Answer:
Step-by-step explanation:
You already have this set up to answer your question. This quadratic is in work form, aka vertex form, where the vertex is (3.5, 15). The first coordinate of the vertex is the time it takes to reach its max height, which is the second coordinate of the vertex. So it takes 3.5 seconds to reach a max height of 15 meters.
Answer:
Proved
Step-by-step explanation:
Given
Required
Prove by induction
Increment n by 1 on both sides
Simplify the right hand side
Group the left hand side
Recall that
----[Given]
So; Substitute for on the left hand side
Open All Brackets
Collect Like Terms
<em>Notice that the expression on both sides are equal;</em>
<em>Hence, the given expression has been proven</em>
Answer:
P(144.5≤X≤155.5)= 0.4176
Step-by-step explanation:
Hello!
Your study variable is:
X: Tensile strength of artificial silk fibers. (MJ/m³)
X~N(μ;σ²)
μ= 150 MJ/m³
σ= 10 MJ/m³
Since the only tabulated normal distribution is the standard normal, to obtain the probability that the tensile strength will be between 144.5 and 155.5 MJ/m³ you need to transform the study variable in terms of the standard normal distribution.
To do this transformation, known as standardization, you have to subtract the variable its mean and divide it by its standard deviation.
The first step is to present the probability symbolically:
P(144.5≤X≤155.5)= P(X≤155.5) - P(X≤144.5)
Now you standardize each term using the standard normal Z=(X-μ)/δ
P(Z≤(155.5-150)/10) - P(X≤(144.5-150)/10)
P(Z≤0.55) - P(Z≤-0.55)
The next step is to look for the values in the table to reach the cumulative probability for each of them.
The standard normal table has two sides, the left one shows the accumulated probabilities for negatives values of Z and the right one shows values of accumulated probabilities for positive values of Z. The first column shows the values of the integer plus first decimal of the Z value, the first row shows the second decimal of the Z value, by crossing them both you reach the probability value. (see attachment)
P(Z≤0.55) - P(Z≤-0.55)= 0.7088 - 0.2912= 0.4176
I hope it helps!
The probability any one system works is 0.99
So the probability of any one system failing is 1-0.99 = 0.01, so basically a 1% chance of failure for any one system
Multiply out the value 0.01 with itself four times
0.01*0.01*0.01*0.01 = 0.000 000 01
I'm using spaces to make the number more readable
So the probability of all four systems failing is 0.00000001
Subtract this value from 1 to get
1 - 0.00000001 = 0.99999999
The answer is 0.99999999 which is what we'd expect. The probability of at least one of the systems working is very very close to 1 (aka 100%)