Answer:

Step-by-step explanation:

Answer:
46
Step-by-step explanation:
Its adding 12 each time
Answer:
a) 98.01%
b) 13.53\%
c) 27.06%
Step-by-step explanation:
Since a car has 10 square feet of plastic panel, the expected value (mean) for a car to have one flaw is 10*0.02 = 0.2
If we call P(k) the probability that a car has k flaws then, as P follows a Poisson distribution with mean 0.2,
a)
In this case, we are looking for P(0)
So, the probability that a car has no flaws is 98.01%
b)
Ten cars have 100 square feet of plastic panel, so now the mean is 100*0.02 = 2 flaws every ten cars.
Now P(k) is the probability that 10 cars have k flaws and
and
And the probability that 10 cars have no flaws is 13.53%
c)
Here, we are looking for P(1) with P defined as in b)
Hence, the probability that at most one car has no flaws is 27.06%
Answer:
(a) B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
(b) Every function of the form
is an antiderivative of 8x
Step-by-step explanation:
A function <em>F </em>is an antiderivative of the function <em>f</em> if

for all x in the domain of <em>f.</em>
(a) If
, then
is an antiderivative of <em>f </em>because

Therefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of <em>f</em>.
(b) Because

then
is an antiderivative of
. Therefore, every antiderivative of 8x is of the form
for some constant C, and every function of the form
is an antiderivative of 8x.