marcus, a college senior, is considering repayment plans for his student loans. compared with income based repayment plans, the standard repayment plan will generally:

The functions g and h, have values for the inverse functions g⁻¹(9) = 1 and h⁻¹(-1) = -1. The composite function (h o h⁻¹)(-1) is equal to -1.

A function is said to have an inverse if it is both one-to-one and onto

for the function g using y = mx + c, when x = 1 and y = 9

m = 8/5 and c = 37/5

g(x) = (8/5)x + 37/5

g⁻¹(x) = (5x - 37)/8

g⁻¹(9) = [5(9) - 37]/8

g⁻¹(9) = (45 - 37)/8

g⁻¹(9) = 8/8

g⁻¹(9) = 1

for the function h(x) = -3x - 4, the inverse;

h⁻¹(x) = -(x + 4)/3

h⁻¹(-1) = -(-1 + 4)/3

h⁻¹(-1) = -3/3 = -1

(h o h⁻¹)(-1) = -[3(-1)] - 4

(h o h⁻¹)(-1) = -(-3) - 4

(h o h⁻¹)(-1) = 3 - 4

(h o h⁻¹)(-1) = -1.

Therefore, for the functions g and h, the values for the inverse functions g⁻¹(9) = 1 and h⁻¹(-1) = -1. The composite function (h o h⁻¹)(-1) is equal to -1.

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Answer:

The range is 25

Step-by-step explanation:

Answer:

25 is the range

Step-by-step explanation:

173-148 is 25

Answer:

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Step-by-step explanation:

The equation for the area of a triangle (\(A_{\bigtriangleup}\)) is:

\(A_{\bigtriangleup} = \frac{1}{2}\cdot b \cdot h\)

Where:

\(b\) - Base, dimensionless.

\(h\) - Height, dimensionless.

The expression for each triangle are described below:

First Triangle (\(b = 3\cdot x + 7\), \(h = 5\cdot x - 1\))

\(A_{\bigtriangleup,1} = \frac{1}{2}\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

Second Triangle (\(b = 3\cdot (3\cdot x+7)\), \(h = 2\cdot (5\cdot x -1)\))

\(A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is:

\(\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}\)

\(\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)\)

\(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\)

The difference between the area of the original triangle and the area of the new triangle is \(\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)\).

Answer: I think it's a relflection over x-axis followed by a rotation of 180 degrees which is b

Step-by-step explanation:

The transformations would generate the image of ΔABC with the coordinates A'(-2,-5), B'(-2,-2), C'(-6, -2) is a reflection over the x-axis followed by a rotation of 180° about the origin

There are three types of translations -

Given is to find the set of transformations would generate the image of ΔABC with the coordinates A'(-2,-5), B'(-2,-2), C'(-6, -2).

The transformations would generate the image of ΔABC with the coordinates A'(-2,-5), B'(-2,-2), C'(-6, -2) is a reflection over the x-axis followed by a rotation of 180° about the origin.

Therefore, the transformations would generate the image of ΔABC with the coordinates A'(-2,-5), B'(-2,-2), C'(-6, -2) is a reflection over the x-axis followed by a rotation of 180° about the origin.

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Only statement (i) must be true in this case.

Given that an ≤ bn ≤ cn for all positive integers n, and the series ∑[infinity]n=1bn converges, we can determine the following:

(i) ∑[infinity]n=1an converges: This statement must be true. Since an ≤ bn for all n, and the series for bn converges, the series for an must also converge. This is because if the sum of the larger terms (bn) converges, then the sum of the smaller terms (an) should also converge. This is a consequence of the Comparison Test for convergence of series.

(ii) ∑[infinity]n=1cn converges: This statement is not necessarily true. Just because the series for bn converges, it doesn't guarantee that the series for cn will also converge. The cn terms could still be large enough such that their sum diverges.

(iii) ∑[infinity]n=1(an+bn) converges: This statement is not necessarily true. The convergence of the bn series does not guarantee the convergence of the (an+bn) series. The terms an, although smaller than bn, could still be large enough such that the sum of (an+bn) diverges.

So, only statement (i) must be true in this case.

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The given expression is

First, we solve the subtraction

Now we subtract 2 on each side to get x-2

Let's solve the difference

Answer:

X - 84.2

Step-by-step explanation:

Given that:

Amount spent per ticket = $21.05

Number of tickets = 4

The effect of the spending on the tourist bank account :

Let initial amount in his account = x

Change or effect on bank account after spending on 4 tickets :

X - (cost per ticket * number of tickets)

X - (21.05 * 4)

X - 84.2

Answer:

1212

Step-by-step explanation:

9790

The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

9(2x + 1) < 9x - 18

18x + 9 < 9x - 18

18x - 9x < -18 - 9

9x < -27

x < -3

x = (-∞, -3)

Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.

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Answer: -4

Step-by-step explanation: edge2020

The gift wrap needed by Damarcus = total surface area of a rectangular box = 1,048 in.².

Total surface area (TSA) = 2(wl+hl+hw), where:

The amount of gift wrap needed to cover the whole box = total surface area of the rectangular box

l = 20 in.

w = 8 in.

h = 13 in.

Plug in the values into the formula for total surface area of a rectangular box:

TSA = 2(8×20 + 13×20 + 13×8)

TSA = 1,048 in.²

Therefore, the gift wrap needed by Damarcus = total surface area of a rectangular box = 1,048 in.².

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Answer: D

Step-by-step explanation: to know symmetry you must draw line from vertices of the figure ad the triangle has 3 vertices so you will draw 3 lines

Answer:

circumference

Step-by-step explanation:

circumference shows us how sowmthing goes around. like have you ever been to the doctor and they said theyre checking a babys head circumference? theyre checking it all over.

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer:

The answer is B. 600

Step-by-step explanation:

Hope that helps!

Answer:

B. $600.00

Step-by-step explanation:

every 10hrs worked you are getting $120.00 so just add $120.00 every 10 hrs

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission is:P(X ≥ 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003≈ 0.323 or about 32.3%

To find the probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission, we need to use the binomial probability formula which is given by: P(X = x) = nCx * p^x * q^(n-x)where, n is the total number of trials x is the number of successful trials p is the probability of success

q = 1 - p is the probability of failure n Cx = n! / x!(n-x)! is the binomial coefficient In this case, since we want to know the probability of at least 11 boats operating for the mission, we can find the probability of 11 boats, 12 boats, 13 boats, 14 boats, 15 boats and 16 boats operating, and then add them up.

So, we have: P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)where, n = 16 (since there are 16 patrol boats)p = 0.9 (since the probability of a patrol boat operating is 0.9)q = 0.1 (since the probability of a patrol boat not operating is 0.1)

Using the formula above, we get:P(X = 11) = 4368 * 0.9^11 * 0.1^5 = 0.174P(X = 12) = 1365 * 0.9^12 * 0.1^4 = 0.097P(X = 13) = 455 * 0.9^13 * 0.1^3 = 0.039P(X = 14) = 136 * 0.9^14 * 0.1^2 = 0.011P(X = 15) = 35 * 0.9^15 * 0.1^1 = 0.002P(X = 16) = 1 * 0.9^16 * 0.1^0 = 0.00003

Thus, if at least 11 of the 16 patrol boats are required to operate throughout the mission, the chance of mission success is P(X 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003 0.323 or roughly 32.3%.

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a) The ratio of the distance Colton has traveled to the amount of time he has been traveling is; 14 mph which represents the average velocity

b) The value of d when travelling for 6 hours at the same velocity is; 84 miles

c) The value of h when he bikes 200 miles is; 14.3 hours

a) We are given;

Distance traveled = 49 miles

Time taken = 3.5 hours

Ratio of distance to time = 49/3.5 = 14 mph

This represents the average velocity

b) We are told that he traveled the same rate for 6 hours. Thus;

Distance is gotten from the formula;

d = velocity * time

d = 14 * 6

d = 84 miles

c) He wants to bike 200 miles. When h is the number of hours taken, then; h = d/v

h = 200/14

h = 14.3 hours

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We can write a proportion to solve

82 guests 91 guests

------------------- = -------------

656 dollars x dollars

Using cross products

82x = 91 * 656

82x =59696

Divide each side by 82

82x/82 = 59696/82

x =728

The party with 91 guests will cost 728 dollars

Answer:

midpoint = (3,3.5)

distance = 5

Step-by-step explanation:

midpoint = (x1+X2/2, y2+y2/2)

=(5+1/2, 5+2/2)

=(6/2, 7/2)

=(3, 3.5)

distance= √(x2-x1)^2 -(y2-y1)^2

=√(1-5)^2 -(2-5)^2

= √ 16+9 =√25 =5

Answer:

Angle BFC.

Step-by-step explanation:

Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles

Answer:

what is the variable

Step-by-step explanation:

Area of surface that is obtained by rotating the curve Y = 0.25X²-0.5 Log_e X, 1≤X ≤2 , area is A = 2π ∫[1,2] (0.25x² - 0.5ln(x)) √(1 + [(4\(e^{(4y)}\) * x²) / (2x\(e^{(x^{2})}\) - 2\(e^{(4y)}\) * x)]²) dy

To find the area of the surface obtained by rotating the curve y = 0.25x² - 0.5ln(x), 1 ≤ x ≤ 2, about the y-axis, we can use the formula for the surface area of revolution:

A = 2π ∫[a,b] y √(1 + (dx/dy)²) dy

First, let's find the derivative of x with respect to y by solving for x in terms of y:

y = 0.25x² - 0.5ln(x)

Rearranging the equation, we have:

0.25x² = y + 0.5ln(x)

x² = 4y + 2ln(x)

Taking the exponential of both sides:

e^(x²) = e^(4y + 2ln(x))

e^(x²) = e^(4y) * e^(2ln(x))

e^(x²) = e^(4y) * (e^ln(x))²

e^(x²) = e^(4y) * x²

Now, let's differentiate both sides with respect to y:

d/dy (e^(x²)) = d/dy (e^(4y) * x²)

2xe^(x²) dx/dy = 4e^(4y) * x² + e^(4y) * 2x * dx/dy

Simplifying, we get:

2xe^(x²) dx/dy = 4e^(4y) * x² + 2e^(4y) * x * dx/dy

2xe^(x²) dx/dy - 2e^(4y) * x * dx/dy = 4e^(4y) * x²

Factor out dx/dy:

(2x\(e^{(x²)}\) - 2e^(4y) * x) dx/dy = 4\(e^{(4y}\) * x²

Divide both sides by (2x\(e^{(x^{2})}\) - 2\(e^{(4y)}\) * x):

dx/dy = (4\(e^{(4y)}\) * x²) / (2x\(e^(x^{2})\) - 2\(e^{(4y) }\)* x)

Now, we can substitute the expression for dx/dy into the surface area formula:

A = 2π ∫[a,b] y √(1 + (dx/dy)²) dy

A = 2π ∫[1,2] (0.25x² - 0.5ln(x)) √(1 + [(4e^(4y) * x²) / (2x\(e^{(x^{2})\) - 2e^(4y) * x)]²) dy

Unfortunately, this integral does not have a closed-form solution and needs to be evaluated numerically. Using numerical methods or a computer program, we can approximate the value of the integral to find the area of the surface.

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The length x of a diagonal support, to the nearest tenth of a foot is; 11 ft

Let us say the side opposite to the 25° angle is a, in both triangles. The side opposite to the 65° angle is b, but we already know the length of b as it is 20/ 2 = 10 ft.

We should find the length of a using trigonometric ratios, and by Pythagorean Theorem, determine the length of x.

Thus;

a = tan 25 * ( 10 )

a ≈ 4.663 ft

b = 10 ft

By Pythagorean Theorem,

a² + b² = x²

4.663² + 10² = x²

21.74 + 100 = x²

x² = 121.74

x  ≈ 11 ft ( to the nearest foot )

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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False. The total shrink for a three- and four-bend saddle is equal to that of an offset.

The statement "total shrink for a three- and four-bend saddle is twice that of an offset" is true.

1. Shrink: Shrink refers to the amount of extra conduit length needed to account for bends in the conduit, so it maintains the required distance between two points after bending.

2. Offset: An offset is a two-bend conduit configuration used to navigate around obstacles while maintaining a straight path. The total shrink for an offset can be calculated using the formula: Shrink = offset height x (multiplier for the specific angle).

3. Saddle: A saddle is a conduit configuration with either three or four bends. It is used to navigate over or under obstructions while maintaining a straight path.

4. Comparison: For both three- and four-bend saddles, the total shrink is twice that of an offset. This is because a saddle consists of two sets of bends (either two offsets or an offset and a U-bend) and requires additional conduit length to accommodate these extra bends.

In conclusion, the statement is true, as the total shrink for a three- and four-bend saddle is indeed twice that of an offset.

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E = cos(kz - ωt) is a solution to the wave equation.   Bmag = 1000i / 3 x 10⁸ = 3.33 x 10⁻⁶i T/m.

By explicit substitution, we need to verify that E = cos (kz - ωt) is a solution to the wave equation:∂²E/∂t² - c² ∂²E/∂z² = 0Given k²ω² = c², we have the following relationships: k = ± ω/c and ω = kc.

Substituting E = cos(kz - ωt) into the wave equation, we have the following:∂²E/∂t² = - ω² cos(kz - ωt)∂²E/∂z² = - k² cos(kz - ωt)Thus, the wave equation becomes: - ω² cos(kz - ωt) - c² (- k² cos(kz - ωt)) = 0.

This can be simplified as follows: ω² cos(kz - ωt) + c²k² cos(kz - ωt) = 0Multiplying both sides by cos(kz - ωt), we get: (ω² + c²k²) cos(kz - ωt) = 0.

Since cos(kz - ωt) ≠ 0, we must have:ω² + c²k² = 0 ⇒ ω² = - c²k²Therefore, E = cos(kz - ωt) is a solution to the wave equation.  

Given Emag = 1000i V/m, ω = 10¹⁵ rad/s. We need to find Bmag and Savg.Using the relationship: c = fλ, we have:ω = 2πf, so f = ω/2πTherefore, c = ωλ/2π, so λ = 2πc/ωSince v = fλ, we have v = c

Hence, Emag/Bmag = c ⇒ Bmag = Emag/c= 1000i / 3 x 10⁸ = 3.33 x 10⁻⁶i T/mSavg = ½ ε₀ c Emag²where ε₀ is the permittivity of free space.

Thus, we have: Savg = ½ (8.85 x 10⁻¹²) (3 x 10⁸) (1000)²= 1.32 x 10⁻³ W/m²If the frequency is doubled, ω → 2ω, so λ → λ/2 and Emag → 2Emag. Hence, Bmag → 2Bmag, andSavg → 4Savg.

Thus, either Bmag or Savg increases by a factor of 2

The given wave equation is ∂²E/∂t² - c² ∂²E/∂z² = 0. We need to show that E = cos(kz - ωt) is a solution to this wave equation.

Using the relationships k²ω² = c² and ω = kc, we obtain k = ± ω/c.

Substituting E = cos(kz - ωt) into the wave equation, we get ∂²E/∂t² = - ω² cos(kz - ωt) and ∂²E/∂z² = - k² cos(kz - ωt).

Thus, the wave equation becomes - ω² cos(kz - ωt) - c² (- k² cos(kz - ωt)) = 0, which simplifies to ω² cos(kz - ωt) + c²k² cos(kz - ωt) = 0.

Multiplying both sides by cos(kz - ωt), we get (ω² + c²k²) cos(kz - ωt) = 0. Since cos(kz - ωt) ≠ 0, we must have ω² + c²k² = 0 ⇒ ω² = - c²k².

Therefore, E = cos(kz - ωt) is a solution to the wave equation. In problem 2, we are given Emag = 1000i V/m, ω = 10¹⁵ rad/s.

To find Bmag, we use the relationship Bmag = Emag/c. Since c = 3 x 10⁸ m/s, we obtain Bmag = 1000i / 3 x 10⁸ = 3.33 x 10⁻⁶i T/m.

To find Savg, we use the relationship Savg = ½ ε₀ c Emag², where ε₀ is the permittivity of free space.

Substituting the given values, we get Savg = ½ (8.85 x 10⁻¹²) (3 x 10⁸) (1000)² = 1.32 x 10⁻³ W/m².

If the frequency of the wave were doubled, ω → 2ω, so λ → λ/2 and Emag → 2Emag. Hence, Bmag → 2Bmag, and Savg → 4Savg.

Thus, either Bmag or Savg increases by a factor of 2.

In conclusion, E = cos(kz - ωt) is a solution to the wave equation ∂²E/∂t² - c² ∂²E/∂z² = 0, where k²ω² = c². For a plane light wave with Emag = 1000i V/m and ω = 10¹⁵ rad/s, we found that Bmag = 3.33 x 10⁻⁶i T/m and Savg = 1.32 x 10⁻³ W/m². If the frequency of the wave were doubled, either Bmag or Savg would increase by a factor of 2.

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To find the prior probabilities of winning for these four teams, we can use the formula:

Prior probability = 1 / (odds against + 1)

For Spain: Prior probability = 1 / (9/2 + 1) = 2/11 or approximately 0.18

For Brazil: Prior probability = 1 / (11/2 + 1) = 2/13 or approximately 0.15

For England: Prior probability = 1 / (6/1 + 1) = 1/7 or approximately 0.14

For the United States: Prior probability = 1 / (90/1 + 1) = 1/91 or approximately 0.01

Therefore, the corresponding prior probabilities of winning for Spain, Brazil, England, and the United States are approximately 0.18, 0.15, 0.14, and 0.01, respectively.

To find the corresponding prior probabilities of winning for the four teams, you'll need to convert the given odds into probabilities. Here's the calculation for each team:

1. Spain (9/2 odds)
Probability = 1 / (9/2 + 1) = 1 / (11/2) = 2/11 ≈ 0.1818 or 18.18%

2. Brazil (11/2 odds)
Probability = 1 / (11/2 + 1) = 1 / (13/2) = 2/13 ≈ 0.1538 or 15.38%

3. England (6/1 odds)
Probability = 1 / (6/1 + 1) = 1 / 7 ≈ 0.1429 or 14.29%

4. United States (90/1 odds)
Probability = 1 / (90/1 + 1) = 1 / 91 ≈ 0.0110 or 1.10%

So, the prior probabilities of winning for the four teams are approximately 18.18% for Spain, 15.38% for Brazil, 14.29% for England, and 1.10% for the United States.

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The research team, after formulating the hypothesis that exercise increases happiness, needs to design and conduct an experiment to test this hypothesis.

The next step would be to plan and implement a study that allows them to collect data and analyze whether exercise has a positive impact on happiness.

Define the variables: Clearly define the variables involved, such as the independent variable (exercise) and the dependent variable (happiness).

Design the study: Determine the study design that will best test the hypothesis. This could involve selecting the sample population, deciding on the duration and intensity of exercise, and considering control groups or randomization techniques.

Collect data: Implement the study by gathering data on exercise habits and measuring happiness levels. This may involve surveys, questionnaires, or other measurement techniques.

Analyze the data: Use statistical analysis methods to examine the collected data and determine if there is a significant relationship between exercise and happiness. This could involve comparing means, conducting correlation analyses, or employing other appropriate statistical tests.

Draw conclusions: Based on the analysis, interpret the findings and draw conclusions regarding the hypothesis. Determine whether the data supports or refutes the hypothesis that exercise increases happiness.

Communicate the results: Share the findings with the scientific community through research papers, presentations, or other appropriate channels. This step allows other researchers to review and replicate the study.

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It is obtained that the equivalent fraction with the largest numerator is \(\frac{15}{12},\) therefore the largest fraction is \(\frac{5}{4}.\)

To compare fractions, we must work with their equivalent expressions, which lead to expressing them through a single denominator.

That equivalent fraction that has the smallest denominator is the smaller of the two fractions studied.

To determine which is the largest of 4 fractions we must first find the least common multiple of the denominators and then calculate the equivalent fractions by applying the least common multiple.

To equivalent fraction that has the largest numerator is the largest.

Let's see what we have outlined above with an example

If we have the following fractions

\(\frac{1}{2},\frac{2}{3},\frac{5}{4} and \frac{7}{6}\)

Now let's calculate which of the 4 given fractions is the largest one.

So, we have:

The L.C.M of 2, 3, 4 and 6 is \(2^2.3=12\)

Then, L.C.M (2, 3, 4, 6) = 12.

Now, we apply the L.C.M to each of the fraction to obtain the equivalent ones.

Thus, we have:

For \(\frac{1}{2}\) the equivalent fraction is \(\frac{6}{12}.\)

For \(\frac{2}{3}\), the equivalent fraction is \(\frac{8}{12}.\)

For \(\frac{5}{4}\), the equivalent fraction is \(\frac{15}{12}\)

For \(\frac{7}{6},\) the equivalent fraction is \(\frac{14}{12}.\)

It is obtained that the equivalent fraction with the largest numerator is \(\frac{15}{12},\) therefore the largest fraction is \(\frac{5}{4}.\)

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The given question is incomplete, So we take the similar question :

If you have 4 fractions with different denominators, and you have to determine which is greater. What should you do to figure that out?