Answer: C. 625 and 81
Step-by-step explanation: A relatively prime pair is a pair in which in both numbers given, the only number that can go into each number is one. In 112 and 36, we know 2 can evenly go into each number because they both end in a positive number (112/2 is 56 and 36/2 is 18.) This means A is incorrect. As for B, 11 can evenly go into each number, leaving you with 25 and 7. B is incorrect. And then there's D. 5 can go into each number giving you 160 and 19. D is incorrect.
C is correct because the only numbers that can go evenly into 81 is 1, 3, 9, 27, and 81. None of these numbers, except one can go into 625 also.
Okay so whats the question?
Answer:
0.0492
Step-by-step explanation:
Based on the tree diagram we need to tell the the probability that the test for lice returns a false positive. False positive means that the student has no lice but still the test shows a positive result.
So for this we have to first look for the branch, from the starting node, which shows that student has no lice. From the starting point, the upper branch represents the students that have lice and lower branch represents the students who have no lice. So, we will consider the lower branch with probability mentioned as 0.82
Now, the lower branch is divided into two branches further. We have to look for the branch which shows positive test result. This would be the upper branch with probability mentioned as 0.06.
The overall probability of this event is mentioned at the end of the branch which is 0.0492
This is the probability of the combined event: Student has no lice but tests shows positive result which is the False positive.
Thus, the probability that the test for lice returns a false positive is 0.0492
Answer: It's a 180 degree angle.
Step-by-step explanation:
F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
