Answer:
true
Step-by-step explanation:
10 - 5x < 6x - 8
We can treat this inequality like a normal algebraic equation.
<em><u>Add 5x to both sides</u></em>
10 < 11x - 8
<em><u>Add 8 to both sides</u></em>
18 < 11x
<em><u>Divide both sides by 11</u></em>
1.64 < x
X is greater than the value 1.64.
Let's plug the number 2 into each value of x to verify.
10 - 5x < 6x - 8
10 - 5*2) < (6 * 2) - 8
10 - 10 < 12 - 8
0 < 4
It's correct.
Now let's plug 1, which is less than 1.64.
10 - 5x < 6x - 8
10 - 5 < 6 - 8
5 < -2
This is not correct, which means that our answer was correct.
For #2, the proportion would be .40/.25 and x/15, then you would cross multiply to find x. and for #3 the proportion would be 15/6 and 75/x and again you would cross multiply to find x. (:
Answer:
47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth
Step-by-step explanation:
For each individual, there are only two possible outcomes. Either they cover their mouth when sneezing, or they do not. The probability of an individual covering their mouth when sneezing is independent of other individuals. 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.
According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.
This means that 
What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth
10 individuals, so n = 10.

In which





47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth