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antiseptic1488 [7]
2 years ago
14

498,147,846,267+ 32,870,714,538​

Mathematics
1 answer:
san4es73 [151]2 years ago
4 0

Answer:

531018560805

Step-by-step explanation:

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How many ways can 5 people be arranged in a line?
Rasek [7]

Answer: 120 ways

Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.

Let's start by drawing 5 blanks to represent the 5 different positions in the line.

Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have <u>5</u> <u>4</u> <u>3</u> <u>2</u> <u>1</u>.

Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.

5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.

So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.

I have also shown my work on the whiteboard in the image attached.

7 0
3 years ago
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If the
notsponge [240]

Answer:

<u>The area of the rectangular field is 20,000 square meters.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of times a person jogged along the rectangular field = 10

Speed of the person jogging = 12 km per hour

Time he/she jogged = 30 minutes = 0.5 hours

Length of the field = twice its width

2. Find the area of the field in square meters.

Step A: Let's calculate the distance the person jogged

Let's recall the formula of the speed:

Speed = Distance/Time

Distance = Speed * Time

Replacing with the values we know:

Distance = 12 * 0.5

<u>Distance = 6 kilometers</u>

Step B: Let's calculate the perimeter of the rectangular field

Distance jogged = ¨Perimeter * 10

6 kilometers = Perimeter * 10

Perimeter = 6/10

<u>Perimeter = 0.6 kilometers = 0.6 * 1,000 = 600 meters</u>

Perimeter = 2 * Length + 2 * Width

x = Width of the rectangular field

2x = Length of the rectangular field

600 = 2 * 2x + 2 * x

600 = 4x + 2x

600 = 6x

<u>x = 600/6 = 100 meters ⇒ 2x = 200 meters</u>

Step C: Let's calculate the area of the rectangular field

Let's recall the formula of the area of a rectangle:

A = Length * Width

A = 200 * 100

<u>A = 20,000 m² (square meters)</u>

7 0
3 years ago
Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown.
andreev551 [17]
Do u have any answer choices?
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5 0
3 years ago
A high school held an election for class president. Exactly 1,000 votes were cast and they were all for either Gillian or Clive.
lisov135 [29]

Answer: 60%

1000÷2=500

Clive: 500-100= 400

Gillian: 500+100= 600 (Because Gillian has 100 more votes than Clive)

\frac{600}{1000} \times 100\%  = 60\%

8 0
2 years ago
Read 2 more answers
A rectangle has a fixed perimeter of 350 but the length and width of the rectangle can vary. Define a function g that determines
Verdich [7]

Answer:

g(L) = 175L - L²

Step-by-step explanation:

350 = 2(length + width)

length + width = 175

Let L be the length,

L + width = 175

width = 175 - L

Area = length × width

g(L) = L(175 - L)

g(L) = 175L - L²

5 0
3 years ago
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