Given: F(x) = 3xˆ2+ 1, G(x) = 2x-3, H(x) = x F(-2) =

heeeelp

This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of  Bonds = 1 - 0.646628

Weight of  Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,

Best feasible CAL = (12.88% - 5.5%)/ 23.34%

Best feasible CAL = 0.3162

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Full Question

See the attached spread sheet for additional information related to the questions.

The number must be between 20 and 30.

The square of the whole number can be found as follows;

The square of the whole number is between 500 and 900. The number must be between 20 and 30.

The number is an whole number.

Therefore, the number will be between 20 and 30.

20² = 400

30² = 900

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Answer:

See below

Step-by-step explanation:

GCF (greatest common factor ) of 42 and 30   is  6

  each row will have 6 seedlings

     there will be  (  42+30) / 6 = 12 rows

                   7 pine rows    5 juniper rows

The approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 5.

Hence, Mean,μ=46 and Standard deviation,σ=5.

To find the probability of daily phone calls numbering between 36 and 56,

P(36≤X≤56)

To convert the X score to Z score, use the formula, Z=(X-μ)/σ

Then we get,

P((36-46)/5 ≤ Z ≤ (56-46)/5) = P(-2 ≤ Z ≤ 2)

By using the property of the normal bell curve, we get

P(-2 ≤ Z ≤ 2) = P(2 ≤ Z) - P(-2 ≤ Z)

As per the normal distribution table,

P(2 ≤ Z) - P(-2 ≤ Z) = 0.9772-0.0228

∴ P(36≤X≤56) = 0.9544

Hence, the approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.

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The answers to the questions are

a. From the table the probability of having 6 girls in 8 birth is given as

0.109.

b. The probability of 6 or more girls in 8 births

p(6) + p(7) + p(8)

= 0.109 + 0.016 + 0.002

= 0.127

c. The result from b is the relevant factor given that it includes the probability of getting 6, 7 and 8 girls.

D. No six is not a significantly high number of girls in 8 births. This conclusion is from the fact that 0.109 is greater than 0.05.

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Answer:

X=-14

Step-by-step explanation:

16+22+x=24

38+x=24

x=24-38

x=-14

The solution to the expression is 18

The area of the poster is  28.75 feet square.

Note that the area of a rectangle is given as;

Area = length × width

Length = 11. 5 feet

Width = 2. 5 feet

Area = 11. 5 × 2. 5

Area = 28. 75 feet square

Thus, the area of the poster is  28.75 feet square.

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The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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Answer: The spin of the wheel by the contestant is an illustration of a sine function whose equation is y = -1.25sin(0.8x + 0.25)

The equation that represents the function will be; y = -1.25sin(0.8x) + 0.25

Suppose that we've got

[tex]f(x) = a\sin(bx + c) + d[/tex]

Amplitude or maximum height from average motion horizontal axis

= a + d

Thus, the minimum low from horizontal axis is –a + d (sin ranges from -1 to 1, and multiplying a to it make it range from -a to a).

A sine function is represented as:

y = Asin(B(x+C)) + D

Now, Substitute the calculated values,

y = -1.25sin(0.8(x+C)) + 0.25

The horizontal shift (C) is 0.

So, the function will be;

y = -1.25sin(0.8x) + 0.25

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Answer:

A

Step-by-step explanation:

If you were to substitute 2 or -3 into equation A, the denominator would be zero and you would have to divide by zero. Thus there are asymptotes for this function at -3 and 2, matching the graph

a. The equation of the tangent at (1,3) is y = -x/3 + 10/3

b. The equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

Since x² + y² = 10, we differentiate the equation with respect to x to find dy/dx which the the equation of the tangent.

So, x² + y² = 10

d(x² + y²)/dx = d10/dx

dx²/dx + dy²/dx = 0

2x + 2ydy/dx = 0

2ydy/dx = -2x

dy/dx = -2x/2y

dy/dx = -x/y

At (1,3), dy/dx = -1/3

Using the equation of a straight line in slope-point form, we have

m = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

-1/3 = (y - 3)/(x - 1)

-(x - 1) = 3(y - 3)

-x + 1 = 3y - 9

3y = -x + 1 + 9

3y = -x + 10

3y + x = 10

y = -x/3 + 10/3

So, the equation of the tangent at (1,3) is y = -x/3 + 10/3

Since the tangent and normal line are perpendicular at the point, for two perpendicular line,

mm' = -1 where

So, m' = -1/m

= -1/(-1/3)

= 3

Using the equation of a straight line in slope-point form, we have

m' = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

3 = (y - 3)/(x - 1)

3(x - 1) = (y - 3)

3x - 3 = y - 3

y = 3x - 3 + 3

y = 3x + 0

y = 3x

So, the equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

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Answer:36

Step-by-step explanation:

Let name the missing angle in the triangle w.

We know that x+z+w=180

We also know that z+w=3z=y.

That means that w=2z.

x=2z, so, 2z+2z+z=180

z=36

Answer:

Z=36 degrees

Step-by-step explanation:

Since angles x and y are supplementary, you know that they add up to 180 degrees.

Since we know that:

=x+y

=2z+3z

=5z

=180 degrees

180/5=36 degrees, so Z=36 degrees

Answer:

The temperature was 3 degrees colder in the afternoon

Step-by-step explanation:

numbers on the left of zero on the number line are arranged in decreasing order and as such -2 is greater than -5.

The true statement is The temperature was 3 degrees colder in the afternoon.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

Given that, Darcy read her thermometer in the morning and the temperature was -2° C. In the afternoon, the same thermometer showed a temperature of -5° C.

-2-3 = -5

We see, that, the temperature is falling from -2 to -5, that means, there was a fall in temperature from morning to afternoon.

Hence, the temperature was 3 degrees colder in the afternoon.

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The type of reflection performed and the scale factor of dilation of the diagram are; Reflection over the x-axis and a scale factor dilation of 2.

From the given diagram, we are told that triangle ABC is transformed into Triangle A"B"C".

Now, we are told that both triangles are similar and as such if they are similar then, it means each corresponding side has the same ratio. Thus, there was a dilation by a scale factor of 2.

Now, the reflection that took place after the dilation would be a reflection over the x-axis.

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The pricing scheme of the function is (a) The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.

The points are given as:

The constant interval implies that the first two hours cost $2

Next, we calculate the slope/rate of the other points.

This is done using

m = (y2 - y1)/(x2 - x1)

So, we have:

m1 = (10 - 2)/(6 - 2) = 2

m2 = (11 - 10)/(7 - 6) = 1

This means that:

Hence, the pricing scheme of the function is (a)

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g(x) is a translation of f(x), we have:

g(x) = f(x) - 3

We have the two functions:

[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]

We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):

[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]

So we have:

g(x) = f(x) - 3

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Answer:

Step-by-step explanation:

Answer: 11

Step-by-step explanation: 40-28= 12-1=11

Answer:

11 apples are left.

Step-by-step explanation:

Since Billy ate 28 apples from the 40 apples he had at the start, you have to subtract 40-28, which equals 12. Lastly, you subtract 12-1, since a kid asks Billy for an apple.

The 53,000 units produced and the increase in sales of 50,400 - 48,000 = 2,400 units, give an impact (increase) in profit of $168,000

Price per unit = $70

Number of units produced = 53,000

Number of units sold = 48,000

Material cost per unit = $21

Labour cost per unit = $10

Manufacturing overhead = $2

Selling and administrative overhead = $4

Fixed cost = $1,060,000

Administrative expenses = $557,000

Advertising cost = $43,000

Percentage increase in sales = 20%

Number of units sold in Year 2 = 1.2 × 12,000 = 14,400

Total cost = 53000×(21+10+2+4) + 1,060,000 + 557,00 = 3,578,000

Total revenue in Year 1 = 70 × 48,000 = 3,360,000

Profit in Year 1 = 3,360,000 - 3,578,000 = -218,000

Total revenue in Year 2 = 70 × (36,000+14,400) = 3,528,000

Profit in Year 2 = 3,528,000 - 3,578,000 = -50,000

The impact on the profit is therefore;

-50,000 - (-218,000) = 168,000

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Answer:

y = 21

Step-by-step explanation:

When x is directly proportional to y:

When x increases, y also increases.

In this case, it is so you write,

1. Write down the formula: y=kx

k being the constant.

Let's use "When x = 4, y = 7" to work out the constant.

2. Substitute the 'when' values: 7=k×4

3. Rearrange to find the constant: 7÷4=k

4. Find k: k=1.75

Now let's see the new problem, 'what is y when x = 12'.

5. Substitute the values now but keep the constant: y = 1.75 × 12

6. Rearrange if needed.

7. Find the missing value: y = 21

Hope this helped and if you require further assistance from me please comment below! :)

Ps: If it was inversely proportional then the formula would be y = k / x

with k still being the constant.

The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.

Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.

Thus in the given question, it can be deduced that;

The population of people living in White Plains =56,853

The population of people living in Elmira = 29,200

So, the difference in the population between the two cities can be determined as;

                         = 56,853 - 29,200

                         = 27,653

Thus, the number of fewer people living in Elmira than in White Plains is 27,653

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The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

It should be noted that from the information given, we are given the information about three salesmen and their sales.

The total earnings for salesman A will be:

= (1300 × 3) + 65 × (11 + 14 + 16)

= 3900 + 2730

= 6630

The total earnings for salesman B will be:

= 300 × 3 + 40 × (14 + 15 + 13)

= 900 + 1680

= 2580

The total earnings for salesman C will be:

= 900 × 3

= 2700

Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

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Step-by-step explanation:

2y - x = 6

2y = x + 6

y = (x + 6) / 2

the slope is 1 and the y int is 3

The half-life of the given exponential function is of 346.57 years.

It is the value of t when A(t) = 0.5A(0).

In this problem, the equation is:

[tex]A(t) = A(0)e^{-0.002t}[/tex].

In which t is measured in years.

Hence the half-life is found as follows:

[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]

[tex]e^{-0.002t} = 0.5[/tex]

[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]

[tex]0.002t = -\ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]

t = 346.57 years.

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The true statements about terms in geometry that are undefinable are;

Three undefinable terms in geometry are;

1) Point

2) Line

3) Plane

The above terms do not have a formal definition but they can be described based on their properties.

The other geometric terms are defined based on the above undefinable terms.

A point can be described as a location in space that is dimensionless and can be specified on the coordinate plane as an ordered pairs (x, y).

True statements about a point are therefore;

A line is infinitely long, that has no beginning or end. It has one dimension, with no thickness or height.

Given that a point is dimensionless, a line can be considered a set of points.

A true statement is therefore;

A plane is a two dimensional geometric figure that have infinite length and width.

An infinite set of lines that forms a two dimensional figure can be used to describe a plane.

The true statement with regards to a plane is therefore;

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