Question 18 of 25
1 answer:
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Answer:
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
Step-by-step explanation:
If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it sweeps an area of 48 cm, we will follow the steps below;
area of a sector = Ф/360 × πr²
where Ф is the angle, r is the radius π is a constant
from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5
Ф =? area of the sector= 48 cm² π =
we can now go ahead to substitute the values into the formula and solve Ф
area of a sector = Ф/360 × πr²
48 = Ф/360 × × (3.5)²
48 = Ф/360 × ×12.25
48 = 269.5Ф / 2520
multiply both-side of the equation by 2520
48×2520 = 269.5Ф
120960 = 269.5Ф
divide both-side of the equation by 269.5
448.8≈Ф
Ф = 448.8°
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
Answer:
a)
b)
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable that represent "life lengths of automobile tires of a certain brand" and we know that the distribution is given by:
The cumulative distribution function is given by:
Part a
We want to find this probability:
and for this case we can use the cumulative distribution function to find it like this:
Part b
For this case w want to find this probability
We have an important property on the exponential distribution called "Memoryless" property and says this:
On this case if we use this property we have this:
We can use the definition of the density function and find this probability: