Answer:
The equation can define y as a function of x and it also can define x as a function of y.
Step-by-step explanation:
A relation is a function if and only if each value in the domain is mapped into only one value in the range.
So, if we have:
f(x₀) = A
and, for the same input x₀:
f(x₀) = B
Then this is not a function, because it is mapping the element x₀ into two different outputs.
Now we want to see it:
x + y = 27
defines y as a function of x.
if we isolate y, we get:
y = f(x) = 27 - x
Now, this is a linear equation, so for each value of x we will find an unique correspondent value of y, so yes, this is a function.
Now we also want to check if:
x + y = 27
defines x as a function of y.
So now we need to isolate x to get:
x = f(y) = 27 - y
Again, this is a linear equation, there are no values of y such that f(y) has two different values. Then this is a function.
Answer:
Continuous random variables: c and e
Discrete random variables: a, b, d
Step-by-step explanation:
We have to identify whether the random variable is discrete or continuous.
- A discrete variable is a variable whose value is obtained by counting.
- A continuous random variable X takes all values in a given interval of numbers.
- Thus, a continuous variable can have values in decimals but a discrete random variable cannot take values in decimals.
a. The number of statistics students now reading a book.
Discrete random variable since number of students cannot take decimal values.
b. The number of textbook authors now sitting at a computer.
Discrete random variable since number of textbooks cannot be expressed in decimals but counted.
c. The exact time it takes to evaluate 27 plus 72.
It is a continuous random variable as it may take all values within an interval of time.
d. The number of free dash throw attempts before the first shot is made.
It is a discrete random variable since the number of throws can always be whole number.
e. The time it takes to fly from City Upper A to City Upper B.
Time is a continuous random variable.
Answer:
The probability that a ship that is declared defecive is sound is 0.375
Step-by-step explanation:
Let P(A|B) denote the conditional probability of A given B. We will make use of the equation
P(A|B) = P(A) × P(B|A) / P(B)
We have the probabilities:
- P(Declared Defective (detected) | Defective) = 0.95
- P(not Detected | Defective) = 1-0.95=0.05
- P(Declared Sound | Sound) = 0.97
- P(Declared Defective |Sound) = 1-0.97=0.03
We can calculate:
P(Declared Defective)= P(Detected | Defective)×P(Defective) + P(Declared Defective |Sound) ×P(Sound) = 0.95×0.05 + 0.03×0.95=0.076
P(S | Declared Defective) =
(P(Sound) × P(Declared Defective | Sound)) / P(Declared Defective)
=0.95×0.03 /0.076 =0.375
Answer:
x=8
Step-by-step explanation:
44-20=24
24/4=8
