Write y - 4 = 1 ( x - 4) in slope intercept form.

Answer:

Step-by-step explanation:

24 - 3 = 21 • 4 = 84

The relationship between arithmetic mean return, geometric mean return, and variability of returns is they all provide different insights into the performance of an investment.

The arithmetic mean return and geometric mean return are two commonly used measures of investment returns. The arithmetic mean return is calculated by adding up all the returns over a period of time and dividing by the number of returns. The geometric mean return, on the other hand, takes into account the compounding effect of returns over time. It is calculated by multiplying all the returns over a period of time and taking the nth root, where n is the number of returns.

The variability of returns refers to the degree of fluctuation in investment returns over a period of time. This variability can be measured using standard deviation or variance.

The relationship among arithmetic mean return, geometric mean return, and variability of returns is that they all provide different insights into the performance of an investment. The arithmetic mean return is a simple measure of the average return over a period of time, while the geometric mean return takes into account the effect of compounding. The variability of returns, measured by standard deviation or variance, provides an indication of the risk associated with an investment.

Investments with high variability of returns are generally considered riskier than those with low variability. When comparing two investments with the same arithmetic mean return, the one with a higher geometric mean return will generally be preferred because it indicates that the investment has been compounding at a higher rate. Overall, it is important to consider all three measures when evaluating the performance of an investment.

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The Weighted Average Cost of Capital (WACC) for Snuggly Baby Corp. is calculated based on the company's capital structure, including common equity, preferred equity, and bonds. The WACC is influenced by the expected returns and prices of these securities.

To calculate the WACC, we need to determine the proportion of each component in the capital structure and multiply it by its respective cost of capital.

For Snuggly Baby Corp., the capital structure consists of 6,130,000 shares of common equity, 1,006,000 shares of preferred equity, and 81,400 bonds.

The cost of common equity is calculated using the expected return and the price of the shares. Similarly, the cost of preferred equity is calculated using the expected return and the price of the preferred shares. The cost of debt, represented by the bonds, is calculated using the yield-to-maturity.

Once we have the costs of each component, we multiply them by their respective proportions in the capital structure and sum them up to determine the overall WACC. Please note that to provide an accurate calculation of the WACC, additional information is required, such as the market value of each component and the weights assigned to them in the capital structure. Without this information, it is not possible to provide an exact WACC calculation.

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Answer:

anywhere from 169 to 220 metres,

Step-by-step explanation:

Answer:

\(7x^{8}\)

Answer:

I think B is the right one.

Step-by-step explanation:

Hope this helped

Based on the information given the average speed for his trip is 64 miles.

Using this formula

d=rt

r=d/t

Where:

r=rate=?

d=distance=512 miles

t=time=8 hours

Let plug in the formula

r=512/8

r=64 miles

Inconclusion the average speed for his trip is 64 miles.

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Answer:

In order to solve this, we need to transform the equation into R = D/T

Plug in the numbers into this equation

R = 512/8

So after we divide these two numbers, we get an answer of 64 mph as Adam's average speed.

Answer:

5%

Step-by-step explanation:

Percent error = (actual - estimated) / actual x 100

(240 - 228) / 240 x 100 = 5%

Answer:

50.3 square units

Step-by-step explanation:

area of rectangle: 11 x twice the radius

radius = 2

A(rect): = 11(4) = 44 sq units

A (semi-circle) = (π·r²) / 2

A = 4π / 2 = 2π = 6.28 sq units

44.0 + 6.28 = 50.28

Answer:

68.1

Step-by-step explanation:

3.14*3²=28.26

28.26/2=14.13

3*2=6

9*6=54

54+14.13=68.13

68.1

Answer:

x = 2

Step-by-step explanation:

4x + 3 = 11

(4x + 3) - 3 = 11 - 3

4x = 8

4x/4 = 8/4

x = 2

As you can see, to isolate x, we must do the opposite operations to both sides.

\(\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}\)

c=9 makes the given expression a perfect square trinomial.

The given expression is:

\(x^{2} +6x+c\)

We can rewrite it as:

\(x^{2} +2*x*3 + c\).....(1)

The expansion of \((a+b)^2\) is \(a^{2} +2ab+b^{2}\)

Comparing (1) with \(a^{2} +2ab+b^{2}\)

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

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By using the concept of maxima, it can be calculated that

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.

Let the length of the rectangle be l m and width of the rectangle be w m

Perimeter (P) = 2(l + w)

By the problem,

2(l + w) = 72

l + w = \(\frac{72}{2}\)

l + w = 36

w = 36 - l

Area (A) = l \(\times\) w

A = l \(\times\) (36 - l) = \(36l - l^2\)

Differentiation with A with respect to l

\(\frac{dA}{dl} = 36 - 2l\)

For maximum area,

\(\frac{dA}{dl} = 0\)

36 - 2l = 0

2l = 36

l = \(\frac{36}{2}\)

l = 18 m

\(\frac{d^2A}{dl^2} = -2 < 0\)

Hence area is maximum

w = 36 - 18 = 18 m

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

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Answer:

n = \(\frac{1}{3}\)

Step-by-step explanation:

for the equation to be true for all values of x , then both sides have to be the same.

expand both sides and equate like terms

left side

12(3n - \(\frac{1}{2}\) x) ← distribute each term in the parenthesis by 12

= 36n - 6x

right side

- \(\frac{2}{3}\) (9x - 18) ← distribute each term in the parenthesis by - \(\frac{2}{3}\)

= - 6x + 12

we require

36n - 6x = - 6x + 12

that is

36n = 12 ( divide both sides by 36 )

n = \(\frac{12}{36}\) = \(\frac{1}{3}\)

for the equation to be true for all x then n = \(\frac{1}{3}\)

The remainder when dividing 4x⁴ - 8x³ - x + 10 by x² - 4 is -33x + 74.

To find the remainder when the polynomial 4x⁴ - 8x³ - x + 10 is divided by x² - 4, we can use polynomial long division.

             4x² - 8x + 16

         ___________________

x² - 4 |  4x⁴- 8x³ - x + 10

         - (4x⁴ - 16x²)

         ______________

                - 8x³ + 16x² - x + 10

                -(- 8x³ + 32x)

                ______________

                          16x² - 33x + 10

                        - (16x² - 64 )

                          ______________

                                    -33x + 74

Therefore, the remainder when dividing 4x⁴ - 8x³ - x + 10 by x² - 4 is -33x + 74.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

3 and 1/3 pounds = flour

5 = containers

Step 02:

We must apply the algebraic rules to find the solution.

The answer is:

2/3 pounds of flour

Answer:

24 cm

Step-by-step explanation:

The volume of the prism with given dimensions in the figure is equal to 612√3 cubic millimeter.

The dimensions of the triangular prism are,

Base of the triangle  'B' = 12mm

let us consider 'h' be the height of the triangle base.

Which intersect base at midpoint

height of the triangle 'h' = √ 12² - 6²

                                        = √108

                                        = 6√3mm

Side length of the prism 'l' = 17mm

Volume of the triangular prism

= ( 1/2 ) × Base × height × length of the side

= ( 1/2 ) × B × h × l

Now , substitute the values we have,

⇒ Volume of the triangular prism  = (1/2) × 12 × 17 × 6√3

⇒ Volume of the triangular prism  = 612√3 cubic millimeter.

Therefore, the volume of the triangular prism is equal to 612√3 cubic millimeter.

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The volume of the rectangular pyramid with a length of 8m, width of 5m and height of 12m is 160 m³.

A rectangular pyramid is simply a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

From the diagram:

Length l = 8 meters

Width w = 5 meters

Height h = 12 meters

Volume V = ?

Plug the given values into the above formula and solve for the volume:

V = (1/3) × l × w × h

V = (1/3) × 8 × 5 × 12

V = 160 m³

Therefore, the volume of the pyramid is 160 m³.

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Answer:

5

Step-by-step explanation:

20 divided by 4 easy

Answer:

b) 5

Step-by-step explanation:

20 ÷ 4 = 5

5 pages per day

Answer:

A 1/3

Step-by-step explanation:

I hope this helps, let me know if you need the work

Refilling the container on a day with a temperature of 26.0°C would result in an additional profit of 1.232 pennies per gallon.

Initial temperature: \($4.0^\circ \text{C}$\)

Final temperature: \($26.0^\circ \text{C}$\)

Coefficient of volume expansion: \($2.80 \times 10^{-6}\) °C ⁻¹

First, we calculate the change in volume \(($\Delta V$)\) using the coefficient of volume expansion:

\(\[\Delta V = V \cdot \beta \cdot \Delta T\]\)

Where:

\($V$\) is the initial volume (1 gallon)

\($\beta$\) is the coefficient of volume expansion \(2.80 \times 10^{-6}\) °C ⁻¹

\($\Delta T$\) is the change in temperature \(($26.0^\circ \text{C} - 4.0^\circ \text{C} = 22.0^\circ \text{C}$)\)

\(\[\Delta V = 1 \cdot (2.80 \times 10^{-6}) \cdot 22.0 = 6.16 \times 10^{-5} \, \text{gallons}\]\)

Next, we calculate the price difference by multiplying the change in volume by the price per gallon:

\(\text{Price difference} = \Delta V \cdot \text{Price per gallon} = (6.16 \times 10^{-5}) \cdot 2 = 0.0001232 \, \text{dollars}\)

To convert this to pennies, we multiply by 100:

\(\text{Price difference in pennies} = 0.0001232 \times 100 = 0.01232 \, \text{dollars}\)

Therefore, you would make an additional 0.01232 dollars, or 1.232 pennies, per gallon by refilling the container on a day when the temperature is \($26.0^\circ \text{C}$\).

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Step-by-step explanation:

5 % decrease means 95 %  (.95)  remain

Year 1

   800 * .95

   year 2  800 * .95  * .95

       .

       .

        year 5 = 800(.95)^5 = 619 deer after year 5

The major axis lies along the z-axis, while the minor axis lies along the x-axis.

Given quadric surface is ( 3x)² − y + (2z)² = 0.

The equation of a quadric surface can be given by Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0, where A, B, C, D, E, F, G, H, I, J ∈ ℝ and (x, y, z) ∈ ℝ³.

(a) Type of quadric surface defined by the above equation is an elliptic paraboloid.

(b) The trace obtained by intersecting the surface with the xy-plane can be obtained by replacing z with 0. So, the equation is 9x² - y = 0, which can be written as y = 9x².

The trace is a parabola which opens upwards and intersects the y-axis at the origin.

(c) The trace obtained by intersecting the surface with the plane y = 1 can be obtained by replacing y with 1.

So, the equation is 9x² + 4z² = 1.The trace is an ellipse in the xz-plane, centered at the origin.

The major axis lies along the z-axis, while the minor axis lies along the x-axis.

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Answer:B.Sample space

Step-by-step explanation:

Answer:

Age of Kim's sister is 12 and that of kim is 24.

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

Ok so this is how I got it:

Since we know the lengths of sides NO, MN, and JK, but we don't know the length of KL, we can use what we know.

To get from MN to JK, we multiply MN (2) by 1.5 to get 3. So you can go the same thing to get from NO to KL.

Just go ahead and multiply 5 by 1.5

5 × 1.5 = 7.5

Hope this helps!

Answer:

KL = 7.5

Step-by-step explanation:

MN : JK = NO : KL

⇒ 2 : 3 = 5 : KL

\(\implies \dfrac23=\dfrac{5}{KL}\)

⇒ 2 · KL = 5 · 3

⇒ 2(KL) = 15

⇒ KL = 15 ÷ 2

⇒ KL = 7.5

When a 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5, the length of the shortest part is 11.25 inches.

Therefore, the answer is 11.25in.

A line segment is cut into two parts, say of length x and y in inch. As they are cut in ratio 3 is to 5, x/y = 3/ 5.

Therefore, 5x = 3y implies x = 3y/5 = 0.6y

Also total length of the line segment is 30in, that is x + y = 30.

Therefore, 0.6y + y = 30

y = 30/ 1.6

= 18.75

Thus, x = 0.6y = 11.25

Therefore the 30in line segment is divided into lengths of 11.25in and 18.75in.

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