answer, I was just guessing.)

Answers

The coordinates of points A and B are (-4, 5) and (2, 6) respectively. Point B is close to the origin by 0.1 unit

How to locate points A and B in the coordinate plane?

The positions or coordinates of points A and B are (-4, 5) and (2, 6) respectively

In order to use the Pythagorean Theorem to find the straight-line distance from each point to the origin (Consider the attached image):

Distance for point A

d = √((-4)²+5²)

d = √41 = 6.40 units

Distance for point A

d = √(2²+6²)

d = √40 = 6.32 units

To find which point is close to the origin and by how much:

The distance of B is less, so point B is close to the origin

Difference of distance =   6.40 - 6.32  = 0.08 ≈ 0.1 unit

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which is true about the product of 10 and 2/3
A The product is less than 2/3
B The product is greater than 10
C The product is less than 10
D The product is between 2 and 3
i don't have anymore points this is all i have

Answers

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The numbers are given below.

10 and 2/3

The product of the numbers 10 and 2/3 will be given as,

⇒ 10 x 2 / 3

⇒ 20 / 3

⇒ 6.67

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

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the mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135. how many numbers are in the set?

Answers

There are 20 numbers in the set.

Given,

Set of numbers is 120

one number is increased by 300

and, mean increases to 135.

To find the how many numbers are in the set?

Now, According to the question:

Let the number of numbers be 'n'

Then, (sum of numbers)/n = 120

or, old sum = 120n

if one number is increased by 300, the new sum = (old sum + 300)

Then, (new sum)/ n= 135

or new sum = 135n = old sum + 300 = 120n + 300

The equation will  be:

135n = 120n + 300

15n = 300

n = 20

Hence, There are 20 numbers in the set.

In the question:

The mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135.

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does there exist a polynomial time reduction from every problem in np-complete to every other problem in np-complete?

Answers

Yes, by definition, every NP problem can be reduced to an NP-complete problem in polynomial time.

All NP-complete problems can be reduced to each other in polynomial time since an NP-complete problem is itself an NP problem.

An NP-complete problem lies in NP, the set of all decision problems whose solutions can be verified in polynomial time. Similarly, NP can be defined as a set of decision problems that can be solved in polynomial time by a non-deterministic Turing machine. A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) to p in polynomial time.

Not sure if all NP issues can be resolved quickly. This is called the P-NP problem. However, if every NP-complete problem can be solved quickly, the definition of an NP-complete problem states that every problem in NP must be rapidly reducible to every NP-complete problem (i.e., it can be solved in polynomial time abbreviated by ). For this reason, NP-complete problems in general are often said to be harder or harder than NP problems.

A decision problem C is NP-complete if:

1. C is in NP and every problem in NP is reducible to C in polynomial time.

2. We can show that C is in NP by showing that the candidate solutions for C can be verified in polynomial time.

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a manufacturer must test that his bolts are 1.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.06cm. he knows that the population standard deviation is 0.22cm. assuming a level of significance of 0.10, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.

Answers

p < 0.10, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.

In this question we have,

The population mean μ = 1.00

The sample size n = 49

The sample mean X = 1.06

The standard deviation σ = 0.22cm

The significance level α = 0.10

So, the hypothesis is:

The null hypothesis: H0: μ = 1

The alternative hypothesis: Ha: μ ≠ 1

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

= (1.06 - 1)/(0.22/√49)

= 0.06 / 0.03142

= 1.91

So, for z = 1.91, the p-value is 0.028067.

The provided significance level of 0.10 is not met by the p-value of (0.028067).

Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.

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Help finding the linear equation for this chart

Answers

The linear equation for the given chart is: y = -3x + 7.

How to Write a Linear Equation?

From the chart given, we can use two pairs of values to find the slope (m) and the y-intercept (b), then plug in their values into the equation that is expressed in slope-intercept form as y = mx + b.

Using two points, (1, 4) and (3, -2), find the slope (m):

Slope (m) = change in y / change in x = (-2 - 4) / (3 - 1)

Slope (m) = -6/2

Slope (m) = -3

Find the y-intercept (b) by substituting m = -3 and (x, y) = (1, 4) into y = mx + b:

4 = -3(1) + b

4 = -3 + b

4 + 3 = b

7 = b

b = 7

To write the linear equation, substitute m = -3 and b = 7 into y = mx + b:

y = -3x + 7

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(5 x 10 ^3 ) x (9 x ^7) in standard form

Answers

The given equation that should be in the standard form should be like a 4.5 x 10¹¹.

The equation in standard form:

Since

The equation is (5 x 10³) x (9 x 10⁷)

Now here we use the commutative property

So,

45 x (10³ x 10⁷)

45 x 10¹⁰

4.5 x 10¹¹

Here, we multiply the number in the 1st bracket, then add, it, and then finally in standard form.

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Answer:

Step-by-step explanation:

(5*10^3)*(9*10^7)

(5*1000)*(9*10000000)

5000*90000000

450000000000

How do you solve 13=8−5d?

Answers

 By solving 13 = 8- 5d we get the value of ‘d ’ is equal to -1.

This equation can be solved by arranging the non – algebraic equations on one side and letting the algebraic number on the other side.

13 = 8 – 5d

5d = 8-13

5d = -5

d = -5/5

d = -1.

While arranging the non - algebraic numbers on one side their signs should be changed after taking the number into another side. Similarly, while arranging the algebraic equations on one side, signs of the numbers should be changed. In an algebraic equation, the terms addition, subtraction, multiplication, division, raising to a power, and extraction of a root are applied to a set of variables to construct a statement of the equality of two expressions.

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Classify each statement as true or false. ∣−3∣>−3

Answers

The inequality of |-3| > -3 is true.

What are inequalities?

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

What is the meaning of modulus sign?

Any expression between the modulus sign | | indicates that the expression will be positive even if it is negative. For example, |-2| = 2.

Using this property of absolute sign,

= |-3| > -3

= 3 > -3

3 is greater than -3. Hence, the statement is true.

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Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.

Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?

Answers

The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

How to obtain the viable solutions?

The variables for this problem are given as follows:

The input variable b represents the number of books ordered.The output variable w represents the total weights of the books, in ounces.

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

Missing Information

The table is given by the image shown at the end of the answer.

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The freight elevator of a building can safely carry a load of at most 4000 lb. A worker needs to move supplies in 50-lb boxes from the loading dock to the fourth floor of the building. The worker weighs 160 lb. The cart he uses weighs 95 lb.
(A) Write and solve an inequality to determine the greatest number of boxes he can move in one trip.
(B) The worker must deliver 310 boxes to the fourth floor. How many trips must she make?

Answers

The inequality that represents the greatest number of boxes he can move in one trip is 255 + 50b ≤ 4000.

The solution of the inequality is 74.

The number of trips he would make to deliver 310 boxes is 5.

What is the solution of the inequality?

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

The form of the inequality is:

Weight of the worker + weight of the cart + (weight of the boxes x number of boxes) ≤ 4000

160 + 95 + (50 x b) ≤  4000

255 + 50b ≤ 4000

In order to determine the value of b, take the following steps:

Combine similar terms:

50b ≤ 4000 - 255

50b ≤ 3745

b ≤ 3745 / 50

b ≤ 74.9

The number of boxes he can carry is 74

Number of trips = total number of boxes / number of boxes he can carry in one trip

= 310 / 74

= 4.1

= 5 trips

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The temperature at noon is -4°F. The temperature at 6:00 pm is -12°F. What is the difference between the noon and the 6:00 pm temperatures?

Answers

-4 - - 12 = -4 +12 = 8

The difference between the temperatures is 8 degrees Fahrenheit. :)

Hope that helps!

a researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. how should we interpret the relationship between these variables?

Answers

In the above condition of positive correlation, the higher a person scores on involvement, the higher they tend to score on life satisfaction. Therefore, the option B holds true.

Positive correlation can be referred to or considered as the correlation, wherein the relationship between two or more elements, that are taken into consideration, is direct. The direct relationship means that the movement of a change in one element leads to an equal movement in the other. Positive correlation also states about the measure of life satisfaction in the above condition.

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Complete question

A researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. How should we interpret the relationship between these variables?

A) There is no relationship between involvement and life satisfaction.

B) The higher a person scores on involvement, the higher they tend to score on life satisfaction.

C) The higher a person scores on involvement, the lower they tend to score on life satisfaction.

D) Involvement and life satisfaction are probably the same variable

The letters and represent nonzero constants. Solve ax+b=37,for x

Answers

The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .

What are arithmetic calculations?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,

Addition : (+)

The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.

Subtraction : (-)

Subtraction is the process in which we remove objects from the original group.

Multiplication : (×)

Multiplication is adding the same number to itself a certain number of times.

Division : (÷)

The division is breaking a large object or group into smaller parts or groups.

Here ,

given equation: ax + b = 37

To calculate value of x :

ax  = 37 - b

As, it is given that a is non-zero constant then,

x = (37 - b)/a

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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin xyzj + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.

Why do we use the line integral form of stokes theorem to integrate this, instead of the stokes variation that uses the curl?

Answers

We can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

What is the Stokes' Theorem?

According to Stoke's theorem, where C = A closed curve, "the surface integral of the curl of a function across a surface limited by a closed surface is equal to the line integral of the particular vector function over that surface."

S = Any surface bordered by C.

So, by utilizing Stokes Theorem to calculate S curl F .dS.

[tex]\iint_s c u r l F \cdot d s=\int_c F d r[/tex]

Parameterize C now.

r(t) = (3 cos t, 3 - 3 sin t)

When t is in [0 2].

Now,

[tex]\begin{aligned}& \int_c F \cdot d r=\int_0^{2 \pi} F(3 \cos t, 3-3 \sin t) \cdot r^{\prime}(t) d t \\& =\int_0^{2 \pi}\left(\left(9 \cos ^2 t\right)(27)(-3 \sin t),(\sin t) \times(-27 \cos t \cdot \sin t) \cdot(-3 \sin t, 0-3 \cos t) d t\right. \\& =27 \int_0^{2 \pi} 81 \cos ^2 t \cdot t \sin ^2 t+3 \cos ^2 t . t \sin t d t \\& =27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2 t+27\left[-\cos ^3 t\right]_0^{2 \pi}\end{aligned}[/tex]

[tex]\begin{aligned}& =27 \times \frac{81}{4} \int_0^{2 \pi}\left(\frac{1-\cos 4 t}{2}\right) \\& =\frac{2187}{8}\left[t-\frac{1}{4} \sin 4 t\right]_0^{2 \pi} \\& =\frac{2187}{8}\left[2 \pi-\frac{1}{4} \sin 4(2 \pi)-0-\frac{1}{4} \sin 4(0)\right] \\& =\frac{2187 \pi}{4}\end{aligned}[/tex]

Therefore, we can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

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Problem: What is the actual distance between two cities if it is drawn to scale of 1:3,000,000 and it is 3 cm on the map?

Answers

Answer:

distance between two cities will be 9 000 000 km

Answer:

Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km

if the number of times you take the test were independent of the chance you fail what could that mean?

Answers

if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.

The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.

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which of the following represents the average rate of change to the function g(x) = 3/2x + 1 over the interval -2 < x < 8

Answers

The average rate of change to the function is (d) 3/2

How to determine the average rate of change to the function?

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

g(x) = 3/2x + 1

Also, we have the interval to be

-2 < x < 8

This interval can be expressed as

a = -2 and b = 8

So, we start by calculating g(-2) and g(8)

Substitute the known values in the above equation, so, we have the following representation

g(-2) = 3/2 * (-2) + 1

g(-2) = -2

Also, we have

g(8) = 3/2 * (8) + 1

g(8) = 13

The average rate of change to the function is then calculated as

Rate = [g(8) - g(-2)]/[8 + 2]

So, we have

Rate = (13 + 2)/(8 + 2)

Evaluate

Rate = 3/2

Hence, the average rate is 3/2

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How do you simplify (−2−i)^2?

Answers

[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.

Multiply the integer by itself.

[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]

[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]

Simplify

[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]

[tex]=4+4i-1[/tex]

Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.

[tex]4+2i+21i+1(-1)[/tex]

Simplify and use the a+bi formula in standard form.

[tex]3+4i[/tex]

A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.

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a researcher states that he expects that there will be a significant difference between 20- and 30-year- olds after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance. what kind of hypothesis is being used in this study?

Answers

The kind of hypothesis is being used in this study is Research hypothesis

Hypothesis

In statistics, a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon is known as hypothesis.

Given,

Here we know that a researcher states that he expects that there will be a significant difference between 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.

And we need to find the kind of hypothesis is being used in this study.

While we looking into the given question we know that a researcher contacts the research on 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.

And her record the result accordingly.

Basically this one refers his research hypothesis.

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At the circus, the McCartney family bought bags of cotton candy and funnel cakes for. The Lennon family bought bags of cotton candy and funnel cakes for. Which system of equations could be used to find the cost of each item?

Answers

The system of equations which is used to find out the cost of each item (i.e cotton candy and funnel cake) bought by two families McCartney and Lennon Family is

3c + 2f = $24

2c + 4f = $32

We have given that

McCartney family bought

total number of bags of cotton = 3

total number of funnel cakes = 2

total cost of 3 bags and 2 funnel cakes is $24.

Lennon Family bought

total number of bags = 2

total number of funnel cake = 4

total cost of 2 bags and 4 funnel= $32

we have to find out the system of equations which used to find the cost of each item.

let the cost of each funnel cake be f and cotten candy be c .

then, using the above data we get

3c + 2f = $24 ---(1)

2c + 4f = $32 --(2)

Hence, equation (1) and (2) make a system of linear equations which is used to determine the cost of each item.

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Complete question:

HEME At the circus, the McCartney family bought 3 bags of cotton candy and 2 funnel cakes for $24. The Lennon Family bought 2 bags of cotton candy and 4 funnel cakes for $32. Which system of equations could be used to find the cost of each item? Let f represent funnel cake and c represent cotton candy

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