Given:
It is stated that
PQ ⊥ PS and
∠QPR = 7x-9
∠RPS = 4x+22
To find the measure of ∠QPR.
Formula
According to the problem PR sits between PQ and PS,
Consequently,
∠QPR+∠RPS = 90°
Now,
Inserting the values for ∠RPS and ∠QPR yields
or,
or,
or,
or,
Substituting the value of into ∠QPR gives us
∠QPR =
or, ∠QPR =
So,
The measure of ∠QPR is 40°.
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.
Answer:
Yes, the cost in dollars and the quantity of yogurt
are indeed proportional.
The relationship can be expressed as:
Step-by-step explanation:
1. If varies directly with
, it can be represented as:
Here, represents the constant of proportionality.
2. We'll calculate the proportionality constant. Given that and
, we have:
3. Thus, the equation becomes:
4. Now, we need to verify proportionality. Substituting , which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:
5. They are indeed directly proportional.