The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.
Step-by-step explanation:
Let,
The longer leg = x
The shorter leg = x-7
Hypotenuse = x+7
Using Pythagoras theorem;
Either,
x= 0
Or,
x-28=0 =>x=28
As length cannot be zero, therefore,
Longer side = 28cm
Shorter side = x-7 = 28-7 = 21cm
Hypotenuse = x+7 = 28+7 = 35cm
The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.
Keywords: triangle, pythagoras theorem
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Answer:
There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
The problem states that:
The number of phone calls that Actuary Ben receives each day has a Poisson distribution with mean 0.1 during each weekday and mean 0.2 each day during the weekend.
To find the mean during the time interval, we have to find the weighed mean of calls he receives per day.
There are 5 weekdays, with a mean of 0.1 calls per day.
The weekend is 2 days long, with a mean of 0.2 calls per day.
So:
If today is Monday, what is the probability that Ben receives a total of 2 phone calls in a week?
This is . So:
There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.