The sets of numbers 7, 24, 25 and 9, 40, 41 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean Triples. Be sure to show your work for each set of triples! ​

Answer:

The answer is A.

Step-by-step explanation:

Answer: Remember, the formula to calculate combinations is nCr = n! / r! * (n - r)!, where n represents the number of items, and r represents the number of items being chosen at a time.

Step-by-step explanation:

Answer: clockwise

Step-by-step explanation:

hope this helps<3

The required diagram could be used to represent the context if x represents how much each bottle of juice cost is D. Option D is correct.

Given that,
She bought a bag of popcorn for $3.39 and a 4-pack of juice bottles. The total cost before tax was $7.43.
To determine the diagram could be used to represent the context if x represents how much each bottle of juice costs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the cost of each juice bottle be x.
Now,
accoding to the question,
4x = 7.43 - 3.39

Thus, the required diagram could be used to represent the context if x represents how much each bottle of juice cost is D. Option D is correct.

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Answer:

here side of cube is 3 cm..

Step-by-step explanation:

side = 3 cm

we know that...

volume of cube =s^3

=3^3

=27Cubic cm

Answer:

9

Step-by-step explanation:

3x3=9 think about it should be right

Answer:

Step-by-step explanation:

9x^2+kx+1=0

k= -9x-1/x

The area of the figure is 13 cm².

We have,

From the figure,

We can make two rectangles.

Now,

Length = 5 cm

Width =  1 cm

Area of one rectangle.

= 5 x 1

= 5 cm²

Length = 4 cm

Width = 2 cm

Area of another rectangle.

= 4 x 2

= 8 cm²

Now,

Area of the figure,

= 5 + 8

=  13 cm²

Thus,

The area of the figure is 13 cm².

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Answer:

step 3

Step-by-step explanation:

it's C on edg

Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

Using the substitution method, the solution to a system of equations is solved by finding one variable in one of the equations, then substituting it to find the other variable.

Given, the systems of equations as:

Thus, Ernesto made his first error in Step 3 because he failed to apply the distribution property properly. It should be 3y + 21 - 2y = 8 instead of 3y + 7 – 2y = 8.

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The solution of the linear system using the Gauss-Jordan elimination method is x = 2, y = -3, z = -1.

To solve the system, we can start by representing the given equations in augmented matrix form:

| 1 1 -1 | 5 |

| 3 -1 1 | -9 |

| 1 0 4 | 3 |

Next, we'll perform row operations to transform the matrix into row-echelon form. The goal is to create zeros below the leading coefficient in each row. We'll achieve this by multiplying rows by appropriate factors and adding or subtracting them from other rows. The steps involved in performing the Gauss-Jordan elimination method are as follows:

Step 1: Multiply the first row by 3 and subtract it from the second row to eliminate the x-term below the leading coefficient in the second equation.

| 1 1 -1 | 5 |

| 0 -4 4 | -24 |

| 1 0 4 | 3 |

Step 2: Multiply the first row by 1 and subtract it from the third row to eliminate the x-term below the leading coefficient in the third equation.

| 1 1 -1 | 5 |

| 0 -4 4 | -24 |

| 0 -1 5 | -2 |

Step 3: Multiply the second row by -1/4 to make the leading coefficient of the second equation equal to 1.

| 1 1 -1 | 5 |

| 0 1 -1 | 6 |

| 0 -1 5 | -2 |

Step 4: Multiply the second row by 1 and add it to the first row to eliminate the y-term below the leading coefficient in the first equation.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 -1 5 | -2 |

Step 5: Multiply the second row by 1 and add it to the third row to eliminate the y-term below the leading coefficient in the third equation.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 0 4 | 4 |

Step 6: Multiply the third row by 1/4 to make the leading coefficient of the third equation equal to 1.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 0 1 | 1 |

Step 7: Multiply the third row by 2 and add it to the first row to eliminate the z-term above the leading coefficient in the first equation.

| 1 0 0 | 13 |

| 0 1 -1 | 6 |

| 0 0 1 | 1 |

Step 8: Multiply the third row by -1 and add it to the second row to eliminate the z-term above the leading coefficient in the second equation.

| 1 0 0 | 13 |

| 0 1 0 | 7 |

| 0 0 1 | 1 |

The resulting matrix represents the row-echelon form of the system. Now, we'll perform back substitution to find the values of x, y, and z.

From the row-echelon form, we can deduce that x = 13, y = 7, and z = 1.

Therefore, the solution to the given system of equations is x = 2, y = -3, z = -1.

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A diverse workforce can provide a source of competitive advantage by suggesting goods and services that will allow the company to increase its market by catering to a broader customer base.

When an organization embraces diversity and inclusion, it brings together individuals from different backgrounds, cultures, experiences, and perspectives. This diverse pool of employees can offer unique insights and ideas that might otherwise go unnoticed, leading to innovative product development and improved customer experiences.

By having a workforce that represents a wide range of demographics, including race, ethnicity, gender, age, sexual orientation, and more, a company can better understand the needs and preferences of various customer segments. This understanding enables them to develop and market products and services that resonate with a larger audience, ultimately increasing market share and revenue.

A diverse workforce enhances creativity and problem-solving abilities within the organization. Diverse teams bring different ways of thinking and approaching challenges, fostering an environment of innovation and adaptability. This can lead to the development of groundbreaking solutions that meet the evolving demands of an increasingly diverse consumer market.

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Answer:

\(\huge\boxed{\sf m = 11}\)

Step-by-step explanation:

-7m + 10m - 8 = 25

3m - 8 = 25

Add 8 to both sides

3m = 25 + 8

3m = 33

Divide 3 to both sides

m = 33/3

m = 11

\(\rule[225]{225}{2}\)

(a) the lοcal maximum fοr the revenue functiοn οccurs at x = 50.

(b) the range οf x is 0 < x < 80, there are nο intervals οn which the graph οf the revenue functiοn is cοncave upward.

(c) the range οf x is 0 < x < 80, the graph οf the revenue functiοn is cοncave dοwnward fοr the interval 0 < x < 80.

revenue is the tοtal amοunt οf incοme generated by the sale οf gοοds and services related tο the primary οperatiοns οf the business.

a. Tο find the lοcal extrema fοr the revenue functiοn R(x) =\(1275x - 0.17x^3,\) we need tο find the critical pοints by taking the derivative οf the functiοn and setting it equal tο zerο.

\(R'(x) = 1275 - 0.51x^2\)

Setting R'(x) = 0 and sοlving fοr x:

\(1275 - 0.51x^2 = 0\)

\(0.51x^2 = 1275\)

\(x^2 = 2500\)

x = ±50

We have twο critical pοints: x = -50 and x = 50.

Tο determine whether these critical pοints are lοcal maxima οr minima, we can examine the secοnd derivative οf the functiοn.

R''(x) = -1.02x

Evaluating R''(x) at the critical pοints:

R''(-50) = -1.02(-50) = 51

R''(50) = -1.02(50) = -51

Since R''(-50) > 0 and R''(50) < 0, the critical pοint x = -50 cοrrespοnds tο a lοcal minimum, and x = 50 cοrrespοnds tο a lοcal maximum fοr the revenue functiοn.

Therefοre, the lοcal maximum fοr the revenue functiοn οccurs at x = 50.

b. The graph οf the revenue functiοn is cοncave upward when the secοnd derivative, R''(x), is pοsitive.

R''(x) = -1.02x

Fοr R''(x) tο be pοsitive, x must be negative. Since the range οf x is 0 < x < 80, there are nο intervals οn which the graph οf the revenue functiοn is cοncave upward.

c. The graph οf the revenue functiοn is cοncave dοwnward when the secοnd derivative, R''(x), is negative.

R''(x) = -1.02x

Fοr R''(x) tο be negative, x must be pοsitive. Since the range οf x is 0 < x < 80, the graph οf the revenue functiοn is cοncave dοwnward fοr the interval 0 < x < 80.

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The fishing boat traveled for 14 hours before the cruise ship caught up.

We have,

Let's assume that the fishing boat traveled for x hours before the cruise ship caught up.

In that time, the fishing boat covered a distance of 10x km.

During the same 10 hours, the cruise ship traveled 14 x 10 = 140 km.

Since both the fishing boat and the cruise ship covered the same distance, we can write:

10x = 140

Solving for x, we get:

x = 14

Therefore,

The fishing boat traveled for 14 hours before the cruise ship caught up.

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U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A = {1, 3, 5, 7, 9}

B = {2, 4, 5, 6, 7}.

A = {1, 3, 5, 7, 9}

B' = {1,3,8,9,10}

A U B' = {1,3,5,7,8,9,10}

Answer:

A U B' = {1,3,5,7,8,9,10}

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

Answer:

Step-by-step explanation:

1) a + a

2) 2n+4 = 6n

3)   1

4n = 4

n = 1

The standard deviation for the given probability distribution is approximately 1.13.

To find the standard deviation for the given probability distribution, follow these steps:

1. Calculate the mean (μ): μ = Σ[x × P(x)]
2. Calculate the variance (σ²): σ² = Σ[(x - μ)² × P(x)]
3. Find the standard deviation (σ): σ = √σ²

Using the given probability distribution:

1. Calculate the mean (μ):
μ = (0 × 0.37) + (1 × 0.05) + (2 × 0.13) + (3 × 0.25) + (4 × 0.20) = 0 + 0.05 + 0.26 + 0.75 + 0.80 = 1.86

2. Calculate the variance (σ²):
σ² = [(0 - 1.86)² × 0.37] + [(1 - 1.86)² × 0.05] + [(2 - 1.86)² × 0.13] + [(3 - 1.86)² × 0.25] + [(4 - 1.86)² × 0.20] = 1.2782

3. Find the standard deviation (σ):
σ = √1.2782 ≈ 1.13

So, the standard deviation for the given probability distribution is approximately 1.13.

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According to the given statement the teenagers went to the zoo = 300

First order equations include linear equations. In the coordinate system, the linear equations have been defined for lines. A linear equation throughout one variable is one in which there is a homogeneous variable having degree 1 (i.e., only one variable). many  variables have present in a linear equation.

6a+4c+5t = 5300......................(equation)

a+c+t = 1200

3c-8t = 0

So,

Putting the value a= 1/6

6a+4c+5t = 5300

0.333c+0.167t = 316.667

3c-8t = 0

solving for the value of t:

6a+4c+5t = 5300

3c-8t = 0

1.056t = 316.667

So,

t = 316.66666667/1.05555556

= 300

According to the given statement the teenagers went to the zoo = 300.

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The diameter of the circle is 12.5 inches

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: 157 breaks required to make a circular garden and cover the boundary.

Now each brick is 4 inches long

Thus total length of the circumference of the circular garden we get

157/4=39.25 inches long

Thus the circumference of the circle is given by

2πr=39.25

2r=39.25/3.14

d=12.5 inches

Thus the diameter is 12.5 inches.

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Answer:

the answer you are looking for is -5<n<4

Answer:

−6<3n+9<21

−6+−9<3n+9+−9<21+−9(Add -9 to all parts)

−15<3n<12

−15

3

<

3n

3

<

12

3

(Divide all parts by 3)

−5<n<4

Step-by-step explanation:

hello

from the point on the graph, we can notice that it is in between (-3) and (-2) value. this corresponds to -(2 1/2).

But then the absolute value of this number would be

the value of the answer corresponds to option D

We can determine that events A and B are dependent.

Based on the given information, we can determine if the events A and B are dependent or not. Two events are considered dependent if the occurrence of one event affects the probability of the other event occurring.

In this case, we know that the probability of event A occurring given that event B happens is 0.7. This suggests that the occurrence of event B affects the probability of event A occurring. Therefore, we can conclude that events A and B are dependent.

Moreover, we can use the formula for conditional probability to calculate the probability of both events occurring together. The formula states that the probability of A and B occurring together is equal to the probability of A given B multiplied by the probability of B.

P(A and B) = P(A | B) x P(B)
P(A and B) = 0.7 x 0.2
P(A and B) = 0.14

This means that the probability of events A and B occurring together is 0.14, which is relatively low. However, since the events are dependent, it is important to consider the occurrence of event B when calculating the probability of event A.

In conclusion, based on the given information, we can determine that events A and B are dependent, and we can calculate the probability of both events occurring together using the formula for conditional probability.

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Answer:

A. Inside the circle

Step-by-step explanation:

K(0, 0), U (6, - 4), V (\( \sqrt 2,\: 7)\)

In order to determine whether point V lie inside, outside or on the circle, first we will find the distances between points K & U and then K & V.

KU would be radius of the circle.

\(d(KU) = \sqrt{ {(6 - 0)}^{2} + {( - 4 - 0)}^{2} } \\ = \sqrt{ {6}^{2} + {( - 4)}^{2} } \\ = \sqrt{36 + 16} \\ \red{ \bold{ d(KU)= \sqrt{52} }} \\ \\ d(KV) = \sqrt{ {( \sqrt{2} - 0)}^{2} + {( 7 - 0)}^{2} } \\ = \sqrt{ {( \sqrt{2)} }^{2} + {(7)}^{2} } \\ = \sqrt{2 + 49} \\ \purple{ \bold{ d(KV)= \sqrt{51} }} \\ \\ \because \: d(KU) > d(KV) \\ \)

Hence point V lie inside of the circle.

The plumber bought 10 pieces of copper pipe and 6 pieces of plastic pipe. Let's start by assigning variables to the unknown quantities.

- Let's call the number of copper pipes that the plumber bought "c". Let's call the number of plastic pipes that the plumber bought "p".

We can then use this information to set up two equations:
- The total number of pipes bought is 16:

c + p = 16

- The total length of the pipes bought is 40 meters:

7c + 1p = 40

Now we have two equations with two variables, which we can solve using algebra.

First, let's solve for one of the variables in terms of the other. We'll use the first equation:

c + p = 16

c = 16 - p

Now we can substitute this expression for "c" into the second equation:

7c + 1p = 40

7(16 - p) + p = 40

112 - 6p = 40

-6p = -72

p = 12

So the plumber bought 12 pieces of plastic pipe. We can substitute this value back into our expression for "c":

c = 16 - p

c = 16 - 12

c = 4

So the plumber bought 4 pieces of copper pipe.

To check our answer, we can verify that the total length of the pipes is indeed 40 meters:

7c + 1p = 7(4) + 1(12) = 28 + 12 = 40

So our solution of 4 copper pipes and 12 plastic pipes is correct.

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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The diameter of Mikayla's cereal bowl, is 5.7 in

The distance from one point on a circle through the center to another point on the circle. It is also the longest distance across the circle.

Given that, the rim of Mikayla’s cereal bowl has a circumference of 18 inches. we need to determine the diameter of the cereal bowl,

Since, the rim is circular, therefore,

Circumference of circle = π × diameter

Therefore,

π × diameter = 18

Diameter = 18 / 3.14

Diameter = 5.7

Hence, the diameter of Mikayla's cereal bowl, is 5.7 in

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Answer: 9

Step-by-step explanation: