12
What is the expected share return given the following macro-economic probabilities? Probability of
recession 20% - Share return 5%; Probability of steady state 60% - Share return 10%; Probability of
boom 20% - Share return 15%

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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Answer:

4x+6+4x+6=180[straight line]

8x=180-12

x=168/8

x=21° is a required answer.

The graph is missing, so i have attached it.

Answer:

From 0 hours to 2 hours.

Step-by-step explanation:

From the attached graph, we can see that on the y-axis, denotes the level of ibuprofen in the patient’s bloodstream while the x-axis denotes the amount of hours after the ibuprofen was taken.

Now, looking at the graph, we can see that the curve goes up from a time of 0 hours which corresponds to 0 mg of ibuprofen to a time of 2 hours which corresponds to 400 mg of ibuprofen.

After that point, the curve begins to to go down. Since we are concerned with increase, we will make do with the first statement.

Thus, we can say the period at which the level of ibuprofen increased was from 0 hours to 2 hours.

The given function has one root i.e. -3.

The Synthetic approach can speed up polynomial division, especially when the result needs to be divided by a linear factor. It is often used to find polynomial roots or zeroes rather than dividing components.

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

We've f(x) = x³-4x+15

               = (x+3) ( x²-3x+5) + 0

which implies that it has remainder as 0, So -3 is a root of given f(x).

Since x²-3x+5 can't be factorized more, the given function has only one root i.e. -3.

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Answer:

A

Step-by-step explanation:

the first one in the picture

Answer:

1.97497

Step-by-step explanation:

Using my calculator, I just put in log(94.4).

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:(-2,2)

Step-by-step explanation:

Answer:

96

320

Step-by-step explanation:

V = (1/3)Bh

where V = volume of pyramid; B = area of base; h = height of the pyramid

B = 8 cm * 12 cm = 96 cm^2

V = (1/3)(96 cm^2)(10 cm)

V = 320 cm^3

Answer:C and A

Step-by-step explanation:

If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.

A real number is any number that can be expressed as a decimal or fraction and exists on the number line.

If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.

Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.

From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.

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Answer:

12

Step-by-step explanation:

75 divided by 6 1/4 is 12.

Answer:

30 & 60°

Step-by-step explanation:

2x + X + 90 = 180

3x = 90

X = 30°

so the accute angles are 30° and 60°

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

Answer:

12.0625 pounds.

Step-by-step explanation:

To find your answer, divide the number of ounces by 16. The quotient is the number of pounds.

Answer:

No

Step-by-step explanation:

3 × \(\frac{2}{5}\) = \(\frac{6}{5}\) = 1 \(\frac{1}{5}\) cups required to triple her recipe

she only has 1 cup

so does not have enough to triple her recipe

Answer:

No

Step-by-step explanation:

If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.

Answer:

10 feet

Step-by-step explanation:

This is a problem of scale

where scale is

actual height of any object/ height of that object on drawing

given

actual height = 24 feet

this is represented 1/2 inch on drawing

thus

scale = actual height/ height on drawing = 24 feet/1/2 inch = 24*2 feet/ 1 inch

scale = 48 feet / 1 inch

given actual  height of a building = 480 feet

let the height on drawing be x inch

thus

48 feet / 1 inch = 480 feet/ x inch

=> x inch/ 1 inch = 480 feet / 48 feet

=> x = 10 feet

Thus,  the  height of  building on the drawing is 10 feet

Answer:

\(\dfrac{1}{\sqrt{42}}(i+4j-5k)\) and \(-\dfrac{1}{\sqrt{42}}(i+4j-5k)\)

Step-by-step explanation:

The two vectors are

\(a=i+j+k\)

\(b=5i+k\)

Unit vector is given by

\(\dfrac{a\times b}{|a\times b|}\)

\(a\times b=\begin{vmatrix} i & j & k\\1 & 1 & 1\\5 & 0 & 1\end{vmatrix}\\ =i(1-0)-j(1-5)+k(0-5)\\ =i+4j-5k\)

\(|a\times b|=\sqrt{1^2+4^2+(-5)^2}=\pm\sqrt{42}\)

\(\dfrac{a\times b}{|a\times b|}=\dfrac{i+4j-5k}{\sqrt{42}}\\\Rightarrow \dfrac{a\times b}{|a\times b|}=\pm\dfrac{1}{\sqrt{42}}(i+4j-5k)\)

The two unit vectors that are orthogonal to both given vectors is \(\dfrac{1}{\sqrt{42}}(i+4j-5k)\) and \(-\dfrac{1}{\sqrt{42}}(i+4j-5k)\).

A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.

In this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.

By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.

Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

1.45528455285

Step-by-step explanation:

Round it up to nearest 10. So it's C

Answer:

Option (2)

Step-by-step explanation:

A function 'f' has been given as,

f(x) = 3x + 1

And the inverse of this function is,

\(f^{-1}(x)=\frac{x-1}{3}\)

We have to find the value of f(2).

So we will use the expression: f(x) = 3x + 1

By substituting x = 2 in this function,

f(2) = 3×2 + 1

     = 6 + 1

     = 7

This result tells us the value of the function at x = 2.

Therefore, Option (2) will be the answer.

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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Step-by-step explanation:

867.5x ×2.8

is is equal to 2429x

Answer:

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

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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