Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then sele

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.

Solution:

We know, g(x) = f(x) + k --------(1)

It is given that f(x) = (x+2)

and g(x) = (x+5)

Substituting f(x) and g(x) into equation (1):

→ (x+5) = (x+2) + k

→ = k

→ k =

Thus, the value of k is 1.

The true value is 25.7 ml.
The calculated error is 15.6%.
Thus, the error amount equals 0.156 times 25.7, which calculates to 4.0092 ml.

The percentage error indicates that the student's measurement could either exceed or fall short of the true value by this error amount.

This leads to two potential readings:
one possibility is: 25.7 + 4.0092 = 29.7092 ml
the other possibility is: 25.7 - 4.0092 = 21.6908 ml