Is -0.3 a rational number? is 3.14144144414444... a rational number?
1 answer:
I will try to make this as simple as possible.
First off, we need to know what a rational number is: A rational number is any number that can be made by dividing 2 integers. For example:
1.5 would be a rational number because 1.5 = 3/2 (3 and 2 are both integers)
With that being said, let's begin.
First off, let's start with -0.3, let's ask ourselves, can we make this number by dividing 2 integers, the answer is yes, we can, by doing we have the equivalent of -0.3, so now we know it's a rational number.
As for the second one, it can't be a rational number because it can't be made by dividing to integers, so the answer is:
-0.3 is a rational number, but 3.14144144414444 is not.
Hope this helped! c:
You might be interested in
Answer:
(a) P(X 20) = 0.9319
(b) Expected number of defective light bulbs = 15
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.