Fill in the missing values to make the equations true.

The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:

Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500

Next, we can calculate the weight of each stock in the index portfolio as follows:

Weight of Stock A = $3,000 / $6,500 = 0.4615

Weight of Stock B = $2,000 / $6,500 = 0.3077

Weight of Stock C = $1,500 / $6,500 = 0.2308

The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:

Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081

The mean excess return of the index portfolio can be calculated using the single-index model as:

Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio

= 1.081 x 18%

= 19.458%

Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:

Mean Return = Mean Excess Return + Risk-Free Rate

= 19.458% + 2%

= 21.458%

Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

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The range is the difference between the maximum and minimum values in the data set. From the box plot, we can see that the maximum value is 52 and the minimum value is 16, so the range is:

Range = Maximum value - Minimum value

Range = 52 - 16

Range = 36

The IQR (interquartile range) is the difference between the first and third quartiles of the data set, which is represented by the length of the box in the box plot. From the box plot, we can see that the length of the box is:

Box length = Upper quartile - Lower quartile

Box length = 45 - 27

Box length = 18

Therefore, the range is 36, and the IQR is 18.

So the correct answer is:

The range is 36, and the IQR is 18.

Step-by-step explanation:

Notice how we have 3 relative extrema , this means our equation has a degree of 4.

Notice how at root 1, our graph bounces off the curve.

This means we have a multiplicity of 2 there so one of our roots are

[tex](x - 1) {}^{2} [/tex]

For roots -3, and 4, our graph just passes through the x axis so those are roots with a multiplicity of 1.

[tex](x + 3)[/tex]

[tex](x - 4)[/tex]

So our equation is

[tex]y = (x - 1) {}^{2} (x + 3 )(x - 4)[/tex]

The graph passes through(-1,-2) so let see if we need any constant

[tex] - 2 = a( - 2) {}^{2} (2)( - 5)[/tex]

[tex] - 2 = - 40a[/tex]

[tex] \frac{1}{20} = a[/tex]

So our equation now is

[tex] \frac{1}{20} (x - 1) {}^{2} (x + 3)(x - 4)[/tex]

The equation that best represents the graph is p(x) = (x + 3)(x - 4)(x - 1)²

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following properties

So, the base equation of the function is

p(x) = a(x + 3)(x - 4)(x - 1)²

Set a = 1

So, we have

p(x) = (x + 3)(x - 4)(x - 1)²

Hence the function is p(x) = (x + 3)(x - 4)(x - 1)²

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The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.

Rearranging the Given equation and Putting all values on other side of Zero.

x^2+2x=6

x^2+2x-6=0 ____________(1)

It can be seen that we can not have the multiples that counts of 6 so that they have a subtraction value 2. therefore, Using the Quadratic Formula for the above equation,

x=(-b±√(b²-4ac))/(2a)  ___________(2)

where

a=1

b=2

c=-6

putting the values of a,b,c in the equation (2)

x=(-2±√(4²-4*1*(-6)))/(2*1)

x=(-2±2√7)/2

x=(-1±√7)/2

Solving the Values of x in simplified form, we get x=1.645 and -3.654.

Therefore, The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.

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The value of the expression l/2 when l=50 is 25.

Given information:

The expression l/2 means "half of l".

The expression is l/2 where l is variable.

In this case, the value of l is given as 50. So to calculate the expression, you just need to substitute 50 for l in the expression and simplify:

If l = 50, then

l/2 = 50/2 = 25

Therefore, the value of the expression l/2 when l=50 is 25.

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Answer:

A

Step-by-step explanation:

sqrt 5 ( 4pi - 2pi) =   2 pi sqrt 5  for the numerator

then     2 pi sqrt (5)  / 3 sqrt (5)      the sqrt (5) 's cancel out and you have

          2pi / 3

Answer:

All real numbers

The necessary information to carry out the hypothesis are given below.

For carrying out a hypothesis examination on the information, we need to do the following steps:

Step 1: Express the null and alternative hypotheses

Step 2: Pick the pertinent measure of value and significance level

Step 3: Compute the test statistic

Step 4: Estimate the p-value

Step 5: Draw a conclusion and interpret the results

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The area of the square given in the diagram is: 25 square units.

Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Using Pythagoras theorem, we can find the length of a side of the square:

AB = √(3² + 4²)

AB = √(9 + 16)

AB = √25

AB = 5

Area of a square is given by the formula:

A = side * side

Thus:

A = 5 * 5

A = 25

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On solving the "equation" written as "5x² - 8x + 12 = 3x + 10" by using "factoring-method" , the "solutions" are x = 1/5 and x = 2.

To solve "5x² - 8x + 12 = 3x + 10" by using the "factoring-method", it should first be rearranged in "standard-form", where one side of the equation is = 0,

First, we combine the constant terms on the right side of the quadratic:

⇒ 5x² - 8x + 2 = 3x,

⇒ 5x² - 11x + 2 = 0,  Now, we factor the quadratic expression on the left side of the equation as :

⇒ 5x² - 10x -x + 2 = 0,

⇒ 5x(x - 2) -1(x - 2) = 0,

⇒ (5x - 1)×(x - 2) = 0

By applying the zero product property, we know that either "5x - 1 = 0" or "x - 2 = 0";

⇒ 5x - 1 = 0 , We get x = 1/5,

⇒ x - 2 = 0, We get x = 2;

Therefore, the solution are x = 2, and x = 1/5.

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The given question is incomplete, the complete question is

Solve the quadratic-equation "5x² - 8x + 12 = 3x + 10" by factoring.

perimeter of the shape

Area of the shape

The shape is a composed of two simpler parts which consists of, namely:

Therefore, the perimeter of the shape includes perimeter of semicircle and the perimeter triangle

To complete the perimeter of the triangle we add two sides of the triangle. the opposite and the adjacent of the right triangle is given so we solve for the hypotenuse.

The hypotenuse of the triangle = [tex]\sqrt{ 7^2 + 6^2}[/tex] = 9.22 units

perimeter of the shape

= perimeter of triangle side + perimeter of semicircle side

= (9.22 + 6) + (3.142 * 3.5)

= 167.37 units

Area of the shape

= area of triangle + area of semicircle

= 1/2 x 7 x 6 + 1/2 x 3.142 x 3.5^2

= 21 + 19.24

= 40.24 square units

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The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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a.) [tex]135 + 89 + \text{C} \geq 325[/tex]

[tex]224 + \text{C} \geq 325[/tex]

b.) [tex]224 + \text{C} \geq 325[/tex]

[tex]\text{C} \geq 325 - 224[/tex]

[tex]\text{C} \geq 101[/tex]

The number of pages that can be printed in half a minute is 90 pages

From the question, we have the following parameters that can be used in our computation:

The graph represents a  proportional relationship

Where

x = minutes

y = pages

When the time is half a minute, we have

x = 0.5

So, we have the following ordered pair

(0.5, y)

From the question. we have

(4, 720)

So, we have

(0.5, y) = (4, 720)

Express as an equation

So, we have

y/0.5 = 720/4

This gives

y = 0.5 * 720/4

Evaluate

y = 90

Hence, the number of pages is 90

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All three values (I, II, and III) are solutions to the inequality, so the correct answer is "I, II and III."

To solve the inequality -10 + 3x ≥ -4, we can follow these steps:

Add 10 to both sides of the inequality:

3x ≥ 6

Divide both sides by 3:

x ≥ 2

Now, let's check which of the given values satisfies the inequality:

I. 8:

x ≥ 2, and 8 ≥ 2, so 8 is a solution.

II. 2:

x ≥ 2, and 2 ≥ 2, so 2 is also a solution.

III. 6:

x ≥ 2, and 6 ≥ 2, so 6 is a solution as well.

All three quantities (I, II, and III) fulfill the requirements of the inequality; hence, the right you have to select is "I, II and III."

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A = s^2, where A is the area and s is the length of one side of the square gives the area of a square base. The correct option is true

If s^2 = 144, then s = √144 = 12 feet. The correct option is false

A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex.

Therefore, s^2 = 144 is a valid equation to find the length of one side of the base. The correct option is true

Therefore, one side of the pyramid's base is 12 feet, not 72 feet.

The correct option is false

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The value of the infinite series expression [tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] is -30.

Given information:

[tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

The required series form can be rearranged as,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i[/tex]

Substitute the provided values of [tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

We get,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = 29(-10) - 13(-20)

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -290+ 260

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -30.

As a result, the required value is -30.

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The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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The angle between the slant height and the base of the cone is 30.2°.

Recall the formula of the volume of a cone:

V = (1/3)πr²h

where

V = volume,

r = radius,

h = height.

To get the h, we use the volume formula and substitute:

264 = (1/3)π(6²)h

Make h the subject of the formula and simplify:

h = (3/π)(264/36) = 8.8

Therefore, h = 8.8 m.

Now, we find the slant height using the Pythagorean theorem:

s² = r² + h²

Plugging in the values, we get:

s² = 6² + 8.8² = 102.64

s = √(6² + 8.8²)

s = 10.13

To find the angle between the slant height and the base, we use trigonometry:

tan θ = r / s

r = radius of the base

s = slant height

Plugging in the values, we get:

tan θ = 6 / 10.13

tan θ = 0.5925

Find the arctan of θ

θ = tan⁻¹(0.5925)

θ = 30.2°

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Area= 69π or 216.77 square units.

Remember that the formula for the area of a circle is the following:

[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.

Hence, the area of the white circle is:

[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]

Here you can use the same formula, just need to change the value of the radius:

[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]

[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]

The area of the shaded region is 69π or 216.77 square units, approximately.

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Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a A

The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2

From the question, we have the following parameters that can be used in our computation:

The functions f(x), g(x) and h(x)

Solving the composite functions, we have

f(g(2)) = f(3) i.e. g(2) = 3

This gives

f(g(2)) = 5.5

Next, we have

h(f⁻¹(5))

Here, we have

f⁻¹(5) = 4

So, we have

h(f⁻¹(5)) = h(4)

Evaluate

h(f⁻¹(5)) = 1

Next, we have

f(h(x)) = 7

From the graph, we have

f(0) = 7

This means that

h(x) = 0

From the table, we have

h(5) = 0

This means that

x = 5 for f(h(x)) = 7

Evaluating R(x) at x = 4. we have

R(x) = 2f(x) - 3g(x) + h(x)

This means that

R(4) = 2f(4) - 3g(4) + h(4)

So, we have

R(4) = 2 * 9 - 3 * 5 + 1

R(4) = 4

Evaluating k(x) at x = 5. we have

k(x) = h⁻¹(g(f⁻¹(x)))

This means that

k(x) = h⁻¹(g(f⁻¹(5)))

From the graph, f⁻¹(5) = 4

So, we have

k(x) = h⁻¹(g(4))

Next, we have

g(4) = 5

So, we have

k(x) = h⁻¹(5)

From the table, we have

h⁻¹(5) = 2

This means that

k(x) = 2

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The regression equation is:

y = 20.85 + 0.735 * x

Year Motor registration (000 nos.) No. of tyres sold (000 nos.)

2 62 65

3 65 70

4 48 53

5 53 73

6 60 68

7 68 60

8 60 8

9 9 10

10 65 82

11 72 62

12 62 80

13 40 52

(a) In order to ascertain the coefficient of correlation between the registration of the motor and the number of tires sold, we can apply the following formula:

r = Σ[(xi - x_mean)(yi - y_mean)] / √[Σ(xi - x_mean)^2 * Σ(yi - y_mean)^2].

To do this, we need to determine the mean values for the motor registration (x) and the number of tyres purchased (y).

[tex]x_m_e_a_n = (62 + 65 + 48 + 53 + 60 + 68 + 60 + 9 + 65 + 72 + 62 + 40) / 12 = 664 / 12 = 55.33\\y_m_e_a_n = (65 + 70 + 53 + 73 + 68 + 60 + 8 + 10 + 82 + 62 + 80 + 52) / 12 = 733 / 12 = 61.08[/tex]

Now, we can calculate the required sums for the correlation formula:

Σ(xi - x_mean) = -39

Σ(yi - y_mean) = -39

Σ(xi - x_mean)^2 =3543

Σ(yi - y_mean)^2 = 6649

Σ[(xi - x_mean)(yi - y_mean)] = 2604

Now, we can calculate the correlation coefficient:

r = 2604 / √(3543 * 6649) ≈ 0.556

(b) Interpret your result:

With a correlation coefficient, r, between -1 and 1 going up to 0.556, it shows up as a significant positive relationship.

So when the number of car registrations augments, the sales of tires will also go up.

(c) Test the significance of the result:

As the t-statistic is listed as 1.934, we can analyze it using the critical t-value from a t-distribution table which is around 2.228.

Consequently, since the t-statistic (1.934) is lower than the critical t-value (2.228), the correlation between them is not statistically significant at the 0.05 level.

(d) Compute the two regression coefficients:

The two regression coefficients can be calculated using the following formulas:

b1 = Σ[(xi - x_mean)(yi - y_mean)] / Σ(xi - x_mean)^2

b0 = y_mean - b1 * x_mean

Using the previously calculated values:

b1 = 2604 / 3543 ≈ 0.735

b0 = 61.08 - 0.735 * 55.33 ≈ 20.85

The regression equation is:

y = 20.85 + 0.735 * x

(e) Estimate the number of tyres to be sold when the expected motor registration is 92,000:

Using the regression equation, we can predict the number of tyres to be sold when the expected motor registration is 92,000 (92 in thousands):

y = 20.85 + 0.735 * 92 ≈ 87.81

We estimate that when the expected motor registration is 92,000, approximately 87,810 tyres will be sold.

It should be stated that the relationship was not considered to be statistically relevant so care is advised.

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The statements that are always true are:

i. m∠5 + m∠6 = 180°

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.

From the given question and information, the statements that are always true regarding the diagram are:

i. m∠5 + m∠6 =180°  

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

The required diagram is attached to this answer as a guide

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The solution is : The price per unit is $48, when 30 units are demanded.

Here, we have,

Since we have given that

At price of $12 per unit, the number of units demanded = 40 units

At price of $18 per unit, the number of units demanded = 25 units.

So, the coordinates would be

(40,12) and (25,18)

As we know that x- axis denoted the quantity demanded.

y-axis denoted the price per unit.

So, the slope would be

m = -2/5

So, the equation would be

5y + 2x = 140

So, if 30 units are demanded, the price per unit would be

y = $48

Hence, the price per unit is $48, when 30 units are demanded.

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complete question:

Suppose consumers will demand 40 units of a product when the price is $12 per unit and 25 units when the price is $18 each. Find the demand equation assuming that it is linear. Find the price per unit when 30 units are demanded.

Answer: 15 square units

Step-by-step explanation:

Area of a triangle is 1/2bh

x = b = 6

H=5

1/2(6)(5)

1/2(30)

Area = 15 square units

Answer:

These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid

The values are expressed as;

1. radius = 13cm

2. Diameter = 27.2cm

3. Diameter = 24m

4.  Radius = 24. 5m

It is important to note the formula for calculating the circumference and area of a circle.

The formula for calculating area of a circle is expressed as;

A = πr²

Such that the parameters are given as;

Also, the formula for circumference is expressed as;

C = 2πr

To determine the formula for diameter is expressed as;

Diameter = 2Radius

1. Substitute the values

r = d/2

r = 26/2

r = 13cm

2. If r= 13.6m

d= 2(13.6)

d = 27.2m

3. If r = 12m

d = 2(12)

d = 24m

4. If d = 49m

Then, r = 49/2 = 24. 5m

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Answer:

2((4.5)(6) + (4.5)(4) + (6)(4))

= 2(27 + 18 + 24) = 2(69) = 138 square cm