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Answers

Answer 1

Answer:

All integers are rational numbers

Step-by-step explanation:

Since any integer can be written as the ratio of two integers, all integers are rational numbers. Remember that all the counting numbers and all the whole numbers are also integers, and so they, too, are rational.

Answer 2

Answer:

True

Step-by-step explanation:

An integer is a number including positive and negatives with 0 that are whole numbers and are not fractions or decimals


Related Questions

What is 2+2 minus 32 multiplied by 438? is the answer a squareroot, yes or no?​

Answers

The answer is -14012

In the figure below, m LMK = 26° and m KLM = 33° What is m MKJ? A. 52° B. 66° C. 59° D. 121°​

Answers

Answer:

option c

Step-by-step explanation:

first use angle sum property, then use

linear pair axiom

Answer:

D: 121

Step-by-step explanation:

Step One: To do this problem, you must understand the rule that all angles in a triangle add up to 180 degrees.

Step Two: Now that we know the rule, we know this triangle equals 180 degrees. First, we must add the angles we DO know together: 26+33= 59.  

Step Three: We can subtract 59 from 180 to find the missing angle: 180-59= 121.

Consider the following equation: 4 + 6x = 6x + 4. Explain why the equation has many solutions.

Answers

since x is basically any number, there are many solutions when you replace x. such as 1,3,4 etc. and it will always be true.

Find the missing length 3 9 c

Answers

Answer:

Step-by-step explanation:

c²  =  a² + b²

c   =  √(a² + b²)

    =  √(9² + 3²)

    =  √(81 + 9)  

c   =  √90             = √(9)(10)       =   3√10  simplified








Determine the perimeter and area of the shape shown below. 4 ft 16.5 ft 4 ft 20 ft Perimeter: feet Area: square feet Round your answer to the nearest hundredth as needed.

Answers

The perimeter of the shape is approximately 44.00 feet, and the area is approximately 160.50 square feet.

To determine the perimeter of the shape, we add up the lengths of all its sides. The given sides are 4 ft, 16.5 ft, 4 ft, and 20 ft. Adding these lengths together, we get a perimeter of 44.5 ft. However, since we are asked to round to the nearest hundredth, the perimeter becomes approximately 44.00 feet.

To find the area of the shape, we need to know its specific shape. Since the given measurements do not provide enough information, it is not possible to accurately determine the area. In order to calculate the area, we need to know the shape's dimensions, angles, or additional side lengths. Without this information, we cannot determine the area accurately.

In conclusion, the perimeter of the shape is approximately 44.00 feet, but the area cannot be determined without further information.

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Which of the following decimals would be found between 5 and 5
on a number line?
А
5.50
5.40
-16/3 -21/4
B
С
5.30
D
5.20

Answers

None of them. Any number 5-5 can only be 5.

Which statement is true concerning the vertex and axis of symmetry of h(x)=−2x2+8x?

The vertex is at (0, 0) and the axis of symmetry is x = 2.
The vertex is at (0, 0) and the axis of symmetry is y= 2.
The vertex is at (2, 8) and the axis of symmetry is x = 2.
The vertex is at (2, 2) and the axis of symmetry is y = 2.

Answers

Answer:

C.) The vertex is at (2, 8) and the axis of symmetry is x = 2.

Step-by-step explanation:

I got a 100 on edge

The vertex is at (2,8) and the axis of symmetry is x = 2

What is vertex and axis of symmetry of a curve?

The vertex of a curve is the point where the curve passes its axis of symmetry. While the axis of symmetry is the line that divides the curve into two equal halves.

Analysis:

if y = a[tex]x^{2}[/tex]+bx +c.  then the axis of symmetry occurs at  [tex]\frac{-b}{2a}[/tex] and the vertex occurs at [tex]\frac{-b}{2a}[/tex] and the value of y at [tex]\frac{-b}{2a}[/tex].

comparing the above with the equation h(x) = -2[tex]x^{2}[/tex]+8x

x coordinate for vertex = [tex]\frac{-8}{2 x -2}[/tex]  = 2

y coordinate at x = 2

-2[tex](2)^{2}[/tex] + 8(2) = 8

vertex is at point (2,8)

axis of symmetry is the x coordinate of the vertex which is at x = 2

In conclusion, the axis of symmetry is at x = 2 and vertex at point (2,80 option c

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(4) |-5 + (-2)| _____ |5 + 2|
<
>
=

Answers

Hi

The answer would be =

Why?

The `| |` symbols mean actual value, which makes every number inside of it positive. That would mean, following the rules of actual value, the equation would look like:

5 + 2 _____ 5 + 2

Both add up to 10, so both equations are equal.

Answer:

>

Step-by-step explanation:

(4)| -5 + (-2)|  ____ |5 + 2|

         (4)| -7|  ____ |7|

            (4)(7) ____ 7

                28     >   7

A TV originally priced at $948 is on sale for 35% off. 4.a) Find the discount amount 4.b) Find the price after discount X There is then a 9.2% sales tax. 4.c) Find the tax amount 4.d) Find the final price after including the discount and sales tax

Answers

The discount amount is $331.80. The price after discount is $616.20. The sales tax amount is $56.63. The final price is $672.83.

A TV originally priced at $948 is on sale for 35% off. We are to find the discount amount and the price after discount.

The original price of the TV = $948

The percentage discount = 35%.

Let X be the price after discount.

We can find X as follows:

Discount = 35% of original price

= 35% of 948= (35/100) × 948= $331.80

Price after discount (X) = Original price - Discount

= $948 - $331.80= $616.20

Therefore, the price after discount is $616.20.

Now we are to find the tax amount and the final price after including the discount and sales tax.

The sales tax is 9.2%.

We can find the tax amount as follows:

Tax amount = 9.2% of price after discount

= 9.2% of $616.20= (9.2/100) × 616.20= $56.63

Now, the final price after including the discount and sales tax = Price after discount + Tax amount

= $616.20 + $56.63= $672.83

Therefore, the final price after including the discount and sales tax is $672.83.

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3. Audrey measures the distance around the lid of her aquarium. The picture shows the shape of the lid. If the perimeter of the lid is 56 inches, what is the missing side length? * Brainliest and 20 points

Answers

Answer:

18 in

Step-by-step explanation:

in the circuit given below, r1 = 4 ω and r2 = 4 ω. note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part.

Answers

In the given circuit, there are two resistors, R1 and R2, both with a resistance of 4 Ω. The circuit analysis and determination of various electrical quantities, such as current and voltage, can be performed based on this information.

The circuit consists of two resistors, R1 and R2, each with a resistance of 4 Ω. To analyze the circuit and determine various electrical quantities, we can apply principles such as Ohm's law and Kirchhoff's laws.

Firstly, we can calculate the total resistance in the circuit by combining the resistors in series or parallel based on their connection. If R1 and R2 are in series, their total resistance, RT, would be the sum of their individual resistances, i.e., RT = R1 + R2 = 8 Ω.

Once we know the total resistance, we can use Ohm's law (V = IR) to calculate the voltage across the resistors or the current flowing through them. If the circuit is connected to a power source or a given voltage, we can determine the current flowing through the resistors using Ohm's law and Kirchhoff's laws.

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4(x3 + xy2) dV, where E is the solid in the first octant that lies beneath the paraboloid z = 1 − x2 − y2.

Answers

To calculate the given volume integral, 4(x^3 + xy^2) dV, over the solid E in the first octant beneath the paraboloid z = 1 - x^2 - y^2, we need to set up the integral in cylindrical coordinates. The integral will involve integrating over the appropriate limits and applying the volume element in cylindrical coordinates.

In cylindrical coordinates, we have x = r cos θ, y = r sin θ, and z = z.
The equation of the paraboloid, z = 1 - x^2 - y^2, can be expressed as z = 1 - r^2.
The given volume integral becomes 4(x^3 + xy^2) dV = 4(r^3 cos^3 θ + r^3 cos θ sin^2 θ) r dz dr dθ.
To determine the limits of integration, we need to consider the region of the solid E in the first octant. Since the solid lies beneath the paraboloid z = 1 - x^2 - y^2, the upper limit for z is given by z = 1 - r^2.
The limits for r and θ depend on the region in the first octant. We need to set appropriate limits to cover the desired region.Once we have the limits for r, θ, and z, we can set up the triple integral using the volume element in cylindrical coordinates.
By evaluating the integral with the corresponding limits, we can find the value of the given volume integral over the solid E in the first octant beneath the paraboloid.

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There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the classroom?
3 to 4
4 to 3
4 to 7
7 to 4

Answers

Answer:

3 to 4

Step-by-step explanation:

12÷4=3

16÷4=4

so that makes it 3 to 4

12 = a (-6 + 5) (-6 - 6)

Answers

Answer:

a=1

Step-by-step explanation:

12 = a (-6 + 5) (-6 -6)
12 = a ( -1) (-12)
12 = a * 1 * 12
12 = 12a
divide 12a with 12
a = 1




Construct a simple graph with vertices F, G, H, I, J, K, L that has an Euler trail, the degree of I is 1 and the degree of K is 3. What is the edge set?

Answers

Edge set of the graph with vertices F, G, H, I, J, K, and L that has an Euler trail, the degree of I is 1 and the degree of K is 3 is: {(F, H), (G, H), (G, I), (H, J), (I, K), (J, K), (K, L), (K, F)}.

To construct a simple graph with vertices F, G, H, I, J, K, L that has an Euler trail, the degree of I is 1 and the degree of K is 3 and the corresponding edge set, we can follow this method

1: Draw the vertices of the graph. We have 7 vertices, F, G, H, I, J, K, and L.

2: Draw edges between the vertices to form the graph. Since the degree of I is 1 and the degree of K is 3, we can connect I to some other vertex and K to three other vertices.

3: Check if the graph has an Euler trail. A graph has an Euler trail if all vertices have an even degree or if exactly two vertices have an odd degree. Here, the degree of I is 1 and the degree of K is 3, so the graph has two vertices with odd degrees. Therefore, the graph has an Euler trail.

4: Write down the edge set. The edge set of the graph can be written as follows: {(F, H), (G, H), (G, I), (H, J), (I, K), (J, K), (K, L), (K, F)}

5. Here's one possible graph that satisfies the conditions:

  I

   /

F--G--H--J

   \

    K--L

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A bag contains 9 and 54 blue marbles. If a representative sample contains 3 white marbles, then how many blue marbled would you expect to contain? Explain

Answers

Answer:

There should be 18 blue marbles in the representative sample.

Step-by-step explanation:

Given that a bag contains 9 white and 54 blue marbles, if a representative sample contains 3 white marbles, to determine how many blue marbles would you expect to contain the following calculation must be performed:

9 = 3

54 = X

54 x 3/9 = X

162/9 = X

18 = X

Therefore, there should be 18 blue marbles in the representative sample.

In one second, approximately 150,000 gallons of water spill over the American Falls, and approximately 600,000 gallons spill over the Horseshoe Falls. About how many more gallons of water spill over the Horseshoe Falls than over the American Falls in one minute?

Answers

Answer:

O-O

Step-by-step explanation:

XD i took the last comment

Answer:

its D

Step-by-step explanation:

Neutering dogs is a common surgical practice. The mean time to recover from the general anesthetic used is 26 hours. A veterinarian believes that since changing to a new anesthetic, the mean recovery time is shorter than before. From a random sample of 40 surgeries with the new anesthetic, she finds the mean recovery time was 25 hours with a standard deviation of 2.5 hours. What is the p-value for her hypothesis test

Answers

Answer:

0.005719

Step-by-step explanation:

H0 : μ = 26

H1 : μ < 26

Given that:

Population mean, μ = 26

Sample mean, xbar = 25

Sample standard deviation, s = 2.5

Sample size, n = 40

The test statistic :

(xbar - μ) / s/sqrt(n)

Test statistic :

(25 - 26) / 2.5/sqrt(40)

-1 / 0.3952847

Test statistic = - 2.5298

Using a Pvalue calculator from Z test statistic:

Pvalue = 0.005719

In a​ one-tail hypothesis test where you reject H0 only in the lower ​tail, it was found that the p-value is 0.9699 if ZSTAT=+1.88.

What is the statistical decision if you test the null hypothesis at the 0.10 level of​ significance?

Choose the correct answer below.

A. Reject the null hypothesis because the​ p-value is greater than or equal to the level of significance.

B. Reject the null hypothesis because the​ p-value is less than the level of significance.

C. Fail to reject the null hypothesis because the​ p-value is greater than or equal to the level of significance.

D. Fail to reject the null hypothesis because the​ p-value is less than the level of significance.

Answers

The null hypothesis is not rejected since the p-value is higher than or equal to the level of significance.

We assess the statistical conclusion based on the given data by comparing the p-value to the level of significance ().

Given: ZSTAT is 1.88 and p-value is 0.9699.

Level of significance () = 0.10

In a one-tail hypothesis test, the null hypothesis is only rejected in the lower tail if the p-value is less than the level of significance ().

The p-value is greater in this instance (0.9699) than the level of significance (0.1).

Therefore, the proper reaction is

C. The null hypothesis is not rejected since the p-value is higher than or equal to the level of significance.

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How far from the tower can it be placed, to the nearest foot?

Answers

Answer:

43 feet would be the correct answer.

Step-by-step explanation:

help me please lol I will report if you troll​

Answers

Y = mx + b
m = slope, b = y intercept
Plug in the values

Solution: y = -2x + 3

At what value(s) of x does fx) x4-18x2 have a critical point where the graph changes from decreasing to increasing? (4 points) 0 and -3 only 0 and 3 only 0 -3, and 3 only 0 only DELL

Answers

The correct answer is: 0, -3, and 3. At  0, -3, and 3 of x does fx) x4-18x2 have a critical point where the graph changes from decreasing to increasing.

To find the critical points where the graph of the function f(x) = x^4 - 18x^2 changes from decreasing to increasing, we need to find the values of x where the derivative of the function is equal to zero or does not exist.

Let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 36x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 36x = 0

Factor out 4x:

4x(x^2 - 9) = 0

Now we have two factors:

1) 4x = 0, which gives x = 0

2) x^2 - 9 = 0, which gives x = ±3

So, the critical points where the graph changes from decreasing to increasing are x = 0, x = -3, and x = 3.

Therefore, the correct answer is: 0, -3, and 3.

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anyone know the answer?

Answers

I legit can’t see it

what all is equivalent to 75:50

Answers

Answer:

Not sure what you mean by "all". If you literally meant all the ratios that are equivalent to 75:50, the answer would be basically infinite. Maybe you mean in simplest terms, which is most commonly answered. In that case, the answer is 3:2

7. Would you expect the world population growth to be best modeled be a linear, quadratic, or exponential function?

Answers

Answer:

exponential

Step-by-step explanation:

since the rate of our population growth is relative to the amount of people already on our planet, the numbers will grow exponentially

Answer: exponential

Step-by-step explanation: exponential function don’t grow at a constant rate, like the world population

Choose all the values that are solutions to the inequality x > -4.
A. 2
B. 10
C. -8
D. -6
E. -3​

Answers

This is really simple any of the values that are larger than -4 should be correct, those values would be -3, 2, 10 (A,B,E)

Which represents a quadratic function?

Answers

Answer:

B

Step-by-step explanation:

a is a cubic. A cubic is an equation that has 3 on its base x to become x^3 as it's highest power. That is not a quadratic. A cubic and a quadratic are not the same thing.

b is a quadratic The highest power is 2 on the base (x)  to become x^2. That is how a quadratic is defined.

c is a reciprocal. It has its highest power in the denominator, and that is not a quadratic. A quadratic is an equation whose highest power is 2 on its base (x) and whose highest power is in the numerator, not the denominator. This choice is rather tricky because the quadratic formula can be used on it if you change x = 1/z. Then the equation becomes f(x) = 4z^2 - 2z + 1. But as it is given and likely as you have been told, this is not a quadratic. This will factor into  (2z - 1)(2z - 1). If I were a student, I'd question this one. It would be interesting to see how your instructor would eliminate it.

d is just a linear function. Since x^2 is multiplied by 0, it disappears. What is left is f(x) = -9x + 7 which is a linear function.

Consider the following double integral 1 = {2 -xzdy dx. By converting 1 into an equivalent double integral in polar coordinates, we obtain: 1 = 420 Sär dr de 1 = S" Sr dr de This option O This option None of these 1 = " S dr de

Answers

The equivalent double integral in polar coordinates is: 1 = ∫∫(2 - r²cosθ) rdr dθ.

In polar coordinates, we can express the given double integral as 1 = ∫∫(2 - r²cosθ) rdr dθ. To convert from rectangular coordinates to polar coordinates, we substitute x = rcosθ and y = rsinθ. The element of area in polar coordinates is given by dA = rdr dθ.

By making these substitutions and adjusting the limits of integration accordingly, we obtain the equivalent double integral in polar coordinates.

The integral becomes 1 = ∫∫(2 - r²cosθ) rdr dθ. This form allows us to integrate with respect to r first and then with respect to θ, simplifying the evaluation process.

Polar coordinates provide an alternative way to express integrals, particularly when dealing with problems involving circular or radial symmetry.

They use the distance from a fixed point (the origin) and the angle measured from a reference direction (usually the positive x-axis) to represent points in the plane.

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• A neighborhood threw a fireworks celebration for the 4th of July. A bottle rocket was launched upward from the ground with an initial velocity of 160 feet per second. The formula for vertical motion of an object is h(t) = 0.5at2 + vt +s, where the gravitational constant, a, is -32 feet per square second, v is the initial velocity, s is the initial height, and h(t) is the height in feet modeled as a function of time, t.

Part A: What function describes the height, h, of the bottle rocket after t seconds have elapsed?


Part B: What was the maximum height of the bottle rocket?​

Answers

Answer:

poopy

Step-by-step explanation:

Answer:

h(t)=0.5at^2+v+5

Step-by-step explanation:

If you know how to do math you should know

A spinner is divided into 8 equal sections and each section contains a number from 1 to 8. What probability of the spinner landing on 5?

Answers

Answer:

1/8

Step-by-step explanation:

1 number out of eight possible choices.

Answer:

1/8

Step-by-step explanation:

the answer

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The previousCFO already committed to one project down the road as follow:The project is about to start on January 1, 2025 (that is three years from today) and lasts for 5 years (it is closed down on December 31, 2029). On January 1, 2025 an investment of $5.0 million is necessary to finance the start of the project. No other financing is necessary after January 1, 2025.The project provides cash flow of $2.0 million on December 31 of each of the years 2025 to 2029. The discount rate for cash flow generate by the project is 20.0%.Further, the former CFO already arranged for the financing of the project such that iSoftCloud borrows $5.0 million on January 1, 2025 and immediately uses that amount to start the project. Under the arrangement iSoftCloud is required to repay the following amounts: $1.0 million on December 31, 2025, $1.4 million on December 31, 2026, $1.6 million on December 31, 2027, $1.8 million on December 31, 2028 and $2.0 million on December 31, 2029. The repayments are made out of the cash flow generated by the project.Under the current arrangement:i. What is the cost of financing?ii. What is the NPV and IRR of the project? Would you cancel the project if you could?You are looking for an alternative financing strategy. Today January 1, 2022 you discuss with ABB Bank the following arrangement: on January 1, 2025 you borrow $5.0 million from ABB Bank and you commit to repay a constant amount A on December 31 of each of the years 2025 to 2029. ABB Bank provides to you the interest rates for each maturity from one year to five year that you should use in calculating A such that the present value of your payments exactly equal to the amount you borrow:One-year Interest 12.5%Two-year Interest 13.5%Three-year Interest 14.5%Four-year Interest 15.5%Five-year Interest 16.5%(To clarify: an amount borrowed on January 1, 2025 and repaid on January 1, 2026 requires an interest rate of 12.5% and so one for the other periods)Calculate A.What is the cost of financing under this new financing arrangement?Assume that you would be able to cancel the financing arrangement that the previous CFO set and enter into the new financing arrangement with ABB Bank. Use an incremental analysis to analyze whether it would be better to switch from the previous financing arrangement to the new one. What is our decision? Which steps would you recommend to an organization interested in providing more patient- and family-centered care? we can avoid problems of adverse selection by part 2 a. screening potential customers. b. gathering more information about products. c. estimating the probability of an event'sd. all of the above What encryption standard is utilized with kerberos on windows server 2016 and windows 10? Which of the following statements is most CORRECT? a. Tax considerations often play a part in mergers. If one firm has excess cash, purchasing another firm exposes the purchasing firm to additional taxes. Thus, firms with excess cash rarely undertake mergers. b. Managers who purchase other firms often assert that the new combined firm will enjoy benefits from diversification, including more stable earnings. However, since shareholders are free to diversify their own holdings, and at what's probably a lower cost, research of U.S. firms suggests that in most cases, diversification through mergers does not increase the firm's value. c. The smaller the synergistic benefits of a particular merger, the greater the scope for striking a bargain in negotiations, and the higher the probability that the merger will be completed. d. Since mergers are frequently financed by debt rather than equity, a lower cost of debt or a greater debt capacity are rarely relevant considerations when considering a merger. e. Research of U.S. firms suggests that managers' personal motivations have had little, if any, impact on firms' decisions to merge. a playground of merry go roung is essintial a uniforn disk thats roattes about vertical xis theough cwnter radius TRUE or FALSE: To determine whether or not to reject the null hypothesis, we compared the p-value to the test statistic. Explanation: If you answered TRUE above, describe how we used the p-value to determine whether or not to reject the null hypothesis. If you answered FALSE above, explain why the statement is false and then describe how we use the p-value to determine whether or not to reject the null hypothesis. A chain of upscale deli stores in California, Nevada and Arizona sells Parmalat ice cream. The basic ingredients of this high-end ice cream are processed in Italy and then shipped to a small production facility in Maine (USA). There, the ingredients are mixed and fruit blends and/or other ingredients are added and the finished products are then shipped to the grocery chains' distribution centers (DC) in California by refrigerated trucks. Given that the replenishment lead time averages about five weeks, the replenishment managers at the DCs must place replenishment orders well in advance. The DC replenishment manager is responsible for forecasting demand for Parmalat ice cream. Demand for ice cream typically peaks several times during the spring and summer seasons as well as during the Thanksgiving and Christmas holiday season. The replenishment manager uses a "straight line" (i.e. simple) regression forecast model (typically fitted over a sales history of about two to three years) to predict future demand. Of the options listed below, what would be the best forecasting technique to use here? Simple average Simple exponential smoothing, Four-period moving average. Holt-Winter's forecasting method. Last period demand (naive) DISCUSS the information security governance and risk management In an effort to reduce the impact of overpopulation, from the late 1970s to the early twenty-first century, the Chinese government If you borrow $22108 at 20% interest rate for 6 years, what is your ordinary simple interest in this case? Question 8 12.3. Calculate the IRR, given a discount rate of 10% and the table below: Operating Cash Flow Change in Net WC Terminal Cash Flow Initial Cost Net Cash Flow CFO 0 -35 0 -150 CF1 130 0 0 0 The Census counts the number of inhabitants in the country and provides a statistical profile of the population and households. In Singapore, the Census of Population is conducted once in ten years and the Census 2020 was launched on 4 February 2020 where a sample enumeration of some 150,000 households will be conducted over a period of six to nine months. Data from the Census are key inputs for policy review and formulation and the Census is considered an exercise of national importance.(a) Describe the sampling frame used for Census 2020 and discuss how samples are selected. Specifically, explain(i) Explain what a census is;(ii) Describe the sampling frame for Census 2020;(iii) Explain in detail how samples are selected for this census. If firms decide to purchase less U.S.-produced investment goods like trucks, railroad cars, jet engines etc., ceteris pariba O a. the decrease in investment will have no effect on U.S. income or consumption. O b. the decrease in investment will cause U.S. income to decrease, which will cause consumption to decrease. O c. the decrease in investment will cause U.S. income to increase, which will cause consumption to increase. QUESTION 8 If foreigners decide to increase their purchases of U.S.-made goods by $15 million real GDP will, ceteris paribus, O a. decrease by more than $15 million. Ob. increase by more than $15 million. Oc. increase by less than $15 million. O d. increase by $15 million. O e. remain unchanged. the average value of a function f over the interval [2,3] is 6 , and the average value of f over the interval [3,5] is 20. what is the average value of f over the interval [2,5] ?A.2B.7C.10/7D.5 The owner of an office building wants to know if it is less costly - in terms of both up-front costs and in paying the electric bills - for a new energy efficient fluorescent lighting system, compared to the present lighting system. The time period that the owner wants to consider is 7 years, since the new lighting system could be installed using an equipment lease. The interest rate that the owner will pay on the lease is 10%, so this is the minimum attractive rate of return on this investment. The annual costs that can be compared by economic analysis methods are:- Capital cost of lighting systems: Zero for the existing lighting system compared to $20,000 for the new.- Energy costs for lighting systems: $16,000 per year for the existing lighting, $10,400 per year for the new lighting. Cost for operations and maintenance: $500 per year for the existing lighting, zero for the new lighting. - Cost of equipment repair: $2000 per year for the existing lighting, zero for the new lighting.- Cost for equipment replacement: $300 per year for the existing lighting, zero for the new lighting.What is the difference in the NPV after 7 years when comparing the new lighting system to the old?]Is the investment worth making?What is the NPV when a discount rate equal to the IRR is used for n = 7 years?What is the IRR after 7 years? One disadvantage of Gaussian quadrature rules is that they cannot be refined as easily as Newton- Cotes rules, because the nodes move if the number of subintervals is increased. a. trueb. false