Suppose that the economy is experiencing a recession with an estimated recessionary gap of $10 billion. Congress is considering the use of fiscal policy to ease the recession, but due to current political sentiments, it has determined that the maximum spending increase the government is willing to support is $3 billion. It wants to make up the remainder of the recessionary gap using tax cuts.
If a spending increase of $3 billion is approved and the MPC is 0.6, by how much will taxes need to be reduced to close the remainder of the recessionary gap?
Answer:
4.66 billion
Step-by-step explanation:
arange the number line in the following spending order 20,-40,5-1,10
What postulate proves the two triangles are congruent?
Answer:
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent
Step-by-step explanation:
I'm not sure the answer
Find the value of x.
Find the value of y.
Y
61
X
Answer:
61=x ( vertical opposite angle)
61=y (corresponding angle)
Step-by-step explanation:
y = 61°( corresponding angles)
x = y = 61°(vertically opposite angles)
A park shaped like a rectangle. The diagram shows the how the park is split into a sports field and a playground. Let x represent the length in meters of the sports field. Write an expression to represent the area of the park as the sum of the areas of the sports field and the playground.
Answer:
20r + 310
Step-by-step explanation
For the first part.
The required expression is 20x + 310 which represents the area of the park as the sum of the areas of the sports field and the playground.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Let x represent the length in meters of the sports field.
Here, the area of the sports field = 20 × x = 20x units
And, the area of the playground = 15.5 × 20 = 310 units
Now, the required expression to represent the area of the park will be :
⇒ area of the sports field + area of the playground
⇒ 20x + 310
Thus, the required expression is 20x + 310.
Learn more about Expressions here :
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What is 3250 divided by 1/2
Answer:
6500
Step-by-step explanation:
KCF
3250/1 ÷ 1/2
3250/1 x 2/1
3250 x 2= 6500
1 x 1 = 1
final answer 6500/1 or 6500
Write an equation of the line that passes through (-1,3) and is parallel to the line y=2x+2
Answer:
The new line will be parallel to the line represented by y =2x +2
The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope. So the slope of this line is 2. A line parallel to y = 2x + 2 will have the same slope. This means the slope of the new line will also be 2.
To determine the equation of the new line, we can use the given point to find the y intercept of the new line:
y = 2x + b
Use x = -1 and y =3 to find b (or the y intercept ) of the new line:
3 = 2 * (-1) + b
3= -2 + b
b=5
Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be: y = 2x + 5
(Hope it can help)
Answer:
y=2x+5
Step-by-step explanation:
hope you understood
Monthly, Juan's net earnings are $6,000, and expenses are $5,000. If Juan saves the difference, how much will Juan have saved after 6 years
Answer:
$72,000
Step-by-step explanation:
6000-5000=1000
1000x6 =6000
6000x12=72,000
Mr. Williams drove 440 miles in 8 hours, on the highway, at a steady speed. How far could he drive in five hours at the same average speed?
Answer:
275 miles
Step-by-step explanation:
A hot air balloon is rising at a speed of 100 m/min. If an observer is standing 200 m from the lift-off point, what is the rate of change of the angle of elevation of the observer’s line of sight when the balloon is 600 m high?
Answer:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
Step-by-step explanation:
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Let θ be the angle of elevation of the line of sight from the horizontal. Since the hot air balloon is rising at a speed of 100 m/min, its vertical distance in time, t is d = vt = 100t.
Since the point of the observer is 200 m away( the horizontal distance), then tanθ = vertical rise/horizontal distance = 100t/200 = t/2
tanθ = t/2
To find the rate of change of the angle of elevation, we differentiate with respect to t.
So, dtanθ/dt = d(t/2)/dt
sec²θdθ/dt = 1/2
dθ/dt = 1/(2sec²θ)
At 600 m high, tanθ = vertical rise/horizontal distance = 600 m/200 m = 3
Given that tan²θ + 1 = sec²θ
dθ/dt = 1/(2sec²θ)
dθ/dt = 1/(2[tan²θ + 1])
Since tanθ = 3
dθ/dt = 1/(2[tan²θ + 1])
dθ/dt = 1/(2[3² + 1])
dθ/dt = 1/(2[9 + 1])
dθ/dt = 1/(2[10])
dθ/dt = 1/20
dθ/dt = 0.05 rad/min
So, the rate of change of the angle of elevation of the observer’s line of sight when the balloon is 600 m high is 0.05 rad/min.Learn more about rate of change of angle of elevation here:
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AB×6=BBB (playing with numbers.)
Answer:
A = 7
B = 4
Step-by-step explanation:
If u wanna know how i got this answer plz look at the comments below since it will delete my answer U-U
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
18 cm
30 cm
24 cm
22 cm
what is one thousandth less than 0.061
Answer:
one thousandth is greater than 0.061
Step-by-step explanation:
Urn 1 contains 4 green and 5 yellow marbles. Urn 2 contains 7 green and 4 yellow marbles. An experiment consists of choosing one of two urns at random then drawing a marble from the chosen urn. Urn 1 is more likely to be chosen than Urn 2 with probability 0.63.
Required:
a. What is the probability that a green marble was chosen?
b. What is the probability that a yellow marble was chosen, if it is known that Urn 2 was chosen?
c. What is the probability that Urn 1 was chosen, if it is known that a yellow marble was drawn?
Answer:
a
[tex]P(N_g) = 0.5155[/tex]
b
[tex]P(K ) = 0.36364[/tex]
c
[tex]P(U1 | N_y ) = 0.7223[/tex]
Step-by-step explanation:
From the question we are told that
The number of green marbles in Urn 1 is [tex]N_g = 4[/tex]
The number of yellow marbles in Urn 1 is [tex]N_y = 5[/tex]
The number of green marbles in Urn 2 is [tex]n_g = 7[/tex]
The number of yellow marbles in Urn 1 is [tex]n_y = 4[/tex]
The probability of choosing Urn 1 is [tex]P(U1) = 0.63[/tex]
The probability of choosing Urn 2 is [tex]P(U2) = 1- 0.63 =0.37[/tex]
Generally the total marble in Urn 1 is
[tex]N_t = N_g +N_y[/tex]
=> [tex]N_t = 4 + 5[/tex]
=> [tex]N_t = 9[/tex]
Generally the total marble in Urn 2 is
[tex]n_t = n_g +n_y[/tex]
=> [tex]n_t = 7+4[/tex]
=> [tex]n_t = 11[/tex]
Generally the probability of choosing green marble is
[tex]P(N_g) = P(U1 ) * \frac{N_g}{N_t} + [P(U2 ) * \frac{n_g}{n_t} ][/tex]
=> [tex]P(N_g) = 0.63 * \frac{4}{9} + [0.37 * \frac{7}{11} ][/tex]
=> [tex]P(N_g) = 0.5155[/tex]
Generally the probability that a yellow marble was chosen, if it is known that Urn 2 was chosen is mathematically represented as
[tex]P(K ) = \frac{n_y}{n_t}[/tex]
=> [tex]P(K ) = \frac{4}{11}[/tex]
=> [tex]P(K ) = 0.36364[/tex]
Generally the probability of choosing yellow marble is
[tex]P(N_y) = P(U1 ) * \frac{N_y}{N_t} + [P(U2 ) * \frac{n_y}{n_t} ][/tex]
=> [tex]P(N_y) = 0.63 * \frac{5}{9} + [0.37 * \frac{4}{11} ][/tex]
=> [tex]P(N_y) = 0.4845[/tex]
Generally the probability that Urn 1 was chosen, if it is known that a yellow marble was drawn is mathematically represented as
[tex]P(U1 | N_y ) = \frac{ P( U1 \ n N_y)}{P(N_y)}[/tex]
=> [tex]P(U1 | N_y ) = \frac{0.63 * [\frac{5}{9} ] }{0.4845 }[/tex]
=> [tex]P(U1 | N_y ) = 0.7223[/tex]
What is the value of square root 30 is between witch two integers
A-4and5
B-5and6
C-6and7
D-7and8
Answer:
b
Step-by-step explanation:
because
A theater has 384 seats. Each row has 16 seats. The area model represents this situation.What is the value of x in the area model? Enter your answer in the box.
Answer:
X = 4 because 20 times 16 is 320 than if you add 4 to the 20 you will get 24. 24 times 16 is 384. BOom thats your answer and i know because i just answered it.
Step-by-step explanation:
Please answer the screenshot I attached below
Answer:
i think the answer is
[tex] \frac{1}{ {x}^{ \frac{4}{3} }} [/tex]
solve this question step by step
Answer:
BE = 49
Step-by-step explanation:
In triangle BDC
65^2=56^2+BD^2
65^2-56^2=BD^2
4225-3136=BD^2
1089=BD^2
33=BD
In triangle FDE
65^2=63^2+DE^2
4225-3969=DE^2
256 = DE^2
16=DE
since ED+DB=BE
THEREFORE
16+33=BE
49=BE
Below are two parallel lines with a third line intersecting them.
Answer:
x = 132
Step-by-step explanation:
180 - 48 = 132
Annalise withdraws $20.50 each day from her account for a week. how can you represent the change in the account for the week
Answer:
you can get some fries and chickent aint enough for me keep it going people
Step-by-step explanation:
Miguel is multiplying 58 by 12.
Answer:
696
Step-by-step explanation:
At a local baseball game, the concession stand has two different meal choices. You can get 7 hotdogs and 5
drinks for $41.00 or you can get 4 hotdogs and 8 drinks for $44.00. If the price of hotdogs and drinks is the
same for each meal, find how much it costs for an individual hotdog and how much it costs for an individual
drink.
per hotdog:
per drink:
Answer:
Each hotdog is $3 and each drink is $4.
Step-by-step explanation:
Let h be the number of hotdogs and d the number of drinks,
7h + 5d = 41
4h + 8d = 44
Let's eliminate h. Multiply the first by 4 and the second by 7.
28h + 20d = 164
28h + 56d = 308
Subtrat the first from the second.
36d = 144
d = 4
Substitute back into one of the equations.
7h + 5(4) = 41
7h + 20 = 41
7h = 21
h = 3
Help me with this please it says how can you isolate the term f/3 in f/3 + 22 = 17
Answer:
Given:[tex]\sf {\dfrac {f}{3}}+22=17 [/tex]
To find:-[tex]\sf {\dfrac {f}{3}}[/tex]
Solution:-First write the equation[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}+22=17 [/tex]
Now take 22 to the other side by which the "+"sign will turn "-".[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=17-22 [/tex]
Simplify[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=-5 [/tex]
[tex]\therefore[/tex][tex]{\underline{\boxed{\bf {\dfrac {f}{3}}=(-5)}}}[/tex]
Answer: Subtract 22 from both sides.
Step-by-step explanation:
f/3 +22 = 17
f/3 +22 -22 = 17 -22 Subtracting the same value from both sides keeps the equation equal.
Then simplify. The +22 and -22= 0 They "cancel" 17-22 = -5
f/3 = -17 f/3 is now isolated-- by itself-- in the equation.
If you had to solve for f, the next step would be to multiply both sides by 3.
A bag contains 5 RED beads, 3 BLUE beads, and 4 GREEN beads. If a single bead is picked at random, what is the probability
Answer:
total number of beads :-
5+3+4=12
probability is :-
number of times a specific outcome has occurred
total number of possible outcomes
red beads - 5/12
blue beads - 3/12
green beads - 4/12
the above given fractions are the probabilities of each color bead.
Step-by-step explanation:
hope this helps, if yes please can u give me a brainly?
i would really apreciate it...
have a great day ahead :)
can i get help here ?
Some algae contains up to 50% oil by weight. How much oil is in a 7.3-ounce sample of this type of algae?
This would help if you could solve anyone.
Answer: 3.65
Step-by-step explanation:
This question is asking basically what is 50% or 1/2 of 7.3.
Let's expand the number 7.3
Then, we end up getting 7.30.
We have to find 1/2 of 7.30.
[tex]\frac{1}{2}[/tex] of 7.30 = [tex]3.65[/tex]
Hope this helps you!
Veronica take 1/3 of an hour to write 1/4 of a page of calligrahpy how long will it take Veronica to write one page
Answer:
b because it takes 1 hour to complete 3/4 of a page so 3/3 = 1 hour 1 1/3 =1 and a third of an hour
Step-by-step explanation:
Each week as part of her workout, Monica walks 0.5 mile, runs 1.6 miles, and then walks 0.75 mile.
How many total miles will Monica walk and run in a year? Reminder: there are 52 weeks in a year.
Enter your answer in the box.
miles
Answer:
-2 or -5
Step-by-step explanation:
( shown in photo below )
9 ⋅ (-.5) what is the answer
Answer:
-45
Step-by-step explanation:
9x5=45, and since there is a negative, you put it before 45.
Hope I helped!
Please mark Brainliest!!!
Helpp meee!?!!!!!
?!!?!
!?!
Answer:
You have to draw we cant draw 4 you sorry i cant help
Step-by-step explanation: