First of way to many questions, but Ill answer them
1) 5/9, 75/135 2) 5/11 3) 10/3 4) 13 quarts 5) 120 6) in 108 minutes
7) 3/4<33/40 8) 3/8<2/3<19/24
It is given the probability that a dancer like ballet is 0.35
So, P(B) = 0.35
It is given the probability that a dancer like tap is 0.45
So, P(T)= 0.45
The probability that he likes both ballet and tap is 0.30
So, 
the probability that the dancer likes ballet if we know she likes tap. This is the case of conditional probability.
So, 
= 0.666
= 0.67
Therefore, the probability that the dancer likes ballet if we know she likes tap is 0.67.
Option 3 is the correct answer.
2 inches : 6 feet is the same as 1 inch : 3 feet
It could also be written:
1 inch : 36 inches
1 foot : 36 feet
Answer:
The two equations are
y = x - 3 and
3y = x + 9
Step-by-step explanation:
The options are not well stated. I'll answer the question without the options but however, my answer will be a reflection of one of the given options.
Given:
2 statements
Required
Write equivalent of both statements as equations
Let the large number be represented by x.
From the first statement (y, is equal to the difference of a larger number and 3)
Difference means minus (-); so, this statement is represented as follows to give us the first equation:
y = x - 3
From the second statement (The same number is one-third of the sum of the larger number and 9).
This is also represented as follows to give us the second equation
y = ⅓(x + 9)
Multiply both sides by 3
3 * y = 3 * ⅓(x + 9)
3y = x + 9
So, the two equations are
y = x - 3 and
3y = x + 9
