MATHEMATICIANS. HELP ME Out!?

Question

I want any one who can help me to know that i fully appreciate their help. EVEN if it's one two or 3.


1. We toss a coin seven times.
(a) How many outcomes are possible?
(b) How many different ways can we get two times heads and five times tails?

2. We throw a die twice.
(a) How many outcomes are possible where the sum of the two numbers rolled is less than
…five?
(b) How many outcomes are possible where the two numbers rolled are different?

3, (This problem is about the fact that 20+20 is not always 40:) Ten years ago, the population
of a town was 60 000. After five years, the population has increased by 20%. After another five years, the population again has increased by 20%.
(a) How many people live in the town today?
(b) By what percent did the population grow in the last ten years?

Answer 1

1. We toss a coin seven times.
(a) How many outcomes are possible?

Each flip results in two possible outcomes so the number of possible outcomes is 2^7 = 128.

(b) How many different ways can we get two times heads and five times tails?

7C2 = 7!/(2!*5!) = 6*7/2 = 21
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2. We throw a die twice.
(a) How many outcomes are possible where the sum of the two numbers rolled is less than five?

The only possibilties are sums of 2, 3, and 4.
The number of ways to get
Sum 2 = 1 and is {1,1}
Sum 3 = 2 and are {1,2} and {2,1}
Sum 4 = 3 and are {1,3}; {2,2}; and {3,1}

For a total of 6.

(b) How many outcomes are possible where the two numbers rolled are different?

There are 6^2 = 36 possible outcomes altogether. All but doubles results in different numbers being rolled. There are 6 possible doubles. So the possible number of non-doubles is

36 - 6 = 30
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3) (This problem is about the fact that 20+20 is not always 40:) Ten years ago, the population of a town was 60,000. After five years, the population has increased by 20%. After another five years, the population again has increased by 20%.
(a) How many people live in the town today?

To increase something by 20% multiply by 1.2. If this happens twice you have multiplied by 1.20² = 1.44

Population today is 60,000*(1.2²) = 86,400

(b) By what percent did the population grow in the last ten years?

Percentage Growth = 100*[(86,400-60,000)/60,000]
= 100*[(26,400)/60,000] = 44%

Answer 2

1.
(a) 2^7=128
(b) number of combinaisons of 2 in 7
6x7/2=21


2. We throw a die twice.
(a) 1+1, 1+2, 1+3, 2+1, 2+2, 3+1 =6 possibilities
(b) 4 possibilities

3.
(a) now=60000*1.2*1.2=86400
(b) 86400/60000=1.44 => 44%

Answer 3

My first thought became they have been a base-7 society via fact that there have been 7 symbols (a,b,e,l,n,p,r) of their "huge style" equipment. even nonetheless, while i attempted to return up with values for each letter I have been given caught. including a 5 digit huge style to a 4 digit huge style could basically effect in a 6 digit huge style that starts off with 10...., yet that should mean that A = 0, B = a million. yet that now makes APPLE initiate with a nil and that messes each little thing up. i will could think of a splash extra in this...

Answer 4

I'll take #3, since most other people will take #1 or #2, I think.

Start with 60,000 people. 20% more is 60,000 times 20% = 12,000.
Now you have 60,000 + 12,000 = 72,000 people.
Then, you add 20% more
72,000 times 20% = 14,400 people
72,000 + 14,400 = 86,400 people

The total increase for 10 years is 12,000 + 14,400 = 26,400.

What % is 26,400 of 60,000 ?
26,400 / 60,000 = 44%