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4 years ago

1. Increase £92 by 40%

Mathematics

1 answer:

yanalaym [24]4 years ago

5 0

Answer:

1. Increase £92 by 40% = £128.8

2. Increase £150 by 13% = £169.5

3. Decrease £75 by 80% = £15

4. Decrease £440 by 18% = £360.8

Step-by-step explanation:

1. Increase £92 by 40%

40/100 + 92

0.4X92

36.8

92+36.8

£128.8

2. Increase £150 by 13%

13/100 X 150

0.13X150

19.5

150+19.5

£169.5

3. Decrease £75 by 80%

80/100 X 75

0.8X75

75-60

£15

4. Decrease £440 by 18%

18/100 X 440

0.18X440

79.2

440-79.2

£360.8

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1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

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