Luke invested $69,000 in an account paying an interest rate of 5.1% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 19 years?

Note that [tex]U(W) = W^{0.5}[/tex]

Answer:

Mary's risk premium is $0.9375

Step-by-step explanation:

Mary's utility function,  [tex]U(W) = W^{0.5}[/tex]

Mary's initial wealth = $100

The gamble has a 50% probability of  raising her wealth to $115 and a 50% probability of lowering it to $77

Expected wealth of Mary, [tex]E_w[/tex]

[tex]E_{w}[/tex] = (0.5 * $115) + (0.5 * $77)

[tex]E_{w}[/tex] = 57.5 + 38.5

[tex]E_{w}[/tex] = $96

The expected value of Mary's wealth is $96

Calculate the expected utility (EU) of Mary:-

[tex]E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75[/tex]

The expected utility of Mary is $9.75

Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where

U(EW - P) is equal to Mary's expected utility from the risky gamble.

U(EW - P) = EU

U(94 - P) = 9.63

Square root (94 - P) = 9.63

If Mary's risk premium is P, the expected utility will be given by the formula:

[tex]E_{u} = U(E_{w} - P)\\E_{u} = U(96 - P)\\E_u = (96 - P)^{0.5}\\(E_u)^2 = 96 - P\\ 9.75^2 = 96 - P\\95.0625 = 96 - P\\P = 96 - 95.0625\\P = 0.9375[/tex]

Mary's risk premium is $0.9375

Answer:

She is 215 m from the starting point

Step-by-step explanation:

Let's begin by constructing a figurative representation of the information given (figure attached)

We know 2 sides of the triangle and the inner angle, we can therefore use the Cosine Rule

Mathematically represented as:

b² = a² + c² - 2ac(CosB)

b = ?, a = 60 m, c = 180, B = 118° (the sum of the 90° right angle at B + the interior angle of 28° from A)

b² = 60² + 180² - 2(60)(180)Cos 118°

b² = 3600 + 32400 - (- 10140.586)

b² = 46140.586 ⇒ b = [tex]\sqrt{46140.586}[/tex]

b = 214.8 m ≈ 215 m

b = 215 m (to the nearest whole number)

∴ the student is 215 m from the starting point

Answer:

Step-by-step explanation:

Apply the  priority rule,

(458+56)-134=514-134=380

Answer:

C)

Step-by-step explanation:

3x+2>5

3x>3

x>1

I believe that you mistyped C so I think its C

Answer:

(c) Observational Distribution

(d) Diet Choice

Step-by-step explanation:

Out of 1033 American adults interviewed in July 2018, 5% consider themselves to be vegetarian.

Since the poll observes the diet habit of the respondents, the cited 5% is part of the Observational distribution of whether the respondent is a vegetarian or not (which is the Diet Choice).

If on the other hand, the poll seeks to manipulate the conditions of the study, it would have been an experimental distribution.

Answer:

9.1 Inches

Step-by-step explanation:

Length of the proposed box=11 Inches

Width of the proposed box=8 Inches

Required Volume, [tex]V \geq 800 $ cubic inches.[/tex]

Volume of a Rectangular Prism =Length X Width X Height

Therefore:

[tex]800\\11*8*Height\geq 800\\88*Height \geq 800\\$Divide both sides by 88\\Height \geq 800 \div 88\\Height \geq 9.\overline{09}$ inches[/tex]

Therefore, the minimum height to the nearest tenth of an inch is 9.1 Inches.

Answer:-111

Step-by-step explanation:

Answer: choice D

Step-by-step explanation:

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

in this exampke the constant(d) is -3

Answer:

D is the correct answer.

Step-by-step explanation:

because the numbers are decreased by -3

 Defination: in arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

Answer:

The degree would be 4

Step-by-step explanation:

When you add polynomials without multiplying bases, you cannot add or subtract the degree. So the highest degree would be 4 in this case.

Question:

The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or afternoon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius.At 5 p.m, the temperature is halfway between the temperature at 2 p.m. and the temperature at 8 p.m.

What coordinates represent the temperature at 5 p.m.?

Answer:

(5, 2)

=> At 5pm, the temperature is at 2⁰C

Step-by-step Explanation:

Coordinates of any point on a cartesian/coordinate plane is represented by (x, y). Where x is the number at the point on z-axis, while y is the number at the same point on the y-axis.

From the diagram of the coordinate plane attached below, we can simply find out what coordinates represent the temperature at 5pm.

==> Given that the temperature at 5pm is half way between the temperature at 2pm (y=7) and temperature at 8pm (y=-3), the point that is being referred to = [7+(-3)] ÷ 2 = ⁴/2 = 2 (i.e. 2 on the y axis representing temperature)

*The position of the point is indicated in the second picture that is attached below.

At that position of the point, we have 2 as the coordinate for the y axis representing temperature, and at that same position, we have 5 on the x-axis representing the number of hours.

Therefore, coordinates of the point (x, y) representing 5p.m = (5, 2)

==> At 5pm, the temperature is at 2⁰C

Answer:

Look above for a good answer!

Step-by-step explanation:

The coordinates are 5,2

Answer:

D

Step-by-step explanation:

Let's derive the equations for the two graphs;

For the graph towards the right,

The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)

Let's choose points;

(2,1) and (3,2)

The slope = 2-1/ 3-2 = 1/1 = 1

From the general equation of a line

y = mx + c = 1× x + (-1) = x-1

y = x-1

Similarly for that towards the left we have;

The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)

Let's choose points;

(2,1) and (3,2)

The slope = 2-1/ 3-2 = 1/1 = 1

From the general equation of a line

y = mx + c = 1× x + (-1) = x-1

y = x-1

Similarly for that towards the left we have;

The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)

Let's choose points;

(-7,0) and (-4,-3)

Slope = -3-0/ -4-(-7) = -3/ 3 = -1

From the general equation of a line

y = mx + c = -1× x + c = -x + c

Since c is not obvious we can find the equation by picking just a point along the graph along side an arbitrary (x,y) point hence we have for slope;

If we pick (-7,0)

y-0 / x-(-7) = -1

y / x+7 = -1

y = -x -7

The equations of the graphed lines are;

y=x-1

y=-x-7

Look at option D you we see it's the same as the equation of the graph towards the right y=x-1

For the records

y=[x+3]-4 = x+3-4 = x-1

Answer:

The correct answer is c. 29

Step-by-step explanation:

Answer:

[tex]4x^2+3x-2[/tex]

Step-by-step explanation:

We are given that

[tex]\frac{8x^3+2x^2-7x+2}{2x-1}[/tex]

We have to divide the polynomials.

We have

Divisor polynomial=[tex]2x-1[/tex]

Dividend polynomial=[tex]8x^3+2x^2-7x+2[/tex]

[tex]\frac{8x^3+2x^2-7x+2}{2x-1}=4x^2+3x-2[/tex]

Quotient=[tex]4x^2+3x-2[/tex]

Remainder=0

Answer:

3.93% probability that both say service is poor

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The customers are chosen without replacement, and the order in which they are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability that both say service is poor?

Desired outcomes:

Two saying it is poor, from a set of 66. So

[tex]D = C_{66,2} = \frac{66!}{2!(66-2)!} = 2145[/tex]

Total outcomes:

Two customers from a set of 331. So

[tex]T = C_{331,2} = \frac{331!}{2!(331-2)!} = 54615[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{2145}{54615} = 0.0393[/tex]

3.93% probability that both say service is poor

Answer:

no

Step-by-step explanation:

Answer:

5.029ft

Step-by-step explanation:

[tex](titer \div 360) \times \pi \times diameter[/tex]

Answer:

Step-by-step explanation:

Answer:

The best estimate of the proportion for all eligible voters in the​ town, that is, the best estimate for the population, is 0.47.

Step-by-step explanation:

Since the sample is large enough, the proportion from the sample is the best estimate for the proportion of the population.

In this question, we have that:

For the sample, the proportion who say that they plan to vote in the next mayoral election is 0.47

So the best estimate of the proportion for all eligible voters in the​ town, that is, the best estimate for the population, is 0.47.

Answer:

There are 4 treatments

Step-by-step explanation:

In this study, there are four treatments. Each sample from 1 to 3 was subjected to each treatments which in this case are the methods; Lind's Method, Szabo's Method, Carl's Method and Manley's Method.

Thus, the methods in this study are the treatments the samples are subjected to.

Answer: D

Step-by-step explanation: y int is when x=0, thus when there are no chirps.

Y=(1/6)x + 50

put in 0

Y=(1/6)*0 + 50

Y=50

Slope is the rate at which x changes, in this case, 1/6

Answer:

The midpoint of (-2,1) is -1. The midpoint for (-1,1) is 0.

Step-by-step explanation:

To find the midpoint you will have to add x+y then divide by 2.

Step-by-step explanation:

here is the answer u can get help from it.....

The solution to the equation (2x-4)/5 = 4 is x = 12.

To solve the equation (2x-4)/5 = 4, we will use the following steps.

Multiply both sides of the equation by 5 to eliminate the denominator as;

5[(2x-4)/5] = 5 x 4

This simplifies to:

2x - 4 = 20

Add 4 to both sides of the equation to isolate the term with x:

2x - 4 + 4 = 20 + 4

This simplifies to:

2x = 24

Divide both sides of the equation by 2 to solve for x:

(2x)/2 = 24/2

This simplifies to:

x = 12

Thus, the solution to the equation (2x-4)/5 = 4 is x = 12.

Learn more about simplification here: https://brainly.com/question/28008382

#SPJ2

The percent of daily calories does one serving of walnuts provide is 9%.

This question is solved using proportions.

We have:

-----------------

Walnut:

Thus, the amount of calories of fat is:

[tex]A = 20 \times 9 = 180[/tex]

-----------------

Percentage:

180 calories out of a daily diet of 2000 calories, so:

180*100%/2000 = 9%

The percent of daily calories does one serving of walnuts provide is 9%.

A similar question is found at https://brainly.com/question/10491646

Solution,

Given data=15,8,11,16,10,5,10

Highest score= 16

lowest score= 5

Range=highest score- lowest score

=16-5

=11

Answer:

[tex]10[/tex]

Step-by-step explanation:

Given data =

[tex]15 \: \: 8 \: \: 11 \: \: 16 \: \: 10 \: \: 5 \: \: 10[/tex]

[tex]range = height \: \: - \: lowest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: score \: \: \: \: \: \: \: \: \: \: \: \: \: score \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \: \: \: \: \: - \: \: \: \: 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 10[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

The person receives 10000 every month

for one year total principal 10000 * 12 = 120000

r= 12%p.a and t is 1yr

simple interest= 120000*12*1/100 = 14400

total money received in present year 120000 + 14400 = 134400

for 20 yrs principal becomes 10000*12*20= $2400000

simple interest = 2400000*12*20/100= $5760000

total amount received for 20 yrs = 2400000+ 5760000=8160000.

present value of principal as money receive 10000 for 10 yrs = 10000*10 = 100000

si = 100000*10*12/100= 120000

amount = $220000

Answer:

0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection

Step-by-step explanation:

For each truck, there are only two possible outcomes. Either they pass the inspection, or they do not. The probability of a truck passing the inspection is independent of other trucks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

80% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection.

This means that [tex]p = 0.8[/tex]

17 trucks:

This means that [tex]n = 17[/tex]

What is the probability that at least 10 but fewer than 13 trucks pass the inspection

[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{17,10}.(0.8)^{10}.(0.2)^{7} = 0.0267[/tex]

[tex]P(X = 11) = C_{17,11}.(0.8)^{11}.(0.2)^{6} = 0.0680[/tex]

[tex]P(X = 12) = C_{17,12}.(0.8)^{12}.(0.2)^{5} = 0.1361[/tex]

[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12) = 0.0267 + 0.0680 + 0.1361 = 0.2308[/tex]

0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection

Substitute [tex]y=x-8[/tex] into the second equation to get [tex]2x+3(x-8)=1,[/tex] which simplifies to [tex]5x=25,[/tex] so [tex]\boxed{x=5}.[/tex] It easily follows that [tex]\boxed{y=-3}.[/tex]

Answer:

x=5, y=-3

Step-by-step explanation:

Answer:

219.91cm²

Step-by-step explanation:

The question is not properly structured. Here is the complete question.

A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.

Area of a sector = theta/360 × πr²

theta is the angle substended by the circle

r is the radius of the circle.

Given radius = 10cm

theta = 252°

Area of a sector = 252°/360° × π(10)²

Area of a sector = 252/360 × 100π

Area of a sector = 79168.13.360

Answer:

Step-by-step explanation:

The question is not properly structured. Here is the complete question.

A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.

Area of a sector = theta/360 × πr²

theta is the angle substended by the circle

r is the radius of the circle.

Given radius = 10cm

theta = 252°

Area of a sector = 252°/360° × π(10)²

Area of a sector = 252/360 × 100π

Area of the sector = 219.91cm²

Answer:

70pi

Step-by-step explanation:

That is the answer on khan academy