Answer:
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
16%
Step-by-step explanation:
First, calculate the z-score.
z = (x − μ) / σ
where x is the value,
μ is the mean,
and σ is the standard deviation.
z = (12.5 − 11) / 1.5
z = 1
What this means is that 12.5 is 1 standard deviation above the mean.
According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations. That means 32% is outside of that range. Since normal distributions are symmetrical, we can say that 16% is less than -1 standard deviations, and 16% is greater than +1 standard deviations.
Therefore, the probability that a man's shoe is greater than or equal to 12.5 (greater than +1 standard deviations) is 16%.
Answer:
The solution of the differential equation is .
Step-by-step explanation:
The first step is to take Laplace transform in both sides of the differential equation. As usual, we denote the Laplace transform of as . Then,
In the last step we use that and .
Notice that our differential equations becomes an algebraic equation for , which is more simple to solve.
In the expression we have obtained, we can write in terms of :
which is equivalent to
.
Now, we make a partial fraction decomposition for the term . Thus,
.
Substituting the above value into the expression for we get
) in both hands of the above expression. Recall that . So,
.
To obtain this we have used the following identities that can be found in any table of Laplace transforms