Profitability ratios show the combined effects of liquidity, asset management, and debt management on a firm's operating results. True or False?

Answers

Answer 1

Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.

Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios

Profitability ratios- are used to assess ability of a business to generate earnings with respect to revenue, operating cost, equity to shareholders, balance sheet assets etc.Liquidity ratio - is the ability of a company to pay of its debts for short term.Debt ratios- Calculated by dividing total debt by total assets.Coverage ratio -Companies ability to pay debts and other financial obligations like dividend.

So the statement given is true.

 

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Related Questions

I need help solving x

Answers

Answer:

x = 12

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles.

5x+20 = 20 + 6x-12

Combine like terms.

5x+20 = 6x +8

Subtract 5x from each side.

5x+20-5x = 6x+8-5x

20 = x+8

Subtract 8 from each side.

20-8 = x+8-8

12 =x

i need this ASAP!!!!

Answers

In accordance with Side-Angle-Side theorem of congruence, the triangles seen in choices A and C are congruent.

How to find two congruent triangles

In this problem we need to determine what triangles are congruent, that is, two triangles whose sides and angles are the same in measure and distribution. We can prove congruence by means of Side-Angle-Side theorem, where given angle is between two given sides.

Then, by direct inspection, the triangles from choices A and C are congruent, because sides and in-between angle are the same in measure and distribution.

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The triangles that are certainly congruent in the diagram are triangle A and triangle C.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape, such that the lengths of the three sides in one triangle are equivalent or have same length as the lengths of the three sides of the other triangle.

The congruent triangles can be obtained by using the congruence rules, or conditions for congruence, which includes; ASA, SAA, SSS, SAS

Where;

ASA is an acronym for Angle-Side-Angle

SAA is an acronym for Side-Angle-Angle

SSS is an acronym for Side-Side-Side

SAS is an acronym for Side-Angle-Side

The lengths of two sides and the measure of the included angle in triangle A are congruent to the length of two sides and the measure of the included side between the two sides in triangle C.

Therefore, the triangle in option A is congruent to the triangle in option C by the Side-Angle-Side, SAS, congruency rule.

The angle 62° is the non included angle to the 14 m and 10 m long side in option B and D, while the 14 m long side is the adjacent side to the 62° angle in option B. In option D the 10 m long side is adjacent to the 62° angle, which the orientation of triangles B and D to be different

The only two congruent triangles are triangles in option A and option C

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ken bought a bike that was priced at $450.He was offered a 25% discount what was the discount on the bike.

Answers

Answer:

You just want to find what 25% of 450 is. To do so, you can change 25% into a decimal, and then multiply:

25% as decimal is 0.25.

0.25 * 450 = 112.5

The discount is $112.50.

Step-by-step explanation:

Hope it helps! =D

1. It is claimed that less than 25% of adults prefer Italian food as their favorite ethnic food. A
survey of 1122 adults resulted in 314 who say that Italian food is their favorite ethnic food.
Find the value of the test statistic z using

z=^p-p
——-
Square root of pq
—-
n


Oz=2.31
Oz=-2.31
Oz=2.01
Oz=-2.01

Answers

The value of the test statistic z is, 2.31.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

It is claimed that less than 25% of adults prefer Italian food as their favorite ethnic food.

And,  A survey of 1122 adults resulted in 314 who say that Italian food is their favorite ethnic food.

Now,

⇒ P = 25%

⇒ q = 100% - 25% = 75%

⇒ n = 1122

Hence, We get;

⇒ z = (314/1122 - 25%) / √(25% 75% / 1122)

⇒ z = 2.31

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use the fundamental theorem of calculus to find the exact value of the definite integral `\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx`. a correct solution must: - clearly state an antiderivative of the integrand, - show where the fundamental theorem of calculus is used and - give an exact value (do not approximate).

Answers

By using fundamental theorem of calculus  The exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

First, we can find an antiderivative of the integrand by using the power rule and the constant multiple rule of integration:

∫(3x^(-1/2)) dx = 3 ∫(x^(-1/2)) dx = 3 (2x^(1/2)) + C = 6√(x) + C

where C is the constant of integration.

Now, we can use the fundamental theorem of calculus to evaluate the definite integral \int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx. The theorem states that if f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x), then

∫[a, b] f(x) dx = F(b) - F(a)

In this case, f(x) = 3x^(-1/2) and F(x) = 6√(x) + C. Therefore,

∫{1}^{π} (3x^(-1/2)) dx = F(π) - F(1) = 6√(π) + C - 6√(1) - C = 6√(π) - 6√(1) = 6(√(π) - 1)

So the exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

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How many solutions does the system of
equations below have?
-2x - 3y + z = 7
-x - y + 3z = -10
-2x - y - z = 13
no solution
one solution
infinitely many
solutions

Answers

The system of equations has infinitely many solutions.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:

-2x - 3y + z = 7

-x - y + 3z = -10

-2x - y - z = 13

We have to how many solutions the system of equations has.

Arranging the above equations in form of a matrix and finding the determinant, we get,

Δ = [tex]\left|\begin{array}{ccc}-2&-3&1\\-1&-1&3\\-2&-1&-1\end{array}\right|[/tex]

= -2(1+3) +3(1+6) +1(1-2)

= - 4 + 21 -1 = 16

Δ₁ = [tex]\left|\begin{array}{ccc}7&-3&1\\-10&-1&3\\13&-1&-1\end{array}\right|[/tex]

= 7(1+4) +3(10-39) +1(10+13)

= 35 - 87 + 23

= -29

Hence, the system of equations has infinitely many solutions.

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the number is divisible by 6, 8, and 10 and has no repeated digits

Answers

120 is the number divisible by 6, 8, and 10.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The common multiples to 6, 8, and 10.

6 x 20 =  120

8 x 15 = 120

10 x 12 = 120

So,

120 is divisible by 6, 8, and 10.

Thus,

120 is the number.

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Determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius:

Answers

The ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius is 1/2

We know that the formula for the volume of a paraboloid is:

V = 1/2 × π × r²  × h

where r is the Radius of Paraboloid

and h is Height of Paraboloid

Let us assume that V₁ represents the volume of a paraboloid (a parabola rotated about the y axis)

So, V₁ = 1/2 × π × r²  × h

Also, we know that the formula for the volume of a cylinder is:

V = π × r²  × h

Let us assume that V₂ be the volume of a cylinder with the same height h and base radius r.

So, V₂ =  π × r²  × h

consider the ratio of the volume of a paraboloid to the volume of a cylinder with the same height and base radius,

V₁ / V₂

= (1/2 × π × r²  × h) / (π × r²  × h)

= 1/2

Therefore, the required ratio is 1/2

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What is the difference of 8/3x+5 -2x/3x+5

Answers

The difference of  8/3x+5 -2x/3x+5 is (8 - 2x) / (3x+ 5).

The correct option is (A).

What is Expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

We have the Expression as:

8/3x+5 -2x/3x+5

Now, Simplifying the expression as:

=  8/3x+5 -2x/3x+5

= (8 - 2x) / (3x+ 5)

= 8/(3x+ 5) - 2x/ (3x+ 5)

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The average of any three odd integers is an odd integer. What proof method would you use to show that the statement is true, or false? Prove true by exhaustion. Prove true by contraposition. O Prove false by counterexample. O Prove true by direct proof. Theorem: The difference between any odd integer and any even integer is odd. In an attempted proof of this statement a student wrote the following lines: Suppose n is any odd integer, and m is any even integer. By definition of odd integer, n = 2k + 1 where k is an integer. By definition of even integer, m = 2k where k is an integer. Then n m = (2k + 1) – 2k = 1 and 1 is odd. Therefore, the difference between any odd integer and any even integer is odd. Which one of the following best describes the reason the proof is not correct? O The proof does not prove that 1 is odd. O The proof violates the parity property. The proof violates the zero-product property. The proof assumes m and n are consecutive integers.

Answers

The proof method to show that the statement "The average of any three odd integers is an odd integer" is true is "Prove true by direct proof."

To prove that the statement is true by direct proof, we can assume that the three odd integers are a, b, and c, where a = 2k + 1, b = 2m + 1, and c = 2n + 1 for some integers k, m, and n. Then, the average of these three odd integers is:

(a + b + c)/3 = (2k + 1 + 2m + 1 + 2n + 1)/3

= (2k + 2m + 2n + 3)/3

= 2(k + m + n) + 1

Since k, m, and n are integers, k + m + n is also an integer. Therefore, the average of any three odd integers is of the form 2x + 1, where x is an integer, which is an odd integer.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property." The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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The original price of a lawn mower was $199.99. During a midsummer sale, the lawn mower is on sale for $139.99. What is the discount rate?

Answers

Answer:

60 dollars

Step-by-step explanation:

I say this because it's simple math 199.90 - 139.99 its obviously 60

The cost of going to the movie theater for Elissa and 11 of her friends is shown in the table. The total cost is divided equally among each person. How much does each person pay?

Answers

The cost for each person is $12.

So, each person paid $12 for a movie ticket.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The cost of going to the movie theater for Elissa and 11 of her friends is $144.

The total cost is divided equally among each person.

The number of total people is 12.

So, the cost of each person,

= total cost/ the number of total people

= 144/12

= 12

Therefore, 12 is the required value.

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What is D(50) − (D(15) ∪ D(20))?

Answers

The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).

The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.

What is Set Theory?

Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.

In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.

The union of sets, represented by the symbol , is the operation that gives you the set of all elements that are in at least one of the sets being considered.

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A rectangle has a length of 30 feet less than five times its width if the area of the rectangle is 360 ft.² find the length of the rectangle

Answers

Answer:

[tex]l = 30[/tex]     OR     [tex]l=-60[/tex]

Step-by-step explanation:

We can solve this problem with a system of equations by creating 2 equations from the information given.

1. "a length of 30 feet less than 5 times its width"

[tex]l = 5w - 30[/tex]

2. "the area of the rectangle is 360 ft²"

[tex]l\cdot w = 360[/tex]

To solve for the rectangle's length, we can create a substitution for w by dividing both sides of the second equation by length ([tex]l[/tex]).

[tex]l\cdot w = 360\\\overline{\ \ l\ \ } \ \ \ \: \ \overline{\ l \ \ }[/tex]

[tex]w = \dfrac{360}{l}[/tex]

Then, we can substitute this value back into the first equation and solve for [tex]l[/tex].

[tex]l = 5(\dfrac{360}{l}) - 30[/tex]

↓ distribute the 5

[tex]l(l) = \left(\dfrac{1800}{l} - 30\right)l[/tex]

↓ multiply both sides by [tex]l[/tex]

[tex]l^2 = 1800 - 30l[/tex]

↓ move all [tex]l[/tex]'s to one side

[tex]l^2 + 30l = 1800[/tex]

To solve this quadratic, we can complete the square.

    ↓ add (30/2)² to both sides

    [tex]l^2 + 30l + \left(\dfrac{30}{2}\right)^2 = 1800 + 15^2[/tex]

    ↓ simplify 15²

    [tex]l^2 + 30l + 225 = 1800 + 225[/tex]

    ↓ factor the left side as a perfect square

    [tex](l + 15)^2 = 2025[/tex]

    ↓ take the square root of both sides

    [tex]l + 15 = \pm \sqrt{2025}[/tex]

    [tex]l + 15 = \pm 45[/tex]

↓ split into 2 equations

[tex]l + 15 = 45[/tex]     OR     [tex]l + 15 = -45[/tex]

[tex]\boxed{l = 30}[/tex]          OR     [tex]\boxed{l=-60}[/tex]

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.
y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05
(a) Compute E(Y).
E(Y) =
(b) Suppose an individual with Y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharge.
$
Expert A

Answers

(a) The value of E(Y) will be = 0.8

(b)  The expected amount of the surcharge is $165.

(a) The expected value of Y is given by:

E(Y) = 0(0.5) + 1(0.25) + 2(0.2) + 3(0.05)

= 0.25 + 0.4 + 0.15

= 0.8

Therefore, the expected number of moving violations for which the individual was cited during the last 3 years is 0.8.

(b) The amount of the surcharge for an individual with Y violations is $110[tex]y^{2}[/tex]. The expected surcharge is given by:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

To calculate E([tex]y^{2}[/tex]), we use the formula:

E([tex]y^{2}[/tex]) = Σ [tex]y^{2}[/tex] p(y)

where the sum is taken over all possible values of Y.

E([tex]y^{2}[/tex]) = [tex]0^{2}[/tex](0.5) + [tex]1^{2}[/tex](0.25) + [tex]2^{2}[/tex](0.2) + [tex]3^{2}[/tex](0.05)

= 0 + 0.25 + 0.8 + 0.45

= 1.5

Therefore, the expected surcharge is:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

= $110 * 1.5

= $165

So, the expected amount of the surcharge for an individual with moving violations is $165.

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A tent is in the shape of a triangular prism. About how much canvas, including the floor, is used to make the tent? Draw a net if necessary.

Answers

The total area of the canvas needed would be 21.4 square yards.

What is the surface area of triangular pyramid?

The formula to calculate the total surface area of a triangular pyramid is -

T.S.A. = {1/2}(a × b) + {1/2}(b × s).

Given is a tent is in the shape of a triangular prism.

The total area of the canvas would be -

A{C} = 2{1/2 x 2 x 1.7} + 2{3 x 2} + {3 x 2}

A{C} = (2 x 1.7) + 12 + 6

A{C} = 3.4 + 18

A{C} = 21.4 square yards

Therefore, the total area of the canvas needed would be 21.4 square yards.

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Answer:6

Step-by-step explanation:beacuse it it

make w the subject of the formula y-aw=2w-1
dont answer y+1/a+2 cuz it doesnt work

Answers

Refer to the attached image.

What is the y-intercept of the graph of y = 2.5*?
a. 2.5
b. 1
ΟΑ
О в
О с
OD
C. 0
d. -1
OT
Ü
Please select the best answer from the choices provided

Answers

Point of  y-intercept is (0,1)

What is y-intercepts?

In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.

Given the function is [tex]y=2.5^{x}[/tex]

y-intercept is the point where the graph of the function crosses the y-axis.

To find the point of y-intercept put x=0 in the given function, we get

if x=0  then [tex]y=2.5^{0}[/tex] ⇒ y=1.

The function crosses at the point 1 in the  y-axis.

Hence, point of  y-intercept is (0,1)

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Anthony painted 2triangles of the same size on the top corners of his house flag for sports day. What is the total area of both triangles?

Answers

The total area of both triangles is the product of the height and base of the flag.

What is a triangle?

The connecting of three noncolinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.

Given, Anthony painted 2triangles of the same size on the top corners of his house flag for sports day.

We are aware of A parallelogram can be divided into two comparable triangles by dividing it along its diagonal.

A planar figure with opposite sides that are parallel and of equal length is called a parallelogram.

Since the area of a parallelogram is equal to its base times its height, the combined area of the two triangles will be the same.

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Grade 5 18 is 15% what number

Answers

Answer:

120

Step-by-step explanation:

18 = .15x  Divide both sides by .15 (15% as a decimal is .15)

[tex]\frac{18}{.15}[/tex] = [tex]\frac{.15x}{.15\\}[/tex]

120 = x

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answers

The statements that are true about the quadratic function f(x) = x^2 - 5x + 12 and its graph are:

The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph does not contain the point (20, -8).
The statement "The value of f(–10) = 82" is false, because:

f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162, not 82.

The statement "The graph of the function opens down" is also false, because:

The coefficient of the quadratic term is positive, so the parabola opens upwards.

Prove that a nonempty set W is a subspace of a vector space V if and only if ax + by is an element of W for all scalar a and b and all vectors x and y in W.In one direction, assume W is a subspace and show by using closure axioms that ax + by is an element of W. In the other direction, assume ax + by is an element of W for all scalars a and b and all vectors x and y in W, and verify that W is closed under addition and scalar multiplication.(i) If W is a subspace of V, then use scalar multiplication closure to show that ax and by are in W. Now, use additive closure to get the desired result.(ii) Conversely, assume ax + by is in W. By cleverly assigning specific values to a and b, show that W is closed under addition and scalar multiplication.

Answers

If W is a subspace of V, then ax + by is an element of W since it satisfies the closure axioms of a vector space. Specifically, scalar multiplication closure confirms that ax and by are in W, and additive closure confirms that their sum, ax + by, is also in W.

Conversely, if ax + by is an element of W for all scalars a and b and all vectors x and y in W, then W must be closed under both addition and scalar multiplication.

To demonstrate this, we can assign a particular value to a or b, set the other to 1, and substitute the corresponding vectors x and y from W to get the equation ax + by = a(x) + b(y). This equation confirms that W is closed under addition and scalar multiplication, making it a subspace of V.

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mike tyson is high no ee aiqidj​

Answers

Answer:

Jakaur7889 on inta

Step-by-step explanation:

Babahaja

Take a picture or describe a place/instance/event that might influence your heart rate. Start with a heart rate of 90bpm, decide how many beats per minute your situation might increase or decrease your heart rate – DO NOT DISCLOSE YOUR NUMBER. Calculate the number of 0.04s boxes there would be between R-R intervals on an ECG trace. Write that number in your answer. - choose something that might increase your heart rate

Answers

Using unitary method, we can calculate the number of 0.04s boxes between R-R intervals on an ECG trace for our chosen event.

The unitary method is a mathematical technique that involves finding the value of one unit of a given quantity and then using it to find the value of a different quantity. In this case, we want to find the change in heart rate per second, so we need to determine how many beats per second our chosen event increases our heart rate by.

To calculate the duration of each R-R interval, we can use the following formula:

R-R interval duration = 1 / heart rate (in seconds)

Assuming our starting heart rate is 90 bpm and our event increases our heart rate by y beats per second, we can calculate the new heart rate as follows:

New heart rate = 90 bpm + (y * 60) bpm

We can then calculate the duration of each R-R interval using the formula above.

Finally, to find the number of 0.04s boxes between R-R intervals on an ECG trace, we can convert the R-R interval duration to a number of 0.04s boxes. Each 0.04s box on an ECG trace represents 0.04 seconds, so we can use the following unitary method:

1 second = 25 0.04s boxes

R-R interval duration (in seconds) = x seconds

Number of 0.04s boxes = x * 25

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A bond has a 1,9% interest rate compounded quarterly. A stock has a 7.2% interest rate compounded
annually.
Which of the following shows how to transform the function representing the value of the bond from
quarterly compounding interest to annually compounding interest? Assume t is the time in quarters, and
that there is an initial investment of $1 in each account.

Answers

The way to transform the function such that the bond goes from quarterly compounding interest to annually compounding interest is = 1 + ( 1 + rate / 4 )ⁿ ˣ ⁴.

How to find the value ?

The bond is said to be compounded quarterly. There would therefore be four compounding periods in a single year because there are four quarters in a year.

The formula would have been:

= Initial investment + ( 1 + rate ) ^ number of years

The adjusted formula to account for the quarters becomes :

= 1  + ( 1 + rate / 4 )ⁿ ˣ ⁴

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Which of the following is/are assumptions for linear regression? Please select all that apply. It's possible that there is only one correct answer. Y| X = x (the conditional distribution of Y given X = x) is a normal distribution. X and Y are independent. The errors e1,e2, e; have the same variance. The expectation of each error e; is O

Answers

As per the information provided, option B) The errors e1,e2, e; have the same variance is the assumptions for linear regression.

Regression analysis is a linear technique used to model the relationship between a scalar response and/or one or more explanatory variables, also known as the dependent and independent variables here.

Simple linear regression and multiple linear regression are two terms used to describe the process when there is only one explanatory variable present. This statement is different from multivariate linear regression, which thus predicts multiple correlated dependent variables as opposed to a single scalar variable present.

The first regression analysis technique that attracted a lot of research attention and was frequently applied in practical situations was linear regression. This is because models with linear rather than non-linear dependence on their unknown parameters are easier to fit, and it is also easier to determine the statistical properties of the resulting estimators.

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1. What is the equation for a line in slope-intercept form that is perpendicular to y= 1/4x-5

2. Write the equation of the line in slope-intercept form that goes through (3,8) and is parallel to y=-3x+1.

Answers

Answer:

1) y = - 4x + b;2) y = - 3x + 17.

--------------------------------

Question 1

Given line:

y = 1/4x - 5

We know that perpendicular lines have opposite-reciprocal slopes.

Perpendicular line to the given has a slope of m = - 1 / (1/4) = - 4.

Let the y-intercept be b, then the line is:

y = - 4x + b

Question 2

Given line:

y = - 3x + 1

We know parallel lines have equal slopes.

The parallel line to the given has a slope of m = - 3 and passes through point (3, 8).

Set the point-slope equation:

y - 8 = - 3(x - 3)

Convert this into slope-intercept form:

y - 8 = - 3x + 9y = - 3x + 9 + 8y = - 3x + 17

the base of a triangle is 8 ft less than its height. if the area is 120 ft2, find the base and the height of this triangle. use an equation to solve this problem.

Answers

The height of the triangle is 20 and base of the triangle is 12.

"Information available from the question"

The base of a triangle is 8 ft. less than its height.

If the area is 120 [tex]ft^2.[/tex]

We have to find the base and the height of this triangle.

Now, According to the question:

Let the height be x then if the base is 8 ft. less, then the base is x - 8.

We know that:

Area of the triangle is :  (b × h)/2

Area of the triangle is : (x (x - 8)) /2

120 [tex]ft^2[/tex] = ([tex]x^{2} -8x[/tex])/2

240 = [tex]x^{2} -8x[/tex]

[tex]= > x^{2} -8x-240=0[/tex]

For solving equation, Use the quadratic formula :

x = (-b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a

a = 1

b = -8

c = -240

x = (-(-8) ± [tex]\sqrt{(-8)^2-4.1(-240)})/2.1[/tex]

By solving, we get

x = (8 ± 32)/2

We get the values :

x = 20 and x = -12

We know x = −12 can't be a solution as length can't be negative.

Base = x - 8

Base = 20 - 8

Base = 12

Hence, The height of the triangle is 20 and base of the triangle is 12.

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determine the amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST

Answers

The total amount of cash collected is $10,418.6.

What is a percentage?

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

The amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST is,

Rate of interest on the sales amount is 13%

13% of 9220 = [tex]\frac{13}{100}*9220=1198.6[/tex]

Here, sales price = $9,220

The total amount of cash collected = 1198.6+9220

                                                          = 10,418.6

Hence, the total amount of cash collected is $10,418.6.

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Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v, and w.u=i+jv=j+kw=i+k

Answers

The volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is: 1.

The triple scalar product can be used to find the volume of the parallelepiped formed by three non-coplanar vectors u, v, and w. The triple scalar product is defined as:

u · (v × w)

where × represents the cross product and · represents the dot product.

Given that u=i+j, v=j+k, and w=i+k, we can first find the cross product of v and w as:

v × w = (j+k) x (i+k)

= i x (j+k) + k x (j+k)

= i x j + i x k + k x j + k x k

= -k + i -j

Next, we can find the dot product of u with the cross product of v and w as:

u · (v × w) = (i+j) · (-k+i-j)

= i · (-k) + i · i + i · (-j) + j · (-k) + j · i + j · (-j)

= -ik + i^2 - ij - jk + ji - j^2

= i^2 - j^2 - k(i+j)

= 1 - 0 - (1+0)

= -1

The absolute value of this result gives the volume of the parallelepiped, so the volume is:

|u · (v × w)| = |-1| = 1

Therefore, the volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is 1.

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