A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:
Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL.

Answer: To find the gradient of a curve at a given point, we need to find the derivative of the function with respect to x and then evaluate it at the desired x-coordinate.

Given the function y = 3x^4 - 2x^2 + 5x - 2, we can find its derivative dy/dx as follows:

dy/dx = d/dx(3x^4) - d/dx(2x^2) + d/dx(5x) - d/dx(2)

Taking the derivative of each term:

dy/dx = 12x^3 - 4x + 5

Now, let's evaluate the derivative at the given points:

Point (0, -2):

Substituting x = 0 into the derivative:

dy/dx = 12(0)^3 - 4(0) + 5

dy/dx = 0 - 0 + 5

dy/dx = 5

Therefore, the gradient at (0, -2) is 5.

Point (1, 4):

Substituting x = 1 into the derivative:

dy/dx = 12(1)^3 - 4(1) + 5

dy/dx = 12 - 4 + 5

dy/dx = 13

Therefore, the gradient at (1, 4) is 13.

Answer:

6/MN = 8/9

8MN = 54

MN = 6 3/4

The correct answer is B.

The HCF (highest common factor) of 20 and 10 is 10.

To determine the 20 and 10's highest common factor (HCF).

We must identify the highest number that can divide both 20 and 10 without producing a remainder in order to determine the HCF.

1, 2, 4, 5, 10, and 20 are the variables that make up 20.

1, 2, 5, and 10 make up the number 10.

The biggest element that both 20 and 10 have as a shared component is 10.

The HCF of 20 and 10 is hence 10.

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Answer:

3)  A = 35.2°, B = 38.6°, C = 106.2°

4)  B = 70.4°, C = 31.6°, a = 18.7

Step-by-step explanation:

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{12^2+13^2-20^2}{2(12)(13)}[/tex]

[tex]\implies \cos(C)=\dfrac{-87}{312}[/tex]

[tex]\implies \cos(C)=-\dfrac{29}{104}[/tex]

[tex]\implies C=\cos^{-1}\left(-\dfrac{29}{104}\right)[/tex]

[tex]\implies C=106.191351...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{12^2+20^2-13^2}{2(12)(20)}[/tex]

[tex]\implies \cos(B)=\dfrac{375}{480}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{375}{480}\right)[/tex]

[tex]\implies B=38.6248438...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{20^2+13^2-12^2}{2(20)(13)}[/tex]

[tex]\implies \cos(A)=\dfrac{425}{520}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{425}{520}\right)[/tex]

[tex]\implies A=35.1838154...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 12, b = 13 and c = 20 are:

[tex]\hrulefill[/tex]

Given values of triangle ABC:

First, find the measure of side a using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is A, change C for A in the formula and swap a and c:

[tex]\implies a^2=c^2+b^2-2cb \cos (A)[/tex]

Substitute the given values and solve for a:

[tex]\implies a^2=10^2+18^2-2(10)(18) \cos (78^{\circ})[/tex]

[tex]\implies a^2=424-360\cos (78^{\circ})[/tex]

[tex]\implies a=\sqrt{424-360\cos (78^{\circ})}[/tex]

[tex]\implies a=18.6856038...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles B and C.

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{(18.6856038...)^2+18^2-10^2}{2(18.6856038...)(18)}[/tex]

[tex]\implies \cos(C)=0.852040063...[/tex]

[tex]\implies C=31.565743...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{(18.6856038...)^2+10^2-18^2}{2(18.6856038...)(10)}[/tex]

[tex]\implies \cos{B}=0.334888270...[/tex]

[tex]\implies B=\cos^{-1}(0.334888270...)[/tex]

[tex]\implies B=70.434256...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

The algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

The four translation rules are defined as follows:

Comparing the equivalent vertices, the translations for this problem are given as follows:

Hence the algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

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A function that has a degree of 5 must have the following: d. at least one real 0.

In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using specific mathematical operations.

Generally speaking, the degree of a polynomial function is sometimes referred to as an absolute degree and it is the greatest exponent (leading coefficient) of each of its term.

In conclusion, a function that has a degree of 5 is referred to as a quintic function and it is characterized by an odd degree, can't have more than 4 turning points, and must have at least one real zero.

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Answer:

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

Use midpoint equation to find each coordinate:

and

So the midpoint is (12, 16).

Answer:

Step-by-step explanation:

76 RPMs

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

Step-by-step explanation:

let the number of apples represent x

3x^2 - 22x + 35

John will need 36 feet of fence to enclose his 9-foot square garden.

A sqaure is simply a polygon made up of four equal sides, with all the interior angles measuring 90 degrees.

The perimeter of a square is expressed as:

Perimeter = 4 × side length

Given that, the side length of the square garden is 9 ft.

To calculate the amount of fence John will need to enclose his 9-foot square garden, we need to determine the perimeter of the square.

Perimeter = 4 × side length

Plug in the side length

Perimeter = 4 × 9 ft

Perimeter = 36 feet

Therefore, the perimeter of the garden is 6 feet.

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The solution is, the values are, -3, -2, [tex]\left[\begin{array}{ccc}-2&0\\0&-3\\\end{array}\right][/tex], 6.

Here, we have

given that,

the matrices are:

A = [tex]\left[\begin{array}{ccc}-1&0\\0&3\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}2&0\\0&-1\\\end{array}\right][/tex]

now, we have to find the determinant of them

|A| = -1*3 - 0

    = -3

|B| = -1*2 - 0

    = -2

Now, we have to find AB ,

we get,  A×B = [tex]\left[\begin{array}{ccc}-2&0\\0&-3\\\end{array}\right][/tex]

So, we have, the determinant value is :

|AB| = -2 * -3 - 0

      = 6

Hence, The solution is, the values are, -3, -2, [tex]\left[\begin{array}{ccc}-2&0\\0&-3\\\end{array}\right][/tex], 6.

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Answer: If 34% of the mixed fruit juice is apple juice, then 66% of it is a combination of other fruit juices. We can assume that the ratio of apple juice to other fruit juices remains the same in the ice cream and mixed fruit juice mixture.

Let the volume of ice cream in each batch be 3x litres and the volume of mixed fruit juice be 2x litres. Then the total volume of mixture in each batch is 5x litres.

If 34% of the mixed fruit juice is apple juice, then the volume of apple juice in each batch is 0.34 × 2x = 0.68x litres. The volume of other fruit juices in each batch is 2x − 0.68x = 1.32x litres.

The ratio of ice cream to mixed fruit juice is 3 : 2, so we have:

3x : 2x = ice cream : mixed fruit juice

Simplifying, we get:

ice cream = 1.5 × mixed fruit juice

Substituting the values we obtained earlier, we have:

3x = 1.5 × 2x

x = 0.75

Therefore, the volume of ice cream in each batch is 3x = 2.25 litres, and the volume of mixed fruit juice is 2x = 1.5 litres.

To make 1.5 litres of mixed fruit juice, we need 0.68 litres of apple juice and 0.82 litres of other fruit juices.

To make 12.5 litres of smoothies, we need 2.25 litres of ice cream and 10.25 litres of mixed fruit juice. Of this, 0.68 litres is apple juice and 9.57 litres is other fruit juices.

Therefore, to make 12.5 litres of smoothies, we need 0.68/1.5 × 12.5 = 5.67 litres of apple juice.

To make 51 litres of apple juice, we can make a maximum of 51/5.67 ≈ 9 batches of smoothies.

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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Answer:

A

Step-by-step explanation:

If you look at the angles or use something to measure it you can tell that a and b are opposite sides that are parallel to each other. So they are equal.

Answer:

4(1/2)(3)(5) + (3^2) = 30 + 9 = 39 ft^2

Based on the assumptions, the estimated Federal Withholding Tax for Franklin Lyons would be approximately $191.68.

Determine Franklin's taxable income:

To calculate the taxable income, we need to subtract any deductions or exemptions from his gross pay. We'll consider his gross pay as the taxable income.

Taxable Income = Gross Pay = $958.38

Estimate the Federal Withholding Tax rate:

The Federal Withholding Tax rate depends on the taxable income and the individual's filing status. Let's assume a general tax rate of 20% for this estimation.

Federal Withholding Tax rate = 20%

Calculate the Federal Withholding Tax:

To find the withholding tax, multiply the taxable income by the tax rate:

Federal Withholding Tax = Taxable Income * Federal Withholding Tax rate

= $958.38 * 0.20

= $191.68

Thus, the answer is $191.68.

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Answer:

x = 9

Step-by-step explanation:

6/(x - 1) = 21/(3x + 1)

21(x - 1) = 6(3x + 1)

21x - 21 = 18x + 6

3x = 27

x = 9

Answer:

Step-by-step explanation:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

This helped me when i was learning to solve for x

Answer:

220 in²

Step-by-step explanation:

surface area = [area of the 4 vertical faces] + area of the base + area of top.

surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)

= (80 + 100) + 20 +  20

= 220 in²

Answer:

-10

Step-by-step explanation:

The required y-intercept of the line y = 4x - 10 is -10.

What is the intercept in the equation?

In the equation, the intercept is the value of the linear function where either of the variables is zero.

Here,

The equation y = 4x - 10 is in slope-intercept form, where the coefficient of x is the slope of the line, and the constant term is the y-intercept.

So, the y-intercept of the line y = 4x - 10 is -10. This means that the line intersects the y-axis at the point (0,-10). When x is 0, the value of y is -10, which is the y-intercept.

Thus, the required y-intercept of the line y = 4x - 10 is -10.

Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

The equation of the quadratic function is y=x2−4x, the correct option is E

We are given that;

x=-4,-2,1

y=5,-5,0

Now,

The first three rows of the table, we get:

​y=−4 when x=−5y=5 when x=−2y=−3 when x=1​

Substituting into the general form, we get:

​−4=25a−5b+c5=4a−2b+c−3=a+b+c​

Solving this system of equations, we get:

​a=1b=−4c=0​

Therefore, the equation of the quadratic function is y=x2−4x.

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Answer:

a=25

b=92

Step-by-step explanation:

Because the average of the five numbers is 51, the sum of the five numbers is 255.

a+b+73+65=255

138+a+b=255

a+b=117

a+67=b

Therefore,

a=25

b=92

Feel free to tell me if I made a mistake! :)

Using the z-score values given, the area under the standard normal distribution curve is 0.123 squared units

The total area under the standard normal distribution curve is 1. Therefore, if we have a z-score, i.e., how far a value is above or below the mean, we can determine the probability of a value less than or greater than that.

The points are

A = z₂ - z₁

z₂ = 0.6230

z₁ = 0.5000

A = 0.6230 - 0.5000

A = 0.123 squared units

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MRP Scheme: Determine demand, calculate gross requirements, consider lead time, determine scheduled receipts, calculate planned order receipts, determine planned order release, monitor inventory levels, repeat process periodically. Lot-for-lot ordering, no safety stock.

MRP (Material Requirements Planning) Scheme:

Determine the Demand:

Gather the demand forecast or sales orders for the upcoming period.

Calculate the net demand by subtracting any existing inventory from the total demand.

Calculate the Gross Requirements:

Gross requirements are the total quantity of materials needed to fulfill the net demand.

Consider the lead time of two weeks when calculating the gross requirements.

Determine the Scheduled Receipts:

Check if there are any open purchase or production orders scheduled to arrive within the lead time.

Include the quantities of materials expected to be received during this period.

Calculate the Planned Order Receipts:

Subtract the scheduled receipts from the gross requirements to determine the planned order receipts.

If the planned order receipts are negative, no action is required as the scheduled receipts are sufficient.

If the planned order receipts are positive, create a purchase or production order for that quantity.

Determine the Planned Order Release:

The planned order release specifies when the purchase or production order should be initiated.

It is typically based on the lead time, taking into account any constraints or preferences.

The planned order release should ensure that the materials arrive in time to meet the net demand.

Monitor Inventory Levels:

Keep track of inventory levels regularly to identify any deviations from the plan.

If the actual inventory falls below the net demand, adjust the planned order releases accordingly.

If the actual inventory exceeds the net demand, consider reducing the planned order releases.

Repeat the Process:

Review and update the MRP scheme periodically based on the changing demand and inventory levels.

Continuously adjust the planned order releases to align with the updated requirements.

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The difference of the two polynomials is [tex]2x^3 + 2x[/tex]. Therefore option no 2 is correct from the image given.

A polynomial is a mathematical expression along with variables and coefficients, combined using only addition, subtraction, multiplication, & non-negative integer exponents.

To discover the distinction of those two polynomials, we want to carry out polynomial subtraction.

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

[tex]= x^4 + x^three + x^2 + x - x^4 + x^3 + x^2 + x ([/tex] distribute the negative sign to every term inside the 2nd set of brackets)

[tex]= 2x^3 + 2x[/tex] (integrate like terms)

Therefore, the difference of the two polynomials is [tex]2x^3 + 2x.[/tex]

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Answer: A  7x2+3y2-4x

Step-by-step explanation:

These atomic formulas represent basic assertions or relationships between elements or sets.

In logic and mathematical logic, "atomic formulas" refer to the simplest, indivisible formulas that do not contain any logical connectives or quantifiers.

They are the building blocks from which more complex formulas are constructed.

In set theory, the atomic formulas are typically statements about membership or equality.

For example, "x belongs to y" (x ∈ y) and "x equals y" (x = y) are atomic formulas in set theory.

Using logical connectives (such as conjunction, disjunction, negation, implication, and equivalence) and quantifiers (such as "for all" (∀) and "there exists" (∃)), we can combine atomic formulas to form more complex formulas, enabling us to express a wide range of logical statements and mathematical properties.

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Answer:

16 tvs

Step-by-step explanation:

Maura's earnings for the week equal her weekly salary (460) plus she earns 6.5% commission x number of flat screens sold x $414.

So: Total Earnings = 460+ 0.065*414*t where t is the number of tvs she has sold.

If total earnings = 890.56, just substitute that above and solve for t.

890.56= 460+ 0.065*414*t

430.56=0.065*414*t

430.56=26.91*t

430.56/26.91 = t

16 = t

She sold 16 tvs to earn 890.56.

A graph of the image of polygon DGF after a dilation centered at the origin with a scale factor of 1.5 is shown below.

In Geometry, a dilation is a type of transformation which typically changes the dimension (size) or side lengths of a geometric figure, but not its shape.

This ultimately implies that, the side lengths of the dilated geometric figure would be enlarged or reduced based on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of the polygon by applying a scale factor of 1.5 that is centered at the origin as follows:

D (-2, 0) → (-2 × 1.5, 0 × 1.5) = D' (-3, 0).

G (0, 2) → (0 × 1.5, 2 × 1.5) = G' (0, 3).

F (2, -2) → (2 × 1.5, -2 × 1.5) = F' (3, -3).

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The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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