In an economy, the price index in 2006 was 100 and the real gross domestic product (GDP) was $1,000. In 2010, the price index was 110 and the nominal GDP was $2,200. Based on that information, which of the
following can be inferred about the economy's nominal GDP in 2006 and real GDP in 2010?
A. Nominal GDP in 2006 = $2,000; Real GDP in 2010 = $1,000
B. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000
C. Nominal GDP in 2006= $1,100, Real GDP in 2010 = $2,420
D. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,420
E. Nominal GDP in 2006 = $1,100; Real GDP in 2010 = $2,200
Please show your work.

The equation of the line is y = -4x -4.

We need to calculate the line which is parallel to y = -4x +3 and passes through the point (4, -20)

The given equation is y = -4x +3

Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation is -4.

Now, When two lines are parallel to each other, their slopes are equal.

So, the slope of the required equation is -4.

Now, the equation of the line which passes through the points, [tex](x_{1} ,y_{1} )[/tex] and has slope m, is given by

[tex]y - y_{1} = m(x-x_{1} )[/tex]

Putting the values in the general equation, we get,

y - (-20) = -4(x - 4 )

y + 20 = -4x +16

y +4x = 16 -20 = -4

The equation of the line is y = -4x -4.

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The statements that are true according to the equation  h (x) = –3 |x – 1| + 4. are

The graph of the described function is attached

The vertex is marked (1, 4) in the graph

The y intercept is marked (0, 1) in the graph

Also from the equation, the y intercept is solved by

h (x) = –3 |x – 1| + 4

plugging the value of x

h (x) = –3 |0 – 1| + 4

h (x) = –3 |– 1| + 4

removing the modulus sign

h (x) = –3 * 1 + 4

h (x) = –3 + 4

h (x) = 1

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Answer:

1. 4√5

2. 3√5

3. √149

4. √58

Step-by-step explanation:

The Pythagorean theorem states "a^2 + b^2 = c^2",  where "a" and "b" are the legs, while "c" is the hypotenuse.

Knowing this, we can substitute each variable with given values on the triangles

1.  "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"

4^2 + 8^2 = c^2

16 + 64 = c^2

80 = c^2

√80 = c

4√5 = c

2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"

6^2 + 3^2= c^2

36 + 9 = c^2

45 = c^2

√45 = c

3√5 = c

3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"

7^2 + 10^2 = c^2

49 + 100 = c^2

149 = c^2

√149 = c

4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

√58 = c

The best firm for the Appliance manufacturer for the repair work is Firm 2 .

In the question ,

it is given that ,

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .

The acceptable range of the repair time is 50 minutes to 90 minutes.

the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .

the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .

the range is calculated using the formula

Range = Mean ± Standard Deviation

So , for firm 1 ,

the Range = 74 ± 4

= 74 [tex]+[/tex] 4       and      74 - 4

= 78     and   70

the range for firm 2 is

= 72 ± 5.1

= 72 [tex]+[/tex] 5.1      and      72 - 5.1

= 7.1        and       66.9  

The second company has a lower range and it should be preferred .

Therefore ,  The best firm for the Appliance manufacturer for the repair work is Firm 2 .

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Answer:

B

Step-by-step explanation:

OR means that they don't overlap and based on the answer you have in you know how to solve the innequality.

Considering the discrete probability distribution, it is found that:

a) The mean is of: 6.3

b)

The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:

E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:

Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.

The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:

S(X) = sqrt(4.01) = 2.

We have that:

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The point Q'(x, y) = (- 1.5, - 1.5) is located in quadrant III and 3 units away from point Q(x, y) = (1.5, - 1.5).

In this question we find the location of an ordered pair on the coordinate plane and we are asked to find a possible solution that is in quadrant III and three units away from the original point.

A point (x, y) is in the quadrant III if x < 0 and y < 0 and we can determine a resulting point by using the following translation formula:

(x, y) → (x - 3, y)

If we know that (x, y) = (1.5, - 1.5), then the resulting point is:

Q'(x, y) = (1.5, - 1.5) + (- 3, 0)

Q'(x, y) = (- 1.5, - 1.5)

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The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

Given,

Consider the interview of a person is a trial.

Lets consider it success if a person  owns a dog and consequently , a person without a dog will be a failure.'

Let the random variable X represent the number of persons to be interviewed to get 5 dog owner: in other words, to get 5 successors.

Probability of a success in each trial is p = 0.3. Therefore probability of a failure in each trial is q = 1 - p = 0.7 .

Because trials are independent. X has a negative binomial distribution with parameters k = 5, p = 0.3

P(X =x ) = b(x: k, p) = [tex][(x-1)(k-1)] p^kq^r^-^k[/tex]

where, x = k , k + 1 , k + 2......(1)

Now, Lets find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog

Using equation (1), we get:

P(X = 10) = b(10: 5, 0.3)

                = [(10-1) (5 - 1)][tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = [(9)(4)] [tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = 0.05146

Hence, The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

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Answer:

Slope is the same thing as gradient

The formula is

y2-y1/x2-x1

where y2 is =8

y1 is =5

x2 is=-7

x1 is =-4

when we substitute, your answers will be

= -1

Answer:

depends on how you peel it

Step-by-step explanation:

if you peel it with one quick peel, you will have only one

if you do it with 2, you will have 2 peels an so on

The amount of peels will be greater in the bigger potato as compared to the smaller potato.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

There are two potatoes, a small one and a bigger one.

If you peel the bigger one, because of the bigger surface area, you will get more peels as compared to the smaller potato because the surface are is small, and you will get less number of peels.

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There will be 319 boards be required

and the total cost be $223,720.

Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.

Now, we have to find the number of boards needed altogether

So, the area of the ceiling is

Area = 6.8×4.7

Area = 319.6 m²

Now, the area of the board is

Area = 1 m²

So, 319 boards will be required to cover the ceiling.

Now, if one board costs $700 then,

the total cost be

= 700×319.6

= $223,720

Hence, There will be 319 boards be required

and the total cost be $223,720.

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Answer:

45.47368421 (round as much as you need)

Step-by-step explanation:

We can model the equation using G(h) = -19h + 872, where -19 is the rate at which the bucket is emptying and 872 is the amount of gallons the bucket starts with.

Since gallons is the output, we would have 8 = -19h + 872 and we simply need to solve for h

[tex](8 = -19h+872)-872\\\frac{(-864=-19h)}{-19} \\h=45.47368421[/tex]

Answer:

[tex]-\frac{1}{2}(x-1)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{3-1}{1-5}=-\frac{1}{2}[/tex].

Using the point (1,3), the equation is [tex]y-3=\boxed{-\frac{1}{2}(x-1)}[/tex].

Making the subject as x, the expression is x = u/9

The given equation is

9x = u

It can be written as

u = 9x

We need to make x as the subject in the given expression

9x = u

u = 9x

here u is the subject

9x = u

x = u/9

Therefore, making the subject as x, the expression is x = u/9

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Answer:tell me the math soulation first

Step-by-step explanation:

The probability of drawing 2 Diamonds is 1/17.

The probability of drawing 1 diamond and 1 heart is 13/204.

How to find probability for a deck of cards?

According to the given question:

Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.

After the first card is drawn, there are just 12 diamonds left.

So, the probability of drawing the diamond now is 12/51.

The total probability is the product of two probabilities

So, P = 13/52 x 12/51 = 1/4 x 4/17

P = 1/17 ≈ 0.058

So the probability of drawing 2 Diamonds is 1/17.

Similarly, we know probability of getting a diamond in first is 13/52.

Also the probability of drawing a heart from 51 cards is 13/51.

The total probability P = 13/52 x 13/51

P = 1/4 x 13/51

P = 13/204 ≈ 0.063

So the probability of drawing 1 diamond and 1 heart is 13/204.

More likely outcome is the one whose probability is closer to unity. Since 13/204 > 1/17 that is 0.063 > 0.058 therefore drawing a heart and a diamond is a more likely outcome.

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Answer:

They spent a total of 1 and 1/2 hours swimming.

Step-by-step explanation:

It is because 1 1/4 plus 1 1/4 equals 1 2/4 which mean 2/4=1/2 so in total they spent 1 1/2 hours swimming

The coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that the image of the point (-3, -6) under a translation is (-1, -8).

The coordinate by which the first given condition is translated as,

(-3, -6) - (x,y) =  (-1, -8)

(x,y) = (-3, -6) - (-1, -8)

(x,y) =(-3-(-1), -6-(-8)

(x,y) =(-3+1),(-6+8)

(x,y) =(-2,+2)

The coordinates of the image of the point (-9, -3) are under the same translation obtained as,

=(−9,−3)- (-2,+2)

=(-9-(-2) , (-3-(+2))

=(-9+2),(-3-2)

= -7,-5

Thus, the coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).

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The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's say the day spend in Benin, Ghana and Togo are B, G, and T respectively.

As per the given,

B + G + T = 30

Here, 2 ≤ B ≤ 12, G ≤ 13, and T ≤ 9.
(12 - B) + (13 - G) + (9 - T) = -30 + 12 + 13 + 9 = 4

Also, B ≥ 2 or B ≤ -2 ⇒ 12 - B ≤ 12 - 2 = 10

Hence "The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible".

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Answer:$27

Step-by-step explanation:

$33.75/15 = $2.25 per book

12 books x $2.25/book =  $27

[tex]p = \frac{kd^{2}}{u}[/tex] is an equation that expresses the relation.

Directly proportion means if variable x and y varies equally.

Increment of one variable result to another one.

The ratio of these variable remains same throughout.

Inversely proportion means if one variable increases the second one will decreases. It is opposite of directly proportion.

According to the question,

p varies directly. with the square of d and inversely with u

p ∝ d²

p ∝ 1/u

Combining both the equation,

p ∝ d²/u

Putting k as the constant

p = kd²/u is our required equation

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The cost of the tomatoes, in dollars per pound, using proportions, is of:

$0.86 per lb.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.

In this problem, the costs is obtained as follows:

Hence the cost in dollars per kg of the tomatoes is obtained as follows:

1.74 x 1.09 = $1.8966 per kg.

The relationship between kg and pounds is given as follows:

1 kg = 2.20 lb.

Hence the cost is written as follows:

$1.8966 per 2.20 lb.

The cost per pound of the tomatoes is of:

1.8966/2.20 = $0.86 per lb.

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Answer: 114

Step-by-step explanation:

firstly, convert meters to centimeters:

2.5m * 100cm in a meter = 250 cm

let the length of the first shelf equal x:

250 = x + (2x + 18) + (x - 12) + (x + 4)

combine like terms:

250 = 5x + ( 18 - 12 + 4) = 5x +10

subtract 10 from both sides:

240 = 5x, then solve for x

240/5 = x

x = 48 cm

the length of the second shelf was 2x + 18, so plug in 48 for x:

2(48) + 18 = 114

Answer:

114 [cm].

Step-by-step explanation:

1) if the length of the 1st shelf is 'x', then

2) the length of the 2d shelf is '2x+18', the 3d shelf is 'x-12' and the 4th shelf is 'x+4';

3) the sum of the all 4 shelves is 250 [cm], then it is possible to make up the equation:

x+(2x+18)+(x-12)+(x+4)=250;

4) the root of the equation above is x=48, then

5) the required length of the 2d shelf is 2*48+18=114 [cm].

The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

Given that,

All real numbers x are defined by the functions f and g.

f(x)=3x+6

g(x)=x-5

We have to find the expression

(f+g)(x), (f-g)(x) and (f.g)(3)

Take the functions,

f(x)=3x+6

g(x)=x-5

Now, First

(f+g)(x)

f(x)+g(x)           (Substitute in the place of f and g functions)

Which is

3x+6+x-5

4x+1

(f+g)(x)=4x+1

Now, second

(f-g)(x)

f(x)-g(x)

Which is

3x+6-(x-5)

3x+6-x+5

2x+11

(f-g)(x)=2x+11

Now, third

(f.g)(3)

f(3)×g(3)

Which is

(3(3)+6)×((3)-5)

(9+6)×(3-5)

15×-2

-30

(f.g)(3)=-30

Therefore, The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

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Answer:

y=12

x=34

Step-by-step explanation:

x+y=46

3y-2=x

(3y-2)+y=46

4y-2=46

   +2.  +2

4y=48

/4.  /4

y=12

x+12=46

 -12.  -12

X=34

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Answer:

sada

Step-by-step explanation:

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The amount that each student will have to raise on average in order to meet the goal would be $40

First, find the remaining amount that the members of the Westview Journalism Club are trying to raise:
= Amount to raise - Amount already raised

= 2, 100 - 1, 180

= $920

The amount that each student in the club will have to raise on average can be found as:

= Amount remaining to be raised / Number of students in the Westview Journalism Club

= 920 / 23

= $40

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