The interior angles of a quadrilateral are in an arithmetic sequence. If the largest angle is 96°, find the other angles.

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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The calculated measure of t from the given equation is 15 degrees

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

10

to

25°

When expressed properly, we have

10° + t° = 25°

Evaluate the like terms

So, we have

t° = 15°

Hence, the value of t° is 25°

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4x + 32

All u need to do is simplify, 4 * x + 4 * 8 = 4x + 32

Answer:

a. unbounded

e. x ≤ 9

Step-by-step explanation:

The interval means all real numbers less than or equal to 9.

Since all numbers to negative infinity are included, it is unbounded.

a. unbounded

e. x ≤ 9

A sketch looks like a number line with a solid dot at 9 and an line pointing left with an arrowhead at the left pointing left.

Answer:

b. unbounded

e. x ≤ 9

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

A bounded interval is an interval that includes both its endpoints.

For the interval (-∞, 9]:

Therefore, the given interval is unbounded.

Inequality notation

Therefore, the given interval is represented by the inequality x ≤ 9.

To sketch the graph on a number line:

To sketch the graph on a coordinate plane:

Answer:

the answer is C, NOT B

Step-by-step explanation:

The system of inequalities will have more solutions than the system of equations , Option C is the corrrect answer.

Inequality is the relation between two unequal numbers or algebraic expression.

The inequality symbols are less than , greater than , less than equal to, greater than equal to.

It is given in the question that

the system of equations y= -1/2x + 1 and y = x - 5.

the system of inequalities y > -1/2x + 1 and y < x - 5.

x-5 = -1/2 x +1

2x+x=6*2

3x = 12

x = 4

x-5 >-1/2 x +1

x>4

The system of inequalities generally have more solutions and in this case definitely have more solutions than the system of equations.

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Answer:

Step-by-step explanation:

The commutative, associative, and distributive properties help you rewrite a complicated algebraic expression into one that is easier to deal with. When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied.

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The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

Answer:

If six people all shake hands with each other, how many hand shakes were made in total?

Publish your book. Become an author in 15 days. Get published.

I assume that no two people shake hands if they've already shaken them earlier, irrespective of who initiated it.

In that case Guest 1 will shake hands with 5 others (Guest 2 to 6)

Guest 2 will shake hands with 4 others (Remember she's already shaken hands with Guest 1).

Guest 3 will shake hands with 3 others (having already shaken hands with Guest 1 and 2)

and so on.....

We end up with 5+4+3+2+1 handshakes or 15 handshakes in all!

Step-by-step explanation:

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Answer:

15 handshakes

Step-by-step explanation:

the 1st person shakes hands with 5 people

the 2nd person shakes hands with 4 people

the 3rd person shakes hands with 3 people

the 4th person shakes hands with 2 people

the 5th person shakes hands with 1 person

the 6th person shakes hands with no one

5+4+3+2+1=15

Answer:

Hope this helps

Step-by-step explanation:

Table one and table four represent a linear function.

A linear function is simply a function that represents a straight line on the coordinate plane.

For a function to be linear, the differences of the y-values must be constant.

For table 1.

Let get the differences of the y-values

-1 - (-2) = 1

0 - (-1) = 1

1 - 0 = 1

2 - 1 = 1

Since the differences of the y-values are all 1 ( constant ), table one is a linear function.

For table 2.

2 - (-3) = 5

0 - 2 = -2

-2 - 0 = -2

3 - (-2) = 5

Since the differences of the y-values are not the same ( constant ), table two is not a linear function.

For table 3.

0 - 2 = -2

-1 - 0 = -1

0 - (-1) = 1

2 - 0 = 2

Since the differences of the y-values are not the same ( constant ), table three is not a linear function.

For table 4.

1 - 3 = -2

-1 - 1 = -2

-3 - (-1) = -2

-5 - (-3) = -2

Since the differences of the y-values are all -2 ( constant ), table four is a linear function.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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A 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73

We can use the chi-square distribution to construct a confidence interval for the population standard deviation, where the lower and upper limits are given by:

\(\sqrt{(n-1)*s^2/chi2(alpha/2,n-1)) }\)         and \(\sqrt{(n-1)*s^2/chi2(1-alpha/2,n-1)}\)

Standard Deviation is a measure that shows how much variation (such as spread, dispersion, spread,) from the mean exists.

Where n is the sample size, s is the sample standard deviation, alpha is the significance level, and chi2 is the chi-square distribution function.

Substituting the given values, we get:

Lower limit

= \(\sqrt{(31-1)*50^2/chi2(0.05/2,31-1)}\)

= 1596.45

Upper limit

= \(\sqrt{(31-1)*50^2/chi2(1-0.05/2,31-1)}\)

= 4466.73

Therefore, a 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73.

Hence, the correct answer is B) 1596.45-4466.73

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The value of Sin(90) is equal to 1.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Sin(90) and to find the value using the unit circle

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.

The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

Hence, Sin (90) is equal to 1.

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Answer:

a(A) = 0

Step-by-step explanation:

is there a picture I can see

Answer:

A or 8

Step-by-step explanation:

So,

Based in the information of the problem given, we could make the following question:

"How many problems does she complete in one week?"

Given that she complete 30 problems for her math homework each night and she has math homework five nights a week, we could multiply:

Therefore, she completes 150 problems per week.

Answer:

\(tan(30) = \frac{A}{B}\)

Step-by-step explanation:

Given

The attached triangle

Required

Find tan(30)

Let the side opposite 30 degrees be A and the side adjacent 30 degrees be B

So [using tangent identity]:

\(tan(\theta) = \frac{Opposite}{Adjacent}\)

This gives:

\(tan(30) = \frac{A}{B}\)

The ordering and transportation cost C for the components used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds.

To find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20.

The rate of change of the cost with respect to x is its derivative.

The differentiation rules to apply are

Quotient Rule: \(\frac{d}{dx} \left[\frac{f(x)}{g(x)}\right] = \frac{g(x)f^{'}(x)-f(x)g^{'}(x)}{\left[g(x)]^{2} }\)

Constant Multiple Rule: \(\frac{d}{dx} \left[cf(x) \right] = cf^{'}(x)\)

Power Rule: \(\frac{d}{dx} \left[x^{n} \right] = nx^{n-1}\)

Constant Rule: \(\frac{d}{dx} [c] = 0\)

So,

\(c^{'}(x) = 100 (\frac{x^{2}(200)^{'}-200(x^{2})^{'}}{(x^{2})^{2} }+\frac{(x+30)(x)^{'}-x(x+30)^{'} }{(x+30)^{2} } )\)

\(c^{'}(x) = 100 (\frac{x^{2}(0)-200(2x) }{x^{4} } + \frac{(x+30)(1)-x(1+0)}{(x+30)^{2} })\)

\(c^{'}(x) = 100 (\frac{0-400x}{x^{4} } + \frac{x+30-x}{(x+30)^{2} })\)

\(c^{'}(x) = 100 (\frac{-400x}{x^{4} } + \frac{30}{(x+30)^{2} })\)

From the above values it appears that the rate of change of the cost increases as the size of the order increases

\(a) c^{'}(10) = -38.13\\ \\b) c^{'}(15) = -10.37\\ \\c) c^{'}(20) = -3.8\)

Hence the above values it appears that the rate of change of the cost increases as the size of the order increases

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The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).

To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.

1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).

Therefore, 3 yards is equal to 3 * 36 = 108 inches.

Now, we can compare 108 inches to 3 yards 16 inches.

108 inches is equal to 3 yards, so it matches the given length.

To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.

Therefore, 3 yards 16 inches is equivalent to:

3 yards

108 inches

3 yards 0.44 yards (or approximately 3.44 yards)

108 inches 0.44 yards (or approximately 108.44 inches)

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Answer:

Total arrangement = 720

Step-by-step explanation:

Given:

Total letter n = 6

Using letter r = 5

Computation:

Total arrangement = nPr

Total arrangement = !n / !(n-r)

Total arrangement = !6 / !(6-5)

Total arrangement = 6 x 5 x 4 x 3 x 2

Total arrangement = 720

Answer:25

Step-by-step explanation:

The distance traveled by Joe in 1 hour is required.

The distance Joe would travel in 1 hour is \(25\ \text{miles}\)

Distance traveled by Joe in 5 hours is 125 miles.

\(5\ \text{hours}=125\ \text{miles}\)

Divide by \(5\) on both sides

\(1\ \text{hour}=\dfrac{125}{5}=25\ \text{miles}\)

The speed of Joe is \(25\ \text{miles/h}\)

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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Answer:

15.6145 meters squared

Step-by-step explanation:

multiply the 2 together

Answer:

15.6145

Step-by-step explanation:

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

Answer:

t = 1.2, -1.2