Which input value produces the same output value for the two functions on the graph?
2 answers:
The input value yielding the same output for both graphed functions is . Choice (b) is the correct answer.
Explanation:
Here are the options:
(a)
(b)
(c)
(d)
Output values correspond to the range of a function, while input values constitute its domain.
A one-to-one function assigns a unique domain value to each range element.
The functions are depicted as . From the graph, the two lines intersect at
.
Therefore, the input that produces identical outputs is , confirming that option (b) is correct.
You might be interested in
Answer:
(A) 0.15625
(B) 0.1875
(C) Cannot be determined
Step-by-step explanation:
The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let's denote X as the duration needed for the student to complete the statistics quiz
Thus, X ~ U(32, 64)
The probability density function (PDF) for a uniform distribution is expressed as;
f(X) = , a < X < b where a = 32 and b = 64
The cumulative distribution function (CDF) is given by P(X <= x) =
(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 - = 1 -
=
= 0.15625
(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) = =
= 0.34375
P(X < 37) = =
= 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) The probability that a student takes exactly 44.74 minutes to complete the quiz
= P(X = 44.74)
This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.
Part A
To identify the values of x that make 2x−1 positive
⇒ 2x - 1 > 0
⇒ 2x > 1
⇒ x >
Part B
To find values of y making 21−37 negative
⇒ 21-3y < 0
⇒ 21 < 3y
⇒ 7 < y
Thus, for all y values exceeding 7, the expression 21-3y is negative
Part C
To identify values of c that digit 5−3c greater than 80
⇒ 5-3c > 80
⇒ -3c > 75
⇒ -c > 25
⇒ c < -25
Therefore, for values of c less than -25, the expression 5-3c surpasses 80