If there is a positive correlation between number of hours spent studying and exam grades, then the _____ time people spend studying, the _____ their exam grades.
less; higher





b.

more; higher





c.

none of the above.



d.
more; lower

Using the exponential probability density function in the given situation the required formula for P(x ≤ x0) would be P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵.

The exponential distribution, sometimes known as the negative exponential distribution, is the probability distribution of the interval between events in a Poisson point process, that is, an event-producing process where events happen continuously and independently at a fixed average rate.

The memoryless feature of the exponential distribution states that future probabilities are independent of any prior knowledge.

According to mathematics, P(X > x + k|X > x) = P(X > k).

The probability that a random variable will fall into a specific range of values as opposed to taking on any value is defined by the probability density function (PDF).

In the given function:

f(x) = 1/5⁻ˣ⁺⁵ for x

Then, the formula for P(x ≤ x0) would be:

P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵

Therefore, using the exponential probability density function in the given situation the required formula for P(x ≤ x0) would be P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵.

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Complete question:

Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0. Write the formula for P(x ≤ x0)

The area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

What is rectangle?

A rectangle is a four-sided two-dimensional geometric shape in which all angles are right angles (90 degrees) and opposite sides are parallel and equal in length. This means that a rectangle has two pairs of congruent sides and its opposite sides are parallel.

To find the area of each part of the figure and the whole figure, we need to use the formulas for the area of a triangle and the area of a rectangle.

First, we can find the area of the triangle:

Area of Triangle A = (1/2) x base x height = (1/2) x 4 x 6 = 12 square units.

Next, we can find the area of the rectangle:

Area of Rectangle B = length x width = 5 x 6 = 30 square units.

To find the area of the whole figure, we can add the area of Triangle A and Rectangle B:

Area of Whole Figure = Area of Triangle A + Area of Rectangle B

= 12 + 30

= 42 square units.

Therefore, the area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

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Therefore, the value of m = 1/ 3, b = -11/6. equation in the form [tex]y = mx+b[/tex].

"Slope-intercept" refers to a method of expressing a linear equation in the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.

The "slope" of a line refers to how steeply it rises or falls as it moves from left to right. It is calculated by dividing the change in y by the change in x between any two points on the line.

The "y-intercept" is the point where the line intersects the y-axis. It is the value of y when x equals zero.

By expressing a linear equation in slope-intercept form, you can easily identify the slope and y-intercept, which can provide useful information about the line's behavior.

To write the equation in the form y = mx + b, we need to solve for y:

[tex]-2x + 6y = -11[/tex]

[tex]6y = 2x - 11[/tex]

[tex]y = (2/6)x - (11/6)[/tex]

[tex]y = (1/3)x - (11/6)[/tex]

So, the equation in slope-intercept form is. [tex]y = (1/3)x - (11/6)[/tex], where the slope m is 1/3 and the y-intercept b is -11/6.

Therefore,

m = 1/3

b = -11/6

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Answer:

hehe

Step-by-step explanation:

Answer:

[tex]2x = 20[/tex]

[tex]x = 10[/tex]

a) The problem can be formulated as a Linear Programming Model (LPM) as follows:

Maximize Z = 400x + 100y

Subject to:

4x + 2y ≤ 1600

2.5x + y ≤ 1200

4.5x + 1.5y ≤ 1600

Where x is the number of units of model A produced, y is the number of units of model B produced, and the constraints represent the production capacities of each department.

b) The LPM can be solved using the graphical method by plotting the constraints on a graph and finding the feasible region, which is the region of the graph where all constraints are satisfied. The corner points of the feasible region are then evaluated to find the optimal solution.

After plotting the constraints and finding the feasible region, the corner points are (0, 0), (0, 800), (266.67, 533.33), (400, 200), and (355.56, 0). Evaluating the objective function at each corner point, we find that the maximum profit of Birr 133,333.33 is achieved at the point (266.67, 533.33), which represents producing 266.67 units of model A and 533.33 units of model B.

The slack time in each department can be found by subtracting the time used for production from the available time. The slack times are 533.33 hours in Department I, 466.67 hours in Department II, and 66.67 hours in Department III.

Answer:

arc ADB = 10π m

A (shaded) = 30π m^2

Step-by-step explanation:

Given:

∠AOB = 60° (it is a central angle, which is equal to the arc on which it rests on)

r (radius) = 6 m

Find: arc ADB - ? A (shaded) - ?

If arc AB is 60°, then arc ADB is (remember, that a full circle forms an angle of 360°):

[tex] \alpha = 360° - 60° = 300°[/tex]

Now, we can find the length of the arc ADB:

[tex]l = \frac{2\pi \times r \times \alpha }{360°} = \frac{2\pi \times 6 \times 300°}{360°} = \frac{3600\pi}{360°} = 10\pi \: m[/tex]

The shaded region is a cutout of a circle

We can find its area by using this formula:

[tex]a(shaded) = \frac{\pi {r}^{2} \times \alpha }{360°} = \frac{\pi \times {6}^{2} \times 300°}{360°} = \frac{10800\pi}{360°} = 30\pi \: {m}^{2} [/tex]

P(x<69.3) = 0.9082. (Rounded to four decimal places.)

P(x ≥ 66.3) = 0.2486. (Rounded to four decimal places.)

(b) We have X ~ N(65, 4²), where μ = 65 and σ = 4. Therefore,

Z = (X - μ) / σ = (69.3 - 65) / 4 = 1.325

Using a standard normal table or calculator, find P(Z < 1.325) = 0.9082. Therefore,

P(X < 69.3) = 0.9082.

(c) Using the same standard normal table or calculator, find P(Z ≥ 0.675) = 0.2486. Therefore,

P(X ≥ 66.3) = 0.2486.

Note that we use the complement rule here, since P(X ≥ 66.3) = 1 - P(X < 66.3), and we have already calculated P(X < 66.3) in part (b).

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Answer:

[tex]286\pi \: {in}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

d (diameter) = 22 in

l = 26 in

Find: A (lateral) - ?

First, let's find the length of the radius:

[tex]r = \frac{1}{2} \times d = \frac{1}{2} \times 22 = 11 \: in[/tex]

Now, we can find the lateral area:

[tex]a(lateral) = \pi \times r \times l[/tex]

[tex]a(lateral) = \pi \times 11 \times 26 = 286\pi \: {in}^{2} [/tex]

Therefore, the equation of the line that is perpendicular to the given line and passes through the point (−3,4) is [tex]y=(-2/3)x+6[/tex].

Parallel lines are two lines in a plane that never intersect, no matter how far they are extended. In other words, they are always at the same distance from each other and never converge or diverge. Parallel lines have the same slope and are always equidistant. In geometry, parallel lines are denoted by a double vertical line symbol (||) placed between them. They are an important concept in geometry and have many real-world applications, such as in architecture, engineering, and computer graphics.

Find the equation of the line that is perpendicular to this line and passes through the point  3, 4.

The given line is −6x + 4y = 5. To find the equation of a line that is parallel to this line and passes through the point (−3,4), we can use the fact that parallel lines have the same slope. The slope of the given line can be found by rearranging it to the slope-intercept form: y = (3/2)x + (5/4), which has a slope of 3/2.

Therefore, the slope of any line parallel to the given line will also be 3/2. We can use this slope and the point-slope form of a line to find the equation of the line we're looking for:

[tex]y - y_1 = m(x - x1)[/tex], where (x1, y1) = (-3, 4) and m = 3/2

[tex]y - 4 = (3/2)(x + 3)[/tex]

[tex]y - 4 = (3/2)x + 9/2\\[/tex]

[tex]y = (3/2)x + 9/2 + 4[/tex]

[tex]y = (3/2)x + 17/2[/tex]

Therefore, the equation of the line that is parallel to the given line and passes through the point (−3,4) is y = (3/2)x + 17/2.

To find the equation of a line that is perpendicular to the given line and passes through the point (−3,4), we can use the fact that perpendicular lines have negative reciprocal slopes. The slope of the given line is 3/2, so the slope of any line perpendicular to it will be -2/3.

Using this slope and the point-slope form of a line, we can find the equation of the line we're looking for:

[tex]y - y_1 = m(x - x1)[/tex], where (x1, y1) = (-3, 4) and m = -2/3

[tex]y - 4 = (-2/3)(x + 3)[/tex]

[tex]y - 4 = (-2/3)x - 2[/tex]

[tex]y = (-2/3)x + 2 + 4[/tex]

[tex]y = (-2/3)x + 6[/tex]

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The equation that is true for all value is : 4(x - 3) = 0

A linear equation is one that has the following form of expression:

y = mx + b

If m is the line's slope, b is the y-intercept, x and y are variables. In this equation, m indicates the steepness of the line and b the point at which it crosses the y-axis to show a straight line on a graph.

The equation that is true for all values of x is:

4(x - 3) = 0

To see why, we can simplify the equation as follows:

4(x - 3) = 0

4x - 12 = 0 (distributing the 4)

4x = 12 (adding 12 to both sides)

x = 3 (dividing both sides by 4)

So we see that the equation simplifies to 4 times the quantity (x - 3), which is equal to 0 if and only if x = 3. Therefore, the equation is true for all values of x if and only if x = 3.

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Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

The area of the circle with a circumference of 8 cm is 16/π square cm.

What are the area and circumference of a circle?

The relationship between the area of a circle and its circumference can be described using the formula:

A = (π/4) x D²

where A is the area of the circle, D is the diameter of the circle, and π is the mathematical constant pi, approximately equal to 3.14159.

Similarly, the circumference of a circle can be calculated using the formula:

C = π x D

If the circumference of a circle is 8 cm, we can use the formula for circumference to find the radius:

C = 2πr

8 cm = 2πr

r = 4/π cm

Now that we know the radius, we can find the area using the formula:

A = πr²

A = π(4/π)²

A = 16/π square cm

So the area of the circle with a circumference of 8 cm is 16/π square cm (or approximately 5.09 square cm if we use 3.14 as an approximation for π).

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The value of X for which 70.54% of the area under the normal curve lies to the right of it is 7.88 (rounded to two decimal place)

To solve this problem, we need to find the value of X such that 70.54% of the area under the normal curve lies to the right of it.

We know that the total area under the normal curve is 1 or 100%. So, if 70.54% of the area lies to the right of X, then 29.46% of the area must lie to the left of X.

We can find the Z-score corresponding to the left tail area of 29.46% using a standard normal distribution table or calculator.

The Z-score is -0.53 (rounded to two decimal places).

Now, we can use the formula for converting a Z-score to an X-value for a normal distribution:

X = μ + Zσ

where;

μ is the mean of the distribution,

σ is the standard deviation, and

Z is the Z-score.

Plugging in the values, we get:

X = 10 + (-0.53)(4)

X = 7.88

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Answer:

Step-by-step explanation:

The probability of getting exactly 25 heads in 50 coin flips would be higher than flipping a coin 6 times and getting exactly 3 heads.

To understand why, we can use the formula for calculating the probability of getting a specific number of heads in a given number of coin flips, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k heads, n is the total number of coin flips, p is the probability of getting heads on a single coin flip, and (n choose k) is the binomial coefficient.

For the first scenario of flipping a coin 50 times and getting exactly 25 heads, we can plug in the values and get:

P(X=25) = (50 choose 25) * 0.5^25 * 0.5^25 = 0.112

For the second scenario of flipping a coin 6 times and getting exactly 3 heads, we can similarly plug in the values and get:

P(X=3) = (6 choose 3) * 0.5^3 * 0.5^3 = 0.3125

As we can see, the probability of getting exactly 25 heads in 50 coin flips is much higher than the probability of flipping a coin 6 times and getting exactly 3 heads. This is because the probability of getting a single head on a coin flip is 0.5, and as the number of coin flips increases, the probabilities of different outcomes converge towards a bell-shaped distribution centered around 0.5. This means that the probability of getting a specific number of heads in a large number of coin flips becomes more likely as the number of coin flips increases.

The value of the quadratic equation when x = 3 is 67.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown number and where a, b, and c represent known values, with a ≠ 0, is a quadratic equation.

We are given a quadratic equation as 3[tex]x^{2}[/tex] + 5x + 25.

Now, when x = 3, we get

⇒ 3* [tex]3^{2}[/tex] + 5 (3) + 25

⇒ 3 (9) + 5 (3) + 25

⇒ 27 + 15 + 25

⇒ 67

Hence, the value of the quadratic equation when x = 3 is 67.

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Question: Evaluate : 3x² + 5x + 25 when x = 3.

Answer:

Step-by-step explanation: Isn't the 3rd one wrong

There is a 65.54% probability that the average age of those doctors is under 48.8 years.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

True mean = mean (or average)+/- Z*SD/sqrt (sample population)

Then,

Mean (average) = 48.0 years

The true mean must be less than 48.8 years.

SD = 6.0 years, and

Sample size (n) = 9 doctors

Using Z as the formula's subject:

Z= (True mean - mean)/(SD/sqrt (n))

Inserting values:

Z=(48.8-48.0)/(6.0/sqrt (9)) = 0.4

From the table of normal distribution probabilities:

At Z= 0.4, P(x<0.4) = 0.6554 0r 65.54%

Therefore, there is a 65.54% probability that the average age of those doctors is under 48.8 years.

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Complete question:

The average age of doctors in a certain hospital is 48.0 years old. suppose the distribution of ages is normal and has a standard deviation of 6.0 years. if 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. assume that the variable is normally distributed.

Answer:

1 / 20 or 0.05

Step-by-step explanation:

1/5 ÷ 4

= 1/5 × 1/4

= 1 / 20

the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

How to solve the probability?

A standard deck of 52 cards contains 12 face cards (4 Kings, 4 Queens, and 4 Jacks) and 40 non-face cards (10s, 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, and Aces). To find the probability that a 5-card poker hand contains exactly 2 face cards, we need to count the number of possible hands that satisfy this condition and divide by the total number of possible 5-card hands.

To count the number of hands with exactly 2 face cards, we can use the following steps:

Choose 2 face cards from the 12 available: 12 choose 2 = 66 ways.

Choose 3 non-face cards from the 40 available: 40 choose 3 = 91,390 ways.

Multiply the results of steps 1 and 2 to get the total number of possible hands with exactly 2 face cards: 66 x 91,390 = 6,270,540.

To count the total number of possible 5-card hands, we can use the formula for combinations: 52 choose 5 = 2,598,960.

Therefore, the probability of getting a hand with exactly 2 face cards is:

6,270,540 / 2,598,960 = 0.0241, or approximately 2.41%.

So the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

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Answer: To show that the function has exactly one zero in the given interval, we need to show that the function changes sign exactly once on the interval.

First, we can see that the function is continuous on the interval (0, pi/2) as it is a polynomial of trigonometric functions.

Next, we can evaluate the function at the endpoints of the interval:

R(0) = sec^2(0) - cos(0) - 1 = 1 - 1 - 1 = -1

R(pi/2) = sec^2(pi/2) - cos(pi) - 1 = undefined

We can see that R(0) is negative, and since the function is continuous on the interval, by the Intermediate Value Theorem, the function must pass through zero at some point in the interval.

To show that it passes through zero only once, we can take the derivative of the function:

R'(theta) = 2sec^2(theta)sin(theta) + 2sin(2theta)

We can see that R'(theta) is positive for all theta in the interval (0, pi/2), as sec^2(theta) and sin(theta) are positive and sin(2theta) is non-negative. Therefore, the function R(theta) is strictly increasing on the interval, and can cross the x-axis at most once.

Thus, we have shown that the function R(theta) has exactly one zero in the interval (0, pi/2).

Step-by-step explanation:

The quadratic equations are classified as follows:

If the discriminant of the quadratic equation is positive, then the equation has two real solutions.

If the discriminant is zero, then the equation has one real solution.

If the discriminant is negative, then the equation has no real solutions (but may have complex solutions).

Let's classify the given quadratic equations based on the number of solutions:

20² +5 = 9 is not a quadratic equation because it does not have a variable with a degree of two. Instead, it is just a number that evaluates to a false statement.

Therefore, it has no solution.

2x² + 3x = 5 is a quadratic equation with a = 2, b = 3, and c = -5. The discriminant is 3² - 4(2)(-5) = 49, which is positive.

Therefore, the equation has two real solutions.

3x² + 2x = 22 is a quadratic equation with a = 3, b = 2, and c = -22. The discriminant is 2² - 4(3)(-22) = 100, which is positive.

Therefore, the equation has two real solutions.

4x² + 12x = 19 is a quadratic equation with a = 4, b = 12, and c = -19. The discriminant is 12² - 4(4)(-19) = 400, which is positive.

Therefore, the equation has two real solutions.

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Drag each equation to the correct location on the table.

Classify the quadratic equations based on the number of solutions.

20² +5 = 9

2x² + 3x = 5

3x² + 2x = 22

4x² + 12x = 19

One Solution

Two Solutions

No Solution

Answer:

2 3/8

Step-by-step explanation:

I am not completely sure because I did it a long while back but correct me if I'm wrong I want to learn please mark me brainliss

Answer:

2°
one solution
(a) The system has no solution

Step-by-step explanation:

Let the smaller angle be x. According to the given condition, the larger angle is forty-four times the smaller angle, which is 44x. Since the angles are complementary, their sum is 90°.

x + 44x = 90

45x = 90

x = 90/45

x = 2

So, the smaller angle is 2°, and the larger angle is 44 times that, which is 88°.

The given system of equations is:

20y = -24x + 40

6x + 5y = 10

To determine the nature of the system, we can compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.

Let's find the slopes of the two equations:

20y = -24x + 40

Dividing by 20, we get: y = (-24/20)x + 2

6x + 5y = 10

Dividing by 5, we get: (5/5)y = (6/5)x + (10/5)

y = (6/5)x + 2

Comparing the slopes, we see that they are equal (both are 6/5), and the y-intercepts are also equal (both are 2). So, the system has infinitely many solutions. The correct answer is (b) The system has infinitely many solutions.

The given system of equations is:

19 = 4y + 12x

12x + 4y = 15

To determine the nature of the system, we can again compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.

Let's find the slopes of the two equations:

19 = 4y + 12x

Dividing by 4, we get: (1/4)(4y + 12x) = 19/4

y + 3x = 19/4

12x + 4y = 15

Dividing by 4, we get: (1/4)(12x + 4y) = 15/4

3x + y = 15/4

Comparing the slopes, we see that they are equal (both are 1/3), but the y-intercepts are not equal. So, the system has no solution. The correct answer is (a) The system has no solution.

The statements that would be true if the length of each side of the square increased by one unit is that the area of the square would be a rational number and the area of the square would be a perfect square.

A perfect square is defined as the number that can be expressed as the product of two equal integers.

The area of the square given = 400

The sides of the square = 20

When an additional unit is added= 21

The new area = 441

This is a perfect square and equally a rational number because it's a real number.

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Answer:

Step-by-step explanation:

Answer:

the answer is 23

Step-by-step explanation:

the equation states that x=3

therefore you have to replace x with 3 so the equation is equal to

6×3= 18+5= 23

The monthly payments for the loan to be paid off at the rate given would be = $1,504.4

The total cost of the house = $243, 950.

The time for the payment of the loan = 25 years.

The rate of the payment = 7.4%

The simple interest = principal×time×rate/100

Si = 243, 950.×25×7.4/100

si = 45130750/100

si = 451,307.50

The total number of months is 25 years = 300

The amount paid per month = 451,307.50/300 = $1,504.4

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1.) Over half of the iguanas measure 14 centimeters or more in length.

The assertion that is most supported by the data is, "More than half of the iguanas measure 14 centimeters or more in length." According to this claim, more than 50% of the iguanas are 14 cm or longer in length. The other two claims describe precise iguana lengths (12 centimeters and 11 centimeters or less, respectively), but they do not mention how common such lengths are in comparison to other lengths. Therefore, out of the available probability, the first statement is the one that is most illuminating and best substantiated.

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Complete question is :

At the zoo, the length of each iguana is measured. Which statement is best supported by the information below?

The result is a polynomial in simplest form [tex]x^{2} -6x -27[/tex]

Polynomials are algebraic formulas with variables and coefficients. Variables are sometimes known as indeterminates.

To calculate (f - g)(x), subtract g(x) from f(x) as follows:

(f - g)(x) = f(x) - g(x)

When we substitute the given functions, we get:

(f - g)(x) =[tex](x^2 - 5x - 36)[/tex] - (x - 9)

When we expand and simplify, we get:

(f - g)(x) = [tex]x^{2} - 5x - 36 - x + 9[/tex]

(f - g)(x) = [tex]x^{2}[/tex] - 6x - 27

As a result, the polynomial is (f - g)(x):

(f - g)(x) = [tex]x^{2}[/tex] - 6x - 27

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Therefore, the length of the third side of the right-angled triangle is 2√55.

Using the Pythagorean theorem to solve for the length of the third side of the right-angled triangle:

So, if we let the third side be x, we have:

6^2 + x^2 = 16^2

Simplifying this equation:

36 + x^2 = 256

Subtracting 36 from both sides:

x^2 = 220

Taking the square root of both sides:

x = √220

Simplifying the square root:

x = 2√55

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