Answers
Answer:
-3^2 = -9
(-3)^2 = 9
Step-by-step explanation:
-3^2 only the 3 is being squared. So he answer is -(3) which is -3
In the second problem (-3)^2 Everything inside the parentheses is being squared. (-3)(-3) = 9
Related Questions
The equation a\(x^{2}\)+b\(x\)+c=0 has roots α, β. Express (α+1)(β+1) in terms of a, b and c.
Answers
Answer:
\(\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)\)
Step-by-step explanation:
We are given the equation:
\(ax^2+bx+c=0\)
Which has roots α and β.
And we want to express (α + 1)(β + 1) in terms of a, b, and c.
From the quadratic formula, we know that the two solutions to our equation are:
\(\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\)
Let x₁ = α and x₂ = β. Substitute:
\(\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)\)
Combine fractions:
\(\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)\)
Rewrite:
\(\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}\)
Multiply and group:
\(\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}\)
Difference of two squares:
\(\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}\)
Expand and simplify:
\(\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}\)
Distribute:
\(\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}\)
Cancel like terms:
\(\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}\)
Factor:
\(\displaystyle =\frac{4a(a+c-b)}{4a(a)}\)
Cancel. Hence:
\(\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)\)
Therefore:
\(\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\)
Solve by the substitution method.
-3x – 3y = 3
y=-5x – 17
Answers
Answer:
postive 6
Step-by-step explanation:cause negative plus a negative equals a postive
Include all topics that you learned with following points: Name of the topic • Explain the topic in your own words. You may want to include diagram/ graphs to support your explanations. • Create an example for all major topics. (Include question, full solution, and properly labelled diagram/graph.) Unit 5: Discrete Functions (Ch. 7 and 8). Arithmetic Sequences Geometric Sequences Recursive Sequences Arithmetic Series Geometric Series Pascal's Triangle and Binomial Expansion Simple Interest Compound Interest (Future and Present) Annuities (Future and Present)
Answers
Unit 5: Discrete Functions (Ch. 7 and 8)
1. Arithmetic Sequences: Sequences with a constant difference between consecutive terms.
2. Geometric Sequences: Sequences with a constant ratio between consecutive terms.
3. Recursive Sequences: Sequences defined in terms of previous terms using a recursive formula.
4. Arithmetic Series: Sum of terms in an arithmetic sequence.
5. Geometric Series: Sum of terms in a geometric sequence.
6. Pascal's Triangle and Binomial Expansion: Triangular arrangement of numbers used for expanding binomial expressions.
7. Simple Interest: Interest calculated based on the initial principal amount, using the formula \(\(I = P \cdot r \cdot t\).\)
8. Compound Interest (Future and Present): Interest calculated on both the principal amount and accumulated interest. Future value formula: \(\(FV = P \cdot (1 + r)^n\)\). Present value formula: \(\(PV = \frac{FV}{(1 + r)^n}\).\)
9. Annuities (Future and Present): Series of equal payments made at regular intervals. Future value and present value formulas depend on the type of annuity (ordinary or annuity due).
Please note that detailed explanations, examples, and diagrams/graphs are omitted for brevity.
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Selling Price: $90.00 Rate of Sales Tax: 3%
Answers
If the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7
The selling price = $90
The rate of sales tax = 3%
The amount of sale tax = The selling price × The rate of sales tax
Substitute the values in the equation
The amount of sale tax = 90 × (3/100)
= 90 × 0.03
= $2.7
The total price = The selling price + The amount of sale tax
Substitute the values in the equation
The selling price = 90 + 2.7
= $92.7
Hence, if the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7
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you choose to put 1-100 marbles in a bag, and i also have the same option. we pick one marble from the bag. if your marble gets picked from the bag you get the amount of marbles you did not put in as your payout. so if you put in 20 marbles and your marble gets picked, you get 80. what is the optimal number of marbles to put in?
Answers
Since you have the option to choose any number from 1 to 100, you need to calculate the expected payout for each case and choose the number that yields the highest expected value.
Let's denote the number of marbles you put in the bag as n. The probability of your marble being picked is 1/n, as there are n marbles in total and only one is chosen. In this case, your payout would be (100 - n). Therefore, the expected payout can be calculated.
To find the optimal number of marbles, we need to maximize the expected payout. We can do this by taking the derivative of the expected payout with respect to n and setting it equal to zero. Solving this equation will give us the value of n that maximizes the expected payout.
However, since the equation is not a simple linear or quadratic equation, solving it analytically might be challenging. Therefore, numerical methods or optimization algorithms can be employed to find the optimal value.
In this scenario, it is difficult to determine the exact optimal number of marbles without further information or assumptions about your preferences or risk aversion. However, through the use of mathematical techniques, you can determine the expected payouts for different numbers of marbles and choose the one that aligns with your desired outcome or risk tolerance.
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Zach and Jessica decide to make lanyards out of 114 feet of string. They decide that for every one foot Zach uses, Jessica needs 5 feet. This would make the part to part ratio equal?
This means that Zach will need______ to make his lanyard?
Answers
Zach will need 19 feet of string to make his lanyard.
Zach and Jessica have 114 feet of string to make lanyards.
According to the given information, for every one foot Zach uses, Jessica needs 5 feet.
Let's assume that Zach uses x feet of string. Since Jessica needs 5 feet for every 1 foot Zach uses, she will need 5x feet of string.
The total length of string used by both Zach and Jessica should equal the total length of string they have, which is 114 feet.
So, we can set up an equation to represent this:
x + 5x = 114
Simplifying the equation:
6x = 114
Divide both sides by 6:
x = 19
Therefore, Zach will need 19 feet of string to make his lanyard.
Zach will need 19 feet of string to make his lanyard.
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9/4 / 3/4 help please I need explanations
Answers
Given the below expression;
\(\frac{9}{4}\frac{.}{.}\frac{3}{4}\)To be able to solve this, we'll need to change the division sign to multiplication sign and find the reciprocal of the denominator;
\(\begin{gathered} \frac{9}{4}\ast\frac{1}{\frac{3}{4}} \\ \frac{9}{4}\ast\frac{4}{3} \end{gathered}\)Let's go ahead and simplify;
\(\begin{gathered} \frac{9}{1}\ast\frac{1}{3} \\ \frac{9}{3}=3 \end{gathered}\)Therefore, our answer is 3.
Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
Answers
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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En una fábrica se pueden etiquetar 4096 envases en 4 días de trabajo. ¿Cuántos días será necesario para etiquetar 9216 envases?
Answers
By applying direct proportion, it would take 9 working days to label 9,216 containers in this factory.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented by the following equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.By applying direct proportion, we have:
4,096 containers = 4 working days.
9,216 containers = X working days.
Cross-multiplying, we have:
4,096X = 4 × 9,216
4,096X = 36,864
X = 36,864/4,096
X = 9 working days.
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Complete Question:
In a factory, 4,096 containers can be labeled in 4 working days. How many days will it take to label 9,216 containers?
First, we need to determine how many containers can be labeled per day in the factory:
Number of containers per day = Total number of containers / Number of working days
Number of containers per day = 4096 / 4
Number of containers per day = 1024
So, we know that the factory can label 1024 containers per day. Now we can use this information to calculate how many days are needed to label 9216 containers:
Days needed = Total number of containers / Number of containers per day
Days needed = 9216 / 1024
Days needed = 9
Therefore, 9 working days will be needed to label 9216 containers in this factory.
When polygons or histograms are constructed, which axis must show the true zero or "origin"?a) The horizontal axis.b) The vertical axis.c) Both the horizontal and vertical axes.d) Neither the horizontal nor the vertical axis
Answers
When polygons or histograms are constructed, the axis that must show the true zero or "origin" is the vertical axis. The correct option is (b).
The vertical axis represents the magnitude or quantity being measured, such as frequency, count, or any other numerical value.
It is important to have a true zero on the vertical axis because it provides a reference point for comparison and interpretation of the data. The zero point indicates the absence or absence of the measured quantity.
For example, in a histogram representing the frequency distribution of a variable, the vertical axis represents the frequency or count of observations falling within each interval.
Having a true zero on the vertical axis ensures that the absence of observations is visually represented as a bar of height zero. This allows for accurate comparisons between different intervals and facilitates the interpretation of the data.
On the other hand, the horizontal axis represents the categories or intervals of the variable being measured.
It does not necessarily require a true zero because it serves as a categorical or qualitative scale rather than a quantitative scale.
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If these numbers represent elevations in meters, which is the farthest away from sea level?
7
-3
1/2
-0.8
0.8
-1/10
-2
Answers
Answer:
The farthest away is 7. ( im not sure though ) sorry if its wrong :(
Step-by-step explanation:
I think its 7 because sea level is at 0 and 7 is the farthest away. You may be thinking that it could be one of the negatives but those aren't it because those aren't as far away as the 7. I AM SO SORRY IF ITS WORNG and please maybe give me brainliest because ive never had it. Please tell me if its worng.
The order is
-3<-2<-0.8<-0.1<0.5<0.8<7The _____ probability function is based in part on the counting rule for combinations.
a. exponential b. Poisson c. uniform d. hypergeometric
Answers
The hypergeometric probability function is based on the counting rule for combinations.
This rule states that if you have two sets of items, with one set containing n1 items and the other containing n2 items, the number of possible combination of r items that can be taken from the two sets is equal to n1+n2 choose n1. This means that you have to select n1 items from the first set, then n2 items from the second set. This function is used in probability calculations to determine the probability of selecting a certain number of items from one set, given a certain number of items from the other set. It is also used to calculate the probability of a certain event occurring when items are randomly selected from two sets.
The hypergeometric probability function can be used to calculate the probability of drawing a certain number of items from a given set. It can also be used to calculate the probability of a certain event occurring. For example, if you are playing a game where you draw 5 balls out of a bag of 20, you can use the hypergeometric probability function to calculate the probability of drawing a certain number of balls from the bag.
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__________ is an adaptation of the divisional structure whereby various divisions or parts of divisions are grouped together based on some common strategic elements, usually linked to distinct product/market differences.
Answers
A matrix structure is an adaptation of the divisional structure whereby various divisions or parts of divisions are grouped together based on some common strategic elements, usually linked to distinct product/market differences.
In a matrix structure, organizations create a dual reporting system where employees report to both functional managers and project or product managers. This structure allows for greater flexibility and collaboration across departments, as individuals from different functional areas come together to work on specific projects or initiatives. The matrix structure is often employed in complex organizations that operate in multiple markets or industries, as it enables efficient resource allocation and coordination. By grouping divisions or parts of divisions based on common strategic elements, organizations can streamline decision-making processes and enhance cross-functional communication and cooperation.
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Point Q is plotted on the coordinate grid. Point P is at (30, −30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q? (1 point)
On a coordinate grid from negative 50 to positive 50 in increments of 10, Point Q is plotted at the ordered pair negative 40, negative 30.
Group of answer choices
Point R is at (−40, 40), a distance of 70 units from point Q
Point R is at (−40, 20), a distance of 10 units from point Q
Point R is at (−40, −40), a distance of 70 units from point Q
Point R is at (−40, −20), a distance of 10 units from point Q
Answers
Answer:
(a) Point R is at (−40, 40), a distance of 70 units from point Q
Step-by-step explanation:
Point Q is on the same horizontal line as P, but is 30 -(-40) = 70 units away. If point R is 70 units above point Q, its y-coordinate will be -30 +70 = 40.
Point R is at (−40, 40), a distance of 70 units from point Q
PLEASEEEEEEEEEEEEEEE HELPPPPPPPPPPPPPP
Answers
Answer:
The equation is x-18 + 8x = 180 (because they form a linear pair of angles.
Each angle measure:-
x-18 + 8x = 180
x + 8x = 180 + 18 (-18 becomes +18)
9x = 198
x = 198/9
x = 22
Angle 1 = x-18 = 22-18 = 4 degrees
Angle 2 = 8x = 8 * 22 = 176 degrees
Hope it helps :')
John is inviting himself, Lucy, and 5 of their closest friends to the party. If there are 3
3/4 cups of yogurt, how many cups of yogurt will John and the rest of the guests at the party each equally receive? PLS ANSWER. I WILL GIVE POINTS TO WHOEVER ANSWERS FIRST.
Answers
Answer:
99
Step-by-step explanation:
For a Student's t-distribution with mean 0, standard deviation 1, and degrees of freedom 49, which of the following Python lines outputs the probability P(t > 0.115)?
Answers
The following line of code in Python calculates the probability P(t > 0.115) for a Student's t-distribution with mean 0, standard deviation 1, and 49 degrees of freedom:
import scipy.stats as stats
1 - stats.t.cdf(0.115, df=49)
The cdf function calculates the cumulative density function (CDF) of the t-distribution, which gives the probability that the random variable (t-statistic) is less than or equal to a given value. To find the probability that it is greater than a given value, we subtract the CDF from 1.
Standard deviation is a statistical measure that calculates the amount of variation or dispersion of a set of data values. It represents how far the data points in a set deviate from the mean.
A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are more spread out.
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Write the following using algebraic notation, using the letter x for any unknown numbers:
i think of a number, halve it, then subtract four.
Answers
Answer:
1/2x-4
Step-by-step explanation:
Since we don't know the number (unknown) we simplify it as a variable, x.
Then since you're taking half of x, place 1/2 next to x. Finally subtract 4, and it concludes to 1/2x-4.
help ASAP HELP PLS HELP PLS HELP PLS HELP
Answers
Answer:
5 and -4.5
Step-by-step explanation:
Since the / is a division sign, 10/2 divides to 5. -9/2 divides to -4.5.
Answer:
Step-by-step explanation:
You would plot it at -4.5 and +5
QUESTION 15 Areej invested BD 14000 12 years ago, today this investment is worth BD 52600, based on this what annualized rate has Areej earned on this investment? O 11.66% O 2.75% 17.43% 8.91%
Answers
To calculate the annualized rate of return, we can use the formula for compound interest. The correct answer is 11.66%.
The formula for compound interest is given by: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.
In this case, the initial investment (P) is BD 14,000, the final amount (A) is BD 52,600, and the time (t) is 12 years. We need to solve for the annual interest rate (r).
\(BD 52,600 = BD 14,000(1 + r)^{12}\)
By rearranging the equation and solving for r, we find:
\((1 + r)^{12} = 52,600/14,000\)
Taking the twelfth root of both sides:
\(1 + r = (52,600/14,000)^{(1/12)}\\r = 0.1166 / 11.66 \%\)
Therefore, Areej has earned an annualized rate of approximately 11.66% on this investment.
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Max completed 12 questions on the exam. This is 40% of the questions. 1. Write an equation representing this situation. 2. How many questions are on the exam? 3. Explain how you got your answer
Answers
Answer:
Step-by-step explanation:
How many questions are on the exam? Represent this by n.
Then 40% of n comes out to 12 questions, or more symbolically,
0.40n = 12, after which we get n = 12/0.40 = 30
Answers:
(1) 0.40n = 12 is the desired equation.
(2) n = 30 is the number of questions on the exam.
(3) See above for explanations.
State if the triangle is a right triangle. (Remember that the largest value is always c)
No
Yes
Answers
Answer:
Yes
Step-by-step explanation:
Right triangles have a 90 degree angle, which this triangle does. The side opposite the 90 degree angle is the hypotenuse. The hypotenuse (in this case 53 m) is the longest side.
PLS HELP! GEOMETRY!!
Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary.
if you're actually willing to help me with my geometry test that would be awesome
Its a win-win!
Answers
Surface area of cuboid is = 312 ,With dedication and effort, you can succeed in your geometry test and feel confident about your understanding of the subject.
Surface area of a cuboid is = 2lw + 2lh + 2 hw
where ; l= length
w= width.
h = height
= 2(10×6)+2(10×6)+2(6×6)
=2(60)+2(60)+2(36)
=120+120+72
=312
Geometry can be challenging, but with the right mindset and approach, you can do well. To start, make sure you understand the basic concepts and definitions.
Then, practice solving problems and applying those concepts. Don't be afraid to ask questions or seek help when you need it. Utilize resources such as textbooks, online tutorials, and practice worksheets.
Also, try to relate geometry to real-life situations to make it more interesting and relevant. Remember to take breaks and stay organized to avoid feeling overwhelmed.
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What number is a multiple of both 5 and 15?
Answers
Answer:
five because 5×3 is 15 and 5×1 is 5
a recent article claims that the state of illinois has low tuition rates for its colleges and universities. cate decides to research the cost of tuition for different colleges in illinois. the average tuition in illinois is $28,950 with a standard deviation of $3,470. which type of inference test should cate use? a.) chi-squared test for goodness-of-fit b.) two-way anova c.) one-sample z-test d.) one-sample t-test
Answers
The correct option c.) one-sample z-test, for the inference test used by the Cate.
What is defined as the one-sample z-test?When determining if a difference between a sample's mean and a population's mean is substantial sufficiently to be statistically significant—that is, because unless it is unlikely to have taken place by chance—we utilize the one-sample z-test. The test is typically used with reasonably large samples (N > 30) or whenever the population variance is known because it is thought to be robust for breaches of normal distribution; otherwise, you can think about using the t-test.As stated in the assertion
In Illinois, the average cost of tuition is $28,950, with a $3,470 standard deviation.This is a one-sample z-test, assuming we have a sizable sample, as we are comparing the mean of one group to an assumed value.As a result, cate uses one sample Z Test.
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What is 5 and 1/2 divided by 1/2 step by step ?? It would mean a lot!
Answers
Answer:
11
Step-by-step explanation:
Use a calculator. Punch in 5.5, then use the divide symbol (÷) and finally put in 0.5, then you will get 11 as your final answer.
Hope this helps!
5x + 2y = 6
3y = 2x +9
Answers
Answer:
x=0, y=3. (0, 3)
Step-by-step explanation:
5x+2y=6
3y=2x+9
-------------
y=2/3x+9/3
y=2/3x+3
----------------
5x+2(2/3x+3)=6
5x+4/3x+6=6
15/3x+4/3x=6-6
19/3x=0
x=0/(19/3)=0
5(0)+2y=6
0+2y=6
2y=6
y=6/2=3
What is the solution of the proportion x-1/2 = x-4/5 ?
A. -2.33
B. 1
C. -1.86
D. -1
Answers
Answer:
x = -1
Step-by-step explanation:
x-1/2 = x-4/5 is ambiguous (subject to misinterpretation).
It should be written with parentheses or with proper fractions:
x - 1 x - 4
---------- = ----------
2 5
Cross multiplying results in 5x - 5 = 2x - 8, or 3x = -3. Then x = -1
Consider the following small open economy: с = 200+ 0.69Y I = 80 - 1,000r G = 20 NX = 850.09Ye e = 90 M = 115 YL = 0.5Y - 200r Y = 300 C is consumption spending, I is investment spending, r is the interest rate, G is govern- ment spending, NX is net exports, e is the nominal exchange rate, M is money supply, YL is demand for money, and Y is long-run output. In this economy, the interest rate does not deviate from the foreign interest rate. The price level is fixed and set to one. Note that, in this problem, a decrease in e is synonymous with a depreciation of the nominal exchange rate. 1. Assuming that the economy is in equilibrium, find the value of the interest rate. (6 points) 2. Going from the equilibrium found in Question (1), assuming fixed nominal exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the size of the nominal money supply in the new short run equilibrium? (6 points) 3. Going from the equilibrium found in Question (1), assuming flexible exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the value of the real exchange rate in the new equilibrium? (6 points)
Answers
The interest rate is 10.89%
1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..
The size of the nominal money supply in the new short-run equilibrium is 121.07.
2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.
Real exchange rate will remain unchanged.
3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.
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