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GREYUIT [131]
3 years ago
9

Question 1 of 10

Mathematics
1 answer:
jekas [21]3 years ago
8 0

Step-by-step explanation:

A density curve for all the possible ages between 0 years and 25 years on the shape of a triangle. 0.04

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Answer choices
Anettt [7]
The answer is D because is you add a one under the 9 you get 9/1 x 2/3 and you can just multiply straight away and get 18/3 but if you need to simplify more you get 6
5 0
2 years ago
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A jewelry is designing a gift box. The sum of the length, width, and height is 12. Graph to find the needed dimensions of the bo
frutty [35]
The Volume of the box has to equal 64

because all the sides have to equal 12

and 12/3 = 4
6 0
3 years ago
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Four girls helped Mr.Day plant garden for their help hr gave the girls $24 to share equally later Mrs day gave each girl $2 for
katrin [286]

Answer:$8

Step-by-step explanation: there is 4 girls and $24 they split it equally so you would do 24/4 and that gives you 6. Then it says Mrs. Day gave each girl $2 so then you add 6+2 and then you get 8.

3 0
3 years ago
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Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do ho
oksano4ka [1.4K]

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

7 0
3 years ago
R leaks out of a barrel so that the rate of change in the water level is proportional to the square root of the depth of the wat
Irina-Kira [14]
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
  y'(t) = k√(y(t)) . . . . for some proportionality constant k
  y(0) = 30
  y(1) = 29

We observe that a function of the form
  y(t) = a(t - b)²
will have a derivative that is proportional to y:
  y'(t) = 2a(t -b)

We can find the constants "a" and "b" from the given boundary conditions.
At t=0
  30 = a(0 -b)²
  a = 30/b²
At t=1
  29 = a(1 - b)² . . . . . . . . . substitute for t
  29 = 30(1 - b)²/b² . . . . . substitute for a
  29/30 = (1/b -1)² . . . . . . divide by 30
  1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
  b = 30 +√870 . . . . . . . . simplify

The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
5 0
3 years ago
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