Answer:
The correct option is C:
C) The representative sample contained more girls than boys.
Step-by-step explanation:
It is given that a random sample is chosen from a total students of 160 students. The sample can be of 10,15 or any small numbers of students as compared to 160. However, a sample cannot be of 160 students as it is defined as a population in this case.
A random sample is always unbiased. Which means that the sample chosen should have around the same proportion of girls to boys as it is in the population of 160.
We know that:
Total boys in 160 = 65
Total girls in 160 = 95
Proportion of girls to boys = 95/65 = 1.462
Which means that for every 1 boy, there are 1.462 of girls.
The same ratio is held in a random sample, hence the total number of girls will be greater than boys
Answer:
0.3891 = 38.91% probability that only one is a second
Step-by-step explanation:
For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
17% of its goblets have cosmetic flaws and must be classified as "seconds."
This means that 
Among seven randomly selected goblets, how likely is it that only one is a second
This is P(X = 1) when n = 7. So


0.3891 = 38.91% probability that only one is a second
Let's represent our number as x.
x is being added to 6 * x², and it equals 12

Factor:

Solve for x:

Therefore,
x = -3/2 and 4/3.
The first mistake was made in step 1 because they took out the x’s it should be 10x-25+2x+8=43
Answer:
7.2
Step-by-step explanation:
Given that in triangle LMN, LO is angle bisector of angle L.
LN =10 and LM =18
By angle bisector theorem for triangles we have
LN/LM = NO/MO
Substitute the values for known things and x for MO
We get
10/18 = 4/x
Or cross multiply to get
10x=72
x=7.2
So answer is 7.2