Your mother takes you to your grandparents house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives another 30 minutes at constant speed for 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?

Answer:the number of cupcakes that Sue purchased is 12

Step-by-step explanation:

Let x represent the number of cupcakes that Sue purchased at the bakery.

Let y represent the number of cookies that Sue purchased at the bakery.

She needs to serve 36 people. This means she would purchase a total of 36 people. Therefore,

x + y = 36

Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. This means that

2.5x + y = 54 - - - - - - - - - 1

Substituting x = 36 - y into equation 1, it becomes

2.5(36 - y) + y = 54

90 - 2.5y + y = 54

- 2.5y + y = 54 - 90

- 1.5y = - 36

y = - 36/ - 1.5

y = =24

x = 36 - y = 36 - 24 = 12

She purchased 24 cupcakes

If she needs to serve 36 people, then;

x + y = 36 ....................  1

if cupcakes cost $2.50 each, cookies cost $1.00 each while she spends $54.00, then;

2.5x + y = 54 ...................... 2

From equation 1, x = 36 - y

Substitute into equation 2;

2.5(36-y) + y = 54

90 - 2.5y + y = 54

-1.5y = - 36

y = 36/1.5

y = 24

Hence she purchased 24 cupcakes

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Answer:

Step-by-step explanation:

Area Of Triangle And Rectangle

Given a triangle of base b and height h (perpendicular to b), the area can be computed by

[tex]\displaystyle A=\frac{bh}{2}[/tex]

A rectangle of the same dimensions has an area of

[tex]A=bh[/tex]

We have a triangle of base 3 cm and a height of 4 cm. Its area is

[tex]\displaystyle A=\frac{(3)(4)}{2}=6\ cm^2[/tex]

That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is

[tex]A=(3)(12)=36\ cm^2[/tex]

The triangle stays in the top of this rectangle, so its area is part of the total swept area:

Total swept area = 6 + 36 = [tex]42\ cm^2[/tex]

Answer:

(fоgоh)(x)=2x³+1

Step-by-step explanation:

Function composition is an operation where two functions, say f(x) and g(x), a new function h(x)=(fоg)(x)=f(g(x)) is generated. In this operation, the function g is applied to the result of the function f. Hence, function f:X→Y and g:Y→Z are joined to form a new function h:X→Z

Given [tex]f(x)=x+1[/tex]

[tex]g(x)=2x[/tex]

[tex]h(x)=x^{3}[/tex]

(fоgоh)(x)=[tex]f(g(h(x)))[/tex]

               =[tex]f(g(x^{3}))[/tex]

               =[tex]f(2x^{3})[/tex]

               =2x³+1

Answer:

Step-by-step explanation:

The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.

a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3

Therefore, the probability of getting a sum of 4 will be

3/36 = 1/12

b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4

Therefore, the probability of getting a sum of 4 will be

4/36 = 1/9

c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5

Therefore, the probability of getting a sum of 6 will be

5/36 = 5/36

The probability that the sum of the results of the throw is 4,5 or 6 would be

1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3

Answer:

800 people a year

Step-by-step explanation:

When there is an increment in an observed value, the increment implies that there is a growth or percentage increase in the observed value. The percentage increase in participation is 33%:

Given that:

[tex]Initial = 2400[/tex] --- last year

[tex]New= 3200[/tex] --- this year

The percentage increase is calculated as:

[tex]\%Increase = \frac{New - Initial}{Initial} \times 100\%[/tex]

So, we have:

[tex]\%Increase = \frac{3200 - 2400}{2400} \times 100\%[/tex]

[tex]\%Increase = \frac{800}{2400} \times 100\%[/tex]

[tex]\%Increase = 0.3333 \times 100\%[/tex]

[tex]\%Increase = 33.33 \%[/tex]

Approximate

[tex]\%Increase = 33 \%[/tex]

Hence, the percentage increase in participation from last year to this year is 33%

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Completed question: A bag of rare spice that weighs 3/5 pounds will be split equally among 15 people. How much spice will each person get?

Answer:

0.04 pounds

Step-by-step explanation:

The number of spice received by each person will be equal to the total number of spice divided by the number of people sharing it.

Amount of spice received per person = (3/5) /15

                                                     = 0.04 pounds

Answer:

0 handshakes

Step-by-step explanation:

There are 8 women of different heights.

Let the eight women be A, B, C, D, E, F, G and H

Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.

If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28

Answer:

0

Step-by-step explanation:

There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.

Answer:

see the explanation

Step-by-step explanation:

Remember that

[tex]1\ week=7\ days[/tex]

To convert weeks to days , multiply by 7

so

[tex]3\ weeks=3(7)=21\ days[/tex]

we know that

Each night Tim's Tacos sell 57 chicken tacos and 89 beef tacos

To find out how many of each type of taco sold after three weeks, multiply the number of taco sold daily by 21 (3 weeks)

Chicken tacos

[tex]57(21)= 1,197\ chicken\ tacos[/tex]

Beef tacos

[tex]89(21)= 1,869\ beef\ tacos[/tex]

Answer:

[tex]A= 125*250=31250 ft^2[/tex]

Step-by-step explanation:

Let's define some notation first :

w= width , l = length , A= Area, P perimeter

For this case we want to maximize the Area given by this function:

A= l w   (1)

With the following restriction P=500 ft

We know that the perimeter on this case is given by:

[tex]P=2w +l[/tex]

Since they are using the creek as one side.

So then we have this:

[tex]500 =2w +l[/tex]   (2)

Now we can solve w in terms of l from eqaution (2) and we got:

[tex]w=\frac{500-l}{2}[/tex]   (3)

And we can replace this condition into equation (1) like this:

[tex]A= \frac{500-l}{2} l =250l - \frac{1}{2} l^2[/tex]

And we can maximize this function derivating respect to l and we got:

[tex]\frac{dA}{dl}= 250 -l=0[/tex]

And then we got that [tex]l=250[/tex]

And if we solve for w from equation (3) we got:

[tex]w=\frac{500-250}{2}=125[/tex]  

And then the dimensions would be:

[tex] l =250ft , w=125ft[/tex]

And the area would be:

[tex]A= 125*250=31250 ft^2[/tex]

To maximize the area of the corral, we can solve a mathematical optimization problem. By expressing the length in terms of the width, we can find the derivative of the area formula and set it to zero. Substituting the resulting value of the width into the area formula gives us the maximum area.

To find the maximum area of the corral, we need to determine the dimensions of the rectangle. Let's assume the length of the corral is L and the width is W.

Since one side of the corral is the creek, we only need to use fencing for the other three sides. This implies that 2W + L = 500 (since there are two widths and one length that need fencing).

To maximize the area, we can express L in terms of W using the formula L = 500 - 2W and substitute it into the area formula A = LW. Simplifying, we get A = W(500 - 2W). To find the maximum area, we can take the derivative of A with respect to W, set it equal to zero, and solve for W. The resulting value of W can be substituted back into the equation to find the corresponding value of L. The maximum area is obtained by multiplying these two dimensions together.

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Answer:

[tex]k=-\frac{2}{7}[/tex]

Step-by-step explanation:

The two equations given represent two straight lines in 2-D graph.

The two lines will not intersect if they are parallel.

Hence the two equations will not have solution if the lines are parallel and not coincident.

The condition for 2 lines given by the equations :

ax+by+c=0

dx+ey+f=0 to be parallel but not coincident is:

[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]

here a=2  b=-3k  c=-1  d=4  e=k+2  f=-5

[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]

But also:

[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]

Hence the value of k is -2/7.

Good evening ,

Answer:

Step-by-step explanation:

GE=2×ZE

Since ZE=XY then ZE=5

therefore GE=2×5=10.

:)

Answer:

[tex]P(x < 535.8) = 0.64[/tex]

[tex]P_{64} = 535.8[/tex]

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.64

P(X<x) = 0.64

[tex]P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64[/tex]  

Calculation the value from standard normal z table, we have,  [tex]p(z<0.358) = 0.64[/tex]

[tex]\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8[/tex]

[tex]P(x < 535.8) = 0.64[/tex]

[tex]P_{64} = 535.8[/tex]

Tyrell's math score is 554.

To find Tyrell's math score, we need to use the z-score formula. The z-score formula is given as z = (x - μ)/σ. In this case, we want to find x, so we rearrange the formula to solve for x: x = zσ + μ. Given that Tyrell's score is in the 64th percentile, we can use the z-score table to find the corresponding z-score. The z-score for the 64th percentile is approximately 0.355. Plugging this into the formula, we get: x = 0.355(100) + 500 = 53.55 + 500 = 553.55. Rounding to the nearest whole number, Tyrell's math score is 554.

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Answer:

The coordinates of  A'(8,-5)

Step-by-step explanation:

we know that

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places

so

The rule of the reflection across the line y=x is

(x,y) -----> (y,x)

we have the point A(-5,8)

Applying the rule of the reflection across the line y=x

A(-5,8) ----> A'(8,-5)

see the attached figure to better understand the problem

Answer:

Step-by-step explanation:

The aquarium is 2 1/2 miles from her hotel. Converting 2 1/2 miles into improper fraction, it becomes 5/2 miles.

She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles. Converting 1 3/4 miles to improper fraction, it becomes 7/4 miles. Therefore the total distance covered by walking and boarding the bus would be

1/4 + 7/4 = 8/4 = 2 miles

She walks the rest of the way to the aquarium. Therefore, the distance that Clara walked after getting off the bus would be

5/2 - 2 = 1/2 miles

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

2x+9y=5

9y = - 2x + 5

y = -2x/9 + 5/9

Comparing with the slope intercept form, slope = -2/9

If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (4,-9) is 9/2

To determine the intercept, we would substitute m = 9/2, x = 4 and y = -9 into y = mx + c. It becomes

- 9 = 9/2×4 + c = 18 + c

c = - 9 - 18 = - 27

The equation becomes

y = 9x/2 - 27

Answer:

The answer to your question is cos A = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Process

1.- Write the formula

[tex]cos A = \frac{adjacent side}{hypotenuse}[/tex]

2.- Identify the legs of the triangle

opposite side = 12

adjacent side = 9

hypotenuse = 15

3.- Substitute the values in the formula

[tex]cos A = \frac{9}{15}[/tex]

4.- Simplification and result

[tex]cos A = \frac{3}{5}[/tex]

Explanation of finding the value of cos A using trigonometric identities and scalar products.

Cosine function: The value of cos A can be determined using trigonometric identities. For example, from the given expressions like cos 4A=8cos^4A-8cos^2A+1, we can find the value of cos A for specific angles.

Trigonometric identities: By manipulating the given equations and using trigonometric relationships like 1 - cos A = 2sin^2A, you can solve for cos A for different angles.

Scalar products: Understanding the concept of scalar products involving cosine functions like AB cos(θ) will help in applying trigonometry in real-world applications.

Answer: d) 0.238

Step-by-step explanation:

We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as

P(x =r) = nCr × q^(n - r) × p^r

Where

p represents the probability of success.

q represents the probability of failure.

n represents the number of samples.

From the information given,

n = 10

p = 65% = 65/100 = 0.65

q = 1 - p = 1 - 0.65 = 0.35

The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P(x = 6). It becomes

P(x =6) = 10C6 × 0.35^(10 - 6) × 0.65^6

P(x =6) = 10C6 × 0.35^4 × 0.65^6

P(x =6) = 0.238

Final answer:

Option d) 0.238

Explanation:

To find the probability that exactly six out of 10 men consider themselves knowledgeable football fans, we can use the binomial probability formula:

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

Where:

Using the formula, we get:

P(X=6) = C(10, 6) * 0.65^6 * (1-0.65)^4

Calculating C(10, 6) which is 210, and then raising 0.65 to the power of 6 and (1-0.65) to the power of 4, simplifies to:

P(X=6) = 210 * 0.1160290625 * 0.1502625 = 0.238

After rounding to three decimal places, we get:

P(X=6) = 0.238

Therefore, the correct answer is (d) 0.238.

Answer:

  6500

Step-by-step explanation:

In 24 hours, there are 12 times 2 hours, so the bacteria count will increase by 500 twelve times. That is, the increase after 24 hours will be ...

  12 × 500 = 6000 . . . bacteria

Since the starting number was 500, the total will be ...

  500 + 6000 = 6500 . . . . bacteria after 24 hours

_____

If you like, you can compute the rate of change as 500 bacteria / (2 hours) = 250 bacteria/hour. Then the equation for the number is ...

  bacteria = 500 + 250h . . . . . where h is the number of hours.

Filling in h=24, we get

  bacteria = 500 + 250(24) = 500 +6000 = 6500 . . . . after 24 hours

The cost of the phone contract will be C = 35 + 12m.

From the information given, the fixed line rental is £35 and the price of calls made is £12, therefore the monthly cost will be represented by:

C = 35 + (12 × m)

C = 35 + 12m

Therefore, the cost of the phone contract will be C = 35 + 12m where m represents the number of months.

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The cost of a monthly phone contract is made up of the fixed line rental and the price of the calls made. This can be represented with the formula: c = l + p, where c is the cost, l is line rental, and p is the price of calls. With a line rental of £35 and call price of £12, the total cost of the phone contract is £47.

In the scenario presented, the cost, c, of a monthly phone contract is constituted by the fixed line rental or l and the price or p of the calls made. This can be represented with the formula: c = l + p. We can substitute in the provided costs - a line rental of £35 and call price of £12 - into the equation to find the total cost of the phone contract. Thus, c = £35 + £12 = £47.

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Answer:

The answer to your question is letter C

Step-by-step explanation:

Process

1.- Find two points of the line

   A ( 0, 1)

   B ( 1, -3)

2.- Find the slope of the line

    [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

    [tex]m = \frac{-3 - 1}{1 - 0}[/tex]

    [tex]m = \frac{-4}{1}[/tex]

           m = -4

3.- Find the equation of the line

            y - y1 = m (x - x1)

            y - 1 = -4( x - 0)

            y -1 = -4x

            y = -4x + 1

Answer:

[tex]Months =\frac{3784}{214 /month}=17.682months\approx 18 months[/tex]

As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months

Step-by-step explanation:

Notation

[tex]P_f =792[/tex] current mortgage payment

[tex]P_i = 578[/tex] reduced mortgage payment

R= 3784 represent the rfinancing charges

Solution to the problem

In order to solve this question we need to find first the difference between the two mortgage payments like this:

[tex]P_f- P_i = 792-578=214[/tex]

And then since the refinancing charges is $3784 we can find the number of months that we will need to remain in the house like this:

[tex]Months =\frac{3784}{214 /month}=17.682months[/tex]

As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months

Answer:

Step-by-step explanation:

Given is the probability distribution of a random variable X

X 4 5 6 7 Total

P 0.2 0.4 0.3 0.1 1

x*p 0.8 2 1.8 0.7 5.3

x^2*p 3.2 10 10.8 4.9 28.9

a) E(X) = Mean of X = sum of xp = 5.3

[tex]Var(x) = 28.9-5.3^2=0.81[/tex]

Std dev = square root of variance = 0.9

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

b) For sample mean we have

Mean = 5.3

Variance = var(x)/n = [tex]\frac{0.81}{{36} } \\=0.0225[/tex]

c) [tex]P(\bar X <5.5)\\= P(Z<\frac{5.5-5.3}{\sqrt{0.0225} } \\= P(Z<1.33)\\=0.908[/tex]

The mean and the variance from the data about the cherries will be 5.3 and 0.81.

The required mean from the information given will be:

= (4 × 0.2) + (5 × 0.4) + (6 × 0.3) + (7 × 0.1)

= 0.8 + 2.0 + 1.8 + 0.7

= 5.3

The variance will be calculated thus:

= (4² × 0.2) + (5² × 0.4) + (6² × 0.3) + (7² × 0.1) - (5.3)²

= 3.2 + 10 + 10.8 + 4.9 - (5.3)²

= 0.81

The variance is 0.81.

The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 will be:

= P(x = 4( + P(x = 5)

= 0.2 + 0.4

= 0.6

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Answer:

  18] not a function; (1, 5), (1, -1)

  19] is a function

Step-by-step explanation:

The graph of a function will pass the "vertical line test." That is, a vertical line will not intersect the graph at more than one point.

18] There are an infinite number of points where a vertical line will cross the graph twice. Two that are recognizable are the ones at the vertical extremes: (1, 5) and (1, -1). This relation is not a function.

__

19] None of the points on the graph are vertically aligned, so the relation is a function.

Answer:

a) the number of miles in 1 kilometer

Step-by-step explanation:

The car converts from miles/hour to kilometers/hour, if we see the time measurement (hours) it stays the same in both units.

So to make the conversion it is enough to know how many miles are in one kilometer.

For example, lets convert 10miles/hour to kilometers/hour.

there are 0.621371 miles in 1 kilometer, so if we divide 10miles/hour by 0.621371 we get kilometers/hour units:

[tex]\frac{10miles}{hour} (\frac{1kilometer}{0.621371miles} )=16.0934\frac{kilometers}{hour}[/tex]

Thus to make the conversion between the two units is needed the number of miles in 1 kilometer.

Answer:

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60

Step-by-step explanation:

Let the total professors be =100

n(tennis) = 60

n( bridge) = 65

n( chess)= 50

n( T U B) = 45, n(BU C) = 45, n(T UC)=45

n( T U B U C)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) +  [tex]n(T\cap B\cap C)[/tex]

100 = 60 + 65 + 50 - 45-45-45 +   [tex]n(T\cap B\cap C)[/tex]

 [tex]n(T\cap B\cap C)[/tex] = 60

Therefore,

a) yes we should get suspicious

b) smallest percentage to like all three sports= 60

Final answer:

The given information suggests that we should be suspicious if told that 20% of all college professors like all three recreations. The smallest percentage who could like all three recreations is 0%.

Explanation:

(a) Yes, we should be suspicious if told that 20% of all college professors like all three recreations. This is because the given information states that 45% of college professors like any given pair of recreations. If 20% of them like all three, it means that the remaining 25% (45% - 20%) would have to like two recreations, which contradicts the given data.

(b) The smallest percentage who could like all three recreations is 0%. Since the information states that 50% of college professors like chess and 65% like bridge, it means that at most, 50% (the percentage who like chess) can like both chess and bridge. Therefore, there is no overlap between those who like chess and bridge, and those who like tennis. Hence, the smallest percentage who could like all three recreations is 0%.

Answer: it would take 3.1 months

Step-by-step explanation:

Let m represent the number of months that that it will take either of the runners to have the same amount of money in their accounts.

Let y represent the total amount that runner 1 saves for m months

Let z represent the total amount that runner 2 saves for m months

The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. This means that the total amount that he will save for m months would be

y = 112 + 45 + 25m

y = 157 + 25m

The second runner has $50 in savings and will save $60 each month. This means that the total amount that he will save for m months would be

z = 50 + 60m

To determine the number of months before the amount in the account of both runners becomes the same, we would equate y to z. It becomes

157 + 25m = 50 + 60m

157 - 50 = 60m - 25m

35m = 107

m = 107/35

m = 3.06

Answer:

Repeaters.

Step-by-step explanation:

This is essential to effective communication because your EMS system must use Repeaters.

These are machines used to carry signals across a great distance. We may be in ambulances or put around an EMS network in different areas. The repeater receives and re transmits signals from lower power systems, such as mobile and handheld phones, to a higher power.

Final answer:

When using portable radios in an EMS system, waiting before speaking is necessary to prevent frequency interference with medical equipment like AEDs. This ensures effective communication and prevents disruptions with critical equipment operations.

Explanation:

When using a portable radio and instructed to push the "press to talk" button and wait one second before speaking, it is essential for effective communication because it ensures that the EMS system has time to establish a clear connection. This waiting period is crucial because communications or medical equipment may use similar radio frequencies. Interruptions and interference on these frequencies can arise from external devices, such as mobile phones operating at 1.9 GHz. Moreover, important medical devices, like automated external defibrillators (AEDs), which provide verbal instructions during cardiac emergencies, rely on these frequencies to function correctly without disruption. Therefore, allowing a small delay ensures that all emergency communication and equipment can operate without interference.

Additionally, speaking slowly and clearly is also vital to ensure that the message is conveyed accurately, especially in situations where there might be wi-fi delays or microphone malfunctions.

Answer:

  30 seats

Step-by-step explanation:

The problem statement tells you 30 seats are broken.

___

It does not say 30 seats in each row are broken.

Answer:

Option C)  Any three numbers, each of which is squared is correct

Step-by-step explanation:

By using Pythagorean Theorem:

 Pythagorean theorem is also called as Pythagoras' theorem. It is a fundamental relation among the three sides of a right triangle.

It states that the length of the square of hypotenuse side is equal to the sum of the lengths of the squares of the opposite side and adjacent side.

[tex]a^{2}+b^{2}=c^{2}[/tex]  

where c is the length of the hypotenuse side and a and b are the lengths of the  opposite and adjacent sides of  triangle's.

Therefore Option C)  Any three numbers, each of which is squared is correct

Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem.

Pythagorean triples are sets of three whole numbers (a, b, and c) that satisfy the equation a² + b² = c². This equation is derived from the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. In a Pythagorean triple, the square of the larger numbers is equal to the sum of the squares of the smaller numbers. For example, the triplet (3, 4, 5) is a Pythagorean triple because 3² + 4² = 5² (9 + 16 = 25).