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Answer:
Step 1
Step 2
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
There are 400 applicants for a job
184 are male
78 are male and have a graduate degree.
Step 1 of 2: What is the probability that a randomly chosen applicant has a graduate degree, given that they are male? Express your answer as a fraction or a decimal rounded to four decimal places.
Desired outcomes:
Number of male applicants with a graduate degree, which is 78
Total outcomes:
Number of male applicants, which is 184
Probability:
Step 2 of 2: If 125 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is male, given that the applicant has a graduate degree? Express your answer as a fraction or a decimal rounded to four decimal places.
Desired outcomes:
Number of male applicants with a graduate degree, which is 78
Total outcomes:
Number of applicants with graduate degrees, which is 115
Probability:
The equation of the pair of lines perpendicular to the lines given equation is .
Solution:
Given equation is .
Let and
be the slopes of the given lines.
Sum of the roots =
– – – – – (1)
Product of the roots =
– – – – – (2)
The required lines are perpendicular to these lines.
Slopes of the required lines are
Required lines also passes through the origin,
therefore their y-intercepts are 0.
Hence their equations are:
Do cross multiplication, we get
Add x on both sides of the equation, we get
Therefore, the joint equation of the line is
Substitute (1) and (2), we get
To make the denominator same, multiply and divide first term by b.
Do cross multiplication, we get
Hence equation of the pair of lines perpendicular to the lines given equation is .