3/4=0.75
Since 3/4 (of the bar) + 1/4 (of the bar) equals a whole bar (1), and 3/4 (of the bar) + 0.75 equals the whole weight of the bar, 0.75 is 1/4 of the bar. 1/4 times 4 equals 1, and 0.75 times 4 equals 3, so the bar of soap weighs 3 pounds.
Answer:
Step-by-step explanation:
(-4,0) ; (-7, -14)
![d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(-7-[-4])^{2}+(-14-0)^{2}}\\\\ =\sqrt{(-7+4)^{2}+(-14)^{2}}\\\\=\sqrt{(-3)^{2}+(-14)^{2}}\\\\=\sqrt{9+196} \\\\=\sqrt{205} \\\\=14.3178](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Csqrt%7B%28-7-%5B-4%5D%29%5E%7B2%7D%2B%28-14-0%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Csqrt%7B%28-7%2B4%29%5E%7B2%7D%2B%28-14%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%28-14%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B9%2B196%7D%20%5C%5C%5C%5C%3D%5Csqrt%7B205%7D%20%5C%5C%5C%5C%3D14.3178)
Answer:
a) 0.1353
b) 0.3679
Step-by-step explanation:
Let's start by defining the random variable T.
T : ''The time (in hours) required to repair a machine''
T ~ exp (λ)
T ~ exp (1)
The probability density function for the exponential distribution is
(In the equation I replaced λ = L)

With L > 0 and x ≥ 0
In this exercise λ = 1 ⇒

For a)





For b)

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur



Answer:
10/8, 20/16
Step-by-step explanation:
Let

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

So, the base case is ok. Now, we need to assume
and prove
.
states that

Since we're assuming
, we can substitute the sum of the first n terms with their expression:

Which terminates the proof, since we showed that

as required