Shalondra was late making her monthly car payment last month and had to pay a late fee. Her car payment was $325.00 and she was
2 answers:
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Answer:
Step-by-step explanation:
Given is a Differential equation as
To bring it to linear form we can divide the full equation by x
This is of the form
y'+p(x) *y = q(x)
p(x) = 1/x
So find
Solution is
Use the initial value as y(e) =1
So solution is
Answer:
(a) P(X 20) = 0.9319
(b) Expected number of defective light bulbs = 15
(c) Standard deviation of defective light bulbs = 3.67
Step-by-step explanation:
We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.
Firstly, the above situation can be represented through binomial distribution, i.e.;
where, n = number of samples taken = 150
r = number of success
p = probability of success which in our question is % of bulbs that
are defective, i.e. 10%
<em>Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.</em>
So, Let X = No. of defective bulbs in a box
<u>Mean of X</u>, =
=
= 15
<u>Standard deviation of X</u>, =
=
= 3.7
So, X ~ N(
Now, the z score probability distribution is given by;
Z = ~ N(0,1)
(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X 20) = P(X < 20.5) ---- using continuity correction
P(X < 20.5) = P( <
) = P(Z < 1.49) = 0.9319
(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = =
= 15.
Standard deviation of defective light bulbs is given by = S.D. = =
= 3.67
Answer:
The correct options are:
- g(x) is shifted three units higher than f(x).
- g(x) has a period that is half the period of f(x).
Step-by-step explanation:
We have to compare the graphs of the function:
and
We have to select the correct options among the following:
As we know that the period of sine function is 2π.
i.e. Period of function f(x) is: 2π.
The period of sin(2 x) is π.
Hence, the period of the function g(x) function is π.
- Hence, the period of g(x) is half the period of f(x).
- Also we could observe that g(x) is shifted 3 units upward.
