Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.

Answer:

  b, c

Step-by-step explanation:

A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.

__

A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.

The value of f(0) is 2, so the y-intercept is 2.

The given function is defined for all values of x, so its domain is all real numbers.

The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.

The function has a stationary point at x=0, so is not decreasing over its entire domain.

_____

Additional comment

The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.

No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.

No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.

If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.

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Answer:

(-5,-7)

Step-by-step explanation:

See image for explanation

Answer:

y=5

Step-by-step explanation:

y+6=-35+26 (+ 3y)

4y+6=26 (-6)

4y=20 (/4)

y=5

The number of intersections of the graphs of the given equations is 0.

To determine the number of intersections of the graphs of the equations:

1. One-halfx + 5y = 6

2. 3x - 30y = 36

We can convert the equations to slope-intercept form (y = mx + b) by isolating y:

1. \(\frac12\\\)x + 5y = 6

  5y = -\(\frac12\\\)x + 6

  y = (-1/10)x + 6/5

2. 3x - 30y = 36

  -30y = -3x + 36

  y = (1/10)x - 36/30

  y = (1/10)x - 6/5

Now, we can observe that both equations have the same slope, which is 1/10, but they have different y-intercepts (6/5 and -6/5).

Since the slopes are the same but the y-intercepts are different, the two lines are parallel.

Parallel lines do not intersect,

so the graphs of these equations have no intersection points.

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Answer:

A or none

Step-by-step explanation:

edge

Answer:

- 4 < x ( or ) x > - 4

Step-by-step explanation:

- 10 < - 6 + x

Add 6 on both the sides,

- 10 + 6 < x

- 4 < x

Answer:

25

Step-by-step explanation:

\(0<5x-35<90 \\ \\ 0<x-7<18 \\ \\ 7<x<25\)

Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.

To quantify the probability of each event, we can define the following events:

Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.

Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:

To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.

Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:

Therefore, the probability of event C can be calculated as follows:

P(C) = P(A) * P(A in order) + P(B) * P(B in order)

= (1/5 * 3/5) + (1/10 * 2/5)

= 3/25

So the probability of selecting a defective unit from the order is 3/25.

To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:

P(D) = 1 - P(C)

= 1 - 3/25

= 22/25

So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.

In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.

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The weight of an adult male blue whale is 22.1 times greater than the weight of an adult male African elephant.

In accordance with the context of this question, the weight is the quantity of mass associated to an object or animal under the influence of gravity, which means that weight is a measure of how "heavy" an animal or an object is. According to databases, the weight of an adult blue whale is approximately 200 tonnes, that is, 2 × 10⁵ kilograms.

Now we find the ratio of the weight of an adult blue whale to the weight of an adult African elephant is defined by the following division:

r = (2 × 10⁵ kilograms) / (9.07 × 10³ kilograms)

r = (2 / 9.07) × (10⁵ ⁻ ³) kilograms

r = 221 × 10⁻³ × 10²

r = 221 × 10⁻¹

r = 22.1

The weight of an adult male blue whale is 22.1 times greater than the weight of an adult male African elephant.

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Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

Given:

• The Financial Goal, A= $35,000

• Rate = 7.5% = 0.075

• Number of compounding period = 12 (Monthly)

• Time, t = 3 years

Substitute into the given formula:

The monthly payment is $870.

Option D is correct.

Answer:

1

Step-by-step explanation:

from the rule of exponents

• \(a^{0}\) = 1 , then

\((5x)^{0}\) = 1

Answer:

$22.50

Step-by-step explanation:

50/100 = x/45

cross multiply

50 × 45 = 100 × x

2250 = 100x

divide both sides by 100

22.5 = x

*note: marksup the price means that $45 should be more than what the value of x is. $45 is more than $22.50. you can also check your work by looking at the fact $22.50 is exactly half (50%) the amount of $45*

The maximum value of the function f(x, y) = 4x + 3y subject to the constraint x² + y² = 1 is 5. Therefore, third option is the correct answer.

To find the maximum value of the function f(x, y) = 4x + 3y subject to the constraint x² + y² = 1, we can use the method of Lagrange multipliers.

Let's define the Lagrangian function L(x, y, λ) as:

L(x, y, λ) = 4x + 3y - λ(x² + y² - 1).

To find the maximum value, we need to find the critical points of L(x, y, λ). We can do this by taking the partial derivatives of L with respect to x, y, and λ and setting them equal to zero:

∂L/∂x = 4 - 2λx = 0, .........(1)

∂L/∂y = 3 - 2λy = 0, ..........(2)

∂L/∂λ = -(x² + y² - 1) = 0. .........(3)

From equation (1), we have 4 - 2λx = 0, which gives λx = 2. ..........(4)

From equation (2), we have 3 - 2λy = 0, which gives λy = 3/2. ............(5)

Now, let's solve equations (4) and (5) simultaneously:

λx = 2 (from equation 4)

λy = 3/2 (from equation 5)

Dividing equation (4) by equation (5), we have:

(λx) / (λy) = 2 / (3/2)

x / y = 4/3.

Substituting this into the constraint equation x² + y² = 1:

(4/3)² y² + y² = 1

(16/9 + 1)y² = 1

(25/9)y² = 1

y² = 9/25

y = ±3/5.

For y = 3/5, using equation (5), we have:

λ = (λy) / y = (3/2) / (3/5) = 5/2.

Substituting y = 3/5 and λ = 5/2 into equation (4), we can solve for x:

(5/2)x = 2

x = 4/5.

Therefore, one critical point is (x, y) = (4/5, 3/5) with λ = 5/2.

Similarly, for y = -3/5, using equation (5), we have:

λ = (λy) / y = (3/2) / (-3/5) = -5/2.

Substituting y = -3/5 and λ = -5/2 into equation (4), we can solve for x:

(-5/2)x = 2

x = -4/5.

Therefore, the other critical point is (x, y) = (-4/5, -3/5) with λ = -5/2.

Now, let's evaluate the function f(x, y) = 4x + 3y at the critical points:

f(4/5, 3/5) = 4(4/5) + 3(3/5) = 16/5 + 9/5 = 25/5 = 5,

f(-4/5, -3/5) = 4(-4/5) + 3(-3/5) = -16/5 - 9/5 = -25/5 = -5.

Therefore, the maximum value of the function f(x, y) = 4x + 3y subject to the constraint x² + y² = 1 is 5.

Hence, the correct option is third one.

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Two times the quantity of the difference m and n is equation to x more than 7

This limit is less than 1 if and only if |x-1| < 1/6, so the interval of convergence is: (1-1/6, 1+1/6) = (5/6, 7/6)

The Taylor series for f(x) = -14/x centered at x=1 is:

\(f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...\)

Taking the derivatives of f(x), we have:

f(x) = -14/x

\(f'(x) = 14/x^2\)

\(f''(x) = -28/x^3\)

\(f'''(x) = 84/x^4\)

Evaluating these at x=1, we get:

f(1) = -14

f'(1) = 14

f''(1) = -28

f'''(1) = 84

Substituting these values into the Taylor series, we get:

\(f(x) = -14 + 14(x-1) - 28(x-1)^2/2! + 84(x-1)^3/3! - ...\)

To determine the interval of convergence, we can use the ratio test:

\(lim_{n- > inf} |a_{n+1}(x-1)/(a_n(x-1))| = lim_{n- > inf} |(84/(n+1))/(14/n)| |x-1| = |6(x-1)|.\)

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The interval of convergence for the Taylor series of f(x) = -14/x at x = 1 is (0, 2) in interval notation.

To determine the interval of convergence for the Taylor series of f(x) = -14/x at x = 1, we first find the Taylor series representation. Since f(x) is a rational function, we can rewrite it as f(x) = -14(1/x) and then use the geometric series formula:

f(x) = -14Σ((-1)^n * (x - 1)^n), where Σ is the summation symbol and n runs from 0 to infinity.

To find the interval of convergence, we use the ratio test. The ratio test involves taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms:

lim (n→∞) |((-1)^(n+1)(x - 1)^(n+1))/((-1)^n(x - 1)^n)|

Simplify the expression:

lim (n→∞) |(x - 1)|

For convergence, this limit must be less than 1:

|(x - 1)| < 1

This inequality gives us the interval of convergence:

-1 < (x - 1) < 1

Add 1 to each part:

0 < x < 2

So, the interval of convergence for the Taylor series of f(x) = -14/x at x = 1 is (0, 2) in interval notation.

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the volume of the pyramid is approximately 593,866.67 cubic meters.

To find the volume of the pyramid, we first need to use the formula for the volume of a pyramid, which is:

\(V = \frac{1}{3} * base area * height\)

Since the pyramid has a square base, the base area can be found by multiplying the length of one side by itself:

base area = 140 m * 140 m = 19,600 m²

Now we can plug in the values for the base area and height into the formula:

V = (1/3) * 19,600 m^2 * 91 m

V = 1/3 * 1,781,600 m³

V = 593,866.67 m³

Therefore, the volume of the pyramid is approximately 593,866.67 cubic meters

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The volume of the pyramid is approximately 594,533.33 cubic meters.

To find the volume of a stone pyramid in Egypt with a square base that measures 140 meters on each side and a height

of 91 meters, you'll need to use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

Calculate the base area by squaring the side length:

Base Area = Side × Side = 140 m × 140 m = 19,600 m²

Multiply the base area by the height:

Base Area × Height = 19,600 m² × 91 m = 1,783,600 m³

Multiply the result by (1/3) to get the volume:

Volume = (1/3) × 1,783,600 m³ = 594,533.33 m³ (rounded to two decimal places)

So, the volume of the pyramid is approximately 594,533.33 cubic meters.

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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z = 0.00, 1.05, 5.24, 6.28

To solve the equation sin(x) - sin(2x) = 0 on the interval [0, 2π), we can use the trigonometric identity:

sin(2x) = 2sin(x)cos(x)

Substituting this into the original equation, we get:

sin(x) - 2sin(x)cos(x) = 0

Factoring out sin(x), we get:

sin(x)(1 - 2cos(x)) = 0

Therefore, either sin(x) = 0 or cos(x) = 1/2.

If sin(x) = 0, then x can take on the values 0, π, and 2π.

If cos(x) = 1/2, then x can take on the values π/3 and 5π/3.

Therefore, the solutions of the equation on the interval [0, 2π) are:

x = 0, π/3, π, 5π/3, 2π

Of these solutions, only x = π is not in the interval [0, 2π).

Therefore, the solutions of the equation on the interval [0, 2π) are:

x = 0, π/3, 5π/3, 2π

Expressed in terms of z and rounded to two decimal places (since it was not specified in the problem statement), these solutions are:

z = 0.00, 1.05, 5.24, 6.28

Answer: z = 0.00, 1.05, 5.24, 6.28

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Answer:

\(22.2 \;meters\)

Step-by-step explanation:

The volume of the hemisphere = 22,778 m³

The volume of a sphere of the same radius
= twice the volume of the hemisphere
= 2 x 22,778 m³
= 45576 m³

The volume of a sphere of radius r is given by the formula:
\(V = \dfrac{4}{3}\pi r^3\)

Plugging in knowns:
\(45576 =\dfrac{4}{3}\pi r^3\)

Switching sides:
\(\dfrac{4}{3}\pi r^3 =45576\)

Multiply both sides by \(\dfrac{3}{4}\)

\(\dfrac{3}{4} \times \dfrac{4}{3}\pi r^3 =\dfrac{3}{4} \times 45576\\\\\pi r^3 = 34,182\)

Divide by π both sides to get
\(r^3 = \dfrac{34,182}{\pi} = 10,880.4685\\\\r= \sqrt[3]{10,880.4685} \\\\= 22.15895\\\\= 22. 2 \text{ meters (to the nearest tenth)}\)

Answer:

The slope is 1/2  :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(10 - 4)/(13 - 1) = 6/12 = 1/2 is the slope of the line

The tοtal cοst fοr the grοup οf 7 friends tο gο tο the mοvie and buy snacks is $81.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο find the tοtal cοst, we need tο multiply the cοst οf οne ticket by the number οf tickets and add the cοst οf snacks:

Tοtal cοst = (Cοst per ticket) x (Number οf tickets) + (Cοst οf snacks)

We knοw that each ticket cοsts $9, and there are 7 friends gοing tο the mοvie.

Therefοre, the number οf tickets is 7.

Tοtal cοst = (9) x (7) + (18)

Tοtal cοst = 63 + 18

Tοtal cοst = 81

Hence, the tοtal cοst fοr the grοup οf 7 friends tο gο tο the mοvie and buy snacks is $81.

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Complete Question:

A group of 7 friends are going to a movie. Each ticket costs $9. They also spend $18 on snacks.

Estimate the total amount of money the group spent.

Choose 1 answer:

А

$37

$50

$90

$150

9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

3:25 pm

Step-by-step explanation:

The distance between New Orleans and Houston is : 353 miles

Departure time of the bus : 12:20 pm

Speed of the bus: 60 mph

After 45 minutes, the bus will be at a distance of : 45/60 * 60 = 45 miles

Distance remaining to cover = 353-45 = 308 miles

Speed of the motorcycle = 72 mph

Relative speed = 60 + 72 = 132 mph

Time the two will meet = 308 / 132 =  7/3 hrs

7/3 hrs = 2 hrs  20 minutes

Time the two will meet is ;

12:20 pm + 45 minutes + 2 hrs 20 minutes

= 3:25 pm

Both the bus and the motorcycle are driving opposite to each other.

From the given data, the time at which both the bus and the motorcycle will pass each other is 3:25 PM

The time at which both the motorcycle and the  bus will pass each other.

Let after t hour from the time when motorcycle starts, they both meet.

Then we have:

353 miles = 45 minute traveled by bus + distance traveled by bus in t hour + distance traveled by motorcycle in t time.

Since 45 minutes is three fourth of an hour, thus:

Distance traveled by bus in 45 minutes is calculated as:

\(D_{Bus}(45 \:\rm min) = 60 \times \dfrac{3}{4} \: \rm miles = 45 \: \rm miles\)

Distance traveled by bus in t hours is:

\(D_{Bus}(t \: \rm hours) = 60 \times t \: \rm miles = 60t \: \rm miles\)

Distance traveled by motorcycle in t hour is:

\(D_{motorcycle}(t \: \rm hours) = 72 \times t \: \rm miles = 72t \: \rm miles.\)

Thus, we have:

\(353 = 60t + 72t + 45\\\\308= 132t\\\\t = \dfrac{308}{132}\\\\t= \dfrac{7}{3}\: \rm hours\\\\t=2 \: \rm hours + 20 \: \rm minutes\)

Thus, time at which they meet was 12:20 PM + 45 minutes + 2 hours + 20 minutes = 3:25 PM

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Answer:

30

Step-by-step explanation:

You can do 36*100=3600 and do 3600/120. This is a very simple way to get 30 out of 100

Answer: $30

Step-by-step explanation: If she saves $36 when she earns $120, then she saves *amount =36/120 ×100

Amount saved with $100 earning is $30

Answer:

14 is the simplified answer, but the whole answer is 17 + -18/6

Step-by-step explanation:

Divide

−

18 by 6. h (−18) = 17 − 3 Subtract  3 from 17. h (−18)= 14

The final answer is 14.

If the racecar travels 8.7 feet in the clockwise direction along the track, the angle's measure in radians is approximately 0.0087 radians.

To determine the angle's measure in radians, we need to use the formula: θ = s / r
where θ is the angle in radians, s is the distance traveled along the arc, and r is the radius of the circle.
In this case, we know that the racecar travels 8.7 feet along the track, but we don't know the radius of the circle. However, we can make an assumption that the track is circular and that the racecar traveled along an arc of the circle.
Let's say that the radius of the circle is r feet. Then, we can use the formula for arc length: s = rθ
where s is the distance traveled along the arc, θ is the angle in radians, and r is the radius of the circle.
We know that the distance traveled along the arc is 8.7 feet. So, we can set up an equation:
8.7 = rθ
To solve for θ, we need to know the value of r. Unfortunately, we don't have that information. So, we can make another assumption that the track is a standard oval shape with a radius of 1,000 feet.
Using this assumption, we can calculate the angle in radians:
θ = s / r
θ = 8.7 / 1000
θ ≈ 0.0087 radians
Therefore, if the racecar travels 8.7 feet in the clockwise direction along the track, the angle's measure in radians is approximately 0.0087 radians.

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Paul and Fred working together can paint the fence in 6/5 hours, which is equivalent to 1 hour and 12 minutes.

To determine how many hours Paul and Fred can paint the fence together, we can use the concept of their individual work rates.

Let's denote the work rate of Paul as P (measured in fence per hour) and the work rate of Fred as F (also measured in fence per hour).

From the given information, we know that Paul can paint the fence in 2 hours, so his work rate is:

P = 1 fence / 2 hours = 1/2 fence per hour

Similarly, Fred can paint the same fence in 3 hours, so his work rate is:

F = 1 fence / 3 hours = 1/3 fence per hour

To find the combined work rate of Paul and Fred when they work together, we can add their individual work rates:

P + F = 1/2 + 1/3 = 3/6 + 2/6 = 5/6 fence per hour

Now, to determine the number of hours it takes for Paul and Fred to paint the fence together, we can use the reciprocal of their combined work rate:

1 / (P + F) = 1 / (5/6) = 6/5

So, Paul and Fred working together can paint the fence in 6/5 hours, which is equivalent to 1 hour and 12 minutes.

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