The volume of the circumscribed cylinder is 2154.04π cm^3. Find the radius of the sphere…show all work and steps.
Answers
The measure of the radius of the sphere is given as follows:
r = 359 cm.
How to obtain the volume of the cylinder?
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h
Which is the base area given by πr² multiplied by the height h.
In the context of this problem, the parameters are given as follows:
The radius of the cylinder is the same as the radius of the sphere, which is of r.The height of the cylinder is twice the radius of the sphere, hence it is or 2r.The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:
πr²h = 2154.04π
2πr³ = 2154.04π
2r³ = 2154.04
r = cube root of (2154.04/2)
r = 359.
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Related Questions
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level. Which one of the following is the value of t?.
Answers
The value of t while considering a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level is ±1.685.
Given:
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level.
we are asked to determine the t value:
The directional hypothesis is:
Hₐ : µ > µ₀
The sample size is, n = 40.
The significance level is:
α = 1-0.95 = 0.05
Use the t-table to compute the right-tailed t-critical value as follows:
tₐ,₍ₙ₋₁₎ = t₀.₀₅,₍₄₀₋₁₎
= t₀.₀₅,₃₉
≈ t₀.₀₅,₄₀
= 1.684
≈ 1.685
The value is positive since the directional hypothesis suggests that the test is right tailed.
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Abiona cannot decide which of two bicycles to buy. The original price of each is $380. The first bicycle is marked down by 50%. The second bicycle is marked down by 30% first and then an additional 20% off. Which bicycle should Abiona buy if the bicycles are the same except for the selling price? Explain your answer.
Answers
Abiona should buy the first bicycle ($190) because it is cheaper than the second bicycle ($212.8)
How to determine which bicycle Abiona should buy?Given that:
The original price of each is $380
The first bicycle is marked down by 50%
The second bicycle is marked down by 30% first and then an additional 20% off
The price of the first bicycle after the discount will be:
price = 380 - (0.5×380)
price = $190
The price of the second bicycle after the discount will be:
After 30% discount:
price = 380 - (0.3×380) = $266
After 20% discount:
price = 266 - (0.2×266) = $212.8
Thus, the price after the discount is $212.8
Therefore, Abiona should buy the first bicycle because it is cheaper
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Find the volume of a right circular cone that ha a height of 13,8 cm and a bae with a circumference of 15. 8 m
Answers
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
PLEASE HELP I AM CONFUSE!!!!!!!!!!
Answers
Answer:
A = $285.45
A = P + I where
P (principal) = $200.00
I (interest) = $85.45
Step-by-step explanation:
there I hope this helps!
Please help now asap !!!!!!!!!
Answers
Answer:
80
usually estimate is rounded 1 significant figure, 0.9 is rounded to 1, and 82 is rounded to 80.
1*80 is 80
Sharon discovered $2.95
worth of nickels and dimes.
If she has a total of 37 coins, how many of each kind of coin does she possess?
Answers
Answer:15 nickels 22 dimes
Step-by-step explanation:
A radioactive compound with mass 100 grams decays at a rate of 5. 8% per hour. Which equation represents how many grams of the compound will remain after 2 hours?.
Answers
On solving the question, we got that - [tex]P(t) = P_{100e^{-0.058t} }[/tex] grams of radioactive compound will remain after 2 hours.
What is Radioactive compunds?Chemicals known as radionuclides (also known as radioactive materials) have unstable atoms in their center. Changes in the nucleus help them maintain stability, spontaneous fission, emission of alpha particles, or conversion of neutrons to protons or the reverse.
Future value is the issue at hand. If weight is measured in grams and time is measured in years, then [tex]P(t) = P_{0e^{-rt} }[/tex] with [tex]P_{0} = 100[/tex] and r = 0.058
Therefore,
[tex]P(t) = P_{100e^{-0.058t} }[/tex]
Will remain after 2 hours.
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the liabilities of departments are normally distributed with an unknown population mean and standard deviation. if a random sample of 36 departments is taken to estimate the mean liabilities, what t-score should be used to find a 95% confidence interval estimate for the population mean?
Answers
Critical value with 35 degrees of freedom at 0.05 Los = 2.030
Given information,
Departmental liabilities have a mean and standard deviation that are unknown for the population. What t-score should be used to establish a 95% confidence interval estimate for the population mean if a random sample of 36 departments is utilized to estimate the mean liabilities?
Here,
By assuming a 95% confidence interval and by considering the t-value we have,
Therefore;
Critical value at 0.05 Los with 35 degrees of freedom =2.030
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9 questions for 30 points!
Answers
Answer:
1. The solution to question one = (2, -6)
2. The solution to question two = (-1, 7)
3. The solution to question three = (1, 12)
4. The solution to question four = (2, -12)
5. The solution to question five = (3, 12)
6. The solution to question six = (-3, 12)
7. The solution to question seven = (-2, -8)
8. The solution to question eight = (-3, 21)
9. The solution to question nine = (2, 16)
Step-by-step explanation:
Steps to solve question 1:
Step 1: Substitute 5x for y in y = x - 8 and solve for y
1. (5x) = x - 8 → 4x = 8 → x = 2
Step 2: Plug 2 in for x in y = x - 8 and solve for x
2. y = (2) - 8 → y = -6
The solution to question one: (2, -6)
Steps to solve question 2:
Step 1: Substitute 3x for y in y = -x - 4 and solve for y
1. (3x) = -x - 4 → 4x = -4 → x = -1
Step 2: Plug -1 in for x in y = -x - 4 and solve for x
2. y = -(-1) - 8 → y = 7
The solution to question two: (-1, 7)
Steps to solve question 3:
Step 1: Substitute 12x for y in y = x + 11 and solve for y
1. (12x) = x + 11 → 11x = 11 → x = 1
Step 2: Plug 1 in for x in y = x + 11 and solve for x
2. y = (1) + 11 → y = 12
The solution to question three: (1, 12)
Steps to solve question 4:
Step 1: Substitute -6x for y in y = x - 14 and solve for y
1. (-6x) = x - 14 → -7x = -14 → x = 2
Step 2: Plug 2 in for x in y = x - 14 and solve for x
2. y = (2) - 14 → y = -12
The solution to question four: (2, -12)
Steps to solve question 5:
Step 1: Substitute 2x for y in y = -x + 9 and solve for y
1. (2x) = -x + 9 → 3x = 9 → x = 3
Step 2: Plug 3 in for x in y = -x + 9 and solve for x
2. y = (3) + 9 → y = 12
The solution to question five: (3, 12)
Steps to solve question 6:
Step 1: Substitute -4x for y in y = x + 15 and solve for y
1. (-4x) = x + 15 → -5x = 15 → x = -3
Step 2: Plug -3 in for x in y = x + 15 and solve for x
2. y = (-3) + 15 → y = 12
The solution to question six: (-3, 12)
Steps to solve question 7:
Step 1: Substitute 4x for y in y = -x - 10 and solve for y
1. (4x) = -x - 10 → 5x = -10 → x = -2
Step 2: Plug -2 in for x in y = -x - 10 and solve for x
2. y = -(-2) - 10 → y = -8
The solution to question seven: (-2, -8)
Steps to solve question 8:
Step 1: Substitute -7x for y in y = x + 24 and solve for y
1. (-7x) = x + 24 → -8x = 24 → x = -3
Step 2: Plug -3 in for x in y = x + 24 and solve for x
2. y = (-3) + 24 → y = 21
The solution to question eight: (-3, 21)
Steps to solve question 9:
Step 1: Substitute 8x for y in y = -x + 18 and solve for y
1. (8x) = -x + 18 → 9x = 18 → x = 2
Step 2: Plug 2 in for x in y = -x + 18 and solve for x
2. y = -(2) + 18 → y = 16
The solution to question nine: (2, 16)
Hope this helps you out :)
Which of the following describes the correct order of events?
A
E
U
D
1. African Americans are denied the right to vote.
2. African Americans organize marches for voting rights in Alabama.
3. The Voting Rights Act is signed.
1. The Voting Rights Act is signed.
2. African Americans are denied the right to vote.
3. African Americans organize marches for voting rights in Alabama.
1. African Americans are denied the right to vote.
2. The Voting Rights Act is signed.
3. African Americans organize marches for voting rights in Alabama.
1. The Voting Rights Act is signed.
2. African Americans organize marches for voting rights in Alabama.
3. African Americans are denied the right to vote.
Answers
Answer:
A
Step-by-step explanation:
describes a good place
If the original quantity i 5 and the new quantity i 3, what i the percent decreae?
Answers
The percentage reduction is 40% if the original number was 5 and the new quantity is 3.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
A percentage is a value expressed as a decimal. Divide the percentage value by 100 to convert percentages to decimals and fractions.
The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates.
The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent."
Per was frequently shortened to "p" and eventually vanished entirely. The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.
According to our question-
5 were originally ordered, however only 3 were added, resulting in a net drop of 1.
(5 - 3) = 2.
Now, we'll divide net change by the initial amount and multiply it by 100% to get the percentage change, which is,
(2/5)×100%.
= 40%,
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A garden has 8 rows of plants. each row has 12 tomato plants and 3 bean plants. how many more tomato plants than bean plants are in the garden?
Answers
Answer: 72
Step-by-step explanation: because 8 x 12 = 96 and 3 x 8 = 24
96 - 24 = 72
if a woodworker builds 3/7 chair in 3/4 hour, how long does it takes the woodworker to build 1 chair
Answers
Answer:
it would take him 4/7 of an hour
Step-by-step explanation:
Mites are discovered in a peach orchard. The Department of Agriculture has determined that the population of mites t hours after the orchard has been sprayed is approximated by N(t)=1600−3tln(0.07t)−t N ( t ) = 1600 − 3 t ln ( 0.07 t ) − t , where 0What is the maximum number of mites in the peach orchard? Round to the nearest whole number.
Answers
The maximum number of mites in the peach orchard are 1564
Given that,
There are found to be mites in a peach orchard. According to research conducted by the Department of Agriculture, the number of mites t hours after the orchard has been sprayed is roughly represented by the equation N(t)=1600-3tln(0.07t)-t
To find : What is the maximum number of mites in the peach orchard? Round to the nearest whole number.
N(t)=1600-3tln(0.07t)-t
N(19)=1600-3(19)ln(0.07(19))-(19)
N(19)=1600- 16.255 - 19
N(19)=1564.74
N(19)≈1564
Therefore, the maximum number of mites in the peach orchard are 1564
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Sam and Rohan's families are driving to Chicago, Illinois, from Orlando, Florida. Sam's
family is driving a direct route of 1,157 miles at 65 mph. Rohan and his family are driving
through Charlotte, North Carolina and will drive 1,250 miles at 70 mph.
1.
2.
At this rate, how many hours will it take Sam's family to get to Chicago, Illinois?
(Round your answer to the tenths place. )
How many hours will it take Rohan's family to arrive in Chicago, Illinois? (Round
your answer to the tenths place. )
Answers
(1) It will take 17.8 hours for Sam's family to get to Chicago, Illinois .
(2) Rohan's family will take 17.9 hours to arrive in Chicago, Illinois .
In the question ,
it is given that ,
For Sam's Family ,
total distance to be covered is = 1157 miles ,
the average speed is given to be = 65 mph .
By the formula of Speed , Distance and Time ,
we get ,
65 = 1157/t
t = 1157/65
t = 17.8 hours .
For Rohan's family ,
total distance to be covered is = 1250 miles ,
the average speed is given to be = 70 mph ,
By the formula of Speed , Distance and Time ,
we get ,
70 = 1250/t
t = 1250/70
t = 17.9 hours
Therefore , Sam's family will take 17.8 hours and Rohan's family will take 17.9 hours .
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the standard error of estimate measures the accuracy of a prediction. group startstrue or falsetrue, unselectedfalse, unselected
Answers
The statement is true that is the standard error of estimate measures the accuracy of a prediction.
Given that,
We have a statement that is the standard error of estimate measures the accuracy of a prediction.
We have to find is the statement is true are false.
We know that,
What is standard error?The SE formula is used to determine how accurately a sample represents a population. The sample mean's departure from the specified population is provided as follows,
Formula for standard error
S.E=S/√n
Where, n is the number of observations and S is the standard deviation.
Therefore, The statement is true that is the standard error of estimate measures the accuracy of a prediction.
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Help PLEASE!!!! Like in the next 15 mins!
Answers
The values of A, B, C and D are 55.04ft² ,9184.50ft , 75.36ft and 38.46ft², the A(C-D)+B= 11214.00
What are circumference and area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2.
Circumference of a circle is the perimeter of a circle. It can be calculated as C= πd or 2πr
calculating A, the area of the circle is 3.14×8²= 200.96
the area of the square= l×l= 16×16= 256
area of the shaded part = 256-200.96= 55.04ft²
calculating B, since the maintenance worker moved round 3 times
3C = 3πd= 3.14×975×3 = 9184.50ft
calculating C
circumference of 3 bowls
= 3πd= 3×3.14×8= 75.36ft
calculating D
area= πr²= 3.14×3.5²
= 38.46ft²
therefore A(C-D)+B= 55(75.36-38.46)+9184.50
= 2029.5+9184.5
= 11214.00
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HELP PLEASE, I’ll give points and mark brainliest
Answers
125x^2/5x+15x/5x
Recall that when dividing exponents, the bases must be the same and the exponents subtract while keeping the base.
Now, we must put 5x in front of the parenthesis to create an equivalent equation:
5x(25x+3)
The whole idea of factoring is deriving an equivalent expression in a simpler form to find the roots of a polynomial, so if we “undo” our factoring by distributing 5x into the parenthesis, we should get 125x^2+15x.
Answer: 5x(25x+3)
a sample of bacteria is decaying according to a half-life model. if the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, after how many minutes will there be 40 bacteria remaining?
Answers
After approximately 113 minutes, there will be only 40 bacteria remaining.
Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.
N(t) = N₀(1/2)^(t/T)
where N(t) = amount of substance remaining after time t
N₀ = initial amount of substance
t = time
T = half-life
If the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, then
N₀ = 500, and N(t) = 350 when t = 16 minutes
Substitute the given values and solve for the half-life.
N(t) = N₀(1/2)^(t/T)
350 = 500(1/2)^(16/T)
T = 31.09 minutes
Using the formula, solve for t when n(t) = 40.
N(t) = N₀(1/2)^(t/T)
40 = 500(1/2)^(t/31.09)
t = 113.30 minutes
t ≅ 113 minutes
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Joey's boat weighs 0.62 tons. What is he weight of the boat measured in pounds?
Answers
Answer:
The answer would be 1240 pounds. The conversion that you would make would be to multiply 0.62 by 2000.
Hope this helps, Have a wonderful day! :D
Step-by-step explanation:
solve for y ! ~
[tex] \rm \: y = 5 \pm58[/tex]
Answers
The solution for y in the expression is y = -53 and y = 63
How to determine the solution for y?From the question, the expression is given as
y = 5 ± 58
We start by expanding the expression
So, we have the following representation
y = 5 - 58 and y = 5 + 58
Evaluate the sum and the difference of the like terms in the above expression
So, we have the following representation
y = -53 and y = 63
Hence, the solution is
y = -53 and y = 63
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For Daniel's lemonade recipe, 4 lemons are required to make 16 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?
Answers
The rate at which lemons being used in lemons per cup of lemonade is 0.25 lemons per cup
RatioA ratio compares values. A ratio says how much of one thing there is compared to another thing.
Rate of Change
Rate of change is the value at which the rest of the time.
Let the rate of lemon per cup of lemonade be x
Total lemon = 4
For a cup of lemonade =16
Rate of lemon per cup of lemonade
x = 4/16
x= 0.25.
Therefore, the required rate of lemon per cup of lemonade is 0.25 lemons per cup
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PLEASE HELP!!!!!!
I need this answered ASAP
Answers
Hope this helps!
Graph the opposite of − 7 on the number line.
Answers
Answer:
Positive seven.
Step-by-step explanation:
Go past zero to normal seven.
Answer:positive 7
Step-by-step explanation:
Make a conjecture about the value
Points A, B, and C are collinear,
and D is between B and C.
Answers
Answer :not fully correct
cStep-by-step explanation:
Complete the equation so that it has no solution.
Enter the correct answer in the box.
6x+5=3 +
plus what to equal to no solution
Answers
Answer:
-3
Step-by-step explanation:
6x + 5 = 0 - there are no solutions...
Answer:
Step-by-step explanation:
-1/3
A piece of paper is to display ~150~ 150 space, 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?.
Answers
The paper's smallest dimensions are height=8.660in and width=17.321in.
What are dimensions?In physics and mathematics, the dimension of space is the smallest set of coordinates needed to specify any point within a mathematical space.
A line has a dimension of one because only one coordinate is needed to specify a point on a line, such as a point at 5 on a number.
So, we have:
Area = 150in²
Side margin = 1 in
Top and Bottom Margin = 2 in
To obtain the smallest dimensions, calculate as follows:
The printed material's area is:
Area = l*w
A1 = h*w
A1 should be changed to 150:
150 = h*w
h = 150/w
The complete paper's topic is:
Area = l*w
A2 = (w+2+2)*(H+1+1)
A2 = (w+4)*(H+2)
For H, substitute 150/W:
A2 = (w+4)*(150/w+2)
A2 = w(150/w+2) + 4(150/w+2)
A2 = 150 + 2w + 600w + 8
A2 = 2w = 600/w + 8 + 150
A2 = 2w = 600/w + 158
Calculate a difference with regard to w and set the outcome to 0:
A'2 = 2-600/w²+0
A'2 = 2-600/w²
0 = 2 - 600/w²
2 = 600/w²
2*w² = 600
w² = 600/2
w² = 300
w = 17.321
Remember that:
h = 150/w
h = 150/17.321
h = 8.660
Therefore, the paper's smallest dimensions are height=8.660in and width=17.321in.
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If there are 48 lollipops and 60 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made
Answers
Answer:
Step-by-step explanation:
The ratio formula is given as a:b = a/b for any two quantities, let's say a and b. Given that a and b are separate amounts for two quantities, the combined total quantity is denoted by (a + b).
There are 48 lollipops and 6 candy bars for a gift bag.
Then the possible ratios of lollipops to candy bars are:
( 48 / 6 ) ÷ ( 2 / 2) = ( 24 / 3 )
( 48 / 6 ) ÷ ( 3 / 3) = ( 16 / 2 )
( 48 / 6 ) ÷ ( 6 / 6) = ( 8 / 1 )
There are 48 lollipops for every 6 candy bars.
There are 24 lollipops for every 3 candy bars.
There are 16 lollipops for every 2 candy bars.
There are 8 lollipops for every 1 candy bar.
There are 4 lollipops for every 5 candy bars (4 :5 ratio)
There are 8 lollipops for every 10 candy bars (8 :10 ratio)
There are 24 lollipops for every 30 candy bars (24:30 ratio)
There are 12 lollipops for every 15 candy bars (12:15 ratio)
Peggy pays an annual fee of $10.75 to belong to an online music club and download songs at a reduced price. Last year she downloaded 105 songs altogether. Non-members pay $0.35 more per song download than members. Suppose Daniel is not a member of the club and downloaded 85 songs last year. If Daniel and Peggy both paid the same total amount, what is the cost per download for members and for non-members? Let x
represent the cost of downloading a song for members. Set up and solve an equation. Show your work.
Help! Due Tonight
Answers
The solution of the algebraic equation for the cost of downloading a song for members is x = $0.95
How to set up and solve an equation for the cost of downloading a song for members?Given that:
1. Peggy pays an annual fee of $10.75. Last year she downloaded 105 songs
2. Non-members pay $0.35 more per song download than members
3. Daniel is not a member of the club and downloaded 85 songs last year
Let x represent the cost of downloading a song for members
Thus, the cost of a song for Peggy will be x
From statement 2: the cost of a song for Daniel will be x+0.35
The algebraic equation for the total amount for Peggy will be:
A = 105x + 10.75
The algebraic equation for the total amount for Daniel will be:
A = 85(x+0.35)
If Daniel and Peggy both paid the same total amount, we can say:
105x + 10.75 = 85(x+0.35)
105x + 10.75 = 85x + 29.75
105x - 85x = 29.75 - 10.75
20x = 19
x = 19/20
x = 0.95
Thus, the cost of a song for member is $0.95
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Suppose Shen is the only seller in the market for bottled water and Manuel is the only buyer. The following lists show the value Manuel places on a bottle of water and the cost Shen incurs to produce each bottle of water:Manuel's Value -------------------------- Shen's CostsValue of first bottle: $7 ------------- Cost of first bottle: $1Value of second bottle: $5 ------- Cost of second bottle: $3Value of third bottle: $3 ------------ Cost of third bottle: $5Value of fourth bottle: $1 ---------- Cost of fourth bottle: $7The following table shows their respective supply and demand schedules:Price ------------ Quantity Supplied --------- Quantity DemandedMore than $7 ----------- 4 ----------------------------- 0$5 to $7 ----------------- 3 ----------------------------- 1$3 to $5 ----------------- 2 ----------------------------- 2$1 to $3 ------------------ 1 ----------------------------- 3$1 or less ---------------- 0 ----------------------------- 4Use Shen's supply schedule and Manuel's demand schedule to find the quantity supplied and quantity demanded at prices of $2, $4, and $6. Enter these values in the following table.Price ----------- Quantity Supplied ---------- Quantity Demanded2 ------------------------- ? ----------------------------- ?4 ------------------------- ? ----------------------------- ?6 ------------------------- ? ----------------------------- ?A price of _____ brings supply and demand into equilibrium.At the equilibrium price, consumer surplus is $___, producer surplus is $___, and total surplus is $___.If Shen produced and Manuel consumed one less bottle of water, total surplus would _____.If instead, Shen produced and Manuel consumed one additional bottle of water, total surplus would _____.
Answers
If Shen produced and Manuel consumed one additional bottle of water, total surplus would be $2
What is the law of Supply and Demand?The law of supply and demand combines two fundamental economic ideas that describe how changes in the price of a resource, commodity, or product affect its supply and demand.
Supply grows as the price rises, but demand drops. In contrast, as the price falls, supply is constrained and demand is increased.
Demand and supply levels for different prices can be displayed as curves on a graph. The intersection of these curves symbolizes the process of price discovery in the marketplace, as it indicates the balance, or market-clearing price, at which demand equals supply.
According to the law of demand, demand for a good or resource will decrease as its price increases and increase as its price decreases.
How to solve?
Price ------ Quantity Supplied ----- Quantity Demanded
2 --------------------- 1 ------------------------- 3
4 --------------------- 2 ------------------------ 2
6 --------------------- 3 ------------------------ 1
4 (quantity supplied = quantity demanded = 2)
4 ($7>$4 and $5>$4, $3<$4<$5, area above price line but under curve if price line was at $4, $7-$4=$3, $5-$4=$1, $3+$1=$4); 4 ($1<$4 and $3<$4, $3<$4<$5, area below price line and under curve if price line at $4, $4-$1=$3, $4-$3=$1, $3+$1=$4); 8 ($4 from consumer surplus + $4 from producer surplus)
fall (equilibrium = 2, 2-1=1, Shen: quantity supplied = 1 -> $2, Manuel: quantity demanded = 1 -> $6, total surplus = producer surplus + consumer surplus = ($4-$1)+($7-$4)=$6, $8>$6)
rise (equilibrium = 2, 2+1=3, Manuel: quantity demanded = 3 -> $2, Shen: quantity supplied = 3 -> $6, total surplus = consumer surplus + producer surplus = ($3-$2)+($7-$6)=$2, $8>$2, $6>$2)
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