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AnnyKZ [126]
3 years ago
15

Katie blows up a balloon and ties it so there is a fixed amount of air in the balloon.

Mathematics
1 answer:
kifflom [539]3 years ago
8 0

Answer:

According to Charles' Law the order of arrangement of the location where the balloon has the smallest size to the location where the balloon has the largest size is given as follows;

A freezer < A cold refrigerator < A normal room temperature classroom < A warm cupboard

Step-by-step explanation:

The parameter of the balloon Katie blows are;

The amount of air in the balloon = Fixed (constant)

The initial size of the balloon = The length of the measured string

The locations in which the balloon can be placed = A freezer, a warm cupboard, a cold refrigerator, a normal temperature classroom

The size of the balloon is given by the volume of the balloon

according to Charles' Law, the volume of a given mass of gas is directly proportional to its temperature

Mathematically, Charles law can be expressed as follows;

V ∝ T

Therefore, as the temperature to which the balloon is subjected decreases, the volume decreases

The locations arranged in order of increasing temperature is given as follows;

Freezer < Cold refrigerator < Normal temperature classroom < Warm cupboard

Given that Katie blow's the balloon in a normal temperature classroom, according to Charles Law, we have;

The temperature of the air in the balloon decreases largely in a freezer, therefore, the size of the balloon largely decreases

The temperature of the air in the balloon increases in a warm cupboard, therefore, the size of the balloon increases

The temperature of the air in the balloon decreases slightly in a cold refrigerator, therefore, the size of the balloon decreases

The temperature of the air in the balloon remains the in a normal temperature classroom, therefore, the size of the balloon remains the same

The size of the balloon reduces the most in a freezer

The size of the balloon increases in a warm cupboard

The size of the balloon decreases slightly in a cold refrigerator

The size of the balloon remains the same in a normal temperature classroom.

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A universal set U consists of elements. If sets​ A, B, and C are proper subsets of U and ​n(U)​, ​n(A ​B)​n(A ​C)​n(B ​C)​, ​n(A
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Answer:

n(A\ u\ B) = 10

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Step-by-step explanation:

Given

n(U) = 12

n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6

n(A\ n\ B\ n\ C)=4

n(A\ u\ B\ u\ C)=10

Required

Solve a, b and c

There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)

Solving (a):

n(A\ u\ B)

This is calculated as:

n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)

From the attachment

n(A) = 0+2+4+2 = 8

n(B) = 0+2+4+2 = 8

n(A\ n\ B) = 4 +2 = 6

So:

n(A\ u\ B) = 8 + 8 - 6

n(A\ u\ B) = 10

Solving (b):

n(A'\ u\ C)

This is calculated as:

n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)

From the attachment

n(A) = n(U) - n(A) = 12 - 8 = 4

n(C) = 0+2+4+2 = 8

n(A'\ n\ C) = 2

So:

n(A'\ u\ C) = 4 + 8 - 2

n(A'\ u\ C) = 10

Solving (c):

n(A\ n\ B)'

This is calculated as:

n(A\ n\ B)' = n(U) - n(A\ n\ B)

n(A\ n\ B)' = 12- 6

n(A\ n\ B)' = 6

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