What is an equation of the lines that passes through (-9, 12) and is perpendicular to the lines whose equation is y= 1/3x + 6

Answer:

C. 8x²+x+3.

Step-by-step explanation:

A and B are not polynomials as they contain a division (A) and a square root (B).

D is a monomial ( just one term).

oc.8x²+x+3

Step-by-step explanation:

Which of the following is a polynomial?

OA. 5+x2²/X

OB. √x+2x-1

OC. 8x²+x+3

OD. 7x

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

The value of the experimental probability of tossing heads is,

⇒ 1 / 3

We have to given that;

Coin Toss Results: T, H, T, H, T, H, T, T, T, T, H, T, H, T, T

Where, H stands for heads and T stands for Tails.

Hence, Total outcomes = 15

And, Head outcomes = 5

Thus, The value of the experimental probability of tossing heads is,

⇒ 5 / 15

⇒ 1 / 3

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This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by the distance;  0.000001 miles

Proportion word problems are simply ways of expressing proportion problems in words. For example we share oranges among three people each receiving 2, 3 and 4 respectively and as such the ratio of the proportion is 2:3:4.

Now, we are told that  after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This is comparable  to shooting an arrow at a target fifty feet away and missing the exact center.

Thus, if the comparable distance missed is x, then we can say that;

x/50 = 6/300000000

x = (6 * 50)/300000000

x = 3/3000000

x = 0.000001

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Answer:

$3,220

Step-by-step explanation:

Add

We can find the coordinates of the point that partitions a line segment into a ratio of 1 to 5 by using the formula:

(x, y) = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and r is the ratio of the distance from the starting point to the point of interest, to the total distance of the line segment. In this case, r = 1/(1 + 5) = 1/6.

We know the coordinates of the two endpoints of the line segment:

(x1, y1) = (-10, 9)

(x2, y2) = (-4, 3)

So, we can substitute these values into the formula and find the coordinates of the point that partitions the line segment into a ratio of 1 to 5:

(x, y) = (-10 + (1/6) * ((-4) - (-10)), 9 + (1/6) * (3 - 9))

= (-10 + (1/6) * (-6), 9 + (1/6) * (-6))

= (-10 -1/6, 9 -1)

= (-10/6 -1/6, 3/2 -1)

= (-16/6, 3/2 -1)

= (-8/3,-1/2)

So, the coordinates of the point on the directed line segment from (-10, 9) to (-4, 3) that partitions the segment into a ratio of 1 to 5 is (-8/3,-1/2)

It is important to notice that this point is a vector and not a point in the Cartesian plane

A statement which is true about the graph include the following: B: The equation y = 0.5x is correctly represented by the graph.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 0.5x) is characterized by a straight line as shown in the image attached below.

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Answer:

Square

9

9 in both boxes

2

\(\sqrt{11}\)

Step-by-step explanation:

Answer:

Here's how I'd do it.

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

(a). The smallest quantity at which marginal cost is equal to 15 dollars per item is 2.76. (b). The positive value of q at which average variable cost is equal to marginal cost is \(\frac{15}{2}\). (c). The longest interval on which marginal revenue exceeds marginal cost is (1.8377, 8.1622). (d). The profit is increasing at 8.1622 at p(q) is maximum. (e). The maximum value of profit is 78.2455 dollars.

The total revenue: TR(q) = 30q

The total cost: Tc(q) = \(q^3-15 q^2+75 q+10$\)

The change in cost is referred to as the change in the cost of production when there is a need for change in the volume of production.

(a).  Marginal cost MC\(=\frac{\partial}{\partial q}(T C)$\)

\($$=3q^2-30 q+75 \text {. }$$\)

According to question.

\($$\begin{aligned}& 3 q^2-30 q+75=15 \\& 3 q^2-30 q+60=0 \\& q^2-10 q+20=0 \\& q= \frac{10 \pm \sqrt{100-80}}{2} \\&= \frac{10 \pm 2 \sqrt{5}}{2}=5 \pm \sqrt{5}\end{aligned}\)

\($$$\therefore \quad q=5+\sqrt{5} \quad$ and $q=5-\sqrt{5}$\)

we have to find smallest quantity.

\($$\therefore \quad q=5-\sqrt{5}=2.76 \text {. }$$\)

b)

\($$\begin{aligned}& F C=T C(0)=10 \\& V C(q)=T C(q)-F C \\& =q^3-15 q^2+75 q . \\& \text { AVC(q) }=\frac{V C(q)}{q}=q^2-15 q+75 .\end{aligned}$$\)

When AVC(q)=MC(q)

\($$\begin{array}{ll}\Rightarrow & q^2-15 q+7 ;=3 q^2-30 q+75 \\\Rightarrow & 2 q^2-15 q=0 .\ \Rightarrow q(2 q-15)=0 . \\\Rightarrow & q=0, \frac{15}{2} \quad \Rightarrow \quad q=\frac{15}{2}\end{array}$$\)

Therefore, the positive value of q at which average variable cost is equal to marginal cost is \(\frac{15}{2}\).

(c).

\(& M R(q)=\frac{d}{d q}(T R)=30 . \\\)

\(& M C(q)=3 q^2-30 q+75 . \\\)

Let MR(a)>MC(q)

\(& \Rightarrow \quad 30 > 3 q^2-30 q+75 \text {. } \\\)

\(& \Rightarrow \quad 3 q^2-3 p q+45 < 0 \\\)

\(& \Rightarrow \quad q^2-10 q+15 < 0 \text {. } \\\)

\(& \because \quad q=\frac{10 \pm \sqrt{100-60}}{2} \Rightarrow q=\frac{10 \pm 2 \sqrt{10}}{2} \\\)

\(& q=(5 \pm \sqrt{10}) \\\)

\(& \Rightarrow \quad(q-5+\sqrt{10})(q-5-\sqrt{10}) < 0 . \\\)

\(& \Rightarrow \(q-5+\sqrt{10}) < 0 \quad \& \quad(q-5-\sqrt{10}) > 0 \text {. } \\\)

\(& \text { or } \quad(q-5+\sqrt{10}) > 0 \quad \& \quad(q-5-\sqrt{10}) < 0 \text {. } \\\)

\(& \therefore \quad \text { other } q < 5-\sqrt{10}=1.8377 ., q > 5+\sqrt{10}=8.1622 \text {. } \\\)

\(& \Rightarrow \quad q < 1.8377 \& q > 0.1622 \text {. } \\\)

\(& \text { or } q > 5-\sqrt{10} \quad \& \quad q < 5+\sqrt{10} \text {. } \\\)

\(& \Rightarrow q > 1.8377 \quad < q < 8.1622 \text {. } \\\)

The Interval is (1.8377, 8.1622).

(d).  P(q) =TR(q)-TC(q)

\(& =30 q-\left(q^3-15 q^2+75 q+10\right) \\& =-q^3+15 q^2-75 q-10+30 q \\& =-q^3+15 q^2-45 q-10 .\)

on (1.8377,8.1622). we have to find a point such that p"(q)=0 and p"(q)<0.

\(& p^{\prime}(q)=-3 q^2+30 q-45 \\\)

\(& \Rightarrow \quad-3\left(q^2-10 q+15\right)=0 \\\)

\(& \Rightarrow \quad q^2-10 q+15=0 . \\\)

\(& \quad q=1.8377 \text { and } \quad q=8.1622 . \\\)

\(& \Rightarrow \quad p^{\prime \prime}(q)=-6 q+30 . \\\)

\(& p^{\prime \prime}(1.8377)=-6(1.8377)+30 \\\)

\(&=18.9738 \\\)

\(& p^{\prime \prime}(8.1622)=-6(8.1622)+30 . &=-18.9732 < 0 .\)

at 8.1622, p(q) is maximum.

(e).

Max profit-P(8.1622)

=78.2455 dollars

Therefore, the maximum value of profit is 78.2455 dollars.

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The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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The number of people at the movie is 340

Let's represent the total number people at the movie as "x".

We know that the number of adults in the movie is 187 and the percentage of children is 45%

So we can write:

187 = (1 - 45%) * x

This gives

187 = 0.55x

To solve for x, we can divide both sides by 0.55:

x = 187/0,55

Evaluate

x = 340

Hence, the number of people is 340

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Answer:

15

Step-by-step explanation:

4 |7 − n| + 5

Substitute n = 12

4 |7 − 12| + 5

4 |-5| + 5

Take the absolute value of -5, which is 5

4 * 5 +5

Multiply

20 -5

15

Answer:

72 miles

Step-by-step explanation:

60% times 45 = 27

27 + 45 = 72

Answer is 72 miles

Answer:

Ema's Family would drive 72 miles

Step-by-step explanation:

Hope this helps :)

And I hope this is correct

Answer:

The answer is 3.19, someone irrationally deleted my answer previously.

Step-by-step explanation:

Simply substract 2.95 from 18.90 and you will get 15.95

Divide this by 5 to get the price of each and you will get $3.19 which is the correct answer.

It should be noted that r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

The radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given.

r = [(s - a)(s - b) (s - c)/s]1/2, where s = (a + b + c)/2.

a, b , c actual lengths of the sides,

s = average length of the sides

So that we can write

L = [(L - L)(L - L) (L - L)/L]^1/2

= [(L)(L) (L)/L]^1/2

= [L^2]^1/2

= L

Therefore r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

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Answer:

The median is 6.

Step-by-step explanation:

Following the Poisson distribution we get values, (i) Mean and standard deviation of monthly visits: mean = 1/3, standard deviation = sqrt(1/3). (ii) Probability of no visits: 0.7165 and (iii) Probability of at least one visit: 0.2835.

To answer the questions, we need to make some assumptions and calculations based on the given information. Let's proceed step by step:

(i) Mean and Standard Deviation:

Given that an average person makes four visits a year to doctors' offices and hospitals, we can calculate the average number of monthly visits by dividing the yearly visits by 12 months:

Average monthly visits = (4 visits/year) / 12 months = 1/3 visits/month

Since the average number of monthly visits is 1/3, the mean is also 1/3.

To calculate the standard deviation, we need to consider the variability in the number of visits. Since the number of visits is discrete and follows a Poisson distribution, the standard deviation is equal to the square root of the mean:

Standard deviation = sqrt(mean) = sqrt(1/3)

(ii) Probability of not making any monthly visits:

To calculate the probability that an average person does not make any monthly visits, we need to use the Poisson distribution formula. In this case, the average number of monthly visits (λ) is 1/3. The probability of not making any monthly visits (P(x = 0)) is given by:

P(x = 0) = (e(-λ) * λ⁰) / 0!

Substituting the value of λ = 1/3:

\(P(x = 0) = (e^(-1/3) * (1/3)^0) / 0!\\P(x = 0) = e^(-1/3) = 0.7165\)

Therefore, the probability that an average person does not make any monthly visits to doctors' offices and hospitals is approximately 0.7165.

(iii) Probability of making at least one monthly visit:

To calculate the probability that an average person makes at least one monthly visit, we can subtract the probability of not making any visits from 1:

P(x ≥ 1) = 1 - P(x = 0)

Substituting the previously calculated value of P(x = 0):

P(x ≥ 1) = 1 - 0.7165

P(x ≥ 1) ≈ 0.2835

Therefore, the probability that an average person makes at least one monthly visit to doctors' offices and hospitals is approximately 0.2835.

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Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Answer:

rectangles, square, and isosceles trapezoids

Step-by-step explanation:

It's asking which shapes always have the property that two pairs of two angles next to each other are congruent.

This would be true for rectangles, square, and isosceles trapezoids.

Answer:

y=29-5x

Step-by-step explanation:

SOLUTION

The slope of a line passing through two points P=(x1,y1) and Q=(x2,y2) is given by m=y2−y1x2−x1.

We have that x1=4, y1=9, x2=7, and y2=−6.

Plug the given values into the formula for a slope: m=−6−97−4=−5.

Now, the y-intercept is b=y1−mx1 (or b=y2−mx2, the result is the same).

b=9−(−5)⋅(4)=29

Finally, the equation of the line can be written in the form y=b+mx:

y=29−5x

A. The area of the triangle is 108 mm².

B. The area of parallelogram is 286√2 in²

A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)

We have:

b = 18 mm

h = 12 mm

Thus:

A = 1/2 * 18 * 12

A = 108 mm²

B. The area of parallelogram is given by:

A = b * h

where b is the base and h is the height

We have:

b = 26 in

Using trig.:

sin 45 = h/22

h = 22 * sin 45

h = 11√2 in

Thus,

A = 26 * 11√2

A = 286√2 in²

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The solution to the triangles whose parameters are given above are:


10. the sides of the triangle are a = 9, b = 7, and c ≈ 12.31, and the angles are A = 108°, B ≈ 46.44°, and C ≈ 25.56°.

11. the sides of the triangle are a = 14, b = 15, and c ≈ 19.23, and the angles are A = 117°, B ≈ 23.7°, and C ≈ 39.3°.

12. the sides of the triangle are a = 18, b = 12, and c ≈ 28.35, and the angles are A = 27°, B ≈ 132.5°, and C ≈ 20.5°.

13. the triangle are a = 35, b = 24, and c ≈ 152.96, and the angles are A = 92°, B ≈ 80.1°, and C ≈ 7.9°.

14. the sides of the triangle are a = 14, b = 6, and c ≈ 36.18, and the angles are A = 145°, B ≈ 24.4°, and C ≈ 10.6°.

15. the sides of the triangle are a = 19, b = 38, and c ≈ 32.76, and the angles are A = 30°, B ≈ 32.1°, and C ≈ 120°.

16. the sides of the triangle are a = 5, b = 6, and c ≈ 7.13, and the angles are A = 63°, B ≈ 62.9°, and C ≈ 54°.

17. the sides of the triangle are a = 10, b = 10√2, and c = 10, and the angles are A = 45°, B ≈ 45°, and C ≈ 90°.

The major rule for solving the above is called the Sine and Cosine rules.

The Sine Rule, also known as the Law of Sines, relates the sides and angles of a triangle. The Cosine Rule, also known as the Law of Cosines, relates the sides and angles of a triangle by using the cosine function.

Let us look an example for each.

10) where  a=9, b = 7, A = 108°
Using the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values:

9/sin(108°) = 7/sin(B)

Solving for sin(B):

sin(B) = 7*sin(108°)/9

Using the fact that the sum of the angles in a triangle is 180°, we have:

C = 180° - A - B

Substituting the given values and the value of sin(B) we just found:

C = 180° - 108° - sin⁻¹(7*sin(108°)/9)

Simplifying:

C ≈ 25.56°

Finally, using the Law of Sines again to find the length of side c:

c/sin(C) = a/sin(A)

Substituting the given values:

c/sin(25.56°) = 9/sin(108°)

Solving for c:

c ≈ 12.31

Therefore, the sides of the triangle are a = 9, b = 7, and c ≈ 12.31, and the angles are A = 108°, B ≈ 46.44°, and C ≈ 25.56°.


11) here we are given: a = 14, b = 15, A = 117°

Using the Law of Cosines:

c² = a² + b² - 2ab*cos(C)

Substituting the given values:

c² = 14² + 15² - 2(14)(15)*cos(C)

Simplifying:

c² = 601 - 420*cos(C)

Using the fact that the sum of the angles in a triangle is 180°, we have:

C = 180° - A - B

Substituting the given value of A and using the fact that a = 14 and b = 15:

cos(B) = (a² + c² - b²)/(2ac)

cos(B) = (14² + c² - 15²)/(214c)

cos(B) = (196 + c² - 225)/(28c)

cos(B) = (c² - 29)/28c

Substituting the value of cos(B) into the equation for C:

cos(C) = cos(180° - A - B)

cos(C) = -cos(A + B)

cos(C) = -cos(A)*cos(B) + sin(A)*sin(B)

Substituting the given values and the value of cos(B) we just found:

cos(C) = -cos(117°)*((c² - 29)/(28c)) + sin(117°)*√(1 - ((c² - 29)/(28c))²)

Simplifying:

cos(C) = -(cos(117°)/28) + (sin(117°)/28)*√(784c² - 4c⁴ - 784)/c

Solving for c using a numerical method, we find that:

c ≈ 19.23

Therefore, the sides of the triangle are a = 14, b = 15, and c ≈ 19.23, and the angles are A = 117°, B ≈ 23.7°, and C ≈ 39.3°.


17) here we are given: a = 10, b =√200, A = 45°
First, we can simplify √200 by factoring out the perfect square 100 from under the square root sign:

√200 = √(100*2) = √100 * √2 = 10√2

Using the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values:

10/sin(45°) = 10√2/sin(B)

Solving for sin(B):

sin(B) = sin(45°) / √2 = √2/2

Using the fact that the sum of the angles in a triangle is 180°, we have:

C = 180° - A - B

Substituting the given values and the value of sin(B) we just found:

C ≈ 90° - 45° = 45°

Finally, using the Law of Sines again to find the length of side c:

c/sin(C) = a/sin(A)

Substituting the given values:

c/sin(45°) = 10/sin(45°)

Solving for c:

c = 10

Therefore, the sides of the triangle are a = 10, b = 10√2, and c = 10, and the angles are A = 45°, B ≈ 45°, and C ≈ 90°.

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Answer:

-9/4, 2.1, -26/13, -13/8

Step-by-step explanation:

The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."

also "get it right please" ?! how rude

Answer:

3

Step-by-step explanation:

The solution has been explained below.

We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.

1. Calculate the pool's diameter and radius:

We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.

The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.

2. Calculate the amount of water in the pool:

Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.

The formula A = πr² can be used to calculate the area of the pool's base,

Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.

3. Determine the pool's total material cost:

There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.

As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.

If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.

4. Calculate the pool's total labour hours:

A pool's construction is estimated to take 2.5 hours for every foot of its radius.

So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.

5. Calculate the total cost of labour for the project:

If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.

6. Find the project's overall cost:

The project's overall cost is the product of its labour and material costs:

Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.

In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.

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Answer:

Use the following Financial Ratios to measure financial performance against standards. In addition, analysts compare these ratios to industry averages (benchmarking), industry standards or rules of thumbs and against internal trends (trends analysis). Furthermore the most useful comparison when performing financial ratio analysis is trend analysis They are derived from thethree following financial

statements:

⚫Balance Sheet

•Income Statement

⚫Statement of Cash Flows

.5 Categories

The five (5) major categori in the financial ratios list include the following:

•Liquidity Ratios

•Activity Ratios

•Debt Ratios

•Profitability Ratios

•Market Ratios

Step-by-step explanation:

Sana makatulong

Ratios dealing with short-term debts are Liquidity Ratios; those gauging efficiency in using assets for sales are Activity Ratios, and those scrutinizing long-term debt handling are Leverage Ratios. Along with the calculations, observations and identification of trends and their driving factors are also necessary.

In finance and business, ratio analysis is a tool used for conducting quantitative analysis on a company's financial statements. It involves the calculation and interpretation of various financial ratios. The following are the answers to the question's blanks:

However, only calculating ratios is not enough; you must also observe and identify trends suggested by the analysis, as well as identify the factors that drive these trends. These additional steps provide context and deeper insights into the company's financial performance.

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