Mathematics
23.11.2022 06:46
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Wich is the result of 23*1/5?

Wich is the result of 23*1/5?
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davisnaziyahovz5sk
davisnaziyahovz5sk
4,8(50 marks)

23/5 as an improper fraction or  4 3/5 as a mixed number

or 4.6 as a decimal or 460% as a percent

Step-by-step explanation:

What I did: 23/1 * 1/5

For this, you just multiply numerators and denominators, getting 23/5 as your answer.

Then I simplified that fraction to get 4 and 3/5 as a mixed number. There's a number of ways you can do this, but I just knew 23 goes into 5, 4 times and added the remaining into the fraction.

For the decimal I knew 4 is just 4 as a whole number and i calculated 3/5 as .6 or 60 percent.

For the percent I just removed the decimal, or in other words, shifted the decimal 2 times to the right.

noor66
noor66
4,9(70 marks)

a) 10 weeks

b) P(k≤2)=0.190

c) P(k>17)=0.167

Step-by-step explanation:

This problem can be solved applying the geometric distribution.

The probability of needing k weeks to find an acceptable apartment can be written as:

P(k)=(1-p)^{k-1}p=0.9^{k-1}\cdot 0.1

a) The expected value of this distribution is:

E(x)=1/p=1/0.1=10

10 weeks

b) The probability of finding an acceptable department in the first 2 weeks is:

P(k\leq2)=P(1)+P(2)=0.1*0.9^0+0.1*0.9^1\\\\P(k\leq 2)=0.1+0.09=0.19

c) We have to calculate P(k>17)

P(k17)=1-\sum_1^{17}P(k_i)\\\\P(k17)=1-(P(1)+P(2)+P(3)+...+P(17))\\\\P(k17)=1-(0.1+0.09+0.081+0.073+0.066+0.059+0.053+0.048+0.043+0.039+0.035+0.031+0.028+0.025+0.023+0.021+0.019)\\\\P(k17)=1-0.833=0.167

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