<h3>
Answer: 17/24</h3>
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Explanation:
We have these four cases or possible outcomes
- Case 1) We select 0 black marbles and 3 red marbles.
- Case 2) We select 1 black marble and 2 red marbles.
- Case 3) We select 2 black marbles and 1 red marble.
- Case 4) We select 3 black marbles and 0 red marbles.
Let's calculate the probability for case 4.
There are 7 black marbles out of 10 total. The probability of picking black is 7/10. If no replacement is made, then 6/9 is the probability of picking black again (subtract 1 from the numerator and denominator separately). Finally, 5/8 is the probability of getting black a third time.
The probability of getting 3 black marbles in a row is
(7/10)*(6/9)*(5/8) = (7*6*5)/(10*9*8) = 210/720 = 7/24.
That fraction 7/24 means that if you had 24 chances, then you expect about 7 of them will lead to getting three black marbles in a row (aka case 4). Therefore, 24-7 = 17 occurrences are expected where we get cases 1 through 3 occur in some fashion (pick one case only).
Notice how cases 1 through 3 encapsulate the phrasing "at most 2 black marbles" which is another way of saying "2 black marbles is the highest we can go".
So that's why the answer is 17/24.
Answer:
20
Step-by-step explanation:
Answer:
Step-by-step explanation:
the constant drain of water is C:
C= (1000-940)/10 = 6 gallons per minute
after x minutes : 1000- 6x ( water left in the tank after x minutes)
for 5 minutes: 1000-6(5)=970
after 20 min.: 1000-6(20)=880
after 30 min.: 1000-6(30)=820
after 27 min.: 1000-6(27)= 838
the rate of flow of water is 6 gallon per minute
Answer:
The position P is:
ft <u><em> Remember that the position is a vector. Observe the attached image</em></u>
Step-by-step explanation:
The equation that describes the height as a function of time of an object that moves in a parabolic trajectory with an initial velocity 
is:
Where 
is the initial height = 0 for this case
We know that the initial velocity is:
82 ft/sec at an angle of 58 ° with respect to the ground.
So:
ft/sec
ft/sec
Thus
The height after 2 sec is:
Then the equation that describes the horizontal position of the ball is
Where
for this case
ft / sec
ft/sec
So
After 2 seconds the horizontal distance reached by the ball is:
Finally the vector position P is:
ft
Answer:
32
Step-by-step explanation:
2(2.5z − 58 + 43) = 176− 46
5z - 116 + 86 = 130
5z -30 = 130
5z = 160
z = 160/5
z = 32
