Coordinates of P = [tex][(3 * xB + xC + 4 * xD) / 8, (3 * yB + yC + 4 * yD) / 8][/tex]
Coordinates of P = [tex][(4 * xC + 2 * xD + 3 * xE) / 9, (4 * yC + 2 * yD + 3 * yE) / 9][/tex]
Leave the directions of point B alone (x1, y1) and the directions of point D be (x2, y2). Then, at that point, the directions of P are:
[tex][(3x1 + x2)/4, (3y1 + y2)/4][/tex]
Let the directions of point A be (x1, y1) and the directions of point E be (x2, y2). Then, at that point, the directions of P are:
[tex][(x1 + 2x2)/3, (y1 + 2y2)/3][/tex]
Leave the directions of point B alone (x1, y1), the directions of point C be (x2, y2), and the directions of point D be (x3, y3). Then, at that point, the directions of P are:
[tex][(3x1 + x2 + 4x3)/8, (3y1 + y2 + 4y3)/8][/tex]
Leave the directions of point C alone (x1, y1), the directions of point D be (x2, y2), and the directions of point E be (x3, y3). Then, at that point, the directions of P are:
[tex][(4x1 + 2x2 + 3x3)/9, (4y1 + 2y2 + 3y3)/9][/tex]
These recipes can be inferred utilizing the weighted typical equation:
[tex][(w1x1 + w2x2 + ... + wnxn)/(w1 + w2 + ... + wn), (w1y1 + w2y2 + ... + wnyn)/(w1 + w2 + ... + wn)][/tex]
where wi is the heaviness of point I and (xi, yi) are the directions of point I. Subbing the given loads and facilitates into the equations for every issue gives the directions of P for each situation.
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The complete question is:
Find the coordinates of P that represent the weighted average of each set of points based on the given conditions. 12. Point B weighs three times as much as point D. 13. Point E weighs twice as much as point A. 14. Point B has a weight of 3 , point C has a weight of 1 , and point D has a weight of 4. 15. Point C has a weight of 4 , point D has a weight of 2 , and point E has a weight of 3.
What are the domain and range of the piecewise function
The domain of the function is, (-4, +∞) - {6}
And the range of the function is, R - [-2,0).
Since, The domain of a function is the set values of x for which the function is defined.
And, The range of a function is the set values of y for which the function is defined.
As we can see that the graph of the function can be defined everywhere except on 6 at the x-axis, and between 0 to -2 on the y-axis. therefore,
Domain = (-4, +∞) - {6}
Range = R - [-2,0)
Hence, the domain of the function is (-4, +∞) - {6} and the range of the function is R - [-2,0).
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5. Find x.
Trapezoids Worksheet
Answer:
(1/2)(x + 4 + 100) = 3x
x + 104 = 6x
5x = 104, so x = 20.8
Input Area
Shares outstanding 8,700,000
Share price $46.50
Purchase price of land $65,000,000
Perpetual earnings increase $14,000,000
Current cost of capital 12.50%
Cost of new debt 8%
Optimal equity weight 70%
Optimal debt weight 30%
Tax rate 21%
Output area:
1. If Stephenson wishes to maximize its total market value, would you recommend that it issue debt or equity to finance the land purchase? Explain.
Assets ?? Equity??
Total assets?? Debt & Equity ??
Perpetual aftertax earnings??
NPV of purchases??
3. Balance Sheet
Old assets??
NPV of Project?? Equity??
Total assets?? Debt & Equity ??
New share price? ?
Shares to issue? ??
4. Balance Sheet
Cash???
Old assets??
NPV of project?? Equity ??
Total assets ?? Debt & Equity ??
Total shares outstanding ? ?
Share price ?? ?
PV of earnings increase ?? ?
Balance Sheet
5. Old assets??
PV of project ??? Equity ?? ?
Total assets ?? ? Debt & Equity ??? ?
Value of levered company ?? ? <---VL = VU+TC*D Note*: TC = Tax rate
Balance Sheet
Value unlevered?? ? Debt ?? ?
Tax shield value?? ? Equity ?? ?
Total assets ?? ? Debt & Equity ?? ?
Stock share price???
6. Which method of financing maximizes the per share stock price of Stephenson's equity?
What is $2.50 divided by 10
Answer:
answer is 0.25
Step-by-step explanation:
2.50/10
there is only one zero in 10 so we move the decimal one digit towards left.
which then the decimal ends up in front of 2.
Jada is the 36th customer. Will she get a prize? If so, what prize will she get? Is it possible for her to get more than one prize? How do you know? Explain your reasoning.
Jada will receive a prize and what prize she will receive depends on the specific details of the prize allocation process.
If there are exactly 36 prizes available and they are being allocated in sequential order, then Jada will receive a prize because she is the 36th customer.
However, if there are fewer than 36 prizes available or if they are being allocated randomly, then Jada may or may not receive a prize.
It is possible that Jada will receive a specific prize designated for the 36th customer, or she may receive a prize that is randomly allocated to any customer.
It is also possible for Jada to receive more than one prize if the prizes are being allocated in a way that allows customers to receive multiple prizes.
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If we set α=0.01, what is the probability that we reject the null hypothesis when it was in fact true?
The probability is  _____
The probability by the given data is 1%.
We are given that;
set α=0.01
Now,
The probability of making a type I error is the significance level, or alpha (α), which is the threshold we set for rejecting the null hypothesis124. It is also known as the false positive rate3.
If we set α=0.01, it means that we are willing to accept a 1% chance of making a type I error. Hence, the probability that we reject the null hypothesis when it was in fact true is 0.01 or 1%.
Therefore, by probability the answer will be 1%.
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A baseball team's cap is selected from 3 different colors, 2 different clasps, and 4 different locations for the team logo. A decision is made not to include or not to include reflective piping.
The calculated value of the number of different outcomes in the sample space is 24
Calculating the number of different outcomes in the sample spaceFrom the question, we have the following parameters that can be used in our computation:
3 different colors, 2 different clasps, 4 different locationsUsing the above as a guide, we have the following:
Colors = 3
Clasps = 2
Locations = 4
So, we have
Outcomes = Colors * Clasps * Locations
Substitute the known values in the above equation, so, we have the following representation
Outcomes = 3 *2 * 4
Evaluate
Outcomes = 24
Hence, the number of different outcomes in the sample space is 24
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i need help with this please
If you choose the baseball workshop, you will need to know the kind of beverage that would be better for the participants after playing baseball, and if we ask participants it is likely they choose water or soda.
What do we know?Information about the workshop is limited; however, it is likely the participants have to play baseball and they will need to drink and eat something after this.
What do we want to know?We want to know the beverage and snack that would be better for hydration. Moreover, it can be expected the participants choose common options such as soda or water.
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In a right triangle, cos(7x) = sin(5x−6). Find the smaller of the triangle’s two acute angles.
The smaller of the triangle’s two acute angles is 34 degrees
Finding the smaller of the triangle’s two acute angles.From the question, we have the following parameters that can be used in our computation:
In a right triangle, cos(7x) = sin(5x−6)
As a general rule in a right triangle,
if cos(a) = sin(b), then
a + b
Using the above as a guide, we have the following:
7x + 5x - 6 = 90
So, we have
12x = 96
Divide
x = 8
Next, we have
Angles = 7x and 5x - 6
So, we have
Angles = 7 * 8 and 5 * 8 - 6
Evaluate
Angles = 56 and 34
Hence, the smaller of the triangle’s two acute angles is 34 degrees
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A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:
The ratio of the cost price and the printed price of the book is 1.2444.
We have,
Let's assume the printed price of the book = P.
As per the problem, the shopkeeper is selling the book at a discount of 10% on the printed price. So the selling price of the book.
= (P - 0.1P)
= 0.9P.
The shopkeeper earns a profit of 12% on selling the book.
So, the selling price of the book is also 112% of the cost price.
That is,
0.9P = 1.12C
where C is the cost price of the book.
Now, let's find the ratio of the cost price and the printed price of the book:
C/P
= (C/0.9P)/(P/0.9P)
= 1.12/0.9
= 1.2444
Therefore,
The ratio of the cost price and the printed price of the book is 1.2444.
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if the angels of a quadrilateral are x, 2x and 3x. what is the value of x.
calculate the size of the largest angel.
Answer:
Step-by-step explanation:
The sum of angles in a quadrilateral is 360 degrees. So, we have:
x + 2x + 3x + fourth angle = 360
6x + fourth angle = 360
fourth angle = 360 - 6x
To find the value of x, we can use the fact that the angles in a quadrilateral add up to 360 degrees:
x + 2x + 3x + (360 - 6x) = 360
6x + 360 - 6x = 360
360 = 360
This equation is true for any value of x, so we cannot solve for x.
To find the size of the largest angle, we can substitute any value of x into the expression for the fourth angle and then find the largest of the four angles. For example, if we choose x = 30, then the angles are:
x = 30 degrees
2x = 60 degrees
3x = 90 degrees
fourth angle = 360 - (x + 2x + 3x) = 180 degrees
So the largest angle is 180 degrees.
Types of discontinuities
Identify and Classify the discontinuities in the function, please.
A function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2) is discontinuous at x = 1 and x = -2. And it is a removable discontinuity.
Consider function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)
We factorise denominator as,
x² + x - 2
= x² + 2x - x - 2
= x(x + 2) - 1(x + 2)
= (x + 2)(x - 1)
So, the function f(x) becomes,
f(x) = (x⁴ - 5x² + 4) / ((x + 2)(x - 1))
A function f(x) is discontinuous when the denominator of f(x) is zero.
i.e., (x + 2)(x - 1) = 0
i.e., x = 1 or x = -2
Also, the factors of the polynomial x⁴ - 5x² + 4 are (x - 2), (x + 2), (x - 1) and (x + 1)
We can write function f(x) as,
f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)
f(x) = ((x - 2) (x + 2) (x - 1) (x + 1)) / ((x + 2)(x - 1))
f(x) = (x - 2)(x + 1)
Now, the function f(x) is continuous.
Therefore, the type of discontinuity is removable discontinuity.
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Heather and Cindy are playing “Guess My Shape.”
Heather has to describe a shape to Cindy accurately enough so that Cindy can draw it without ever seeing the shape.
Heather gives Cindy these clues:
Clue #1: The shape is similar to a rectangle with a base of 7cm and a height of 4cm.
Clue #2: The shape is five times larger than the shape it is similar to.
What are the dimensions of the new shape?
Answer:
The new shape has a base of 35 cm and a height of 20 cm.
Step-by-step explanation:
Since the shape is five times larger than the shape it is similar to, we can simply multiply everything by 5.
7×5=35
4x5=20
The new shape has a base of 35 cm and a height of 20 cm.
Hope this helps (and is correct)! Good luck on your homework!
Use the derivative (x-3)(x+1)(x+4)
to determine the local maxima and minima of f and the intervals of increase and decrease.
The local maximum of f is at (-5/3, 128/27), and the local minimum is at (4/3, -64/27).
To find the neighborhood maxima and minima of the capability f(x) = (x-3)(x+1)(x+4), we really want to take its subordinate:
f'(x) = (x+1)(x+4) + (x-3)(x+4) + (x-3)(x+1)
f'(x) = [tex]3x^2 + 6x - 20[/tex]
Setting f'(x) equivalent to nothing and settling for x, we get:
[tex]3x^2 + 6x - 20 = 0x^2 + 2x - 20/3 = 0(x+5/3)(x-4/3) = 0[/tex]
Thusly, the basic focuses are x=-5/3 and x=4/3.
To decide the time periods and diminishing, we can utilize the principal subsidiary test. Since f'(x) is a quadratic capability with a positive driving coefficient, it is dependably certain for x < - 5/3 and x > 4/3, and consistently negative for - 5/3 < x < 4/3.
Thusly, f(x) is expanding on the spans (- ∞, - 5/3) and (4/3, ∞), and diminishing on the stretch (- 5/3, 4/3).
To find the nearby maxima and minima, we can utilize the subsequent subsidiary test. Taking the subordinate of f'(x), we get:
f''(x) = 6x + 6
Subbing x=-5/3 and x=4/3, we get:
f''(- 5/3) = - 2 < 0, so f has a neighborhood greatest at x=-5/3.
f''(4/3) = 10 > 0, so f has a neighborhood least at x=4/3.
Thusly, the neighborhood limit of f is at (- 5/3, 128/27), and the nearby least is at (4/3, - 64/27).
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What is the answer to this equation need this soon!!!
The measures of the angles add up to 180°, using that we can see that x = 10.
How to find the value of x?Here we can see that the two vertical lines are parallel, thus, the angles in both intersections are equal.
Now, notice that the 75° angle would be an adjacent angle to (11x - 5)°, then their measures add up to 180°, then we can write:
75° + (11x - 5)° = 180°
We can solve that for x.
75 + 11x - 5 = 180°
70 + 11x = 180
11x = 180 - 70 = 110
x = 110/11
x = 10
That is the value of x.
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7. The table below represents the relationship
between cups of flour, fand cups of sugar, s
needed to make cookie dough.
Flour and Sugar in Cookie Dough
Cups of flour (f)
1
2
3.5
5.25
Cups of sugar (s)
2
4
7
10.5
Which equation correctly shows the relationship
between the cups of flour, fand cups of sugar, s
needed to make the cookie dough?
A f = 1/s
B s=²f
C s=3.5f
D f = 2s
The equation that correctly shows the relationship between cups of flour and sugar is f = 1/2s. Option A
How do we form the equation that represents the relationship between flour and sugar?if 1 cup of flour needs 2 cups of sugar.
2 cups of flour need 4 cups of sugar.
3.5 cups of flour need 7 cups of sugar.
5.25 cups of flour need 10.5 cups of sugar.
This only means that the size of sugar is twice the size of flour. Therefore to form our equation, we say
sugar = 2flour. But since the option is not there,
we can also go for
f = 1/2s
3.5 = 1/2 × 7
3.5 = 3.5
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Steven and rebecca ran a race. Rebecca ran 3 times across the center of a circle with the diameter of 40. Steve ran ones around the circle. Who ran futher? By how much did they run futher by?
Steven ran more distance, and the difference is 5.6 units.
Who ran further and by how much?Rebbeca ran 3 times across the center of a circle whose diameter is 40 units, then the distance that she ran is 3 times that:
distance for Rebbeca = 40*3 = 120 units.
While Steven ran one time across the circumference, remember that the circumference is 3.14 times the diameter, so the distance that he ran is:
Distance for Steven = 3.14*40 = 125.6 units.
So Steven ran more, and the difference is:
125.6 - 120 = 5.6 units.
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please help i don’t understand
By completing squares, we can rewrite the quadratic equation as:
(x + 9)^2 = -9
How to complete squares?Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
Here we have the quadratic equation:
x^2 + 103 = -18x + 13
We can rewrite this as:
x^2 + 18x = 13 - 103
x^2 + 18x = -90
x^2 + 2*9*x = -90
We can add 9^2 and subtract 9^2 to get:
x^2 + 2*9*x + 9^2 - 9^2= -90
(x^2 + 2*9*x + 9^2) - 9^2= -90
(x + 9)^2 - 81 = -90
(x + 9)^2 = -90 + 81
(x + 9)^2 = -9
That is the equation we wanted to get.
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please help, i’m very confused
The number of days the family were on vacation is 20 days.
What is the number of days the family was on vacation?The number of days the family were on vacation is calculated as follows;
Let's consider morning and afternoon as a half day.
From the question we will have the following equation;
12 mornings + 13 afternoons = 25 half days.
25 - 15 days of raining = 10 half days
10 half days = 5 mornings and 5 afternoons with no rain.
The number of days they stayed is calculated as;
15 + 5 = 20 days.
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What are the magnitude and direction is u+v+w? ||v|= 60 ||w||=50 ||u||= 80
The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.
How to solveFirst, we calculate the components:
u = (80cos(30°), 80sin(30°)) ≈ (69.28, 40.00)
v = (60cos(60°), 60sin(60°)) ≈ (30.00, 51.96)
w = (50cos(120°), 50sin(120°)) ≈ (-25.00, 43.30)
Now, let's find the resultant vector (u+v+w):
u+v+w = (69.28 + 30.00 - 25.00, 40.00 + 51.96 + 43.30) ≈ (74.28, 135.26)
The magnitude of the resultant vector ||u+v+w|| can be found using the Pythagorean theorem:
||u+v+w|| = √(74.28² + 135.26²) ≈ 152.44
To find the direction, we calculate the angle θ:
θ = atan2(135.26, 74.28) ≈ 61.26°
The total size of the composite vector, obtained by adding u, v, and w, amounts to a value close to 152.44.
The angle formed between this vector and the positive x-axis measures around 61.26° and goes in a counterclockwise direction.
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The three vectors are in two-dimensional space and have the following components:
u = (80cos(30°), 80sin(30°))
v = (60cos(60°), 60sin(60°))
w = (50cos(120°), 50sin(120°))
What are the magnitude and direction is u+v+w? ||v|= 60 ||w||=50 ||u||= 80
please help me i just need this one more
The value of angle S and angle R is 95⁰ and 110⁰ respectively.
What is the value of angle S and angle R?The value of angle S and angle R is calculated as follows;
11y + 7y = 180 (opposite angles of cyclic quadrilateral are supplementary)
18y = 180
y = 180/18
y = 10
(3x - 5) + (3x + 5) = 180 (opposite angles of cyclic quadrilateral are supplementary)
6x = 180
x = 180/6
x = 30
Angle S = 3x + 5
= 3(30) + 5
= 95⁰
Angle R = 11y
= 11 x 10
= 110⁰
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Evaluate the expression. C(11, 0)
The value of C(11, 0) is 1.
We have to find C(11, 0)
Using the definition of Combination
C(n, r) = n!/ r1 (n-r)!
Here, n =11 and r= 0
So, C( 11, 0)
= 11! / 0! (11-0)!
= 11! / 1 x 11!
= 1
Thus, the value of C(11, 0) is 1.
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Ron took 1 1/2 hours to drive to his office. His office was 120 km away from his house. Find his
driving speed.
Answer:
80 miles per hour.
Step-by-step explanation:
120 - 80 = 40 Because 40 is half than 80.
On Monday, one share of a certain stock costs $41.45. On Tuesday, the cost goes up by $0.58. It goes down by $0.26 on both Wednesday and Thursday. On Friday, it goes down by $0.06. Write an expression to represent the cost of one share of the stock on Friday. Then evaluate the expression to find the cost on Friday.
Answer:
The cost of one share of the stock on Friday is $41.45
Step-by-step explanation:
The initial cost of one share of the stock on Monday is $41.45.
On Tuesday, the cost goes up by $0.58, so the cost becomes:
$41.45 + $0.58 = $42.03
On Wednesday, the cost goes down by $0.26, so the cost becomes:
$42.03 - $0.26 = $41.77
On Thursday, the cost also goes down by $0.26, so the cost becomes:
$41.77 - $0.26 = $41.51
Finally, on Friday, the cost goes down by $0.06.
So the expression to represent the cost of one share of the stock on Friday is:
$41.51 - $0.06
To evaluate this expression, we simply subtract $0.06 from $41.51:
$41.51 - $0.06 = $41.45
Therefore, the cost of one share of the stock on Friday is $41.45
Mr.A sells watches. He is paid a monthly commission. received 21% of his first $1,500 in sales and 14% of the balance of his sales. Last month he sold $2,233 worth of watches. How much commission did he earn last month? and show your work.
The amount of commission Mr. A received last month is C = $ 417.62
Given data ,
Let the amount of commission earned be C
Now , the equation is
The first $1,500 in sales are eligible for a commission rate of 21%, so the commission on this portion of his sales is:
0.21 x $1,500 = $315
The remaining portion of his sales is:
$2,233 - $1,500 = $733
This amount is eligible for a commission rate of 14%, so the commission on this portion of his sales is
On simplifying the equation , we get
0.14 x $733 = $102.62
To find Mr. A's total commission, we add the commission on the first $1,500 to the commission on the remaining $733
$315 + $102.62 = $417.62
Hence , Mr. A earned a commission of $417.62 last month
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what is the missing vaule of x on the diagram below
The measure of the missing vaule of x in the diagram is 43
What is the missing vaule of x in the diagramFrom the question, we have the following parameters that can be used in our computation:
The circle
Using the theorem of sum of angles on a circumference, we have
2x + 122 + 152 = 360
Evaluating the like terms, we have
2x = 360 - (122 + 152)
So, we have
2x = 86
Divide by 2
x = 43
Hence, the missing vaule of x in the diagram is 43
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What is the square root of 144?
Answer:
12
Step-by-step explanation:
The square root of 144 is 12. This is because when a number is squared, it means it is multiplied by itself. So, 12 multiplied by 12 is equal to 144. Therefore, the square root of 144 is the value that, when multiplied by itself, gives the result of 144. This value is 12. The square root of 144 is also a perfect square, which means it is a whole number that can be generated by multiplying two equal integers.
Find the equivalent expression of 5^-4
the equivalent expression of 5^-4 is 1/625
What are index forms?Index forms are defined as mathematical forms that are used in the representation of numbers or variables that are too large or too small.
They are also called scientific notation or standard forms.
They are represented as a number or variable that is raised to an exponent.
Examples of index forms are;
a³, c²
5², 6³
From the information given, we have;
5^-4
Note that equivalent expressions are described as expressions that have the same solution but different arrangement of values
Then, we have;
1/5⁴
Find the fourth root
1/625
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Please Help College Algebra
An equation for the line that passes through (-14, 14) and whose slope is undefined is x = -14.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-14, 14) and an undefined slope, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 14 = undefined(x - (-14))
y - 14 = undefined(x + 14)
x = -14
In conclusion, the equation of a line that has an undefined slope represents a vertical line that crosses the x-axis only i.e x = -14.
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cone shaped storage container holds a photographic chemical. if the container is 60 cm wide and 20 cm high how many liters does it hold if 1 liter equal 1000cm3
