Suppose that the natural rate of unemployment in a particular year is 4 percent and the actual unemployment rate is 13 percent. Instructions: Enter your answers as a whole number. a. Use Okun's law to determine the size of the GDP gap in percentage-point terms. percent b. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment? $ billion

Answer:

Two consecutive even terms and LCM = 180

Let’s assume the two terms:

1st term : 2x

2nd term : 2x + 2

There is a rule which states that

If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.

i.e,

a∗b=HCF∗LCM  - (i)

We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.

i.e.,

HCF of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)

Therefore,

from (i) and (ii),

2x∗(2x+2)=  HCF * LCM

2x∗(2x+2)=2∗180  

x∗(2x+2)=180  

2x2+2x−180=0  

Solving the quadratic equation we get,

x=9,−10 (we discard -10 since it is negative)

Therefore, the numbers are

2∗9=18  (1st no.)

2∗9+2=18+2=20  (2nd no.)

Answer :  18,20

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

They got 3x-12 because they took

3(x - 4)

and they distrubuted the 3 to the numbers in parenthesis,

how they did this was they multiplied 3 by x and got 3x then they kept the subtraction sign that is in the parenthesis. Then they multiplied 3 by the 4 and got 12.

then the equation was 3x - 12/2 = 6

Answer:

x=8

Step-by-step explanation:

[tex] \frac{3(x - 4)}{2} = 6[/tex]

Multiply 3 by what's in the bracket

[tex] \frac{3x - 12}{2} = 6[/tex]

Multiply through by the LCM of all the denominators

[tex] \frac{2(3x - 12)}{2} = 2 \times 6[/tex]

=The numerator 2 will cancel the denominator 2

[tex]3x - 12 = 12[/tex]

Grouping like terms

[tex]3x = 12 + 12[/tex]

Dividing both sides by 3

[tex] \frac{3x}{3 } = \frac{24}{3} [/tex]

[tex]x = 8[/tex]

Answer:

Hello,

Step-by-step explanation:

[tex]1.272727....=1.\overline{27}\\\\=1+\dfrac{27}{99} \\\\=1+\dfrac{3}{11} \\\\=\dfrac{11+3}{11} \\\\=\dfrac{14}{11} \\[/tex]

One other way:

Let say x=1.272727...

100x=127.272727...

x=1.272727...

99x=126

x=126/99

x=14/11

Answer:

I assume that the function is:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

Now let's describe the general transformations that we need to use in this problem.

Reflection across the x-axis:

For a general function f(x), a reflection across the x-axis is written as:

g(x) = -f(x)

Reflection across the y-axis:

For a general function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

Then a reflection across the y-axis, and then a reflection across the x-axis is just:

g(x) = -(f(-x)) = -f(-x)

In this case, we have:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

then:

[tex]g(x) = -f(-x) = -\frac{1}{4}*8^{-x}[/tex]

Now we can graph this, to get the graph you can see below:

Some of the sub-questions have been answered. I will provide explanation to the already answered questions and then answer the unanswered parts

1. The graph type

The three graph displayed are stem-and-leaf plots. The single numbers at the left-hand side are referred to as the stem, while the numbers at the right are called leaves.

2. The type of data

The three graphs display numerical data (i.e. numbers). Hence, the data are quantitative

3. The correct graph

To know the correct graph; the leaves on each line must be in ascending order and the delimiter to use is a blank space.

Only graph A obey the above illustration

4. Skewness

In graph A, the length of the leaves increases as we move from one stem to the other. This means that the graph is negatively skewed.

For a negative skewed stem plot, the mean is less than the median

5. The population size

This means that we count the number of leaves in the stem plot

The leaves are:

[tex]Leaves = \{0,8,4,8,0,4,6,2,2,2,6,6,6,0,0,0,0,2,4\}[/tex]

So, the population size is: 19

6. The data set

To do this, we include the stem to the corresponding leaves.

So, we have:

[tex]Dataset= \{50,58,64,68,70,74,76,82,82,82,86,86,86,90,90,90,90,92,94\}[/tex]

Learn more about stem and leaf plots at:

https://brainly.com/question/22141441

Answer:

mate....where is red shaded region....

probably this will help ..... ;)

find the probability that a randomly selected point within the circle falls in the red shaded area

https://brainly.com/question/14113463?utm_source=android&utm_medium=share&utm_campaign=question

Answer:

y=3x

Step-by-step explanation:

The equation of the line is y=3x

Answer:

Step-by-step explanation:

1. arc length

2. semicircle

3. minor arc

4. arc measure

5. circumference

6. radius

7. diameter

HOPE THIS HELPS

Answer:arc length

2. semicircle

3. minor arc

4. arc measure

5. circumference

6. radius

7. diameter

Step-by-step explanation:

Answer:

225 degrees

Step-by-step explanation:

Given the following data;

To find the angle in degrees subtended by an arc;

Mathematically, the length of the arc of a circle is given by the formula;

S = rA

Where;

Substituting the values into the formula, we have;

22 = 5.6 * A

[tex] A = \frac {22}{5.6} [/tex]

A = 3.9286 radians.

Next, we would convert the value of the angle in radians to degrees;

Conversion:

[tex] 1 \; radian = \frac {180}{\pi} \; degrees [/tex]

[tex] 3.9286 \; radians = X \; degrees [/tex]

Cross-multiplying, we have;

[tex] X = \frac {180}{\frac {22}{7}} * 3.9286 [/tex]

[tex] X = \frac {180 * 7}{22} * 3.9286 [/tex]

[tex] X = \frac {1260}{22} * 3.9286 [/tex]

[tex] X = 57.2727 * 3.9286 [/tex]

X = 225.0015 ≈ 225 degrees

Answer:

2(4)^-2

=2/4^2

2/16

1/8

thanks

Answer:

f(- 2) = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

To find f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = 2 [tex](4)^{-2}[/tex] = 2 × [tex]\frac{1}{4^2}[/tex] = 2 × [tex]\frac{1}{16}[/tex] = [tex]\frac{2}{16}[/tex] = [tex]\frac{1}{8}[/tex]

Answers:

=====================================================

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that [tex]-4 < x \le 3[/tex]. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval [tex]-4 < x \le 3[/tex] then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

--------------------------------------------------

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is [tex]-5 < y \le 5[/tex]. This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

Answer:

Hello,

Step-by-step explanation:

Domain(f)= ]-4;3]={x€R | -4<x≤3}

Rang(f)=]-5;5]={y€R | -5< y ≤5}

Step-by-step explanation:

see the answer in attached picture

pls mark me as brainliest pls

Answer:

If two machine works together it takes 180 minute to complete 6480 shirts

Step-by-step explanation:

2400 ÷ 150 = 6

So here,

1st machine produces 20 shirts per minutes

let, x=minutes for shirt's production

Now,

(16+20)x=6480

36x=6480

x=6480/36

Therefor, x=180 minutes

Answer:

1. -4

2. 8/ 5 - 1. 6

Step-by-step explanation:

1 . 3 × -4  

    = (-12)

2. 2/5 × 4

  = 8 / 5

  = 1.6

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

See explanation

Step-by-step explanation:

Maximum weight = 20 kg

Bag 1 = 3.5kg

Bag 2 = 15 kg

Bag 3 = 2kg

Bag 4 = 1.5kg

Total weight of bags = 22 kg

Excess weight of his luggage = Total weight of bags - Maximum weight

= 22 kg - 20 kg

= 2 kg

Express the excess weight as a percentage of his maximum weight allowed = excess weight / maximum weight × 100

= 2/20 × 100

= 0.1 × 100

= 10%

Express the excess weight as a percentage of his maximum weight allowed = 10%

Answer:

1st option, p and q are both negated

Question:- Find

[tex]\left(\frac{5}{12}\right)^{4}\left(\frac{12}{15}\right)^{3}[/tex]

Answer:-

[tex]\left(\frac{5}{12}\right)^{4}\left(\frac{12}{15}\right)^{3}[/tex]

Taking power inside the bracket

[tex] \frac{5^{4} }{ {12}^{4} } \times \frac{ {12}^{3} }{ {15}^{3} } [/tex]

[tex] \frac{ {5}^{4} }{ {12}^{4 - 3} } \times \frac{1}{ {(5 \times 3)}^{3} } \\ \frac{ {5}^{4} }{12} \times \frac{1}{ {5}^{ 3 } \times {3}^{3} } \\ \frac{ {5}^{4 - 3} }{12 \times {3}^{3} } \\ \frac{5}{4 \times 3 \times {3}^{3} } \\ \frac{5}{4 \times {3}^{4} } = \frac{5}{4\times81 } \\ Answer-> \frac{5}{324} [/tex]

[tex]Power\:Form-> \frac{ 5 }{12 \times {3}^{3} } [/tex]

Answer:

40

Step-by-step explanation:

So square A has a side of 4, therefore its area is 16 because you square the side length.

Square B has a side of 2 times Square A's side. So Square B has sidelength 8 as 4*2 = 8.

If Square B has side length 8, it has an area of 64.

The average is found by adding the two area and then dividing by 2. So,

64 + 16 = 80

80/2 = 40

Answer:

B

Step-by-step explanation:

The angle in a semicircle is 90° , then

x = 180° - (90 + 47) = 180° - 137° = 43° → B

Answer:

B. 43

Step-by-step explanation:

ignore the other triangle with the y angle. it is just there to confuse us.

the main information is given already by the main triangle with the angles x and 47 degrees.

because it's baseline is the diameter of a circle, and its top point is also on the circumference of the same circle.

all triangles that can be inscribed into a circle that way are by definition right-angled triangles.

so, the angle at the top point is actually 90 degrees.

and as we know, the sum of all angles in a triangle is always 180 degrees, we can simply calculate :

180 = 90 + 47 + x = 137 + x

x = 43 degrees

that's it.

please mark this answer as brainlist

Answer:

25

Step-by-step explanation:

(-5)^2

(-5)*(-5)

25

Answer:

25

Step-by-step explanation:

(-5)^2 = 25, since -5 x -5 is 25.

Now, if the -5 hadn't been in parenthesis, -5^2 would be read as -(5 x 5), and would equal -25.

Brainliest, please! I'm so close to becoming an Expert!

Answer:

kslskd बोडलालामसूनिविवल

Step-by-step explanation:

sin/cos=tan theta.It is the value of the safety angle

Step-by-step explanation:

1+6k=25

collect like terms

1-25=6k

-24=6k

divide both sides by 6

-4=k

;- k= -4

In this question, an amount is divided between three parts. From this, relations between the variables are used to find the amount corresponding to each part.

Sum of 1110 between A, B and C:

This means that:

[tex]A + B + C = 1110[/tex]

For every rs 8 given to A,B may get Rs 5

This means that:

[tex]\frac{A}{B} = \frac{8}{5}[/tex]

And thus:

[tex]5A = 8B[/tex]

[tex]A = \frac{8B}{5}[/tex]

For every Rs 7 given to B ,C may get rs 4​

This means that:

[tex]\frac{B}{C} = \frac{7}{4}[/tex]

And thus:

[tex]7C = 4B[/tex]

[tex]C = \frac{4B}{7}[/tex]

Amount of B:

Replacing into the original equation:

[tex]A + B + C = 1110[/tex]

[tex]\frac{8B}{5} + B + \frac{4B}{7} = 1110[/tex]

[tex]\frac{56B + 35B + 20B}{35} = 1110[/tex]

[tex]111B = 1110*35[/tex]

[tex]B = \frac{1110*35}{111}[/tex]

[tex]B = 350[/tex]

Amounts of A and C:

A and C are given as functions of B, so:

[tex]A = \frac{8B}{5} = \frac{8*350}{5} = 560[/tex]

[tex]C = \frac{4B}{7} = \frac{4*350}{7} = 200[/tex]

Thus:

The amount given to A is of Rs 560, to B is of Rs 350 and to C is of Rs 200.

For another problem involving divisions given ratios, you can check https://brainly.com/question/23857756.

A, B and C receive RS. 560, RS. 350 and RS. 200, respectively.

In this problem, we must translate the sentences into mathematical expression. Please notice that systems of linear equations are resoluble if the number of formulas equals the number of variables. In other words, we must have three linear equations for three variables:

1) Divide a sum of RS 1110 between A, B, C:

[tex]a + b + c = 1110[/tex] (1) Var: 3, Eqs: 1  

2) So that for every RS 8 give to A, B may get RS 5:

[tex]\frac{a}{b} = \frac{8}{5}[/tex]

[tex]5\cdot a - 8\cdot b = 0[/tex] (2) Var: 3, Eqs: 2

3) And for every RS 7 given to B, C may get RS 4:

[tex]\frac{b}{c} = \frac{7}{4}[/tex]

[tex]4\cdot b -7\cdot c = 0[/tex] (3) Var: 3, Eqs: 3

Now we solve the resulting system, the solution set of the system is:

[tex]a= 560[/tex], [tex]b = 350[/tex], [tex]c = 200[/tex]

A, B and C receive RS. 560, RS. 350 and RS. 200, respectively.

Answer:

y: 1, -3, -7, -11, -15

Step-by-step explanation:

Substitute the value of x in the chart for the formula given:

y = -4x + 1

For the first column in the x-row, do the following

y = -4(0) + 1

y = 1

And...

y = -4(1) + 1

y = -3

And so on.

Answer: 133,827 lb/ft^3

Step-by-step explanation:

V = (4/3) (3.14)(8^3) = 133,827

Answer:

True

Step-by-step explanation:

Office resources can be defined as all those means, facilities or equipments, including manpower that are utilized in the operation of various office procedures on a daily basis. Thus, office resources comprises means of communication, means of transportation, manpower (workers or employees), furniture, computer, etc.

Basically, the proper and efficient utilization of office resources determine the level of success that would be achieved in any office.

In Business management, office resources are generally grouped into five (5) main categories and these include;

I. Communication.

II. Transportation.

III. Material and office supplies.

IV. Sources of income (finance).

V. Manpower (human resources).

Manpower is also referred to as human resources or office personnels and it can be defined as the total number of people working from the lower hierarchy to top hierarchy of an organization, engaged in various jobs or tasks at different levels.

Basically, manpower is considered to be the most important type of office resources because it is vital for achieving the organizational goal.

This ultimately implies that, the most valuable assets of an organization is its qualitative manpower because it comprises human competence, skills and knowledge.