You purchase a t-shirt for $9.55 and a pair of jeans for 18.12 from Old Army at 7% sales tax.

How much change should you receive if you give the cashier two twenty-dollar bills?

a. On the basis of the utility formula above,  if you were risk-averse with A = 4, you would select either investment 3 or investment 4.

b. If you were risk-neutral, you would select investment 4 with an expected return of 0.24.

c.  The variable (A) in the utility formula represents the investor's aversion to risk. The correct answer is B

To determine the optimal investment based on the utility formula, we need to calculate the utility value for each investment option and compare them.

Investment 1:

Expected Return (E(r)) = 0.12

Standard Deviation (σ) = 0.302

Investment 2:

Expected Return (E(r)) = 0.15

Standard Deviation (σ) = 0.503

Investment 3:

Expected Return (E(r)) = 0.21

Standard Deviation (σ) = 0.164

Investment 4:

Expected Return (E(r)) = 0.24

Standard Deviation (σ) = 0.21

Utility formula: U = E(r) - 1/2Aσ^2

(a) Risk-Averse (A = 4):

To calculate the utility value for each investment:

Investment 1:

U1 = 0.12 - 1/2 * 4 * (0.302)^2

U1 ≈ 0.02

Investment 2:

U2 = 0.15 - 1/2 * 4 * (0.503)^2

U2 ≈ 0.02

Investment 3:

U3 = 0.21 - 1/2 * 4 * (0.164)^2

U3 ≈ 0.20

Investment 4:

U4 = 0.24 - 1/2 * 4 * (0.21)^2

U4 ≈ 0.20

Since investments 3 and 4 have the highest utility values of approximately 0.20, if you were risk-averse with A = 4, you would select either investment 3 or investment 4.

(b) Risk-Neutral (A = 0):

When an investor is risk-neutral (A = 0), the utility formula simplifies to U = E(r). In this case, we only consider the expected return.

Comparing the expected returns of the investments:

Investment 1: 0.12

Investment 2: 0.15

Investment 3: 0.21

Investment 4: 0.24

Based on expected returns alone, if you were risk-neutral, you would select investment 4 with an expected return of 0.24.

(c) The variable (A) in the utility formula represents the

b. investor's aversion to risk.

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Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

Answer:

slope is zero

Step-by-step explanation:

slope is the difference of the y-values over the difference of the x-values

(-3-(-3)) ÷ (5-2)

0/3

Answer:

Step-by-step explanation:

x/7 - 13 ≥ -11

x/7 ≥ 2

x ≥ 14

m/-6 + 16 ≥ 19

m/-6 ≥ 3

m/6 ≤ -3

m ≤ -18

Answer:

564.7 cm^3

Step-by-step explanation:

volume of cone =1/3*π*r^2*h

=(1/3)*(22/7)*7^2*11

=564.7 cm^3 (1 d.p.)

Answer:

How tall are you

ez clappp

The given length measurements are converted and given below.

Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.

Given is to convert the given measurements as -

a) 192 km

b) 15500 dam

c) 85000 m

d) 3360 hm

e) 860000 dm

We can write the measurements as -

a) 192 km            

192 Km = 192000 meters

b) 15500 dam

15500 dam = 15500 x 10 = 155000 meters

c) 85000 m

85000 m = (85000/1000) Km = 85 Kilometers

d) 3360 hm

3360 hm = 3360 x 100 = 336000 meters

e) 860000 dm

860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter

Therefore, the given length measurements are converted and given above.

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Answer:

Length of the shorter diagonal is 8.68 cm.

Step-by-step explanation:

Length of the side AB = 11 cm

Length of side BC = 5 cm

Angle between these sides, m∠ABC = 50°

By cosine rule in ΔABC,

AC² = AB² + BC² - 2AB.BC.cos B

AC² = (11)² + 5² - 2(11)(5)cos50°

AC² = 121 + 25 - 70.71

AC = √(75.29)

AC = 8.68 cm

By the property of parallelogram,

m∠B + m∠C = 180° [Interior consecutive angles]

50° + m∠C = 180°

m∠C = 130°

Similarly, In ΔBCD,

BD² = BC² + CD² - 2BC.CD.cos130°

BD² = (5)² + (11)² - 2(5)(11)cos130°

BD² = 25 + 121 + 70.71

BD² = 216.71

BD = 14.72 cm

Therefore, length of the shorter diagonal will be 14.72 cm.

9514 1404 393

Answer:

  x = 50

  y = 33

Step-by-step explanation:

In a right triangle the acute angles are complements of each other.

  x = 90 -40

  x = 50

__

An exterior angle of a triangle is equal to the sum of the remote interior angles. Here, that means ...

  71° +x° = 2y° +55°

  16 +x = 2y . . . . . . . . . . . . . subtract 55°, divide by °

  (16 +50)/2 = y = 33 . . . . . divide by 2 and substitute for x

The values of x and y are 50 and 33, respectively.

Answer:

$71.39

Step-by-step explanation:

So we can go ahead and add the extra money they paid (sales tax and tip).

15% + 6% = 21%

Then we can find 21% of 59 then that will be our extra money we're paying.

59 × 0.21 = 12.39

Then we add that amount to our 59 to get the total amount.

59 + 12.39 = 71.39

Answer:

0.1111

Step-by-step explanation:

That the repeating decimal

Answer:

Quadrant 2

Step-by-step explanation:

-8 - 9 = -17

5 - (-1) = 6

(-17, 6) = second quadrant

Answer:

Given equation:

To plot the line first find two points:

Plot (0, -3) and (5, -1) and connect the points with a line. This will be the required line.

Use Pythagorean to find the missing leg:

The probability of getting two students with the same major is higher for liberal arts majors, followed by business majors, engineering majors, and science majors.

To calculate the probability of getting two specific majors when selecting two students at random, we need to know the total number of students in each major. Let's assume there are 100 engineering majors, 150 business majors, 75 science majors, and 200 liberal arts majors.

The probability of selecting an engineering major as the first student is 100/525 (total number of students). The probability of selecting another engineering major as the second student is 99/524 (one less student in the pool). Multiplying these probabilities gives us 0.036 or 3.6% chance of getting two engineering majors.

Similarly, the probability of getting two business majors is (150/525) * (149/524) = 0.082 or 8.2%, two science majors is (75/525) * (74/524) = 0.023 or 2.3%, and two liberal arts majors is (200/525) * (199/524) = 0.151 or 15.1%.

Therefore, the probability of getting two students with the same major is higher for liberal arts majors, followed by business majors, engineering majors, and science majors.

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Answer:

X x N=C if N>0

Step-by-step explanation:

If C is the total price of all bears x will be a single bear's price, as such x multiplied by the amount of bears will be your answer or X x N = C as long as N is greater than or equal to 0

Answer:

P(B) = 0.46

Step-by-step explanation:

Probability

The complementary event of a given event A is defined as "not A" or the event that A does not occur.

For example, if A is defined as 'getting a job', then the complement of A is 'not getting a job'.

Event A and its complementary event (call it B) must satisfy:

P(A) + P(B) = 1

If we know P(A)=0.54, then

P(B) = 1 - P(A)

P(B) = 1 - 0.54

P(B) = 0.46

Answer: (B)

Step-by-step explanation:

We can see that the rise is 1 because the y value increases by 1 for every increase of the x value.

Using a similar strategy, we can see that the x value increases by 1 for every increase in the y value.
Therefore the run is 1

(B)

Answer:

1)8

2)25

3)20

Step-by-step explanation:

I hope this helps :)

Let me know if you have any questions

Answer:

1. 8

2. 25

3. 20

(a) We have found that if s = Kr and a = -1, then w(x, t) is a solution of the partial differential equation:

wt(x, t) = Kw\(e^{st}\)x

(b) The function w(x, t) = \(e^{-4t^{2} }\)cos(2x) does not satisfy the initial and boundary conditions of the given problem.

To solve this problem, let's go through the steps one by one.

(a) We are given the partial differential equation:

u₂(x, t) = Kur(x, t) + au(x, t)

We introduce a new dependent variable w(r, t) by defining u(x, t) = \(e^{st}\)w(x, t).

First, let's calculate the partial derivatives of u(x, t) with respect to x and t:

∂u/∂x = ∂(\(e^{st}\)w)/∂x = \(e^{st}\)∂w/∂x

∂u/∂t = ∂(\(e^{st}\)w)/∂t = s\(e^{st}\)w + \(e^{st}\)∂w/∂t

Now let's substitute these expressions back into the original equation:

u₂(x, t) = Kur(x, t) + au(x, t)

\(e^{2st}\)w = K\(e^{st}\)rw + as\(e^{st}\)w + a\(e^{st}\)∂w/∂t

Dividing through by \(e^{st}\), we get:

\(e^{st}\)w = Krew + asw + a∂w/∂t

Now, we can differentiate this equation with respect to t:

∂/∂t (\(e^{st}\)w) = ∂/∂t (Krew + asw + a∂w/∂t)

Differentiating term by term:

s\(e^{st}\)w + \(e^{st}\)∂w/∂t = Kr\(e^{st}\)rw + as∂w/∂t + a∂²w/∂t²

Rearranging the terms:

s\(e^{st}\)w - as∂w/∂t - a∂²w/∂t² = Kr\(e^{st}\)rw - \(e^{st}\)∂w/∂t

Now, notice that we have \(e^{st}\)w on both sides of the equation. We can cancel it out:

s - as∂/∂t - a∂²/∂t² = Kr - ∂/∂t

This equation must hold for all values of x and t. Therefore, the coefficients of the derivatives on both sides must be equal:

s = Kr

a = -1

Thus, we have found that if s = Kr and a = -1, then w(x, t) is a solution of the partial differential equation:

wt(x, t) = Kw\(e^{st}\)x

(b) Now, we are given the function w(x, t) =\(e^{-4t^{2} }\)cos(2x). We need to show that it is a solution of the initial-boundary value problem:

wt(x, t) = wrx(x, t), 0 < x < π/2, t > 0

w(x, 0) = 0, 0 ≤ x ≤ π/2

w(0, t) = 0, t ≥ 0

Let's calculate the partial derivatives of w(x, t):

∂w/∂t = -8t\(e^{-4t^{2} }\)cos(2x)

∂w/∂x = -2\(e^{-4t^{2} }\)sin(2x)

Now, let's calculate the partial derivatives on both sides of the given partial differential equation:

wt(x, t) = -8t\(e^{-4t^{2} }\)cos(2x)

wrx(x, t) = -2\(e^{-4t^{2} }\)sin(2x)

We can see that wt(x, t) = wrx(x, t), satisfying the partial differential equation.

Next, let's check the initial and boundary conditions:

w(x, 0) = \(e^{-4(0)^{2} }\)cos(2x) = \(e^{0}\)cos(2x) = cos(2x)

The initial condition w(x, 0) = 0 is not satisfied because cos(2x) ≠ 0 for any x.

w(0, t) = \(e^{-4t^{2} }\)cos(0) = \(e^{-4t^{2} }\)

The boundary condition w(0, t) = 0 is not satisfied because \(e^{-4t^{2} }\) ≠ 0 for any t.

Therefore, the function w(x, t) = \(e^{-4t^{2} }\)cos(2x) does not satisfy the initial and boundary conditions of the given problem.

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Answer: 36 years

Step-by-step explanation:

You can use the Rule of 72 to calculate how long it might take the house to double in value.

The Rule of 72 works by dividing 72 by the interest rate as a whole number and the result will be a rough estimate of the time in years it will take for the investment to double in size:

= 72 / 2

= 36 years

When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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Answer: I agree

Step-by-step explanation:

He right i came too late lol

Answer:

value of n is 3,150 .... .

Answer:

n = 3150 is the answer

Step-by-step explanation:

63 x 50 = 3150/5000

Answer:

There are no solutions

Step-by-step explanation:

Answer:

62.5 degrees

Step-by-step explanation:

180-55= 125

125/2 = 62.5

The value for angle \(x\) will be \(70^0\) .

Angle is when two rays meet together then the space between them is angle.

We have,

\(x=?\)

A triangle with one of its angle equals to \(55^0\) and two sides are equal .

So,

"When two sides are equal then the interior angles opposite to these lines are also equal".

So,

According to the above mentioned theorem the angle other than the angle \(x\) will be \(55^0\) .

Now, Using angle sum property,

\(x+55^0+55^0=180^0\)

\(x=180^0-110^0\)

\(x=70^0\)

So, the value of \(x\) is \(70^0\) which is find out using the angle sum property.

Hence, we can say that the value for angle \(x\) will be \(70^0\) .

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Answer:

20\(\frac{3}{4}\)

Step-by-step explanation:

15.5=15 \(\frac{1}{2}\)

51/4 + 15 1/2

20 3/4

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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The correct answer is:f' (w) = (3w² + 4).

The derivative of f (w)

= w³ + 4w

is given below and we need to enclose the numerators and denominators in parentheses. Thus

,f'(w)

= (d/dw) (w³ + 4w)

= d/dw(w³) + d/dw(4w)

= 3w² + 4.

The correct answer is:f' (w)

= (3w² + 4).

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Answer:

when the #8 lines up with he 40