The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answers
Yo sup??
Since the two figures are similar therefore their sides are in proportion.
for the first one
factor=2/8=1/4
for the second
factor=10/4=5/2
Hope this helps.
Answer: 7
Step-by-step explanation:
Related Questions
Use the following recursive formula to answer the question.
a1=−3/2
an=an−1+1/2
What is a9?
Answers
Answer:
2 1/2
Step-by-step explanation:
Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...
-3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2
a9 is 2 1/2.
I'm pretty sure the answer to
a1=−32
an=an−1+12
is 5/2
Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements: 1. As x increases infinitely, the y-values are continually doubled for each single increase in x. 2. As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine’s statements and her conclusion? a.Statement 1 is incorrect because the y-values are increased by 2, not doubled. b.Statement 2 is incorrect because the y-values are doubled, not halved. The conclusion is incorrect because the range is limited to the set of integers. The conclusion is incorrect because
Answers
The true statement is: d. The conclusion is incorrect because the range is limited to the set of positive real numbers.
The function is given as:
[tex]\mathbf{f(x) =2x}[/tex]
The above function implies that:
When x increases by 1, y increases by 2When x decreases by 1, y decreases by 2The above highlights mean that: Geraldine's claims are incorrect.
Because y increases or decreases by 2, when x increases or decreases by 1
In other words, the value of y does not get doubled or halved.
Hence, both statements are incorrect
Read more about range at:
https://brainly.com/question/21853810
A foot path of uniform width runs all around inside of a rectangle field 45m long and 36m wide.If the area of the path is 234 m , find the width of the path
Answers
Answer:
The width of path is 1.5 m
Step-by-step explanation:
We are given the following in the question:
Field:
Length = 45 m
Width = 35 m
Area of filed =
[tex]\text{Area} = \text{Length}\times \text{Width} = 45\times 36 = 1620[/tex]
The area of rectangular field the is 1620 square meter.
Area of path = 234 m
Let x be the width of path.
Area of field without path = 1620 - 234 = 1386 square meter.
Now, dimensions of field without path is:
Length = [tex]45 -x - x = 45 -2x[/tex]
Width = [tex]36 -x - x = 36 - 2x[/tex]
[tex]\text{Area} = \text{Length}\times \text{Width}[/tex]
Thus, we can write:
[tex](45-2x)(36-2x) = 1386[/tex]
[tex]1620 - 90x - 72x + 4x^2 = 1386\\4x^2 - 162x + 234 = 0\\2x^2 - 81x + 117 = 0\\(2x - 3)(x - 39) = 0\\x = 1.5, x = 39[/tex]
We cannot take the width as 39 m, thus, the width of path is 1.5 m.
A lion hides in one of three rooms. On the door to room number 1 a note reads: „The lion is not here". On the
door to room number 2 a note reads: „The lion is here". On the door to room number 3 a note reads: „2 + 3 = 5".
Exactly one of the three notes is true. In which room is the lion?
(A) Room 1 (B) Room 2 (C) Room 3
(D) It can be in any room. (E) It is either in room 1 or room 2.
Answers
Answer: I will pick B
Step-by-step explanation:
Because it's a logical explanation
Answer:
Room 1.
Step-by-step explanation:
The note on room 3 is true. So The notes on room 1 and room 2 are untrue.
If the lion is in room 1 that would make the note on room 1 untrue - so both room 1 and room 2 notes would be untrue.
Also if the lion is in room 2 that would make both room 1 and room 2 notes true.
So the lion must be in room 1.
Find the present value. Assume there are 360 days in a year.
FV = $83870
t = 226 days
r = 6.8%
Answers
Step-by-step explanation:
[tex]PV = FV \div (1+i)^n[/tex]
Here FV = $83870
i = 6.8% = 0.068
[tex]n = \frac{226}{365}[/tex] =0.62
Therefore,
[tex]PV=\frac{83870}{(1+0.068)^{0.62}}[/tex]
=$80517.91
Therefore the present value = $ 80517.91
Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney. Five-number summary: Minimum: 9 days Q1: 18 days Median: 21 days Q3: 28 days Maximum: 56 days If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the right boundary?
Answers
Answer:
43
Step-by-step explanation:
We have the following data:
Total number of hikers: 136
Minimum: 9 days
Q1 : 18 days
Median: 21 days
Q3: 28 days
Maximum: 56 days
Using the 1.5 Interquartile rule means:
Left boundary: Q1 - 1.5 × IQR
Right boundary: Q3 + 1.5 × IQR
We first calculate the IQR (Interquartile Range): Q3 - Q1
⇒ 28 - 18 = 10
Right boundary: 28 + 1.5 × 10
= 28 + 15
= 43
Hence the right boundary is 43.
A piece of wire 40 cm long is cut into two piece, each to be bent to make a square.The length of a side of one square is to be 4 longer than length of a side of the other. How should the wire be cut
Answers
Answer: the wire should be cut into 12 cm and 28 cm
Step-by-step explanation:
All sides of a square is equal.
The perimeter of a square is the distance around the square.
Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.
The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4
The perimeter of the other square would be 4(L + 4) = 4L + 16
Since the piece of wire is 40 cm long, then
4L + 4L + 16 = 40
8L = 40 - 16 = 24
L = 24/8 = 3
The perimeter of the first square is
4L = 4 × 3 = 12
The perimeter of the second square is
4L + 16 = 4 × 3 + 16= 28
Final answer:
To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.
Explanation:
The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.
Combining the total length of both squares, we have:
4x + 4(x + 4) = 40
This simplifies to:
8x + 16 = 40
Subtracting 16 from both sides, we get:
8x = 24
Dividing both sides by 8, we find:
x = 3
Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:
Smaller square wire length: 4(3) = 12 cm
Larger square wire length: 4(7) = 28 cm
So the wire should be cut into one 12 cm piece and one 28 cm piece.
How many 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard?
Answers
72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Solution:
Given, 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Therefore,
Area of square = 4 x 4 = 16
Thus area of square to be cut is 16 square inches
Rectangular piece of leather measuring 4 feet by two-thirds of a yard
Convert feet to inches
1 feet = 12 inch
4 feet = 4 x 12 = 48 inches
Also,
1 yard = 36 inch
Given is a two-thirds of a yard
[tex]\frac{2}{3} \times 36 = 24\ inches[/tex]
Thus area of rectangular piece of leather is:
[tex]Area = 48 \times 24 = 1152\ square\ inches[/tex]
Total number of squares cut is given as:
[tex]\text{Total number of squares cut} = \frac{\text{area of leather}}{\text{ area of square}}[/tex]
Thus we get,
[tex]\text{Total number of squares cut} = \frac{1152}{16} = 72[/tex]
Thus 72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Answer:
72
Step-by-step explanation:
5 years ago, the age of a man was 7 times the age of his son. After five years, the age of the man will be 3 times the age of his son from now. How old are the man and the son now?
Answers
Answer:
10 years
40 years
Step-by-step explanation:
let present ag e of son=x
5 years ago age of son=x-5
5 years ago age of man=7(x-5)=7x-35
present age of man=7x-35+5=7x-30
after 5 years
age of son=x+5
age of man=7x-30+5=7x-25
also 7x-25=3(x+5)
7x-25=3x+15
7x-3x=15+25
4x=40
x=10
age of son=10 years
age of man=7*10-30=70-30=40 years
Final answer:
By creating equations from the given information and solving them, it was found that the man is currently 40 years old, and his son is 10 years old.
Explanation:
Let's solve the problem using algebra. Suppose the current age of the man is M years and the current age of his son is S years.
According to the problem, 5 years ago, the age of the man was 7 times the age of his son. Therefore, M - 5 = 7(S - 5).
After 5 years, the age of the man will be 3 times the age of his son from now. Therefore, M + 5 = 3(S + 5).
Solving these equations:
M - 5 = 7S - 35
M + 5 = 3S + 15
Simplifying both:
M = 7S - 30
M = 3S + 10
Equating both equations we get:
7S - 30 = 3S + 10
4S = 40
S = 10
Substituting the value of S in the first equation:
M = 7*10 - 30 = 40
Therefore, the man is currently 40 years old, and his son is 10 years old.
Guided Practice
Which of the following is a Pythagorean triple?
A. 15, 20, and 25
B. 15, 16, and 24
O
c. 15, 21, and 28
Answers
Answer:
A. 15, 20, and 25
Step-by-step explanation:
Note that 3-4-5 is a pythagorean triple via following:
[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]
Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.
Find S25 for 1/2 + 1 + 3/2 + 2 + ...
Answers
Step-by-step explanation:
The given sequence:
[tex]\dfrac{1}{2}+1+\dfrac{3}{2}+2+ ...[/tex]
Here, first term (a) = [tex]\dfrac{1}{2}[/tex], common difference(d) =[tex]1-\dfrac{1}{2}=\dfrac{1}{2}[/tex] and
the number of terms (n) = 25
The given sequence are in AP.
To find, the value of [tex]S_{25}[/tex] = ?
We know that,
The sum of nth terms of an AP
[tex]S_{n}=\dfrac{n}{2}[2a+(n-1)d][/tex]
The sum of 25th terms of an AP
[tex]S_{25}=\dfrac{25}{2}[2(\dfrac{1}{2})+(25-1)(\dfrac{1}{2})][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[1+(24)(\dfrac{1}{2})][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[1+12][/tex]
⇒ [tex]S_{25}=\dfrac{25}{2}[13][/tex]
⇒ [tex]S_{25}=\dfrac{325}{2}[/tex]
∴ [tex]S_{25}=\dfrac{325}{2}[/tex]
1.95=z-2.05
Help it is so hard
Answers
Answer:
Z=4
Step-by-step
You just add 2.05 to 1.95 to get z alone
Answer: Z=4
Step-by-step explanation:
Add 2.05 and 1.95 and you get 4.
If you subtract 2.05 from 4 you get 1.95
Please help I've been stuck on this question for a while now. How do I solve (1/2)^4 (1/2)^-2? It has to do with Multiplying and Dividing Expressions with Exponents. Please show work so I may figure it out on my own.
Answers
The value of the expression is [tex]0.25[/tex]
Explanation:
The expression is [tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$[/tex]
Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.
Thus, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{4-2}$[/tex]
Adding the exponents, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{2}$[/tex]
Applying exponent rule, [tex]$\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$[/tex], we have,
[tex]$\left(\frac{1}{2}\right)^{2}=\frac{1^{2}}{2^{2}}$[/tex]
Simplifying, we get,
[tex]\frac{1}{4}[/tex]
Dividing, we have,
[tex]0.25[/tex]
Thus, the value of the expression is [tex]0.25[/tex]
The formula for the perimeter of a rectangle with length and width is as follows. Suppose the length of the rectangle is 5 times the width. Rewrite in terms of only. It is not necessary to simplify?
Answers
Answer:
P = 2(5W + W)
Step-by-step explanation:
P = 2(L +W)
L = 5W
P = 2(5W + W)
P = 10W + 2W
P = 12W
If a line of one billion people standing shoulder to shoulder stretches 420,334 miles what is the average shoulder width in feet of the people in line
Answers
Answer:
2.21936352 feet
Step-by-step explanation:
420334*5280 (thats feet in a mile) divided by 1000000000
Yo sup??
Average shoulder width=total lenght / number of people
since we want it in inches therefore
Final answer=Average shoulder width*63360
=420334*63360/1,000,000,000
=26.62 inches
Hope this helps
A pharmacist has a 6% solution of cough syrup and a 14% solution of the same cough syrup. How many ounces of each must be mixed to make 16 ounces of a 10% solution of cough syrup?
Answers
Answer:
8 ounces of each must be mixed to make 16 ounces of a 10%solution.
Step-by-step explanation:
The careful analysis and detailed calculation is as shown in the attached file.
When using rational expectations, forecast errors will, on average, be ________ and ________ be predicted ahead of time. A) zero; cannot B) negative; can C) positive; can D) positive; cannot
Answers
Answer:
A) zero; cannot
Step-by-step explanation:
In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.
In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?
A. $2,200
B. $3,450
C. $4,200
D. $4,250
E. $5,000
Answers
Answer:
$4200
Step-by-step explanation:
450 - 240 = 210 this is the amount of her commissions for the week.
we are looking for x = sales for the week
x * .05 = 210
x = 210/.05
x = 4200
Answer:c 4200
Step-by-step explanation:
A box of pencils costs $3.25 and a box of colored pencils costs $4.65. However, a box of pencils and a box of colored pencils are sold together at $6.50. If Alex wants to buy 6 boxes of pencils and 9 boxes of colored pencils, what is the least amount of money that Alex can pay?
Answers
Answer:
the least is 40
Step-by-step explanation:
if u multiply each money amount times the amount they bought you get the awnser
HELP!!!! I think its C but I'm not sure!
What does the fundamental theorem of algebra state about the equation 2x2−4x+16=0 ?
A. The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1±i7√2 .
B. The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1±i7√ .
C. The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots are x=1±i7√2 .
D. The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots are x=1±i7√ .
Answers
Answer:
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].
Step-by-step explanation:
Consider the provided information.
Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.
Now consider the provided equation.
[tex]2x^2-4x+16=0[/tex]
The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.
Now find the root of the equation.
For the quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute [tex]a=2,\:b=-4,\:\ and \ c=16[/tex] in above formula.
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}[/tex]
[tex]x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}[/tex]
[tex]x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}[/tex]
[tex]x_{1,\:2}=1\pm i\sqrt{7}[/tex]
Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].
Researchers wanted to know if there is a link between proximity to high-tension wires and the rate of leukemia in children. To conduct the study, researchers compared the rate of leukemia for children who lived within 1/2 mile of high-tension wires to the rate of leukemia for children who did not live within 1/2 mile of high-tension wires. The researchers found that the rate of leukemia for children near high-tension wires was higher than the rate for those not near high-tension wires. Can the researchers conclude that proximity with high-tension wires causes leukemia in children?
Answers
Answer:
COPD
Step-by-step explanation:
COPD is a lung disease caused by tobacco use and other factors
Sam can brew 5 gallons of root beer in an hour or he can make 4 pizzas in an hour. Ben can brew 7 gallons of root beer in an hour or he can make 5 pizzas in an hour.Who has an absolute advantage in making pizza?
Answers
Answer:
Ben
Step-by-step explanation:
Ben has an absolute advantage in making of pizza because he can make five pizzas in one hour which is a greater quantity compared to Sam that makes four pizzas in one hour.
In the diagram, BC⎯⎯⎯⎯⎯∥DE⎯⎯⎯⎯⎯ .
What is AE ?
Enter your answer in the box.
___ in.
THE ANSWER IS 18in
Answers
The length of AE is [tex]18in[/tex]
Explanation:
From the figure, we can see that the two triangles ΔAED and ΔACB are similar. Thus, the legs of the triangle are proportional to each other.
Thus, we have,
[tex]\frac{EC}{DB} =\frac{AE}{AD}[/tex]
Substituting the values of the sides from the image, we get,
[tex]\frac{3}{1} =\frac{AE}{6}[/tex]
Multiplying both sides of the equation by 6, we get,
[tex]6(3)=AE[/tex]
Multiplying, we have,
[tex]18=AE[/tex]
Thus, the length of AE is [tex]18in[/tex]
Answer:
the answer is 18 inches.
Step-by-step explanation:
Y=2x-7, 3x-2=9 solving systems
Answers
x-y=2 and x+y=-2 sove by graphing please and show the solution
Answers
Answer:
The answer to your question is There is only one solution (0, -2)
Step-by-step explanation:
Data
Equation 1 x - y = 2
Equation 2 x + y = -2
Solve for y
Equation 1 y = x -2
y = x - 2
Equation 2 y = - x - 2
See the graph below
These lines cross in point (0 ,-2), that is the only solution.
If the lines have not crossed, they were parallel lines.
State whether the data are best described as a population or a sample. A questionnaire to understand athletic participation on a college campus is emailed to 40 college students, and all of them respond.
Answers
Answer:
Sample
Step-by-step explanation:
The part or portion of a population is called as sample. The given data represents a sample because a questionnaire is given to the selected 40 college students for collecting response on athletic participation rather to all of the college students. Thus, the questionnaire is given to a part of population. So, the given data represents a sample.
An initial investment of $1000 is appreciated for 4 years in an account that earns 4% interest, compounded annually. Find the amount of money in the account at the end of the period.
Answers
Answer: $116.99
Step-by-step explanation:
By using compound interest formula which said:
A = P ( 1 + r/n )^(n×t)
P=Principal= 1000
r=rate=4/100
n=1
t= 4
Apply the above formula
A = P ( 1 + r/n )^(n×t)
A = 1000(1 + 0.04/1)^(1 × 4)
A= 100(1.04)^4
A= 100 × 1.17
A = 116.99
At the county fair,animals are judged for the quality of their breeding and health.The animal pens are arranged in an array,with one animal in each pen .A barn can hold at most 10 rows of pens and at most 6 pens in each row ,with room for people to walk around them.What different ways can the planners of county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?
Answers
Answer:
1 . 60!=8.31*[tex]10^{81}[/tex] ways
The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged
Step-by-step explanation:
At the county fair,animals are judged for the quality of their breeding and health.The animal pens are arranged in an array,with one animal in each pen .A barn can hold at most 10 rows of pens and at most 6 pens in each row ,with room for people to walk around them.What different ways can the planners of county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?
if there are 10 ros and 6 barns. the number of ways animsls can be arrganged becomes
10 *6=60
60
look for 60 factorials, the number of ways
60!=8.31*[tex]10^{81}[/tex] ways
2.Permutation means arrangement . The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged , it makes it possible
For example find the number of ways 12 cows and 18 horses can be arranged in the barns.
we have the number of animals to be=12+18=30
60P30=60[tex]\frac{60!}{960-30)!} =\frac{60!}{30!}[/tex]
31.37*10^48 ways
Final answer:
The planners at the county fair can arrange the animal pens in various ways as long as the total number does not exceed 60, based on a maximum of 10 rows and 6 pens per row. This problem is one of combinatorics, requiring the counting and arranging of objects within given constraints.
Explanation:
The question involves arranging animal pens within a barn that can accommodate at most 10 rows of pens and up to 6 pens per row for animals like horses and cows at a county fair. This is fundamentally a problem of combinatorics, a branch of mathematics dealing with the counting, arrangement, and combination of objects. To determine the different arrangements possible for placing the pens, we would consider the combinations that do not exceed the given maximums for rows and pens per row.
The total number of pens that can fit in the barn is found by multiplying the maximum number of rows by the maximum number of pens per row, which gives us 10 rows × 6 pens per row = 60 pens as the upper limit. Therefore, the planners could arrange the pens in a variety of ways, including all rows filled with 6 pens, fewer rows with 6 pens, or more rows with less than 6 pens each, as long as the total number of pens does not exceed 60.
The quantities given in the problem relate to one another as constraints in a two-dimensional array. The planners have the flexibility to decide how many rows and pens per row to use without exceeding the maximum capacity of the structure. This scenario underscores the practical application of mathematical principles in planning and logistics.
A pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is .5 the size of each of the others. What fraction of the pizza is the smallest piece
Answers
Answer:
1/10 of pizza
Step-by-step explanation:
Let x represent size of equal pieces.
We have been given that a pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is 0.5 the size of each of the others.
This means that size of small piece would be half the size of other pieces, that is [tex]\frac{x}{2}[/tex].
Since the pizza is divided in 5 pieces, so we will divide [tex]\frac{x}{2}[/tex] by 5 as:
[tex]\frac{\frac{x}{2}}{5}=\frac{x}{2\cdot5}=\frac{x}{10}=\frac{1}{10}x[/tex]
Therefore, the smallest piece is 1/10 of the pizza.
Charlie has the utility function u(xa, xb) =xaxb. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle Charlie can afford?
Answers
Answer:
There are 5 apples in the best bundle Charlie can afford
Step-by-step explanation:
If the utility function is u(xa, xb) , where xa represent the quantity of apples and xb is the quantity of bananas then we want to choose the quantity of bananas and apples that maximises the utility of Charlie for the same budget restriction ( get the most benefit for the same money).
The budget restriction is
$4* xa + $2* xb = $40
then
u(xa, xb) =xa*xb
4*xa + 2*xb = 40 → xb = (40 - 4*xa)/2 = 20 - 2*xa
replacing in the utility function
u(xa, xb) =xa* (20 - 2*xa) = 20*xa - 2*xa²
the maximum of this function is obtained when the derivative of the utility function with respect to xa is 0 . Thus
du/dxa = 20 - 4*xa = 0 → xa = 20/4 = 5
then for
xa=5 apples
xb=20 - 2*xa = 20 - 2*5 = 10 bananas
Charlie maximises his utility . Therefore there are 5 apples in the best bundle Charlie can afford
To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. The maximum value of xa represents the number of apples in the best bundle Charlie can afford, which is 5.
Explanation:To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. Let's denote the quantity of apples as xa and the quantity of bananas as xb. Since Charlie's income is $40, we have 4xa + 2xb ≤ 40. Using this inequality, we can find the maximum value of xa, which represents the number of apples in the best bundle Charlie can afford.
To solve for xa, we rearrange the inequality:
4xa ≤ 40 - 2xbxa ≤ (40 - 2xb) / 4Now, let's look at the utility function u(xa, xb) = xaxb. To maximize the utility function, we take the derivative of u with respect to xa and set it equal to zero.
∂u/∂xa = 0(d/da)(xa * xb) = 0xb = 0 / xaSince xb is in the denominator, its value should be greater than zero. Therefore, the best bundle Charlie can afford will have the maximum value of xa such that 4xa + 2(could be anything greater than 0) ≤ 40. Solving for xa, we get xa ≤ 5.
Hence, Charlie can afford a maximum of 5 apples in the best bundle.
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