HELP PLS THIS MATH ADD AND SUBTRACT FRACTION I DING GET BC I FORGET EVERYTHING I LEARN FROM PAST YEARS

HELP PLS THIS MATH ADD AND SUBTRACT FRACTION I DING GET BC I FORGET EVERYTHING I LEARN FROM PAST YEARS

Answers

Answer 1

Answer: 1. 35 5/6 - 4 1/2

2. 1 5/8 - 2/3

3. 1 5/8 + 2/3

4. 35 5/6+4 1/2

Step-by-step explanation:

1. E=Eli. J=Jamison

E=J+4 1/2

35 5/6=J+4 1/2

J=35 5/6 - 4 1/2

2. s=cups of strawberries

b=cups of blueberries

m=more cups of b than s

m=b-s

m=1 5/8 - 2/3

3. o=original length of patio.

i=increase in length of patio

t=total length of patio after increase.

o+i=t

1 5/8 + 2/3=t

4. p=pine tree. a=palm tree. i=inches taller

p+i=a

35 5/6+4 1/2=a


Related Questions

how do you do this help pleaseee due soonnnnnn!!

how do you do this help pleaseee due soonnnnnn!!

Answers

Answer:

they are the same shape and same angles. There was just a dilation.

Step-by-step explanation:

Instructions: Match the linear equation with its graph. Label the slope and -intercept.

Instructions: Match the linear equation with its graph. Label the slope and -intercept.

Answers

Given the following question:

\(y=-3x+1\)

Graph 3 is the same as y = -3x + 1

For part B:

\(\begin{gathered} y=-3x+1 \\ y=mx+b \\ m=slope \\ b=y-intercept \\ m=-3 \\ b=1 \end{gathered}\)

Instructions: Match the linear equation with its graph. Label the slope and -intercept.

Find the root(s) of f(x) = (x+5)3(x-9)2(x+1)

Answers

Answer:

the roots of f(x) = (x+5)3(x-9)2(x+1) are -5 (with a multiplicity of 3), 9 (with a multiplicity of 2)

Step-by-step explanation:

To find the roots of f(x) = (x+5)3(x-9)2(x+1), we need to set the polynomial equal to zero and solve for x.

f(x) = (x+5)3(x-9)2(x+1)

Setting f(x) equal to zero, we get:

0 = (x+5)3(x-9)2(x+1)

The roots of the polynomial are the values of x that make f(x) equal to zero. Therefore, the roots of the polynomial are:

-5 (with a multiplicity of 3), 9 (with a multiplicity of 2), and -1

Therefore, the roots of f(x) = (x+5)3(x-9)2(x+1) are -5 (with a multiplicity of 3), 9 (with a multiplicity of 2),

An instructor is preparing a report showing mid-semester grades and notes that the mean, median, and mode are all exactly 76.00. What can she conclude

Answers

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical. This can also imply that there is no skewness or bias in the data. Answer more than 100 words:When an instructor notes that the mean, median, and mode are all exactly 76.00, it can be inferred that the distribution of grades in the class is roughly symmetrical. This indicates that there are nearly equal numbers of students above and below the average grade.

The mean, median, and mode are three measures of central tendency that are used to summarize the distribution of a dataset. The mean is calculated by adding all the values in the dataset and dividing by the number of observations, while the median is the middle value when the dataset is ordered from smallest to largest. The mode is the value that occurs most frequently in the dataset. When all three measures of central tendency are equal, as in this case, it means that the dataset is roughly symmetrical and there is no skewness or bias. This can also indicate that the dataset is normally distributed, which means that it follows a bell-shaped curve.The instructor can conclude that the class performed around the average, as the mean, median, and mode are all 76.00.

However, it is important to note that this does not give any information about the spread of the dataset. In other words, the instructor cannot tell from this information alone whether the grades were tightly clustered around the average or widely dispersed. For this reason, it may be useful to calculate additional measures of spread, such as the range or standard deviation, to get a better understanding of the distribution.

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical, with no skewness or bias. However, it is important to remember that this information alone does not provide any insight into the spread of the dataset. Additional measures of spread would need to be calculated to determine the degree of variability in the grades.

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a continuous random variable x has a normal distribution with a mean of 12.25. the probability that x takes a value less than 13 is 0.82. Use this information and the symmetry of the density function to find the probability that X
takes a value greater than 11.50
Sketch the density curve with relevant regions shaded to illustrate the computation.

Answers

Given that a continuous random variable x has a normal distribution with a mean of 12.25 and the probability that x is less than 13 is 0.82, we can use the symmetry of the density function to find the probability that x is greater than 11.50.

Since the normal distribution is symmetric, the probability of x being less than 13 is equivalent to the probability of x being greater than the mean minus 13. Therefore, P(x < 13) = P(x > 12.25 - 13).

To find the probability that x is greater than 11.50, we can use the same reasoning. We know that the probability of x being less than 11.50 is equivalent to the probability of x being greater than the mean minus 11.50. Therefore, P(x < 11.50) = P(x > 12.25 - 11.50).

To illustrate the computation, we can sketch the density curve of the normal distribution with the relevant regions shaded. The mean, 12.25, is the center of the distribution. We shade the region to the left of 13, representing P(x < 13), and shade the region to the right of 11.50, representing P(x > 11.50). By using the symmetry of the density function, we can see that the shaded region to the right of 11.50 is equal to the shaded region to the left of 13.

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A professor recieves, on average 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

Answers

The type of distribution that she might use will be Poisson Distribution

We are Given that average = 24.7

Poisson Distribution, the number of occurrences in various types of defined intervals, including distance, area, or volume, can also be calculated using the Poisson distribution.

A call center gets 180 calls on average each hour, every hour of the day due to the calls being separate, the probability that you will receive the next one is unaffected by the one you just received.

To compute the probability of receiving at least 10 e-mails on such a day, the distribution that best suits will be the Poisson distribution.

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how many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?

Answers

There are 63,273,600 different license plates that can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits.

There are two different types of license plates that can be made: one with three letters followed by three digits and one with four letters followed by two digits. To find the total number of different license plates that can be made, we need to calculate the number of possibilities for each type of license plate and then add them together.

For the first type of license plate (three letters followed by three digits), there are 26 possibilities for each letter and 10 possibilities for each digit. So the total number of different license plates of this type is:
26 × 26 × 26 × 10 × 10 × 10 = 17,576,000
For the second type of license plate (four letters followed by two digits), there are 26 possibilities for each letter and 10 possibilities for each digit. So the total number of different license plates of this type is:
26 × 26 × 26 × 26 × 10 × 10 = 45,697,600

Adding these two numbers together gives us the total number of different license plates that can be made:
17,576,000 + 45,697,600 = 63,273,600
Therefore, there are 63,273,600 different license plates that can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits.

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Given that f(x)=x^2=11x+30 and g(x)=x-5, find f(-g)(x) and express the result as a polynomial in simplest form.

Answers

Hey there,

We have,

f(x) = x² + 11x + 30g(x) = x + 6

Now,

(f.g)(x) = f(g(x))

Substituting...

g(x) = x + 6f(g(x)) = f(x + 6)

Now,

f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132

So,The value is x² + 23x + 132

I NEED AN ANSWER ASAP PLEASE

I NEED AN ANSWER ASAP PLEASE

Answers

Step-by-step explanation:

the correct answer is option a 6a-7

PLEASE HELP!! I'LL GIVE OUT BRAINLIEST.

Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed number.
? yards = 3/4 of a mile.

Answers

Answer:

1320 yds

Step-by-step explanation:

1 mile = 1760 yds

3/4 mile * 1760 yds/ 1 mile

1320 yds

Answer:

1 mile = 1720 yard

______ ________

0.75 x

cross multiply and solve for x

1320 yards is the answer

good luck in the future..

how many 7 digit phone numbers can be formed if the first digit canot be 0 or 1 and if on digit can be repeated

Answers

A total of 8,000,000 seven-digit phone numbers that can be formed if the first digit cannot be 0 or 1 and one digit can be repeated.

There are 8 possible choices for the first digit (2-9), and each of the other six digits can have 10 possible choices (0-9). Therefore, 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 possible seven-digit phone numbers.

To better understand this, let's break it down further. For the first digit, there are 8 possible choices since 0 and 1 are not allowed. For the second digit, there are 10 possible choices since any digit (0-9) can be used. For the third digit, there are 10 possible choices again since any digit (0-9) can be used.

The same holds true for the fourth, fifth, sixth, and seventh digits, giving us 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 seven-digit phone numbers.

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Identify which of the twelve basic functions fit the description given.
The six functions that are increasing on their entire domains

Answers

The six functions that are incresing on their domain are : identity, cubing, square root, exponential, natural log and logistic function.

What is Function ?

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.

The logistic function is a function that simulates the exponential expansion of a population while also taking into account variables like the carrying capacity of land and other considerations.

The inverse of an exponential function, the natural log is the logarithm to the base of the integer e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues. The basis of logarithms and natural logs are exponential functions and logarithmic functions.

The six functions that are incresing on their domain are :

identity, cubing, square root, exponential, natural log and logistic.

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Sharon was being paid to paint a mural on a wall in the
gym. The mural was supposed to be at least 6.2 feet tall and
12.8 feet wide. When she measured her completed mural,
the tape measure showed the height as 6 1/4 feet and the
width as 12 7/8 feet. Did the dimensions of Sharon's mural
meet the given requirements? How do you know?

Answers

The dimensions of Sharon's mural meet the given requirements

How to determine if the dimensions of Sharon's mural meet the given requirements?

The given parameters are:

The dimensions of Sharon's mural

Height = 6 1/4 feet

Width = 12 7/8 feet

The required dimensions of the mural

Height = At least 6.2 feet

Width = At least 12.8 feet

Start by representing the dimensions of Sharon's mural in decimals

Height = 6.25 feet

Width = 12.875 feet

By comparing the dimensions of Sharon's mural and the required dimensions of the mural, we have:

6.25 feet is at least 6.2 feet

12.875 feet is at least 12.8 feet

Hence, the dimensions of Sharon's mural meet the given requirements

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Which is the better deal for frozen pizzas?: 3 for $11 or 2 for $8.50.

Answers

the better deal is 3 for $11

Miguel needs to drive a total of 16 miles. So far, he has driven 8.9 miles. How many more miles must Miguel drive?

Answers

Answer:

................

Step-by-step explanation:

Answer:

7.1 miles till Miguel gets to the destination

Step-by-step explanation:

16 miles - 8.9 miles = 7.1 miles

Let C be the counterclockwise closed path around the rectangle with endpoints (0,0),(2,0),(2,1), and (0,1), and let F(x,y)=−y^2i+xj
(a) Use Green's Theorem to rewrite ∫C​F⋅dr as an iterated double integral over the rectangle's interior. (b) Evaluate the double integral you obtained in part (a).
(c) Is the vector field F conservative? Use the information from parts (a) and (b) to support your answer.

Answers

a) The double integral is ∬(0,0)→(2,1)​-y²dA.

b) The value of the double integral is -[1/3].

c) The resulting integral is not zero, the vector field F is not conservative.

(a) Using Green's Theorem, we can rewrite ∫C​F⋅dr as follows:

∫C​F⋅dr=(∬ℐF⋅∇⃗dA)

=∬(0,0)→(2,1)​-y²i+xj⋅(1,0)i+(0,1)jdA

=∬(0,0)→(2,1)​-y²dA

Thus, the double integral is:

∬(0,0)→(2,1)​-y²dA

(b) To evaluate the double integral, we denote the inner and outer bounds as x = 0 to 2 and y = 0 to 1, respectively. Therefore the double integral is:

∫0→1​∫0→2​−y²dxdy

=-∫0→1​y²(2-0)dy

=-∫0→1​y²dy

=-[y³/3]0→1

=-[1/3]

(c) Since the resulting integral is not zero, the vector field F is not conservative. This means that F does not have a conservative potential.  The double integral in part (b) provides us with evidence to support this conclusion.

Therefore,

a) The double integral is ∬(0,0)→(2,1)​-y²dA.

b) The value of the double integral is -[1/3].

c) The resulting integral is not zero, the vector field F is not conservative.

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please help me otherwise I will fail (1/2 + 1/2)* 700​

Answers

Answer: 700

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

copy and paste

Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile and had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job.

Felicia also retiled her kitchen. She bought five boxes of tile, and each box contained the same number of tiles as each of Bruce’s boxes. She also ran out of tile. She had to go back to the store and get five more tiles to finish the job.
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Answers

Expression for the number of tiles Bruce used: 5x+2

Expression for the number of tiles Felicia used: 5x+5

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The first want you'll want to do is translate the question into something easily understood. So for Bruce, we know that he bought three boxes with the same number of tiles in each, so 3, then he had to buy three more, another 3 but didn't finish the last box only using two, 2. So, we know he completely used the first 3 he bought then 2 of the 3 more boxes he bought.

For boxes completely used we can show it like this: 3+2=5 or 5x to represent the not known number of tiles in each box. Now we have to include the last box he bought, but he only used two tiles out of the whole box so it wouldn't be added to the same number as the other five (so not 6x).

To represent those last two tiles we can simply add +2.

Now putting it all together we get 5x+2

5x is the number of boxes multiplied by an unknown number of tiles. so 5x=tiles in 5 boxes. and the 2 are those two tiles that were taken out of the last box.

For Felicia, we go through the same process. We know she bought five boxes with the same number of tiles that Bruce had, 5, then bought five more individual tiles (not in a box), 5.

Not too much to do, so we know she got 5 boxes, so now we add our variable to represent the tiles in the boxes. so that 5 becomes 5x. Now with like we did with the two tiles Bruce only used, we do not add the 5 additional tiles into that number (so not 10x).

Because those were individual tiles they are simply 5.

Putting the whole thing together we get 5x+5

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What is happening to this graph?

What is happening to this graph?

Answers

Answer:  B. Decreasing

Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

The length of a rectangular room is 8 feet more than twice the width. If takes perimeter of the room is 124 feet, what are its dimensions?

Answers

Hey there! I'm happy to help!

Let's call the length and width L and W respectively.

L=2W+8

2W+2L=124

We plug our value of L into the second equation and solve for W.

2W+2(2W+8)=124

We undo the parentheses with the distributive property.

2W+4W+16=124

Combine like terms.

6W+16=124

Subtract 16 from both sides.

6W=108

Divide both sides by 6.

W=18

We plug this W value into the first equation to solve for L.

L=2(18)+8

L=36+8

L=44

So, the length is 44 feet and the width is 18 feet.

Have a wonderful day! :D

Try this!

Arrange the following set of numbers in increasing and decreasing orders.

1.{3, -4, 0, 6, -2}

2.{2.5, 0.3, 5.25, -0.7, 1.2}

3. {2, 0.8 -√8, -4.7, 6⅓}

Decreasing:____________

Increasing:____________

Decreasing:____________

Increasing:____________

Decreasing:____________

Increasing:____________

all time let us have a review about your past topic about multiplying numbers by power of 10

1. 0.042 x 10=

2. 7.331 x 100=

3 0.125 x 1000 =

4. 1.031 x 0.1=

5. 21.5 x 0.001 =

need now
:plss wag nyu na ih answer kung mali rin ih answer nyu huhh!​

Try this!Arrange the following set of numbers in increasing and decreasing orders.1.{3, -4, 0, 6, -2}

Answers

Answer:

23446

76532

12839

09192

29292

The relation ____ a function.
{10,2),(1,3), (2,4),(3,5)}
is or is not

Answers

Answer:

The relation is a function

Step-by-step explanation:

The relation is a function because every x-value has a unique y-value

Right 20 7 and 500/22000 in decimal form

Answers

Answer:

20.7 and 500.200

Step-by-step explanation:

Answer:

20/7 = 2.8571

500/22000 = 0.0227

Step-by-step explanation:

Mario has 160 pizzas and is collecting two pizzas a week. Write the equation for the number of pizzas Mario has

Answers

Answer:

160+2x

Step-by-step explanation:

Answer:

Mario has after 5 weeks 170 pizzas.

Step-by-step explanation:

Each time add to the chart 2 Pizzas and move a week.

Please help me I have been doing this forever.

Please help me I have been doing this forever.

Answers

Point C. And I need more characters

How do you solve 64 divided by 8?

Answers

the answer is 8. To solve 64 divided by 8, we need to find how many times 8 can go into 64 evenly.

One way to do this is through division. We can start by placing the dividend (64) under the division symbol and the divisor (8) outside the division symbol. We then divide 8 into the first digit of 64 (6), which is less than 8. We bring down the next digit (4) to make 64, and we divide 8 into 64. We find that 8 can go into 64 eight times, with no remainder. Therefore, the answer is 8.

Another way to solve this problem is through multiplication. We can ask ourselves, "What number, when multiplied by 8, gives us 64?" We can use simple arithmetic to find the answer. We can start with 8 and multiply it by 1, which equals 8. We then multiply 8 by 2, which equals 16. We continue multiplying by 3, 4, 5, 6, 7, and finally 8, which equals 64. Therefore, the answer is 8.

In summary, to solve 64 divided by 8, we can use either division or multiplication. Division involves dividing the dividend by the divisor to find the quotient, which is the answer. Multiplication involves finding what number, when multiplied by the divisor, equals the dividend. Both methods yield the same answer, which is 8.

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I need help with this math problem
The sum of 3 and b are greater than or equal to -16
Please help me!!!

Answers

Step-by-step explanation:

i believe thats the answer

I need help with this math problemThe sum of 3 and b are greater than or equal to -16Please help me!!!

100 points
there's a runner on 1st base and the batter hits a line drive out to right field, where does the right fielder throw the ball?
this is a "real" question

Answers

Answer:

2nd Base (I think)

Step-by-step explanation:

The right fielder is closer to the 2nd base.

Conditional Statement: If the object has a remote, then it is a television.

Part A: Write the converse to the conditional statement.

Part B: Write a biconditional statement from the conditional statement.

Part C: Validate the biconditional statement from Part B. Use details to support your answer.

Answers

For given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'

Part A:

We need to write the converse to the conditional statement.

The converse of given conditional statement would be:

'If it is a television, then the object has a remote.'

Part B:

We need to write a biconditional statement from the conditional statement.

A biconditional statement of the given conditional statement would be:

'The object has a remote if and only if it is a television.'

Part C:

We need to validate the above biconditional statement.

The biconditional statement is true because the conditional statement and the converse are true.

Therefore, for given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

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Simplify 5ab(a-1) - 5a²(b - c)

Answers

Answer:

-5ab + 5a²c

Step-by-step explanation:

5ab(a-1) - 5a²(b - c)

= 5a²b - 5ab - 5a²b + 5a²c

= -5ab + 5a²c

So, the answer is -5ab + 5a²c

5a^2bc - 5ab the answer
Other Questions
Help me I needs the helps A very common problem in computer graphics is to approximate a complex shape with a bounding box. For a set, s, of n points in 2-dimensional space, the idea is to find the smallest rectangle, R, with sides parallel to the coordinate axes that contains all the points in s. Once s is approximated by such a bounding box, we can often speed up lots of computations that involve s. For example, if R is completely obscured some object in the foreground, then we don't need to render any of s. Likewise, if we shoot a virtual ray and it completely misses R, then it is guarantee to completely miss s. So doing comparisons with R instead of s can often save time. But this savings is wasted if we spend a lot of time constructing R; hence, it would be ideal to have a fast way of computing a bounding box, R, for a set, s, of n points in the plane. Note that the construction of R can be reduced to two instances of the problem of simultaneously finding the minimum and the maximum in a set of n numbers; namely, we need only do this for the x- coordinates ins and then for the y-coordinates in s. Therefore, design a divide- and-conquer algorithm for finding both the minimum and the maximum element of n numbers using no more than 3n/2 comparisons. SCIENCE SUBJECT1. Elma Muros Posadas was one of the country's best Elma Muros Posadas was one of the country best long jumpers. Suppose she makes a 30 angle with the ground before leaping. If her launch speed is 11m/s, compute the time of flight, the range and the maximum height reached.Given:__________Required:_______Solution:Final Answer:_______( Nonsense will be reported! ) A 1210 kg car is driving NE (at45.0) at 15.2 m/s when it isstruck by a moving 1540 kg car.Afterward, they stick together andmove directly east (at 0) at 23.3m/s. 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You may assume that the operation is associative.(c) From class we know that (Z4, +) and (Z2 Z2, +) are two non-isomorphic groups that each have four elements. Which one of these groups is isomorphic to (G, )? Explain your answer briefly. Phishing is not often responsible for PII data breaches If the distance from a magnet is doubled, the magnets force will beA) moreB) the same C) half as much D) one-fourth as much Which of the following statements best describes the Federalists?The Federalists supported the new Constitution because they wanted a strong national government.The Federalists opposed the new Constitution because they opposed a strong national government.The Federalists led the fight to buy the Louisiana Purchase from France.The Federalists remained loyal to Great Britain during the Revolutionary War. The first great awakening did all of the following except:A. Spread a message of personal faithB. Encouraged individuals to bring about their own salvationC. Brought together "old" and "new" lightsD. Saw the rise of several new denominations what are the three possible limiting reagents for this two step synthesis During the School Health week,your teacher wants you to give a speech about the benefits of eating healthy food. Based on the information given, write a speech between 50-80 words. How long does it take for something using 1,902 W ofpower does 19 J of work? Which type of electromagnetic wave has the greatest frequency?(1 point)radio wavesradio wavesX-raysX-raysvisible lightvisible lightultraviolet light The function f(x) = 2x + 3x - 12 on the interval (-3,3) has two critical points, one at I = -1 and the other at 1 = 0. 12. (a)(3 points) Use the first derivative test to determine if has a local maxim n the market for a particular product, the price elasticity of demand is 2/3 , and the price elasticity of supply is + 14/9 . At equilibrium, price is 20 (in dollars) and quantity consumed is 36 (in thousands). (a) Assuming supply and demand are linear, reconstruct and draw the supply and demand curves. Label the intercepts. (b) To help consumers and produces, the government subsidizes the product by $2 per unit. What are the prices paid by buyers PB and prices received by seller PS after the subsidy? What is the new equilibrium quantity? Illustrate them on the same graph. (c) How big is the change in consumer surplus, producer surplus, government expenditure, and deadweight loss? Consider a two agent (agent A and agent B) two good (good x4 and good xz) pure exchange economy. 1 x Suppose preferences for the two agents are U4 = 2x + x^ and UB = x + 2x. Each agent is endowment with an equal amount of each good ex = e = e = e = 5. (3.1.A) For this economy, draw an Edgeworth box diagram with the following: (a) initial endowment, (b) set of Pareto efficient allocations, and (c) core of the economy.