PLEASE SHOW FULL SOLUTIONS FOR BOTH QUESTIONS AND ONLY ANSWER IF YOU KNOW! NO CALCULUS PLEASE! THAT WOULD BE VERY APPRECIATED!!
Answers
Answer:
5. 3 cm × 2 cm × 7 cm
6. f(x) = x³ -3x² -x +3
Step-by-step explanation:
You want the dimensions of a cuboid with edges marked (x-1), (x-2), and (x+3) and a volume of 42 cm³. You also want the coefficients of a monic cubic f(x) with values f(2) = -3, f(-3) = -48, and f(-1) = f(1).
5. CuboidThe volume of the cuboid is the product of its dimensions, so we have ...
V = LWH
42 = (x -1)(x -2)(x +3)
The value of x can be found as the solution to this equation. A graphical solution is attached. It shows x=4, so the dimensions are ...
4 -1 = 3
4 -2 = 2
4 +3 = 7
The dimensions of the cuboid are 3 cm by 2 cm by 7 cm.
Note that the prime factors of 42 are 2, 3, 7, which have the required differences. You don't really need a polynomial to guess these are the dimensions.
The expanded polynomial is x³ -7x -36 = 0, so potential rational roots will be from the set {1, 2, 3, 4, 6, 9, 12, 18, 36}. An estimate of the upper bound of the real root puts it at ∛36 +√7 ≈ 5.9. We require x > 2, so the viable choices for testing are 3 and 4. x=4 is the solution.
6. CoefficientsThe remainder theorem tells you that the remainder from dividing f(x) by (x-a) is f(a). To obtain linear equations in b, c, d, we can rearrange the function to ...
bx² +cx +d = -x³ +f(x)
For x = ±1, we know the remainders f(x) are the same, so we can look at the difference of the equations for these x-values.
(b(-1)² +c(-1) +d) - (b(1)² +c(1) +d) = (-(-1)³ +f(-1)) - (-(1)³ +f(1))
b -b -c -c +d -d = 1 -(-1)
-2c = 2
We can fill in values x=2, x=-3 to get two more equations in b, c, d. The coefficients of the three equations we have for the three unknowns are shown in the second attachment. The third attachment shows the solution of these equations is (b, c, d) = (-3, -1, 3).
The table in the first attachment confirms the remainders using these coefficients.
__
Additional comment
For problem 6, we started out using synthetic division, then realized the resulting equations are the same as those developed using the rearranged form shown above. We like to let calculators and spreadsheets do the tedious arithmetic where possible.
Answer:
5)The dimensions of the rectangular prism are 3 , 7 and 2.
6) f(x) = x³ - 3x² - x + 3
Step-by-step explanation:
5) The volume of rectangular prism = l*w*h.
l*w*h= 42
(x- 1)(x -2)(x+3) = 42
We can find (x - 2) *(x + 3) using the identity (x + a)(x + b) = x² + (a +b)*x + ab
(x - 2)(x + 3) =x² + (-2 +3)x + (-3)*2
= x² + 1x - 6
(x -1)(x + 3)(x - 2) = 42
(x - 1)(x² + x - 6) = 42
x*x² + x*x - 6*x + (-1)*x² + (-1) *x + (-1)(-6) = 42
x³ + x² - 6x - x² - x + 6 - 42 = 0
x³ + x² - x² - 6x - x + 6 -42 = 0
Combine the like terms,
x³ - 7x - 36 = 0
Find the zeros of the cubic polynomial by synthetic division method.
4 1 0 -7 -36
4 16 36
1 4 9 0
x - 4 is zero of the polynomial.
Ignore the quadratic polynomial x² + 4x + 9 as it will have irrational roots(zeros) and dimensions will be always positive integer.
x - 4 = 0
x = 4
length = x - 1 = 4 - 1 = 3
Width = x + 3 = 4 + 3 = 7
Height = x - 2 = 4 - 2 = 2
The dimensions of the rectangular prism are 3 , 7 and 2.
6) f(x) = x³ + bx² + cx + d
It is given that when f(x) is dived by x + 1 and x- 1, the remainders are same.
x + 1 = 0 ; x - 1 = 0
x = -1 ; x = 1
f(-1) = f(1)
-1 + b - c + d = 1 + b + c + d
-1 -1 + b - b - c - c + d - d = 0
-2 - 2c = 0
-2c = 2
c = 2 ÷ (-2)
[tex]\boxed{c = -1}[/tex] -------------(I)
It is given that when f(x) divided by ( x - 2) it leaves a remainder (-3)
f(2) = -3
8 + 4b + 2c + d = -3
8 + 4b + 2*(-1) + d = -3 {from (I)}
8 + 4b - 2 + d = -3
4b + d = -3 + 2 - 8
4b + d = -9 -------------(II)
It is given that when f(x) divided by ( x + 3) it leaves a remainder (-48).
f(-3) = -48
-27 + 9b - 3c + d = -48
-27 + 9b - 3*(-1) +d = -48 {From (I)}
-27 + 9b + 3 + d = - 48
9b + d = -48 + 27 - 3
9b + d = -24 --------------(III)
Subtract equation (III) from equation (II),
(II) 4b + d = -9
(III) 9b + d = -24
- - +
-5b = 15
b = 15 ÷ (-5)
[tex]\boxed{b=-3}[/tex]
Plugin b = -3 in equation (II),
4*(-3) + d = -9
-12 + d = -9
d = -9 + 12
[tex]\boxed{d = 3}[/tex]
[tex]\boxed{\bf f(x) = x^3 - 3x^2 -x + 3 }[/tex]
Related Questions
A system of linear equations and a reduced matrix for the system are given. 1 0 Nm 1 x - y + z = 3 3x + 2z = 7 (x - 4y + 2z = 5 0 1 0 1 Use the reduced matrix to find the general solution of the system, if one exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ( (x, y, z) = *) (b) If multiple solutions exist, find two specific solutions. (Enter your answers as a comma-separated list of ordered triples. If there is no solution, enter NO SOLUTION.) (x, y, z) =
Answers
a) General solution of the system is (x, y, z) = (2, 0, 1).
b) There are no multiple solutions, and we cannot find two specific solutions.
How to evaluate each part of the question?The given system of linear equations is:
1) x - y + z = 3
2) 3x + 2z = 7
3) x - 4y + 2z = 5
The reduced matrix for this system is:
1 0 1
0 1 0
0 0 1
Using the reduced matrix, we can rewrite the system of linear equations as:
1) x + z = 3
2) y = 0
3) z = 1
Now we can solve the system step by step:
From equation (3), we know that z = 1.
Next, we can use the value of z in equation (1) to find x:
x + 1 = 3
x = 3 - 1
x = 2
Finally, from equation (2), we know that y = 0.
So, the general solution of the system is (x, y, z) = (2, 0, 1).
(b) Since there is only one solution to this system, there are no multiple solutions, and we cannot find two specific solutions.
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Place the steps of eukaryotic DNA replication in order, from when a germ cell enters gap 1 (G_1) phase to the cell cycle termination.
Answers
Answer:
The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is : G1-> S Phase ->G2 ->Mitosis ->Cytokinesis ->Cell cycle termination
Step-by-step explanation:
The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is as follows:
Step 1: G1 phase - During this phase, the germ cell is growing and preparing for DNA synthesis.
Step 2: S phase - DNA replication occurs during this phase. The chromosomes duplicate to form two identical chromatids, which remain attached at the centromere.
Step 3: G2 phase - During this phase, the cell checks for any errors in DNA replication and prepares for cell division.
Step 4: Mitosis - The cell divides its replicated DNA and organelles into two identical daughter cells. This process ensures that each daughter cell has the same amount of genetic material as the parent cell.
Step 5: Cytokinesis - The cytoplasm divides, creating two identical daughter cells.
Step 6: Cell cycle termination: After successful completion of mitosis and cytokinesis, the cell cycle is terminated, and the daughter cells may enter a new cycle or enter a non-dividing state (G0 phase).
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How to factor this so that it's in parenthesis? (Please use a detailed explanation thanks)
8n^2 -14n -15
Answers
Answer:
(4n+3)(2n-5)
Step-by-step explanation:
1) Split the second term [tex]8n^2-14n-15[/tex] into two terms.
1- Multiply the coefficient of the first term by the constant term.
[tex]8\times-15=-120[/tex]
2- Ask: Which two numbers add up to -14 and multiply to -120?
6 and -20
3- Split -14n as the sum of 6n and -20n.
[tex]8n^2+6n-20n-15[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2n(4n+3)-5(4n+3)[/tex]
3) Factor out the common term [tex]4n+3[/tex].
[tex](4n+3)(2n-5)[/tex]
A square pyramid has a base with a side length of 4cm and triangular faces with a height of 7cm. Esther calculated the surface area as (4x4)+4(4x7) equals 128cm. Explain Esther's error and find the correct surface area
Answers
Esther missed including the surface area of the square sides of the pyramid. The correct surface area is found by adding the surface area of the four triangular faces, base, and sides. The total surface area is 104cm².
Esther's error was that she only considered the surface area of the triangular faces and the base of the pyramid. She failed to include the surface area of the pyramid's square sides.
To find the correct surface area of the pyramid, we need to add the surface area of the four triangular faces and the surface area of the square base and sides. The surface area of the square base is 4² = 16cm², and the surface area of each triangular face is (1/2)bh = (1/2)(4)(7) = 14cm². The surface area of each square side is 4 x 4 = 16cm².
Therefore, the correct surface area of the square pyramid is:
4 x 14cm² (for the four triangular faces) + 16cm² (for the base) + 4 x 16cm² (for the four square sides) = 104cm².
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Find the sum of the first 48 terms of the following series, to the nearest integer.
5,9,13,. ???
Answers
The sum of the first 48 terms of the following series, to the nearest integer is 4632.
An computation progression( AP) is a sequence of figures where the differences between every two successive terms are the same. In this progression, each term, except the first term, is attained by adding a fixed number to its former term. This fixed number is known as the common difference and is denoted by'd'. The first term of an computation progression is generally denoted by' a' or' a1'.
We have series as,
5,9,13,....48
so we have
First term = a = 5
Last term T = 48
Interval between them as d = 9 - 5 = 4
To find the sum of the first 48 terms we have formula as,
[tex]S = \frac{n}{2} [a+(n-1)d]\\[/tex]
putting the value of the values in the equation,
[tex]S = \frac{48}{2} [5+(48-1)4]\\\\S = 24[5+188]\\\\S = 4632\\[/tex]
Therefore, the sum of the first 48 terms is 4632.
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Helppppppppppppppppp
Answers
Which system of inequalities has the solution shown in the graph?
Answers
y ≥ x - 1
y < 1/2x
Explanation
We can see on the solid line (≥) that the slope is 1 and the y intercept is -1. This will be a greater than or equal because the line is solid and the shaded area is above the line.
We can see on the dashed line (<) the slope is 1/2 and it crosses through (0,0) so no y intercept. It is less than because the line is dashed and the shaded area is below the line.
studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
Answers
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]
Where:
[tex]\(\lambda\)[/tex] is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
[tex]\(\lambda = 5\)[/tex]
[tex]\(k = 0\)[/tex], back to the formula as
[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]
Calculating the probability as
[tex]\[ P(X = 0) = e^{-5}[/tex]
[tex]= 0.0067379[/tex]
Therefore, the probability is 0.0067379 or 0.67%.
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1. Higher Order Thinking Sam made the shape at the right
from colored tiles. What is the area of the shape? Explain
how you found your answer.
1
square in
Answers
The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.
To find the area of the shape, we need to find the area of each of these three shapes and then add them up.
First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.
Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.
Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.
Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.
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a particular triangle has sides of length 14 cm, 8 cm and 9 cm. in centimeters, what is the perimeter of the triangle?
Answers
Answer:
31cm
Step-by-step explanation:
14 + 8 + 9 = 31
Make sure to add the cm on the end!
The perimeter of the triangle is 31cm.
The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.
In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.
In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.
For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.
In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.
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x=10
x-7y=-18 what is the answer
Answers
Answer: y=4
Step-by-step explanation:
you would plug in 10 wherever x would be so your new equation would be 10-7y=-18.
subtract 10 from both sides.
-7y=-28
then divide by -7
y=4
11. To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all? A 32 B 192 C 300 D 1,920
Answers
Joelle has a total of 32 yards of ribbon in all, the correct option is A.
Let's use x to represent Joelle's total amount of ribbon. We know that 24 yards of the ribbon represent 86% of her total amount of ribbon, which can be expressed as:
24 = 0.86x
We can solve for x by dividing both sides by 0.86:
x = 27.91
The response options are all integers, thus we must round to the closest whole number because of this. Since 0.91 is greater than or equal to 0.5, we round up to 28.
Therefore, Joelle has a total of
x = 27.91 / 0.86
= 32.44 yards of ribbon.
Once again, we round to the nearest whole number, which is 32.
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The complete question is:
To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all?
A 32
B 192
C 300
D 1920
i hate math fr but pls help asap
Answers
pi x 11^2 = 380.13in squared
the area is 380.13 inches squared
Answer:
379.94
Step-by-step explanation:
Area of a circle given radius is really easy! The equation for area of a cicle is pi x r^2. So just plug in. Assuming pi is 3.14 your equation would be
3.14x11^2. 11 squared is 121. Then multiply by 3.14 and thats your answer.
what does 4x^{3} ÷ 8 equal
Answers
Answer:
4x^{3} ÷ 8 = x^{3}/2
LMNO id a parallelogram. If NM =c+30 and OL=4x +9, find the value of X NM AND OL
Answers
The value of x is 7, and NM and OL are both equal to 37.
Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,
NM = OL
We also have the following information:
NM = x + 30
OL = 4x + 9
Substituting the first equation into the second equation, we get:
x + 30 = 4x + 9
Simplifying this equation, we get:
3x = 21
Therefore, x = 7.
Substituting this value back into the original equations, we get:
NM = x + 30 = 7 + 30 = 37
OL = 4x + 9 = 4(7) + 9 = 37
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Ellie and Terrell are also putting new
carpeting in their family room,
which is a rectangle having length =
x + 3 and width = x + 1. What is
the area of the family room?
Answers
Answer:
x² +4x + 3
Step-by-step explanation:
Area = length x width
Area = (x + 3)( x + 1)
Area = x² + X + 3x +3
Area = x² + 4x +3
how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
Answers
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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Find the area of a 2.5-by-2.5 square by splitting it into unit squares.
Answers
The area of 2.5 by 2.5 square is given as follows:
6.25 square units.
How to obtain the area of a square?The area of a square of side length s is given by the square of the side length, as follows:
A = s².
For this problem, we have 2.5 by 2.5 square, hence the side lengths are given as follows:
s = 2.5.
Then the area of 2.5 by 2.5 square is obtained applying the formula as follows:
A = 2.5²
A = 6.25 square units.
This means that the entire 2.5-by-2.5 square can be divided into 6.25 unit squares, in which each of them would have a side length of one unit.
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Complete the table and graph the corresponding ordered pairs. Draw the line defined by the points to
represent all solutions to the equation: 4x + 2y = 8
Answers
Plot the x-intercept of (-0.5,0) Plot the y-intercept of (0,-2) Draw a line passing through both intercepts.
To graph 4x + 2y = 8, we'll first look at the x-intercept and y-intercept.
The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.
0 = 4x + 2y => x = -0.5y = 4x + 2(0) => y = -2
From the two equations, we get the ordered pairs(-2,0), and (-0.5,0) as our intercepts.
The line defined by these two points and that represent all solutions to the equation is:
y = -2x + 4
The table would show different values of x for different values of y, but since there are no specific values to solve, you
just have to use the slope-intercept formula to determine the points on the graph.
Here's how to plot the ordered pairs on a graph:
Plot the x-intercept of (-0.5,0)
Plot the y-intercept of (0,-2)
Draw a line passing through both intercepts.
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Please answer with explanation!
Answers
The exact dimensions (in inches) of the cylindrical mailing tube that may be mailed using the postal service is 7 inches radius and a length of 14 inches.
How to calculate radius and length?To find the maximum volume of the mailing tube, maximize the function:
V = πr²L
subject to the constraint:
C = 2πr + L = 84
where C is the girth.
Using Lagrange multipliers, we need to solve the system of equations:
∇V = λ∇C
2πrL = λ(2π)
πr² = λ
2πr + L = 84
Taking the ratio of the first two equations:
L = 2r
Substituting this into the third equation:
4πr + 2r = 84
Simplifying:
r = 7
Substituting this into the equation L = 2r:
L = 14
Therefore, the cylindrical mailing tube of greatest volume that may be mailed using the postal service has a radius of 7 inches and a length of 14 inches.
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Image transcribed:
A package to be mailed using a certain postal service may not measure more than 84 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.)
length
girth
Use Lagrange multipliers to find the exact dimensions (in inches) of the cylindrical mailing tube of greatest volume that may be mailed using the postal service.
radius ______ in
length ______ in
Complete the statements about these similar pyramids. [picture of pyramids]two square base pyramids a and b are represented side-by-side. pyramid a has square base pqrs of side length 5 meters and t is the vertex. pyramid b has square base jklm of side length 25 meters and n is the vertex. the ratio of the heights is _____the ratio of the surface areas is ______the ratio of the volumes is ______
Answers
The ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125
Step-by-step explanation:
We can use the fact that similar pyramids have the same shape, but possibly different sizes. Let's denote the height of pyramid a by h_a, the height of pyramid b by h_b, and the scale factor between the two pyramids by k. Then, we have:
The ratio of the heights is k, since the height is scaled up by the same factor as the base length. That is, k = h_b / h_a.
The ratio of the surface areas is k^2, since the surface area is proportional to the square of the base length and the height. That is, k^2 = (side length of b / side length of a)^2 = (25 / 5)^2 = 5^2 = 25.
The ratio of the volumes is k^3, since the volume is proportional to the cube of the base length and the height. That is, k^3 = (side length of b / side length of a)^3 = (25 / 5)^3 = 5^3 = 125.
Therefore, the ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125.
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Answer:
height ratio- 1:5 surface area- 1:25 volume- 1:125
Step-by-step explanation:
Exercise 3-23A (Algo) Using ratio analysis to assess financial risk LO 3-5
The following information was drawn from the balance sheets of two companies. Company Assets = Liabilities + Equity
East 206,000 91,000 115,000
West 603,000 169,000 434,000
Required
a. Compute the debt-to-assets ratio to measure the level of financial risk of both companies. B. Compare the two ratios computed in requirement a to identify which company has the higher level of financial risk
Answers
The answer based on debt to assets ratio for east and west company are,
East company debt to assets ratio is equal to 0.44.
West company debt to assets ratio is equal to 0.28.
After comparing both the company debt to assets ratio East company is at higher level of financial risk.
Assets = Liabilities + Equity
For East company,
206,000 = 91,000 + 115,000
Assets = 206,000
liabilities = 91,000
Equity = 115,000
For West company,
603,000 = 169,000 + 434,000
Assets = 603,000
liabilities = 169,000
Equity = 434,000
Debt-to-assets ratio = Total liabilities divided by the total assets.
Debt-to-assets ratio for East
= 91,000 / 206,000
= 0.44
Debt-to-assets ratio for West
= 169,000 / 603,000
= 0.28
Comparing the two ratios,
0.44 > 0.28
This implies,
Company East has a higher debt-to-assets ratio is greater than the compared to Company West.
This represents that Company East has a higher level of financial risk.
As larger proportion of their assets are financed through debt.
This shows it is difficult to repay if the company experiences financial difficulties.
Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.
Therefore, the answer of the following questions are,
Debt to asset ratio of east company = 0.44
Debt to asset ratio of west company = 0.28
Company east has a higher financial risk level .
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An empty shipping box has a mass of 2. 75 kilograms. An electronics store is packing 5 identical laptops in the shipping box. Each laptop has a mass of 1. 65 kg. The cost to ship the box was $40. 00 for the first 5 kg and $3. 15 for each kilogram over 5 kg. What was the cost to ship the packed box?
Answers
The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.
The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.
Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.
The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.
The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:
$40.00 + $3.15 * 6 kg = $58.90
Therefore, the cost to ship the packed box is $58.90.
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the probability of drawing a diamond from a deck of cards is 1 4 ; what are the odds in favor of drawing a diamond from an ordinary deck of cards?
Answers
The probability of drawing a diamond from a deck of cards is 1/4. So, the odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.
A deck of cards has 52 cards in it, and there are 13 cards of diamonds in it. So, the probability of drawing a diamond is 13/52. Simplifying 13/52, we get 1/4. The odds of an event happening are the ratio of the probability of an event happening to the probability of an event not happening. It's expressed in the form of x:y.
The probability of an event happening is the probability of success. The probability of an event not happening is the probability of failure. In the current scenario, the probability of drawing a diamond is 1/4. So, the probability of not drawing a diamond is 3/4. Therefore, the odds in favor of drawing a diamond are:
=1/3
The odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.
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which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.
Answers
The following conditions must be met to conduct a two-proportion significance test:
the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.
To conduct the two-proportion significance test, the following conditions must be met:
Populations must be independent.
Sample sizes are greater than 30.
The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.
In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
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two cyclists start from the same point and ride in opposite directions. one cyclist rides twice as fast as the other. in 2 hr, they are 72 mi apart. find the rate of each cyclist.
Answers
From the same starting point, two cyclists ride in different directions. The speed of one cyclist is twice that of the other. They will be 72 miles apart in 2 hours. The rate of each cyclist is 12 miles per hour and 24 miles per hour
Let’s call the rate of the slower cyclist “r”. Then, according to the problem, the rate of the faster cyclist is “2r”.
We can use the formula distance = rate x time to set up two equations, one for the distance traveled by the slower cyclist and one for the distance traveled by the faster cyclist. The sum of these distances is the total distance they are apart after 2 hours, which we know is 72 miles:
2r x 2+r x 2=72
Simplifying this equation, we get:
4r+2r=72
Combining like terms, we get:
6r=72
Dividing both sides by 6, we get:
R=12
So the rate of the slower cyclist is 12 miles per hour. Using the fact that the faster cyclist rides at twice the rate of the slower cyclist, we can find the rate of the faster cyclist:
2r=2 x 12=24
So the rate of the faster cyclist is 24 miles per hour.
Therefore, the two cyclists ride at rates of 12 miles per hour and 24 miles per hour, respectively.
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a dance delegation of 4 people must be chosen from 5 pairs of dance partners. if 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
Answers
There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.
In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).
Therefore, the calculation is as follows:
total number of ways = nCr
= 5C4
= 5! / 4!(5-4)!
= 5! / 4!1!
= 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1
= 5 x 4 x 3 x 2
= 120
Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
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Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x) = 400 - 4x.
a. If revenue = price x demand, write the rule for the
function r(x), which represents the company's
expected revenue in jean sales. Then state the
domain of this function.
b. If the price is $40, how much revenue will the
company earn?
Revenue
Price
Answers
a. The revenue function, r(x), is given by the product of the price x and the demand function d(x):
[tex] \sf r(x) = x \times d(x) = x \times (400 - 4x) = 400x - 4x^2[/tex]
The domain of this function is the set of possible prices that can be charged for the jeans, which is typically a positive real number, or in interval notation: (0, infinity).
b. If the price is $40, we can find the revenue by plugging in x = 40 into the revenue function:
[tex] \sf r(40) = 400(40) - 4(40)^2 = 16,000 - 6,400 = 9,600[/tex]
Therefore, the company will earn $9,600 in revenue if they sell their jeans at a price of 40
When given a set of cards lying face down that spell M, A, T, H, C, L, U, B, determine the probability of randomly drawing a consonant.
six eighths
two sixths
six tenths
one third
Answers
There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)
Answer:
The answer is six eighths
There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)
Step-by-step explanation:
so all you have to do is take out all the vowel and count the letters that are consonant then you make that your top number than you put that over the amount of numbers in total
the equation above relates the number of hours, a, kevin spends doing homework each week and the number of hours he spends watching television each week. if kevin spends a total of 15 hours doing homework and watching television each week, what does the variable b represent?
Answers
Variable b represents the number of hours Kevin spends watching television each week.
Define the term equation?A statement proving the equality of two mathematical expressions is known as an equation.
Given equation a + b = 15 relates the number of hours.
If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").
Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:
homework + watching television = 15 hours
a + b = 15
To find out what b represents, we can rearrange the equation to solve for b:
b = 15 - a
This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.
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Complete question-
The equation is a + b = 15