I also don't know what this shape is lol please help ​

I Also Don't Know What This Shape Is Lol Please Help

Answers

Answer 1

Answer:

Thats an octagon

Step-by-step explanation:

It has 8 sides


Related Questions

Kristin Wilson lives in Spartanburg​, South​ Carolina, and wishes to visit relatives in the following South Carolina​ cities: Sumter comma Columbia comma Charleston commanbspand Greenville. In how many ways can she visit each of these cities and return to her home in Spartanburg question mark

Answers

Answer:

The correct answer is - 24 ways.

Step-by-step explanation:

Kristin Wilson lives in Spartanburg​, South​ Carolina and she wants to visit four cities Sumter, Columbia, Charleston, and Greenville. So there are total of 5 cities we have as she returns to her home back in the end, so the total ways are-

= (5-1)!

= 4x3x2x1

= 24 ways

Thus, the correct answer is - 24 ways

an initial population of fish is introduced into a lake. this fish population grows according to a continuous exponential growth model. there are fish in the lake after years. (a)let be the time (in years) since the initial population is introduced, and let be the number of fish at time . write a formula relating to . use exact expressions to fill in the missing parts of the formula. do not use approximations. (b)how many fish are there years after the initial population is introduced? do not round any intermediate computations, and round your answer to the nearest whole number. fish

Answers

(a)We have to use a continuous exponential growth model to write a formula relating to t and N(t), where t is the time (in years) since the initial population is introduced, and N(t) is the number of fish at time t. Continuous exponential growth models can be expressed as;
N(t) = N₀ * e^(kt)
where N₀ is the initial population, t is the time elapsed, k is the continuous growth rate, and e is Euler's number.

(b)Given that the initial population is introduced into a lake and it grows according to a continuous exponential growth model. The number of fish in the lake is 300 after 4 years. Using N(t) = N₀ * e^(kt);300 = N₀ * e^(4k)So, the formula relating to t and N(t) is;
N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = 300/ e^(4k)We know the number of fish in the lake after 4 years is 300.
Therefore;300 = N₀ * e^(4k)
Dividing by N₀; 300/N₀ = e^(4k)
We have; N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = N₀ * e^(kt)N₀ = N(t) / e^(kt)
At t = 0; N₀ = N(0) / e^(k*0)N₀ = N(0) / e^0
N₀ = N(0)
Now we can substitute the value of N₀ into the formula;
N(t) = N(0) * e^(kt)
Substituting the values in N(t) = N₀ * e^(kt);
N(t) = 1000 * e^(0.23t)

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Find the measures of each exterior angle of a regular 66-gon, the round to the nearest tenth.
Angles: 5.4,6.4,173.6,9720

Answers

The correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

What is Exterior angles ?

In a polygon, an exterior angle is an angle formed by a side and an extension of an adjacent side. The measure of an exterior angle of a regular polygon with n sides is given by 360/n degrees.

To find the measure of each exterior angle of a regular polygon, we use the formula:

Measure of each exterior angle = 360 degrees / number of sides

In this case, the polygon is a regular 66-gon, so the number of sides is 66. Thus,

Measure of each exterior angle = 360 degrees / 66 = 5.454545...

Rounding to the nearest tenth, we get:

Measure of each exterior angle ≈ 5.5 degrees

Therefore, the correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.

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If Sarah uses 3/4 yard of ribbon to make a hair bow. How many yards of ribbon will Sarah use to make 9 hair bows?

Answers

If Sarah uses 3/4 yard of ribbon to make a hair bow, she will need 6 and 3/4 yards of ribbon to make 9 hair bows.

To find out how many yards of ribbon Sarah will use to make 9 hair bows, we need to multiply the amount of ribbon used for one hair bow (3/4 yard) by the number of hair bows she wants to make (9).

So, the equation we need to use is:

3/4 yard of ribbon per hair bow x 9 hair bows = ? yards of ribbon

To solve for the answer, we can simplify the equation:

3/4 x 9 = 27/4

So Sarah will need 27/4 yards of ribbon to make 9 hair bows.

To convert this fraction to a mixed number, we can divide the numerator (27) by the denominator (4) and write the remainder as a fraction:

27 ÷ 4 = 6 with a remainder of 3

In summary, Sarah will need 6 and 3/4 yards of ribbon to make 9 hair bows, if she uses 3/4 yard of ribbon to make one hair bow.

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please help me answer the question in the picture

please help me answer the question in the picture

Answers

Answer:

B

Step-by-step explanation:

formula for equation of line with two given points:

(y-y1)= m(x-x1)

so Its B

It’s B. You’re Welcome

Simplify each algebraic expression. 5(10a−2)

Answers

Answer:

The answer is 50a−10

Step-by-step explanation:

Answer:50a-10

Step-by-step explanation:

multiply 5 into the parenthesis: 5x10 and 5x2

Is 7/45 a terminating decimal

Answers

Answer:

= non-terminating

 

Step-by-step explanation:

The greatest common factor (GCF) of 7 and 45 is 1.

   

7 ÷ 1   = 7

45 ÷ 1       45

prime factors of 45

3 x 3 x 5

A fraction is a terminating decimal if the prime factors of the denominator of the fraction in its lowest form only contain 2s and/or 5s or no prime factors at all. This is not the case here.

7/45

= non-terminating

Which graph represents the equation y^2? = -4x?

Answers

Answer:

\(x=-\frac{y^{2} }{4}\)

Step-by-step explanation:

This graph is in terms of x.

Which graph represents the equation y^2? = -4x?

Write as a sentence as a proportion. Then solve the proportions 5 is to 12 as is to 48

Answers

5:12

x:48

the answer is 20

Please help me with number two and three :)

Please help me with number two and three :)

Answers

The answer to number 2 is:A as there is 1 pear for every three apples and
The answer to number 3: C. Since it also equals 0.6 which is the number eight games won in the first row divided by the number of games played in the first row

The diagram shows a circle with centre O.
A & B lie on the circumference of this circle.
Given that ∠OAB = 40°, evaluate ∠AOB.

Helppp ASAP

The diagram shows a circle with centre O. A & B lie on the circumference of this circle. Given that

Answers

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

What are the properties of circle?

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

What is isosceles triangle?

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Drag and drop the answer into the box to identify each function as linear, exponential, or neither.
(x) 2 3 4
F(x) 5.5 7 8.5

(x) 0 2 4
F(x) 2 5 9

Answers

The first function is a linear function while the second function is neither a linear nor exponential

How to identify whether a function is linear, exponential, or neither?

A linear function is of the form f(x) = mx + c,

where m is the slope (or rate of change) and y-intercept

m = y2-y1 / x2-x1

An exponential function is of the form f(x) = abˣ

where a and b are constants

In a linear function, the slope must be constant. Also, in exponential function a and b must be constants

Given:

(x) 2 3 4

F(x) 5.5 7 8.5

For x = 2 and 3:

slope = 7-5.5 / 3-2 = 1.5

For x = 3 and 4:

slope = 8.5-7 / 4-3 = 1.5

The slope is the same, thus, it is a linear function

Note: f(x) = y

(x) 0 2 4

F(x) 2 5 9

This is not linear, check for exponential

y = abˣ

when x = 0, y =2

2 = ab⁰

a = 2

when x =2, y = 5

5 = 2b²

b² = 5/2

b = √(5/2)

when x =4, y = 9

9 = 2b⁴

b⁴ = 9/2

b = \(\sqrt[4]{(9/2)}\)

Since the b are not the same. Thus, this is an exponential function also

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Find all the points in the form (1, y, z) which are equivalent
to the points (2, -1, 0) and (0, -2, 1)

Answers

The point in the form (1, y, z) that is equivalent to the given points is (1, 3/5, 3/5).

To find all the points in the form (1, y, z) that are equivalent to the points (2, -1, 0) and (0, -2, 1), we can use the concept of vector equivalence.

Let's consider the vector from (1, y, z) to (2, -1, 0). This vector is (2-1, -1-y, 0-z) = (1, -1-y, -z).

Similarly, the vector from (1, y, z) to (0, -2, 1) is (0-1, -2-y, 1-z) = (-1, -2-y, 1-z).

Since these two vectors are equivalent, we can set them equal to each other:

(1, -1-y, -z) = (-1, -2-y, 1-z)

Simplifying this equation, we get:

y - z = 0

2y + 3z = 3

Therefore, all points in the form (1, y, z) that are equivalent to the given points are given by the equations:

y = z

2y + 3z = 3

Solving this system of equations, we get:

y = 3/5

z = 3/5

So the point in the form (1, y, z) that is equivalent to the given points is (1, 3/5, 3/5).

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Which of the following values are solutions to the inequality -6 - x ≤ 7?
I. - 13 II. - 14 III. - 6
O None
II only
O I and II
II and III
O I only
III only
I and III
O I, II and III
Submit Answer

Answers

None none none none none

two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.which functions could be the result of the combinations? select two options.16x – 1217x – 1272x2 – 96x72x2

Answers

The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:

To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.

To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes

(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)

= 6x^2 - 15x + 8x - 20

= 6x^2 - 7x - 20.

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Henry, Laura and Sam share a sum of money in the ratio
13:15:19

Laura got £12
more than Henry.

How much did Henry receive?

Answers

Henry will receive a 3.08%

What is a sum of money?

The time value of money (TVM) is the concept that a sum of money has greater value now than it will in the future due to its earnings potential. Income in its entirety before any deductions are made. surrender value in money. the sum that the insurance provider will pay on a specific life insurance policy if it is canceled before the insured person dies.

Here, we have

Given: Henry, Laura, and Sam share a sum of money in the ratio

13:15:19. Laura got £12 more than Henry.

We have to find the amount Henry will receive.

Henry: Laura: Sam

13: 15: 19

If Laura got £12 more than Henry.

Then, Ratio will become

Henry: Laura: Sam

13: 180: 228

Share of Henry:

= 13×100/421

= 3.08%

Hence, Henry will receive a 3.08%

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solve the linear equation 4x-(2x-1)=x+5+x-6

Answers

The linear equation doesn't have a solution.

How to compute the value?

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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match the terms to their definition. 1. kilometer one thousandth of a meter 2. centimeter one hundredth of a meter 3. millimeter one thousand meters

Answers

A kilometer is a unit of length in the metric system equal to one thousand meters

What is distance in math?

As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

Kilometer: A kilometer is a unit of length in the metric system equal to one thousand meters. It is commonly used to measure long distances, such as the distance between two cities or countries.

Centimeter: A centimeter is a unit of length in the metric system equal to one hundredth of a meter. It is commonly used to measure small distances, such as the length of an object or the distance between two points.

Millimeter: A millimeter is a unit of length in the metric system equal to one thousandth of a meter. It is an even smaller unit of measurement than a centimeter and is commonly used to measure very small distances, such as the thickness of a sheet of paper or the diameter of a small object.

In the metric system, each unit of length is based on powers of 10. This means that each unit is ten times larger or smaller than the one next to it. Hence, This system of measurement makes it easy to convert between units and to measure distances of all sizes.

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Setup a system of equations for the following::

Farmer Swinger started to raise chickens and cows on his farm. Someone asked how many animals he has and Farmer Swinger replies, "I have a total of 35 animals a total number of legs is 102. Can you figure out how many chickens and cows that I have?"

Answers

x + y = 35  and 2x + 4y = 102 represents the required system of equations.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of chickens and y be the number of cows.

Each chicken has 2 legs, so x chickens have 2x legs.

Each cow has 4 legs, so y cows have 4y legs.

The total number of animals is 35 and the total number of legs is 102, so we can set up the following system of equations:

x + y = 35 (the total number of animals)

2x + 4y = 102 (the total number of legs)

Hence, x + y = 35  and 2x + 4y = 102 represents the required system of equations.

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when the second hand moves from halfway between the 1 and the 2 to 4/5 of the way from the 1 to the 2 what is the measure of the arc

Answers

The second hand moves 6 degrees in one second, it will take it: 294/6 = 49 seconds to move from halfway between 1 and 2 to 4/5 of the way from 1 to 2.

The measure of the arc is 144 degrees.

When the second hand of the clock moves from halfway between the 1 and the 2 to 4/5 of the way from the 1 to the 2, it moves a total of 144 degrees.

This can be calculated as follows: The second hand of a clock completes one full revolution every 60 seconds or 1 minute.

This means that in 1 second, it moves 360/60

= 6 degrees.

To find the measure of the arc when the second hand moves from halfway between the 1 and the 2 to 4/5 of the way from the 1 to the 2, we need to find the difference between the two positions in degrees.

The position halfway between the 1 and the 2 is 1.5 on the clock face.

This is equivalent to 45 degrees (since the clock face is divided into 12 hours, each hour marking is 30 degrees apart, so halfway between 1 and 2 is 30+15 = 45 degrees).

4/5 of the way from the 1 to the 2 is 4/5 x 30 = 24 degrees from the 1 mark.

Therefore, the total angle between halfway between 1 and 2 and 4/5 of the way from 1 to 2 is:

24 + (360 - 45)

= 339 degrees.

However, we need to find the difference between these two positions, not the total angle.

Therefore, we need to subtract the position of the second hand at halfway between 1 and 2 from the position at 4/5 of the way from 1 to 2:

339 - 45

= 294 degrees.

Since the second hand moves 6 degrees in one second, it will take it:

294/6 = 49 seconds to move from halfway between 1 and 2 to 4/5 of the way from 1 to 2.

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Determine the range of the following graph:

Determine the range of the following graph:

Answers

Step-by-step explanation:

the domain of a function is the interval or set of all valid x (input) values.

the range of a function is the interval or set of all valid y (function result) values.

we see in the graph that we get for y all continuous values between 0 (max) and -9 (min).

both end points are filled, so we need to include them into the interval of valid values (via the <= or >= signs).

so the range is

-9 <= y <= 0

Select the correct answer.
Arborists use a test to detect the presence of a certain pathogen in fruit trees. The test gives a positive result 96% of the time if a tree has a disease, and it is 97% accurate for trees that do not have the disease.

What is the probability of getting a false-positive result (that is, the tree tests positive for the pathogen but does not actually have the disease)?

Answers

Answer:

0.03

Step-by-step explanation:

Select the correct answer.Arborists use a test to detect the presence of a certain pathogen in fruit

The probability of getting a false-positive result is 0.03 if Arborists use a test to detect the presence of a certain pathogen in fruit trees option (D) is correct.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Arborists use a test to detect the presence of a certain pathogen in fruit trees.

The probability that the tree has a disease = 96%

Or

The probability when the tree has a disease = 0.96

The probability when the tree does not have a disease = 97%

Or

The probability when the tree does not have a disease = 0.97

Probability of getting a false-positive result = 1 - 0.97

Probability of getting a false-positive result = 0.03

Thus, the probability of getting a false-positive result is 0.03 if Arborists use a test to detect the presence of a certain pathogen in fruit trees option (D) is correct.

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Select the correct answer.Arborists use a test to detect the presence of a certain pathogen in fruit

Which statements are true about irrational numbers?
Select all that apply.
1. They are not real numbers.

2.Their decimal form contains a bar over one or more decimal numbers to show that they continue on infinitely.

3.They can be the square root of a non-perfect square.

4.They can be written as simple fractions.

5. Their decimal form contains an ellipsis, 3 dots, to show that they continue on infinitely.

Answers

Answer:

Step-by-step explanation:

the irrational number can't be represented to a fraction number, like pi and square root of 2 , e and so on, the third fourth choice are true

rational number and irrational number are included in real number, the second choice means the decimal numbers with circulating decimal, it is belong to rational number.

the fifth choice only be used to decimal number  with circulating decimal, not the irrational number.

Find the value of this expression if X=-7

Find the value of this expression if X=-7

Answers

Answer:

-9

Step-by-step explanation:

\((-7)^{2}\) = 49

when you have a negative number to any power make sure you plug it in correctly into the calculator.

\(\frac{49+5}{-7+1}\)  = \(\frac{54}{-6}\)

54÷-6= -9

I hope this helps

Answer:

\(-9\)

Step-by-step explanation:

\(\frac{x^2+5}{x+1}\)

If \(x=-7\) then:

\(\frac{-7^2+5}{-7+1} =\\\\\frac{49+5}{-6} =\\\\\frac{54}{-6} =\\\\-9\)

The expression equals \(-9\) if \(x=-7\)

A researcher wants to estimate the mean cholesterol level of people in his city.
A random sample of 21 people yields a mean cholesterol level of 224 and a standard deviation of 12.
Construct a 95% confidence interval.
(219.69, 228.31)
(214.97, 233.03)
(219.60, 228.40)
(218.54, 229.46)
(223.01, 224.99)

Answers

confidence interval: This tells us the degree of certainty or uncertainty that is existent in a sampling method.

To construct a 95% confidence interval for the population mean cholesterol level, we can use the following formula:

CI = x ± t*(s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%.

Substituting the given values, we have:

CI = 224 ± t*(12/√21)

Using a t-table with 20 degrees of freedom (since n-1=20), we find that the t-value for a 95% confidence interval is approximately 2.086.

Thus, the confidence interval is:

CI = 224 ± 2.086*(12/√21)

CI = (219.60, 228.40)

Therefore, the answer is option (c) (219.60, 228.40).

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Is it possible for somebody to help me with a worksheet I will do that Brainly thing please

Is it possible for somebody to help me with a worksheet I will do that Brainly thing please

Answers

Yes send me a message!

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form

Answers

The missing side lengths are x = y =  2sqrt(2) units.

In a 45-90-45 degree triangle, the two legs are congruent. Therefore, if one leg has length x, the other leg must also have length x.

Using the Pythagorean Theorem, we can write:

x^2 + y^2 = (hypotenuse)^2

Substituting the given values, we get:

x^2 + y^2 = 4^2

x^2 + y^2 = 16

We know that the two legs of the triangle are congruent, so we can write:

x = y

Substituting this into the equation above, we get:

x^2 + x^2 = 16

2x^2 = 16

x^2 = 8

x = sqrt(8) = 2sqrt(2)

So the missing side length (base) is 2sqrt(2) units.

To find the perpendicular length (y), we can use the fact that x = y. Therefore:

y = x = 2sqrt(2) units

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The given question is incomplete, the complete question is:

Find the missing side lengths. Leave your answers as radicals in simplest form

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form

The grasshopper jumps either one block to the north, or one block to the west. He needs to reach the point that is located four blocks west and three blocks north of his current position. The grasshopper needs to avoid two dangerous intersections. The first intersection is one block west and one block north of his current position, and the second intersection is two blocks west and two blocks north of his current position. In how many ways can the grasshopper reach the desired destination?

Please help, im kinda new here, so I need answers immediately, I hope brainy doesn't fail me!

Answers

Answer:

The number of ways the grasshopper can reach the desired destination are 9 ways

Step-by-step explanation:

The directions in which the grasshopper can jump are;

One block north  and one block west

By counting, we have;

The number of possible ways are through blocks

1) 1, 2, 5, 6, 8, 10

2) 1, 2, 5, 6, 8, 9

3) 1, 2, 5, 6, 7, 9

4) 1, 2, 3, 6, 8, 10

5) 1, 2, 3, 6, 8, 9

6) 1, 2, 3, 6, 7, 9

7) 1, 2, 3, 4, 7, 9

8) 15, 14, 16, 12, 11, 10

9) 12, 13, 16, 12, 11, 10

Therefore, there 9 ways the grasshopper can reach the desired destination.

The grasshopper jumps either one block to the north, or one block to the west. He needs to reach the

Answer:

9

Step-by-step explanation:

answer with real answer otherwise you will be reported
Under a microscope, Ms. Kapinski studies a culture with bacteria. As the number of hours progresses, Ms. Kapinski sees that the bacteria can be modeled by the function b(t)=1290(1.76)^t where b represents the number of bacteria t hours after Ms. Kapinski begins her study.
(a)What does the value 1.76 represent in this situation? Be sure to explain.
(b)What does the value 1290 represent in this situation? Be sure to explain.
(c) The number of bacteria in a second study is modeled by the function b_2 (t)=1180(1.76)^t.
What does the value of 1180 represent in this situation?
What does the difference of 1290 and 1180 mean between the two studies?

Answers

Answer: A-We looked up the Z Score for 1.76 in our Normal Distribution Tables with Z Scores so you don't have to!

First, note that a Z Score of 1.76 means that your statistic is 1.76 standard deviation to the right of the mean on a bell curve. Here is a Bell Curve so you can visualize where 1.76 is on a bell curv

B-The numerical value of 1290 in Chaldean Numerology is: 0. Pythagorean Numerology. The numerical value of 1290 in Pythagorean Numerology is: 0

C-Since 2^10 is the same as 2^5 * 2^5 he was just breaking it down into something easier to calculate to verify that he had the right answer for 2^10 before working the rest of the equation.

Step-by-step explanation:

Consider a variant of the hamburger and figs example from class. Rachel has $50 in income, the price per hamburger is $3 and the price per bag of figs is $2. a) Write out an expression for Rachel's budget line. Sketch a graph, with hamburgers on the x axis. b) Suppose the price of figs increases to $3. Write out the new budget line equation and illustrate in your graph. c) Suppose income is $50, the price per hamburger is $3 and the price per bag of figs is $3. Rachel also receives $10 in cash from a friend. Write out a new budget line equation and illustrate in a graph. d) Suppose income is $50, the price per hamburger is $3 and the price per bag of figs is $3. Instead of cash, Rachel's friend gives her a gift basket containing 3 free bags of figs. Sketch Rachel's new budget line? Has the slope of the budget line changed? Can you write out a new budget line equation?

Answers

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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