Answer:
x = 2
Step-by-step explanation:
Using Pythagoras' identity on each of the 3 right triangles
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Outer right triangle
x² + z² = (9 + 4)² = 13² = 169, that is
x² + z² = 169 → (1)
Left right triangle
y² + 4² = x²
y² + 16 = x² ⇒ y² = x² - 16 → (2)
Right right triangle
z² = y² + 9²
z² = y² + 81 → (3)
Substitute (3) into (1)
x² + y² + 81 = 169 ← substitute (2) into here
x² + x² - 16 + 81 = 169
2x² + 65 = 169 ( subtract 65 from both sides )
2x² = 104 ( divide both sides by 2 )
x² = 52 ( take the square root of both sides )
x =
=
= ×
= 2
Answer:
Step-by-step explanation:
We have the compound inequality:
Let's solve each of them individually first:
We have:
Divide both sides by 2:
Add 1 to both sides:
We have:
Subtract from both sides:
Divide both sides by -4:
Hence, our solution set is:
Answer:
19.51% probability that none of them voted in the last election
Step-by-step explanation:
For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. 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.
42% of Americans voted in the previous national election.
This means that
Three Americans are randomly selected
This means that
What is the probability that none of them voted in the last election
This is P(X = 0).
19.51% probability that none of them voted in the last election