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3 years ago

If 5 tennis balls are put into 4 boxes, use the Pigeonhole principle to show that at least one box will contain 2 tennis balls

Mathematics

2 answers:

docker41 [41]3 years ago

5 0

Answer:

Step-by-step explanation:

Well one of the first things you could do is put all 5 into one box. That means that that box contains at least 2 tennis balls.

Next being given to experiment, you put 2 balls in 1 box and 3 in another and the condition of 1 box containing at least 2 balls is still met.

So you do the best thing you can. You take 4 balls and put one in each box. So far you have not met the condition of the problem.

But you have one ball in your hand. Wherever you put the tennis ball, it must be in one of the boxes. That will meet the condition of the problem. One box has to have 2 balls in it.

Nataly_w [17]3 years ago

4 0

Answer:

If 5 tennis balls are put into 4 boxes, with 5 tennis balls > 4 boxes, then at least one box will contain more than 1 tennis ball.

Step-by-step explanation:

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Anastasia’s mom baked a giant sugar cookie for her birthday. On her birthday, ⅝ of the birthday cookie was eaten. The next day h

devlian [24]

Answer:

9/32 of the cookie was left for Stephanie to eat after lunch

Step-by-step explanation:

Anastasia’s mom baked a giant sugar cookie for her birthday.

On her birthday, ⅝ of the birthday cookie was eaten.

So, remaining cake = $1 - \frac{5}{8}=\frac{3}{8}$

The next day her brother ate ¼ of what remained.

Amount of cake eaten by her brother = $\frac{1}{4}(\frac{3}{8})=\frac{3}{32}$

So, remaining cake = $\frac{3}{8}-\frac{3}{32}=\frac{12-3}{32}=\frac{9}{32}$

Hence 9/32 of the cookie was left for Stephanie to eat after lunch

6 0

3 years ago

Five less than the area of a square is 59 square feet. Find the side length of the square.

In-s [12.5K]

Answer:

4 feet

Step-by-step explanation:

Let the side length of the square be x feet.

x^2 - 5 = 59

x^2 = 64

x = ±4 (reject - 4 since length > 0)

Topic: Areas of polygons

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

6 0

3 years ago

A patio in the shape of a semicircle has a diameter of 21 ft.

nikklg [1K]

The answer is 173 ft²

The area of the patio (A) is half of the area of the circle (A1) with a diameter of 21 ft:
A = A1/2

The area of the circle with radius r is:
A1 = π * r²
π = 3.14
We do not have the radius, but we know that it is a half of the diameter:
r = 21 ft / 2 = 10.5 ft

A1 = 3.14 * (10.5)² = 346.18 ft²

So, the area of the patio is:
A = A1/2
A = 346.18 ft² / 2
A = 173.09 ft² ≈ 173 ft²

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3 years ago

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Shkiper50 [21]

Smallest to biggest % then divide

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3 years ago

What is the order pair for the question y=-3x-3

posledela

Answer:

You get two, (0,-3) and (1,0)

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3 years ago