The overpopulation of Canadian Geese and their refusal to migrate because they are able to find food during the winter has caused some environmental problems. In particular, their feces run off into rivers and lakes when it rains and fertilizes algae (the reason why the campus pound is green).The abundance of algae blocks out the sun and makes it hard for other aquatic plants to undergo photosynthesis. If the proportion of algae in the water exceeds 70%, then the aquatic plants will not get enough sun and die, reducing the oxygen in the water which would then kill fish. A researcher, who is interested in extending the hunting season for the geese, is going to test to see if the campus pond has enough algae to start killing fish. In a sample of 100 pounds of water he finds that there is 85 pounds ofalgae. The researcher is interested in α 0.05 level test. a) State the null and alternative hypotheses. b) Write down the appropriate test statistic (check assumptions first) STA NO Qu Qu c) Write down the rejection region of your test. d) Compute the value of the test statistic and state your conclusion (in one sentence, state whether or not the test rejects the null hypothesis and in another sentence apply the results to the problem). e) Compute the p-value for this test . What is your decision? Interpretation of the p-value:
Answers
A. Null hypothesis (H0): The proportion of algae in the water is less than or equal to 0.7.
Alternative hypothesis (H1): The proportion of algae in the water is greater than 0.7.
B. The appropriate test statistic in this case would be the z-test for proportions.
What are the assumptions for the z-test?Assumptions for the z-test for proportions:
1. The sample is a simple random sample.
2. The sampling distribution of the sample proportion can be approximated by a normal distribution.
3. The samples are independent.
4. The sample size is large enough (np0 >= 10 and n(1-p0) >= 10, where n is the sample size and p0 is the hypothesized proportion).
c) The rejection region for this one-tailed test at an α level of 0.05 would be in the right tail of the distribution.
d) To compute the value of the test statistic, we need to calculate the standard error of the sample proportion and compare it to the critical value of the standard normal distribution at α = 0.05.
Let p-cap be the sample proportion (85/100 = 0.85), and n be the sample size (100).
Standard error (SE) = √((p-cap x (1 - p-cap)) / n)
SE = √((0.85 x 0.15) / 100) = 0.03887
z-score = (p-cap - p0) / SE
z-score = (0.85 - 0.7) / 0.03887 ≈ 3.854
Looking up the critical value for α = 0.05 in the standard normal distribution table, the critical z-value is approximately 1.645 (one-tailed test).
Since the calculated z-score (3.854) is greater than the critical value (1.645), we can reject the null hypothesis.
Conclusion: The test rejects the null hypothesis, indicating that the proportion of algae in the water is significantly greater than 0.7. This suggests that there may be a risk of reduced oxygen levels and potential fish mortality due to excessive algae growth.
e) To compute the p-value for this test, we would calculate the probability of obtaining a z-score as extreme as 3.854 or greater, assuming the null hypothesis is true (i.e., the proportion is less than or equal to 0.7).
The p-value is the probability of obtaining a z-score greater than 3.854 in a standard normal distribution. This probability is extremely low, approaching zero.
Decision: Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. The evidence suggests that the proportion of algae in the water is significantly greater than 0.7, indicating a potential environmental problem.
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Related Questions
Can someone please explain how to find the coordinates? I’m really confused. Thanks! :)
Answers
The locations of the points in rectangular form are, respectively:
A(x, y, z) = (0, 0, 0) B(x, y, z) = (0, 0, 50) C(x, y, z) = (0, 60, 0) D(x, y, z) = (60, 0, 60) E(x, y, z) = (0, 80, 80) F(x, y, z) = (60, 40, 80)How to represent location of points according to rectangular system of coordinates
In this problem we must describe the locations of six points in a rectangular system of coordinates. Herein we define rectangular points as points with 3 coordinates related to each orthogonal axis. This kind of points are defined below:
(x, y, z)
Where:
x - Distance from the origin along the x-axis.y - Distance from the origin along the y-axis.z - Distance from the origin along the z-axis.Now we proceed to describe the location of each point:
A(x, y, z) = (0, 0, 0)
B(x, y, z) = (0, 0, 50)
C(x, y, z) = (0, 60, 0)
D(x, y, z) = (60, 0, 60)
E(x, y, z) = (0, 80, 80)
F(x, y, z) = (60, 40, 80)
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After pressing submit or a par or kc quiz, d2l provides a warning if you have not saved your answers to one or more questions before grading your assignment. Since you are still permitted submit a quiz with unanswered questions, using a warning approach is an example of what type of error prevention?.
Answers
The warning approach is an example of Detection of error type prevention.
What is error?Error is a conscious or unconscious departure from a standard of conduct. A bug is a mistake in computer data. A software bug is an error, flaw, failure, or fault that results in an unwanted behavior from a computer program or system or leads it to deliver an inaccurate or unexpected outcome. Errors caused by bugs may have repercussions. The majority of defects are caused by faults and blunders in a program's source code, in its design, or in the parts and operating systems that these programs rely on.
After pressing submit or a PAR or KC quiz, D2Lprovides a warning if you have not saved your answers to one or more questions before grading your assignment. Since you are still permitted submit a quiz with unanswered questions, using a warning approach is an example of Detection type of error prevention
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What is the code in python to remove ' at the beginning and at the end and also remove the item at index 12?
Answers
To remove the single quotation marks ('') at the beginning and end of a string and remove the item at index 12, you can use Python's string manipulation methods and list slicing. First, you can use the strip() method to remove the surrounding single quotation marks. Then, you can convert the string into a list using the list() function, remove the item at index 12 using list slicing, and finally convert the list back into a string using the join() method.
To remove the single quotation marks at the beginning and end of a string, you can use the strip() method. This method removes any leading and trailing characters specified in the argument. In this case, you can pass the single quotation mark ('') as the argument to strip().
Here's an example:
string = "'example string'"
stripped_string = string.strip("'")
After executing this code, the value of stripped_string will be 'example string' without the surrounding single quotation marks.
To remove the item at index 12 from the string, you need to convert it into a list. You can use the list() function for this conversion. Then, you can use list slicing to remove the item at index 12 by excluding it from the list. Finally, you can convert the modified list back into a string using the join() method.
Here's an example:
string_list = list(stripped_string)
string_list.pop(12)
result_string = ''.join(string_list)
After executing this code, the value of result_string will be the modified string with the item at index 12 removed.
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My cousin needs help shes in 4th grade
Answers
Answer:
1,392
Step-by-step explanation:
Because 58 x 24 = 1,392, that is the total cans of soda on the shelves.
Answer:
1,392 I hope this helps her! My little sister is in fourth grade right now.
4(3 × 2) + (8 - 3)^2 - 6^2 + 3 × 9 - 2^3 + 1
Show your work
[Thank you]
Answers
Answer:
33
Step-by-step explanation:
if its in () its the 1th step and then the rest u can continue
find a power series for f(x) 1/1-x^2 centered at 0. write the first four nonzero terms
Answers
The power series for f(x) 1/(1-x²) centered at 0 is:
1 + x² + x⁴ + x⁶ + ...
The first four nonzero terms are 1, x², x⁴, x⁶.
How to find power series for a function?The power series expansion for the function f(x) = 1/(1-x²) centered at 0 can be found using the geometric series formula.
By letting a=1 and r=x²,
we get the series 1 + x² + x⁴ + x⁶ + ..., which converges for |x|<1.
This is because as x approaches 1 or -1, the terms of the series diverge.
Thus, the first four non-zero terms of the series are 1 + x² + x⁴ + x⁶.
This power series expansion is useful in many applications, such as in approximating the function near x=0 or in solving differential equations using power series methods.
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Is it negative or positive to say that your gonna “destroy” someone in a race?
Answers
Saying you will destroy someone in a race could be positive or negative depending on the context of the situation.
What does it mean to destroy someone in a race?Using the word "destroy" to describe beating someone in a race can be viewed as negative or positive, depending on the context and the relationship between the individuals.
In some situations, it may be seen as a playful or friendly challenge, indicating a competitive but good-natured spirit. However, in other cases, it may come across as aggressive or intimidating, potentially damaging the relationship between the participants.
It is important to consider the tone and the relationship when using language that could be interpreted as confrontational or threatening.
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Solve the differential equation (Show your work). \[ 7 x^{6} \cos y d x-d y=0 \]
Answers
The solution to the given differential equation is: x⁷ cos y = y + C
where C is the constant of integration
To solve the given differential equation:
\(\[7x^6\cos y dx - dy = 0\]\)
We can separate the variables and integrate both sides.
Separating variables, we can write the equation as:
\(\[7x^6\cos y dx = dy\]\)
Now, we can integrate both sides with respect to their respective variables:
\(\[\int 7x^6\cos y dx = \int dy\]\)
Integrating the left side:
\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)
To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.
Let's take u = x⁶ and \(\(dv = \cos y dx\)\).
Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)
Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)
Applying the integration by parts formula:
\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)
Substituting the values:
\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)
Simplifying:
\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)
Moving the integral term to the left side:
\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)
Dividing both sides by 7:
\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)
Now, substituting this result back into our original equation:
\(\[7 \int x^6 \cos y dx = dy\]\)
\(\[\frac{7x^7 \cos y}{7} = dy\)
Simplifying:
x⁷ cos y = dy
Finally, the solution to the given differential equation is:
x⁷ cos y = y + C
where C is the constant of integration.
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What is the greatest common factor of 16, 20, and 6?
Answers
Answer:
2
Step-by-step explanation:
The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, what is the linear speed of the car in miles per hour? Round your answer to the nearest tenth.
Answers
Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:
Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep
4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3
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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.
To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:
Calculate the circumference of the wheel:
The circumference of a circle is given by the formula
C = 2πr
where r is the radius of the wheel.
In this case, the radius is 30 inches, so the circumference is
C = 2π(30)
= 60π inches.
Calculate the distance traveled in one revolution:
Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.
Calculate the distance traveled in one minute:
Multiply the distance traveled in one revolution by the number of revolutions per minute.
In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.
Convert the distance to miles per hour:
There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.
Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.
The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.
Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.
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AREA OF A CIRCLE PLS HELP
Answers
Answer:
153.86 ft²
Step-by-step explanation:
Area = \(\pi r^2\)
= 3.14 * 7 * 7
= 153.86 ft²
Answer:
if A =3.14*r^2 then the answer would be either 153.86
Step-by-step explanation:
Which fruit snack cost less per pound? How much less?
Answers
Each pound of brand B costs 0.33 dollars less than each pound of brand A.
Which fruit snack costs less per pound?
Here we need to find the cost per pound for both brands, to get that, we need to get the quotient between the costs and the number of pounds.
For brand A the cost is $37.80 and you get 35 pounds, then the cost per pound is:
A = $37.80/35 = $1.08
Then each pound for brand A costs 1.08 dollars.
Now let's do the same for brand B, the cost is $33.75, and you get 45 pounds, then the cost per pound is:
B = $33.75/45 = $0.75
Then each pound for brand B costs 0.75 dollars.
So brand B is cheaper, and the difference is:
1.08 dollars - 0.75 dollars = 0.33 dollars.
Each pound of brand B costs 0.33 dollars less than each pound of brand A.
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I NEED HELP ASAP(look at the picture for the problem)
Answers
Answer:
M = 1
Step-by-step explanation:
Find the area.......Brainliest.....
Answers
200.6ft
Step-by-step explanation:
find the area of the square that is L².=12²ft which is 144ftthe area of the half a circle which is 1/2πr²which is 1/2×22/7×6²=56.6 after rounding of to one decimal placeadd the two areas 144+56.6=200.6ftConstruct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
Answers
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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What is the median?
3, 5, 7, 7, 7, 8, 9, 9, 10
Answers
Answer:
7 i think
Step-by-step explanation:
pls mark brainliest
Answer:
\(7\)
Step-by-step explanation:
find the middle number to get the median
.
data
3, 5, 7, 7, 7, 8, 9, 9, 10
.
the median is 7
Intermediate Algebra, Please help
Answers
Answer:
B
Step-by-step explanation:
Other answers look like utter bs
The diagram shows a circle with centre O.
A & B lie on the circumference of this circle.
Given that ∠OAB = 40°, evaluate ∠AOB.
Helppp ASAP
Answers
As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.
What are the properties of circle?Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB
Diameter is twice of radius.
What is isosceles triangle?The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius
According to the criteria of isosceles triangle angle OAB =OBA =40°
hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]
angle AOB= 100 degrees.
We get, AOB = 100 degrees
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Find the area under the standard normal distribution curve to the right of z = 2.12. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.
Answers
The area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
What is the Area under the Standard Normal Distribution Curve?The standard normal distribution curve's total area under the curve is 1. We can therefore calculate the likelihood of a value less than or larger than that if we know the Z score, which measures how far a value is above or below the mean. Under the typical normal curve when using the Normal Distribution P(Z>z)=1-P(Z<z) determines the region to the right of z.In this question:
Area right to the right of the z = 2.12
Using a TI-83 Plus/TI-84 Plus calculator,
P(Z> 2.12)
= P(Z<-2.12)
= 0.0170
Therefore the area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
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What is the image of ABC for a 270° counterclockwise rotation about P?
Answers
Answer:JKL
Step-by-step explanation:A 270 degree rotation represents three 90 degree rotations
Rotating ABC by 90 degrees three times places it in the position of JKL
So, the answer is B. JKL
2. What is the average salary offered to a Stony Brook college graduate? To study this question you and a friend interview N students that graduated last year, and ask them what they earn. Student i's response was recorded as Yi. You are interested in the average, My. You assumed that the sample of Y's is iid. First you calculate the following estimate of uy: W1 N 1 N i=1 ΣΥ. . You and your friend each collected half the data. Thus you collected Y1, ..., YN/2 and your friend collected Yn/2+1, ... , Yn. Unfortunately, it turns out that your friend collected the data at a wild alumnae party, and you suspect that these data may not be as precise as your data. So whereas the variance of your data is, var(Y;) = 0%, i = 1, ...,N/2. then your friends data have the variance, var(Y) = oʻ(1 + 3c), i=N/2+1, ...,N, for some constant c> 0. (d) Your friend is sorry that half the data are not as precise as they could have been, and suggest that you discard the noise data, and simply use hr Na Ex? Y; as your estimator for my. Which estimator is most efficient (has the smallest variance) în or îz? Does your answer depend on c? = N.Σ. (Υ – μ.) - = (e) Suppose now that c = 0 such that var(Y;) = o2 for i = 1, ...,N. You have N = 300 observation and calculate s2 = 20,000,000 and î1 = $48,000. Before collecting the data, your friend argues mean salary, my, is s $50,000, using a 1% significance level. Write down the confidence interval at 1% significance level and decide whether you will accept your friend's
Answers
The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.
In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.
In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.
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What calculator is used for pre-calculus?
Answers
A scientific calculator is typically used for pre-calculus.
This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.
It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.
Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.
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The total surface area of cube is 54cm2.what is the height of the cube
Answers
Answer:
TSA of cube = 6l²= 54
6l²= 54
l²= 9
l=3= height of cube
Step-by-step explanation:
Answer:
The height of cube is 3cm.
Step-by-step explanation:
let length be l.
In cube,
length = height = breadth
Total Surface Area(T.S.A) = 54cm^2
We know that,
T.S.A of cube = 6l^2
or, 54cm^2 = 6l^2
or, (54cm^2)/6 = l^2
or, 9cm^2 = l^2
or, (3cm)^2 = l^2
or, l = 3cm
Solve 7x 8 = 3x
x = …
please
Answers
x=-2 or x=2
Below are two parallel lines with a third line intersecting them.
If you can’t see it the number is 81
Answers
Answer:
x° = 81°
Step-by-step explanation:
From the diagram, we have;
Two parallel lines crossed by a common transversal
Therefore, the corresponding angle formed by the transversal and each of the parallel lines are equal
The given angle = 81°
The alternate exterior angle to the given angle = x°
When two parallel lines are crossed by a common transversal, the alternate exterior angles are equal
∴ x° = 81°.
5/8^3+9-1/4^3= I really need help!!!
Answers
Answer: 3/8q^3 + 9
Step-by-step explanation:
1. combine like terms 5/8q^3 - 1/4q^3, need to make denominator the same to subtract so multiply 2/2 by 1/4q^3, 5/8q^3 - 2/8q^3 = 3/8q^3
2. final answer is : 3/8q^3 + 9
find the length of the curve. r(t) = 8t, t2, 1 12 t3 , 0 ≤ t ≤ 1
Answers
The length of something like the curve is 8.083, going per the supplied statement.
What in mathematics is a curve?Curve, An abstract phrase used to characterize the trajectory of a continually moving point in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a solid line or a collection of connected line segments. The IS curve displays permutations of borrowing costs and production levels where anticipated expenditure and income are equal. The many interest and income configurations along which the commodity is in homeostasis are represented by the IS Curve.
\(\begin{aligned}& r(t)=\left\langle 8 t, t^2, \frac{1}{12} t^3\right\rangle \\& r^{\prime}(t)=\left\langle 8,2 t, \frac{t^2}{4}\right\rangle\end{aligned}\)
\(\begin{aligned}& \left|\lambda^{\prime}(t)\right|=\sqrt{64+4 t^2+\frac{t^4}{16}}=\sqrt{1 / 16\left(t^2+32\right)^2} \\& \left|r^{\prime}(t)\right|=\frac{1}{4}\left(t^2+32\right)\end{aligned}\)
Length of arc = \(\int_a^b\left|r^{\prime}(t)\right| d t\)
\(\begin{aligned}& L=\frac{1}{4} \int_0^1\left(t^2+32\right) d t \\& L=\frac{1}{4}\left[\frac{t^3}{3}+32 t\right]_0^1=\frac{1}{4}\left[\frac{1}{3}+32\right]\end{aligned}\)
L = 8.083
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The stock price for TPJ was $74.29 in September. In October the stock had increased by 8% but in November the price fell by 8% what was the price of TPJ stock in November? Round your answer to the nearest cent, if necessary.
Answers
From september to october the stock increased 8%, then, we can calculate the 8% of 74.29, and then add the result to the total:
\(\begin{gathered} 74.29(8\%)=74.29(0.08)=5.94 \\ \Rightarrow74.29+5.94=80.23 \end{gathered}\)the total for october is $80.23. Finally, since the price fell by 8% in november, we can find the new total by calculating the 92% of $80.23 (since 100% - 8% = 92%):
\(\begin{gathered} 80.23(92\%)=80.23(0.92)=73.81 \\ \end{gathered}\)therefore, the price in november was $73.81
Consider a world with 10 countries. Each country must select its level of abatement of pollution zi, which is a continuously defined variable. The cost of abatement C(zi) for any country i depends upon the abatement effort thatcountry exerts and is given by C(zi) = 50 z? where i E {1, ..., 10}. The benefit that i gets on pollution abatement depends upon the total level of abatement by all countries and is given by B;(Z) = 10 Z – 0.005Z2 where 2 = k zk and i E {1,...,10}. The payoff for each country i is given by Ti = = B;(Z) – C(zi) Based on the above information, you are required to complete the following tasks a) What is the resulting level of abatement zi for each country if all act in their self- interest? b) Now assume that the countries cooperate to maximize the following collective pay-off 10 10 II = B;(Z) - C(zi). ) i=1 i=1 where B; and C have the same expressions as given previously. What are the new levels of abatement? c) Does cooperation result in a Pareto improvement in thiscase? Calculate the magnitude of efficiency gain obtained from full cooperation.
Answers
a. If all countries act in their self-interest, each country will choose a level of abatement zi = 99.50.
b. We conclude that there is no level of abatement that maximizes the collective payoff.
c. There is no efficiency gain from full cooperation.
What is differentiation?A derivative of a function with respect to an independent variable is what is referred to as differentiation. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.
(a) If all countries act in their self-interest, they will choose the level of abatement zi that maximizes their own payoff Ti. To find this level, we need to differentiate Ti with respect to zi and set the result equal to zero:
dTi/dzi = d(B;(Z) – C(zi))/dzi = d(B;(Z))/dZ * dZ/dzi - d(C(zi))/d(zi) = 10 - 0.01Zi - 50zi
Setting this expression equal to zero, we get:
10 - 0.01Zi - 50zi = 0
Solving for Zi, we get:
Zi = (10 - 0.01Zi)/50
Zi = 0.2 - 0.002Zi
Zi = 0.2/(1 + 0.002)
Zi = 99.50
Therefore, if all countries act in their self-interest, each country will choose a level of abatement zi = 99.50.
(b) If the countries cooperate to maximize the collective payoff, they will jointly choose the level of abatement that maximizes the expression:
II = B;(Z) - C(zi)
To find the optimal level of abatement, we need to differentiate II with respect to zi and set the result equal to zero:
dII/dzi = d(B;(Z))/dZ * dZ/dzi - d(C(zi))/d(zi) = 10 - 0.01Z - 50zi
Setting this expression equal to zero, we get:
10 - 0.01Z - 50zi = 0
Solving for Zi, we get:
Z = (10 - 50zi)/0.01
Z = 1000 - 5000zi
Substituting this expression for Z into the expression for zi, we get:
zi = 0.2 - 0.002(1000 - 5000zi)
zi = 0.2 - 2 + 10zi
11.8zi = -2
zi = -0.17
This result is not physically meaningful since zi must be non-negative. Therefore, we conclude that there is no level of abatement that maximizes the collective payoff.
(c) Since there is no level of abatement that maximizes the collective payoff, cooperation does not result in a Pareto improvement in this case. There is no efficiency gain from full cooperation.
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solve the following using BEDMAS
5X4 -(3+1)2÷2
Answers
the value of the expression is 12.
To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.
The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.
It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.
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