Answer:
a. 18 percent
b. $90 billion
Step-by-step explanation:
a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.
First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment
Difference=13%-4%
Difference= 9%
Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.
Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).
Therefore the the size of the GDP gap in percentage-point terms is 18 percent
b. Calculation to determine how much output is forgone because of cyclical unemployment
Forgone Output :
By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,
Hence,
Output forgone = (18/100) ×$500 billion
Output forgone=0.18×$500 billion
Output forgone=$90 billion
Therefore the Forgone Output is $90 billion
Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically.
Answer:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Step-by-step explanation:
Given
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Required
Solve
We have:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Collect like terms
[tex]1.3t^3 + 0.6t^2 + 0.4t^2 - 24t- 18t + 8[/tex]
[tex]1.3t^3 + t^2 -42t + 8[/tex]
So:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Answer:
look at pic
Step-by-step explanation:
What is
4
7
as a decimal rounded to 3 decimal places?
Answer:
4/7 as a decimal is 0.57142857142857.
What is the phase shift of F(x) = 3 sin(2x - 4)?
Answer:
2
Step-by-step explanation:
Use the form asin(bx−c)+d
a=3
b=2
c=4
d=0
Phase Shift: c/b
Phase Shift: 4/2 = 2
What is the answer of this question?
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
Help me with these 3 and explain too thank you :))
Answer:
1) 25
2) 2
3) f(g(1)) = 42
Step-by-step explanation:
1) Given that f(x) = 4x^2 + 9
If x = -2
f(-2) = 4(-2)^2 + 9
f(-2) = 4(4) + 9
f(-2) = 16 + 9
f(-2) = 25
2) Given that f(x) = 4x - 6
y = 4x - 6
Replace y with x
x = 4y - 6
MAke y the subject of the forfmula
4y = x+ 6
y = (x+6)/4
SInce x = 2
f^(-1)(2) = (2+6)/4
f^(-1)(2) = 8/4 = 2
3) If f(x) = 6x and g(x) = x+6
f(g(x)) = f(x+6)
f(x+6) = 6(x+6)
Since x = 1
f(g(1)) = 6(1+6)
f(g(1)) = 6(7)
f(g(1)) = 42
Surface Area of Prisms
Can someone show me how to solve and also what the formula is. Please!
Answer:
400 in.²
Step-by-step explanation:
Surface area of the triangular prism = bh + L(s1 + s2 + s3)
Where,
b = 8 in.
h = 15 in.
s1 = 17 in.
s2 = 15 in.
s3 = 8 in.
L = 7 in.
Plug in the values
S.A = 8*15 + 7(17 + 15 + 8)
S.A = 120 + 7(40)
S.A = 120 + 280
S.A = 400 in.²
help! A new law has support from some Democrats and some Republicans. This two-way frequency table shows the proportion from each political party that does or does not support the new law.
Which conclusions can be made from this table?
Select each correct answer.
For both parties, more members do not support the law than support the law.
Compared to the Republicans, the Democrats have a larger percentage of members who support the law.
More Republicans support than the law than do not support the law.
Among Democrats, a larger percentage do not support the law than support the law.
Support Do not support
Democrat 0.32 0.68
Republican 0.44 0.56
What i can see:
It seems this law isn't particularly majorly favored in either party. In a lot of cases one party will have the majority support and one will have minority support. Although it seems to be more favored amongst democrats.
Like "insert law here" may be more favored by republicans or align more to their usual values.
Another thing is that it seems that it is controversial and a large portion either supports or doesnt support this law in both parties.
Im no master politician ofc but i am interested in politics so, yeah :)
Answer:
Among Democrats, a larger percentage do not support the law than support the law.
For both parties, more members do not support the law than support the law.
Step-by-step explanation:
just finish the test
What is the equation of the line that has a slope of 3 and passes through the point (1, -2)
Answer:
y= 3x -5
Step-by-step explanation:
The equation of a line can be written in the slope- intercept form, y= mx +c (where m is the slope and c is the y- intercept).
Given that the slope is 3, m= 3. Substitute m= 3 into the equation.
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 1, y= -2,
-2= 3(1) +c
-2= 3 +c
c= -2 -3
c= -5
Thus the equation if the line is y= 3x -5.
Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla opuesta es de 25.2°. Calcular el ancho del río
Answer:
El ancho del río es 59.9 metros.
Step-by-step explanation:
El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:
[tex]tan(\theta) = \frac{CO}{CA}[/tex]
En donde:
CA: es el cateto adyacente = Altura de la torre = 28.2 m
CO: es el cateto opuesto = ancho del río =?
θ: es el ángulo adyacente a CA
Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:
[tex]\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}[/tex]
Ahora, el ancho del río es:
[tex]CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m[/tex]
Por lo tanto, el ancho del río es 59.9 metros.
Espero que te sea de utilidad!
SOMEONE PLEASE HELPPPPPPPPPP
Answer:
the formula for the volume of a square pyramid is V=a^2*h/3
so if we just put in the data
12^2*10/3
144*10/3
480
so the answer is B
Hope This Helps!!!
A) { -3 , -1 , 1, 3 , 6 }
B) { 3, -1 , 2, 0, -2}
C) all real numbers
D) {3,-2,-1,0,1,2,3,4,5,6,7,8}
Given the roll of paper towels below how much plastic would be needed to cover the role so it can be sold given the diameter of the role is 10 inches and the height is 13 inches
Answer:
Amount of plastic need to cover paper role = 565.2 inches
Step-by-step explanation:
Given:
Diameter of paper role = 10 inch
Height of paper role = 13 inch
Find:
Amount of plastic need to cover paper role
Computation:
Radius of paper role = Diameter of paper role / 2
Radius of paper role = 10 / 2
Radius of paper role = 5 inch
Amount of plastic need to cover paper role = Total surface area of cylinder
Amount of plastic need to cover paper role = 2πr(h+r)
Amount of plastic need to cover paper role = 2(3.14)(5)(13+5)
Amount of plastic need to cover paper role = (3.14)(10)(18)
Amount of plastic need to cover paper role = 565.2 inches
You're working as a floor rep in the local home improvement store. The store wants to increase its inventory. Last year, 40 lawn mowers cost $4,776. At the same cost, how much will 120 lawn mowers cost this year?
On Monday, 405 students went on a trip to the zoo. All 7 buses were filled and 6 students had to travel in cars. How many students were in each bus
Answer:
57 students
Step-by-step explanation:
Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.
Then, divide that by 7, and you get the answer. 57.
Hope it helps!
Answer:
57 students
Step-by-step explanation:
405-6=399
399÷7=57
Help! Can you please help
Answer:
14)= 2/3/23 × 1/9/14
= 49/23 × 23/14 = 3/1/2
U CAN USE A CALCULATOR to find the rest......If u have one....
Step-by-step explanation:
11. 1.8
12. 22.6
13. 1.66
14. 3.5
Alexandra finished 3/5th of her work. What percentage of work did she complete?
60 percent
Step-by-step explanation:
Covert 3/5th into percentage so the answer will be 60.
#CarryOnLearningIn which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
What is the measure of Arc E B C?
(100 points)
1.One of the addends of 17,300 is 11,210. What is the other addend?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
2. If one of the factors of 954 is 318 , what is the other factor?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
3. HEector bought seven bokes of fruit. Each boc contained 24 fruit. How much fruit did Hector buy?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
Answer:
1a. The other addend of 17,300
1b. 17,300 and 11,210
1c. 17,300-11,210
1d. 17,300-11,210= 6090
1e. 6090
2a. The other factor of 954
2b. 954 and 318
2c. 954-318
2d. 954-318= 636
2e. 636
3a. The total amount of fruit Hector bought.
3b. 7 and 24
3c. 7 x 24
3d. 7 x 24 = 168
3e. 168 fruits
Out of the 30 days in June, you run 13 days and swim 6 days. You lift weights 7 days
and ride a bike 4 days. If you make a pie chart to show this data, how many degrees
of the circle should represent swimming?
9514 1404 393
Answer:
72°
Step-by-step explanation:
In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.
(6 swim days)/(30 days) = (swim pie angle)/(360°)
Multiply by 360° to find ...
swim pie angle = (360°)(6/30) = 72°
72° of the circle should represent swimming.
Determine the area of the triangle.
223.6 square units
248.7 square units
447.1 square units
458.4 square units
Answer:
223.6 square units. or 223.569 square units
Answer:A
Step-by-step explanation:I took the test
Graph the solution of the inequality 3/7(35x-14)<_ 21x/2+3
Answer:
You'll have a closed circle at x = 2, and shading to the left
See the diagram below
=========================================================
Explanation:
The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.
If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.
14*(3/7) = (14*3)/7 = 42/7 = 814*(21/2) = (14*21)/2 = 294/2 = 147So if we multiplied both sides by 14, then we have these steps
[tex]\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\[/tex]
--------------------------
Let's isolate x
[tex]6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\[/tex]
The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.
So either x = 2 or x < 2.
If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).
See the diagram below.
Consider the line 4x + 8y = -4.
a) What is the slope of a line perpendicular to this line?
b) What is the slope of a line parallel to this line?
is (12, 4), (36, 12), (-6, -2), (21, 7) directly proportional?
Answer:
I think yes
Step-by-step explanation:
12/4=3
36/12=3
-6/-2=3
and so on
A square has a perimeter of 36 cm.
What is the length of each side?
Answer:
Step-by-step explanation:
The perimeter of a square has a formula P = s + s + s + s or just P = 4s where s is the length of a side. If this perimeter has a number value, we can plug it in and solve for the length of each side, like this:
36 = 4s so
s = 9 cm. And there you go!
I need help on my math!!!!!!!
Answer:
67
Step-by-step explanation:
GOOD LUCK!!
i13(12)-2give answer
I need help I’m rubbish at maths and I really don’t know
❤️❤️
Answer:
160 cm³
Step-by-step explanation:
→ Write down the formula for the volume
Length × Width × Height
→ Find each value
Length = 4, Width = 4 and Height = 10
→ Substitute into formula
4 × 4 × 10 = 160 cm³
Rewrite this function in equivalent forms to identify the key features of the quadratic function it models.
f(x) = 2x2 - 40 - 6
Type the correct answer in each box.
Key features:
y-intercept: 0,
axis of symmetry: z =
vertex: OD
x-intercepts: (-1,0) and ((,)
Answer:
y int = -6
x = 1 axis symmetry
vertex : (1,-8)
x int: (3,0),(-1,0)
Step-by-step explanation:
The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise money for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.
Answer: [tex]6\sqrt{5}[/tex] miles
This is the same as writing 6*sqrt(5) miles
==========================================================
Work Shown:
P = park
C = city hall
Point P is at the location (10,11)
Point C is at the location (7,5)
Apply the distance formula to find the length of segment PC
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\[/tex]
The exact distance between the park (P) and city hall (C) is [tex]3\sqrt{5}[/tex] miles.
This doubles to [tex]2*3\sqrt{5} = 6\sqrt{5}[/tex] miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.
Extra info:
[tex]6\sqrt{5} \approx 13.41641[/tex] so the runner travels a total distance of roughly 13.4 miles.
