An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Answers
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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Related Questions
convert an effective rate of 14,5% per annum, to a nominal rate per annum compounded half yearly
Answers
The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.
To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:
Nominal rate \(= (1 + r/m)^m - 1\)
Where:
r = effective rate
m = number of compounding periods per year
In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.
Since compounding is done semi-annually, m would be 2.
Plugging in the values:
Nominal rate \(= (1 + 0.145/2)^2 - 1\)
Simplifying the expression inside the parentheses:
Nominal rate \(= (1 + 0.0725)^2 - 1\)
Calculating the exponent:
Nominal rate \(= (1.0725)^2-1\)
Performing the calculations:
Nominal rate = 1.14900625 - 1
Nominal rate = 0.14900625
Converting the nominal rate to a percentage:
Nominal rate = 14.900625%
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Find the missing length of each triangle and round to the nearest tenth.
Answers
Answer: 5 inches
Step-by-step explanation: We must use the Pythagorean theorem to solve this. Since the hypotenuse is always opposite of the right angle, we know that the hypotenuse is 13 and we can substitute the values into this formula: a^2 + b^2 = c^2
12^2 + b^2 = 13^2
144 + b^2 = 169
169 - 144 = 25 (this is b^2)
\(\sqrt{25}\) = 5
Thus, the value of x is 5 inches.
Would appreciate brainliest <3
Translate this sentence into an equation. The product of Mabel's age and 4 is 56. Use the variable m to represent Mabel's age.
Answers
Answer:
4m = 56
Step-by-step explanation:
4 * m = 56
4m = 56
4/4m = 56/4
m = 14
find the area of this.
Answers
Answer:
it's all close and fuzzy
Which equation represents the vertical line passing through (7,-3)?
A
X=-3
B. y=-3
C.
x=7
D.y= 7
Answers
Answer:
a
Step-by-step explanation:
(0,-3)
-3 x axis form a vertical line
Answer:
c. x=7
Step-by-step explanation:
Show the work for the answer
x=³√27
x = 3
Answers
Answer:
x = 3
Step-by-step explanation:
Given that,
\(x=\sqrt[3]{27}\)
We need to show work to solve it.
We know that,
27 = 3×3×3
or
27 = (3³)
So,
\(x=\sqrt[3]{3\times 3\times 3}\\\\=(3^3)^{\dfrac{1}{3}}\\\\x=3\)
Hence, this is the required solution.
The measures of three parts of AABC are given in the diagram. What is AC, correct to two decimal places?
Answers
Answer:
Step-by-step explanation:
Use the Law of Sines to find AC:
\(\frac{sin41.82}{3.61}=\frac{sin67.62}{AC}\) and cross multiply to get:
AC*sin41.82 = 3.61*sin67.62
and divide both sides by sin41.82:
\(AC=\frac{3.61sin67.62}{sin41.82}\) to find that
AC = 5.01 units
Help please!! I’ll give brainliest if you show work as well. Thank you!!!
Answers
Answer:
TWO CRACKERS
Step-by-step explanation:
I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.
Hope this helped
(3, 4, 5, ...} is finite or infinite
Answers
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
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Find the missing values for the exponential function represented by the table below.
Answers
PLEASE HELP! WILL GIVE BRAINLIEST!
1. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on pizza? fill in the blank with the numerical answer only. the family spent $_______ on pizza.
2. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on soda? fill in the blank with the numerical answer only. the family spent $_______ on soda.
3. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend in all? fill in the blank with the numerical answer only. the family spent $_______ in all.
Answers
Answer:
Step-by-step explanation: for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on pizza? fill in the blank with the numerical answer only. the family spent $_______ on pizza.
The family spent 300$ on pizza
Answer:
Answer
Step-by-step explanation:
for pizza: $300.00
for soda: $43.20
In all: 343.20
Which type of sampling method is being employed in the following example?
The principle of Phoenix High School is conducting an in depth study of graduates since
she has been there. Firstm she creates a list of every student that has graduated since
she has been principle and assigns each graduate a number 1 to 1241. She then has a
computer randomly select 40 numbers between 1 and 1241 to determine which
students she will include in her sample.
O Simple Random Sampling
O Stratified Sampling
O Cluster Sampling
O Sampling of Convenience
O Systematic Sampling
Answers
The sampling method used in this problem is classified as:
Simple Random Sampling
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, all the options are assigned a number and then taken, hence a Simple Random Sample is used.
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Choose the inequality that represents the following graph
Answers
Answer:
X ≥ 3 (D)
Step-by-step explanation:
I got it right on Khan Academy :)
I’m a certain magnetic field the cross-sectional area is 0.5 meter square and the flux is 1500 uwb what is the flux density
Answers
The flux density is 3000 uT.
Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.
Hοw tο calculate flux density fοr the given prοblem?It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.
The flux density (B) can be calculated using the fοrmula:
B = Φ / A
where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.
Plugging in the values given, we get:
B = 1500 uWb / 0.5 m²
B = 3000 uT (micrοtesla)
Therefοre, the flux density is 3000 uT.
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I really need help on this and I would really appreciate if anyone would want to help me please and thank you.
Answers
Given the equation of the parabola:
\(y=x^2+6x-12\)To find the vertex of the parabola,
we will substitute with the value (-b/2a) into the function y
\(\begin{gathered} a=1 \\ b=6 \\ c=-12 \\ \\ x=-\frac{b}{2a}=-\frac{6}{2\cdot1}=-3 \\ y=(-3)^2+6\cdot-3-12=9-18-12=-21 \end{gathered}\)so, the coordiantes of the vertex :
x = -3
y = -21
must a function that is decreasing over a given interval always be negative over that same interval?explain.
Answers
Answer:
hijas de usted cómo estás bien
tickets to a movie cost $10.50 for adults and $7.25 for students. you and a few friends purchased 8 tickets for $61.25. how many adult tickets and student tickets were purchased?
Answers
Answer:
1 adult ticket and 7 student tickets were purchased
Step-by-step explanation:
let a represent number of adult tickets purchased and s the number of student tickets purchased, then
a + s = 8 ( subtract s from both sides )
a = 8 - s → (1) ← based on total tickets purchased
10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets
substitute a = 8 - s into (2)
10.5(8 - s) + 7.25s = 61.25
84 - 10.5s + 7.25s = 61.25
84 - 3.25s = 61.25 ( subtract 84 from both sides )
- 3.25s = - 22.75 ( divide both sides by - 3.25 )
s = 7
substitute s = 7 into (1)
a = 8 - 7 = 1
that is 1 adult ticket and 7 student tickets were purchased
if a1 = 6 and an = na(n-1) + 2 then find the value of a3
Answers
The value of a3 is 30.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
We are given that a_1 = 6 and \(a_n = n_a(n-1) + 2\)
Then Substitute as needed and do the arithmetic;
a_1 = 6
\(a_n = n_a(n-1) + 2\)
\(a_2 = -5a_1 +2 \\a_2= -5(6) +2 =-28\)
\(a_ 3 = -5a_2 +2 = -(-28) +2 = 30\)
The value of a3 is 30.
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A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answers
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Alijah had a taxable income of $8450 and filed his federal income tax return with the Single filing status. Using the table below, find the amount he has to pay in taxes.
Single
Taxable income is over
8.350
33 950
82.750
171.550
372,950
But nat over
8,350
33.950
82,250
171.550
372.550
The tax is
Plus
50.00
835.00
4 675.00
16.750.00
41,754.00
108,216.00
10%
15%
25%
20%
33%
35%
Of the
amount over
50
8.350
33.950
82,250
171.550
372,850
O A. $835.00
• B. $850.00
O c. $2087.50
O D. $1252.50
Answers
Answer:
Step-by-step explanation:
67
Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.
Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.
This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.
He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.
Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.
Thus, looking at the provided options, option B ($850.00) would be the correct answer.
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How do I use the graph to evaluate the expression
Answers
Answer:
\((g\circ f)(-2)=1.5\)Step-by-step explanation:
We have that:
\((g\circ f)(-2)=g(f(-2))\)Which means that we first have to find f(-2), and the evaluate the result in g.
Let's take a look at the plot of f(x) to find f(-2):
This way, we can conlcude that:
\(f(-2)=-3\)Now, let's take a look at the plot of g(x) to find g(-3):
This way, we can conclude that:
\(g(-3)=1.5\)Therefore, we can conclude that:
\((g\circ f)(-2)=1.5\)
Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83
Answers
Answer:
S₂₇ = 1188
Step-by-step explanation:
using the given formula for \(S_{n}\) , that is
\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )
with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then
S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188
Calculate the sector area: 16 in 90°
Answers
Therefore , the solution of the given problem of area comes out to be
r = 8.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Here,
A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as
Sector Size/Sector Area = Circle Area/360
16 ft2/90 = n/360
(360) (16 ft2)/90 = n
(4)(16 ft2) = n
The total size of the circle is n = 64 ft2.
Since Area of a Circle equals r2,
∏r2 = 64
r2 = 64/∏
r = √(64/∏)
We multiply by / to get by rationalizing the denominator.
r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of
r = √(64∏)/∏
r = 8
Therefore , the solution of the given problem of area comes out to be
r = 8.
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A boardwalk game of chance costs $1 to play. You have a 25% chance of winning $1 back, a 20% chance of winning $2
(your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). What is the expected value of playing
the game if you lose your bet 45% of the time?
A. -$1.00
B. -$0.25
C.-$0.15
D. $0.15
Answers
Answer:
the answer is c
Step-by-step explanation:
x+4=−14 x= ........................................................................
Answers
Answer: -18
Step-by-step explanation:
Graph the equation
3x + 4y = 12
6
5
4
d
3
2
1
-7-6
-5 4 3 -2 -1
3
4
5
6
7
-2.
-3
4
-6
Clear All Draw
Answers
There ya go, good luck,,,,
Evaluate the function f(x) = -212-3x + 5 for the input value-3.
Answers
Answer:
f(-3)=-198
Step-by-step explanation:
Function: f(x) = -212-3x + 5
x=-3
First substitute -3 for x:
f(-3)=-212-3(-3)+5
Next multiply -3 by -3:
-3*-3=9
f(-3)=-212+9+5
-212+9=-203
f(-3)=-203+5
-203+5=-198
f(-3)=-198
I hope this helped you.
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PLS HELP IVE BEEN ASKING FOR 3 1/2 DAYS IM ABOUT TO FAIL 7th GRADE ITS OVERDUE WILL GIVE BRAINLIEST IF YOU ANSWER THIS TYSM
Answers
Answer:18 days
Step-by-step explanation:
Answer:
18 days to consume the apple
Step-by-step explanation: 18 because it takes 3 days for a half so six days equals 1 whole apple multiply that by 3 an you'll get 18
-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
Answers
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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quadrilateral ABCD is a rhombus. if the measure of ADC equals 60°, then the measure pf EDC equals?
Answers
Answer:
60 divided by 2 = 30
We half it because Angle E halfs Angle D
Step-by-step explanation:
As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, the angles of opposite pairs of vertices are equal, and the sum of the angles of two adjacent vertices is 180 degrees.