Jae is offered the choice of two uncertain investments, each of which will require an Investment of £10,000. Jae's wealth, if they do not invest, is £18,000.
Investment A returns:
+20% with probability 30%
+5% with probability 15%
-15% with probability 45%
+0% with probability 10% Investment B returns:
+30% with probability 41% -20% with probability 59%
Jae has utility of wealth given by the function: U(w) In(w)
a) Show whether either of the investments is a fair gamble
b) Determine which, if any, of the investments Jae will accept.
c) A new investment, also requiring an investment of £10,000, is offered to Jae.
The new investment returns: -10% with probability 40%.
Calculate the return required with probability 60% to ensure that this investment is preferred by Jae to not investing

Expected gain/loss with survey = (p * (probability of success given favorable survey * gain from success + probability of failure given favorable survey * loss from failure)) + ((1-p) * (probability of success given unfavorable survey * gain from success + probability of failure given unfavorable survey * loss from failure))
= (0.4 * (0.6 * $540,000 + 0.1 * -$450,000)) + (0.6 * (0.2 * $540,000 + 0.7 * -$450,000))

he company is considering whether to market a new product. They assess that the probabilities of the outcomes - success or failure - are p and 1-p, respectively. If the product is marketed and it fails, the company will have a net loss of $450,000. If the product is marketed and it succeeds, the company will have a net gain of $540,000. If the company decides not to market the product, there is no gain or loss.
The company can conduct a survey of prospective buyers to determine the market potential. The survey results can be classified as favorable, neutral, or unfavorable. Based on similar surveys for previous products, the company assesses the probabilities of favorable, neutral, and unfavorable survey results to be 0.6, 0.3, and 0.1 for a product that will evntually be a success, and 0.1, 0.2, and 0.7 for a product that will eventually be a failure.
The total cost of conducting the survey is c dollars. The question asks for which values of c, if any, would the company choose to conduct the survey, given that p=0.4.
To determine whether to conduct the survey, we need to compare the expected gains/losses from marketing the product with and without the survey.
If the company markets the product without the survey, the expected gain/loss can be calculated as follows:
Expected gain/loss without survey = (p * gain from success) + ((1-p) * loss from failure)
= (0.4 * $540,000) + (0.6 * -$450,000)
If the company markets the product with the survey, the expected gain/loss can be calculated as follows:
Expected gain/loss with survey = (p * (probability of success given favorable survey * gain from success + probability of failure given favorable survey * loss from failure)) + ((1-p) * (probability of success given unfavorable survey * gain from success + probability of failure given unfavorable survey * loss from failure))
= (0.4 * (0.6 * $540,000 + 0.1 * -$450,000)) + (0.6 * (0.2 * $540,000 + 0.7 * -$450,000))

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Answer:

part c                      hope this helps. :)

Step-by-step explanation:

11/12

2 3/4 = 11/4

11/4 divided by 3

turn the divide to multiply and write 11/4 x 1/3

answer will be 11/12

Answer:

11/12

Step-by-step explanation:

Shelby and her two friends make 3 people.

2 3/4 pies are left over

They decide to share among themselves.[3]

Change 2 3/4 to an improper fraction:2*4+3=11/4

11/4 evenly divide with 3 friends

Change the division sign to multiplication by giving the reciprocal of the number to the right[3]

11/4*1/3=11/12

Answer:

Step-by-step explanation:

If two lines are perpendicular then the product of theirs slopes is equal -1:

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇒    m₁×m₂ = -1

y = 14x - 2   ⇒   m₁=14

14×m₂ = -1        ⇒    m₂ = -¹/₁₄

The line y=-¹/₁₄x+b passes through point (3, 3) so the equation:

3 = -¹/₁₄×3 + b must be true

3 = -³/₁₄ + b

b = 3³/₁₄

Therefore equation in  slope-intercept form:

                                                y = -¹/₁₄x + 3³/₁₄

Answer:

Estimation is useful when finding actual products and real world solving because, it leads you closer to the answer you are going to be aiming for. For example if a question is 23 x 6 + 1= ? you would estimate around the 100 because it is closer to the answer you will mostly likely create and get.

Hope this helps :3

Answer:

Estimation is useful when finding actual products and real world solving because, it leads you closer to the answer you are going to be aiming for. For example if a question is 23 x 6 + 1= ? you would estimate around the 100 because it is closer to the answer you will mostly likely create and get.

Step-by-step explanation:

The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

What is the Present Value of an Annuity?

With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.

To determine the amount needed for retirement, we can use the formula for the present value of an annuity:

  \(PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}\)

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).

Plugging in these values, we get:

\(PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225\)

PV = $405,840.13

Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

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Answer:

36

Step-by-step explanation:

We know all angles in a triangle must add up to 180°

The square in the triangle that angle is equal to 90°

We can now solve for x

90 + 54 + x = 180

144 + x = 180

x = 36

That is your answer

- Kan Academy Advance

There are 6 pennies in a total of 150 coins.

Given that,

Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.

and also,

For every penny, there are five dime.

Total = 150 coins

Out of it, 90 are quarters so the remaining coins are 60

It is said that,

In that 60 coins 40% are nickels which means

40% of 60 is 24

So remaining coins are 36 (by subtracting 24 from 60)

It is said that there are 5 dimes for every penny which means

Using Algebra,

x + 5x = 36

6x= 36

x= 6

Therefore, there are 6 pennies in a total of 150 coins.

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The following probabilities are found under the condition that  a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Now,
Regarding  a national survey concerning the head od households,  only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.

Therefore,

(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.

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Answer:

508.69

Step-by-step explanation:

...

Answer:

The first derivative test is used to examine where a function is increasing or decreasing on its domain and to identify its local maxima and minima.

The method of using a function's first derivatives to analyze it and determine its extremum point is known as the first derivative test.

What does the first derivative test measure?

The first-derivative test evaluates a function's monotonic features, looking specifically at a point in its domain where the function is increasing or decreasing. At that moment, if the function "switches" from increasing to decreasing, the function will reach its maximum value.

What are the first and second derivative tests?

We can determine if a function is increasing or decreasing using the first derivative, but the second derivative can also do this. reveals the direction of the first derivative, either growing or decreasing.

                                   The first derivative follows if the second derivative is positive. The slope of a tangent line to the curve at any given time can be determined using an expression known as the first derivative of a function.

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Answer:

b = 15h

Step-by-step explanation:

15/1 = 15 bikes in 1 hour.

When it turns 2 hours, it will have 30 bikes produced.

30/2 = 30 bikes in 2 hours.

15/1 is 15 and 30/2 is 15.

15/1 = 30/2

This means it is proportional.

b = 15h

b = represents bicycle

h = represents hours

Let's put in h as 2, as in 2 hours. The b should come out as 30, since 30 bicycles are made in 2 hours.

15h = b

b = 15(2)

b = 30

b does equal 30. And so this equation works for this word problem.

Step-by-step explanation:

Hey there!

Follow the steps to get answer.

The equation of a line passing through point (2,3) is;

(y-3)= m1(x-2).......(i).

Another equation is;

\(y = \frac{ - 1}{2} x + \frac{2}{3} \)

2nd equation..

Now, From equation (ii)

We have;

Comparing equation (ii) with y = mx+c.

We get;

Slope = -1/2.

For perpendicular lines,

\(m1 \times m2 = - 1\)

\(m1 \times \frac{ - 1}{2} = - 1\)

Therefore the slope is 2.

Put value of slope (m1) in equation (i). We get;

\((y - 3) = 2(x - 2)\)

Simplify them to get equation.

\((y - 3) = 2x - 4\)

\(y = 2x - 1\)

Therefore the required equation is y = 2x-1.

Hope it helps..

Answer:

Thanks

Step-by-step explanation:

The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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The growth rate of the sloth population when the population is made up of 275 individuals is 99 individuals per year.

To calculate the growth rate of the three-toed sloth population when there are 275 individuals, we will use the logistic growth model formula:

Growth rate = r * N * (1 - N/K)

where r is the maximum per capita growth rate (0.8 per year), N is the current population size (275 individuals), and K is the carrying capacity of the forest (500 individuals).

Growth rate = 0.8 * 275 * (1 - 275/500)
Growth rate = 0.8 * 275 * (1 - 0.55)
Growth rate = 0.8 * 275 * 0.45
Growth rate ≈ 99 individuals per year

So, the growth rate of the sloth population when the population is made up of 275 individuals is approximately 99 individuals per year.

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Answer:

The correct options are;

B. You can easily withdraw funds from a checking account

C. There are many types of checking accounts

E. Some checking account allow for joint use

F. Even if you open a free checking account a bank can still charge penalties on the account

Step-by-step explanation:

A checking, also known as transactional accounts or demand account is an account into which a bank costumer can deposit money and also withdraw from the money from the account. The high liquid nature of checking account makes it easier to access the account for transactions, and the checking account can also be accessed through automated teller machines, electronic debit cards and checks as well as other methods.

Types of checking accounts include;

1) Regular checking account

2) Premium checking account

3) Free checking account

4) Low-balance account

5) Interest- bearing checking account

6) Second-chance checking account

The study conducted by the researcher suffers from several limitations, including the absence of a control group, small sample size, participant bias, and experimenter bias. Furthermore, the sample selection is inadequate, as all the participants are students of one course in a single university.

Moreover, the study fails to account for extraneous variables that might affect the results. Therefore,  that textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. T he study is flawed, and more research is needed to assess the effect of textbooks on learning.

The study conducted by the researcher suffers from several limitations. First, there is no control group, which makes it difficult to determine whether the results are due to the absence or presence of the textbook. Second, the sample size is small, which reduces the generalizability of the findings.

Third, there is participant bias, as some students might have bought the textbook even though it was optional, while others might not have bought it even though it was required. Fourth, there is experimenter bias, as the professor who scored the essays knew which section had the textbook and which did not.

Fifth, the sample selection is inadequate, as all the participants are students of one course in a single university. Moreover, the study fails to account for extraneous variables that might affect the results, such as the students' prior knowledge, motivation, and study habits.

Therefore, the  textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. The study is flawed, and more research is needed to assess the effect of textbooks on learning.

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Answer:

the answer is b

Answer:

Surface Area = 96

Step-by-step explanation:

Area of Triangle: Area = 1/2 * Base * Height

Area = 1/2 * 6 * 2 = 6

Area = 6

Area of Rectange: Area = Length * Height

Area = 7 * 3 = 21

Area = 7 * 6 = 42

Area = 21

Surface Area = TopTri + BotTri + LeftRect + MidRect + RightRect

Surface Area = 6 + 6 + 21 + 42 + 21 = 96

Given a quadratic function y = 36 - x² , the intervals over which the function is increasing is: (-∞ , 0) and the intervals over which the function is decreasing is:  (0, ∞).

The standard form of a quadratic function is given by:

f(x) = ax² + bx + c

If a > 0, the graph of the function opens upward and the extreme point is the minimum one.

If a < 0, the graph of the function opens downward and the extreme point is the maximum one.

In this case, the function is: y = 36 - x²

Since the coefficient of the quadratic term is negative, or a < 0, then the graph opens downward and has a maximum point.

y = 36 - x²  is already in the form of perfect square, hence, we can immediately compute:

x-intercepts : (-6,0) and (6,0)

y-(intercept = maximum point = (0, 36)

Before the maximum point, the function is increasing, while after the maximum point, the function is decreasing.

Hence,

increasing interval = (-∞ , 0)

decreasing interval = (0, ∞)

Your question is incomplete, most likely, it was:

Find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.

y = 36 - x²

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Answer: 5

Step-by-step explanation:

For how many teachers are both p ∧ r true and q false?

(p ∧ r) ∧ (q')

q' = q complement (not in q)

p intersection r = (p ∧ r) = 9

both p ∧ r true and q false = (8+6) - 9

both p ∧ r true and q false = 14 - 9 = 5

OR

p + r - p ∧ r

8 + 6 - 9 = 14 - 9 = 5

Answer:

The answer is C (5) on Edge.

Step-by-step explanation:

Answer:

Maybe the same as the angle of F (46)

Step-by-step explanation:

If you see the two shapes are the same. but different size. so therfore the angles are same.  

The concepts that we use are

1. circumcenter of the circle.

b. Area of the circle  

c. Area of the circle

d. Circumference of the circle.

The circumference of a circle is the distance around its outer boundary, while the area of a circle is the total space enclosed within its boundary.  

The formula we use in a given problem depends on the context of the problem the following situations can be understood as follows

Here we have 5 situations

a. The distance around a circular track.

Here to find the distance around the circular track we need to calculate the perimeter of the circular track i.e circumcenter of the circle.

b. The total number of equally-sized tiles on a circular floor.

The total size of tiles on the circular floor represents the area of the circle. Hence we need to use the area of the circle  

c. The amount of oil it takes to cover the bottom of a frying pan.

The amount of oil that spread on the bottom of the pan will equal the area of the circular surface of the pan

Hence, we need to use the Area of the circle

d. The distance your car will go with one turn of the wheels.

The distance will cover by the wheel will equal to boundary line around the wheel hence, we need to use the circumference of the circle.

Therefore,

The concepts that we use are

1. circumcenter of the circle.

b. Area of the circle  

c. Area of the circle

d. Circumference of the circle.

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Complete Question:

For each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning.

a. The distance around a circular track.

b. The total number of equally-sized tiles on a circular floor.

c. The amount of oil it takes to cover the bottom of a frying pan.

d. The distance your car will go with one turn of the wheels.

Answer:

6

Step-by-step explanation:

\(12h-6=30+6h \\ \\ 6h-6=30 \\ \\ 6h=36 \\ \\ h=6\)

The sequences of transformations can be used to support Sara's claim that is A; a reflection over the y-axis, followed by a reflection over the x-axis.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs), etc.

Given that Sara claims that a sequence of transformations carries Rectangle 1 onto Rectangle 2.

When a graph is reflected along an axis, it says x-axis, then that leads the graph to go just to the opposite side of the axis as if we can see it in a mirror.

If we study it more, then we will find that it is symmetric, however, each point is equidistant from the axis of reflection as that of the image of that point.

Therefore, The sequences of transformations can be used to support Sara's claim that is A; a reflection over the y-axis, followed by a reflection over the x-axis.

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Answer: the answer is $35 per hour

Step-by-step explanation:

at the store worked on the computer for 4 hours and charged her $85 for parts. The

total was $225. Write and solve an equation which can be used to determine x, the

cost of the labor per hour