You can first turn both numbers into a improper fraction so it looks like this: 41/8-11/4.
Then you have to change the denominator so that they are the same, which looks like this: 41/8-22/8.
After, you subtract the numerator and keep the denominator the same, which will then look like this 19/8.
Lastly, you turn your numbers back into a mixed number so it is 2 3/8.
Answer:
0.362
Step-by-step explanation:
When drawing randomly from the 1st and 2nd urn, 4 case scenarios may happen:
- Red ball is drawn from the 1st urn with a probability of 9/10, red ball is drawn from the 2st urn with a probability of 1/6. The probability of this case to happen is (9/10)*(1/6) = 9/60 = 3/20 or 0.15. The probability that a ball drawn randomly from the third urn is blue given this scenario is (1 blue + 5 blue)/(8 red + 1 blue + 5 blue) = 6/14 = 3/7.
- Red ball is drawn from the 1st urn with a probability of 9/10, blue ball is drawn from the 2nd urn with a probability of 5/6. The probability of this event to happen is (9/10)*(5/6) = 45/60 = 3/4 or 0.75. The probability that a ball drawn randomly from the third urn is blue given this scenario is (1 blue + 4 blue)/(8 red + 1 blue + 1 red + 4 blue) = 5/14
- Blue ball is drawn from the 1st urn with a probability of 1/10, blue ball is drawn from the 2nd urn with a probability of 5/6. The probability of this event to happen is (1/10)*(5/6) = 5/60 = 1/12. The probability that a ball drawn randomly from the third urn is blue given this scenario is (4 blue)/(9 red + 1 red + 4 blue) = 4/14 = 2/7
- Blue ball is drawn from the 1st urn with a probability of 1/10, red ball is drawn from the 2st urn with a probability of 1/6. The probability of this event to happen is (1/10)*(1/6) = 1/60. The probability that a ball drawn randomly from the third urn is blue given this scenario is (5 blue)/(9 red + 5 blue) = 5/14.
Overall, the total probability that a ball drawn randomly from the third urn is blue is the sum of product of each scenario to happen with their respective given probability
P = 0.15(3/7) + 0.75(5/14) + (1/12)*(2/7) + (1/60)*(5/14) = 0.362
Answer:
a) y = 16/x²
b) x = 4/5
Step-by-step explanation:
You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.
<h3>(a) Relation</h3>
The wording "inversely proportional to the square" means the form of the equation is ...
y = k/x² . . . . . . where k is the constant of proportionality
The value of k can be found from the given (x, y) pair.
k = x²y = (1)²(16) = 16
The equation is ...
y = 16/x²
<h3>(b) Value of x</h3>
Solving for x gives ...
x = √(16/y)
Then the value of x for y = 25 is ...
x = √(16/25)
x = 4/5
Answer:
(a) 
(b) 
(c) 28.07 minutes
Step-by-step explanation:
A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.
That means sequence formed will be 3, 6, 12, 24............
We can easily say that this sequence is a geometric sequence having common ratio (r) = 
r = 2
Now we know the explicit formula of a geometric sequence is given by
Where a = Initial population = 3 bacteria
r = common ratio = 2
and t = time in hours
So explicit formula will be
(a) Now we have to calculate the size of population after t hours
(b) We have to find the size of population after 7 hours or 420 minutes
=
After 7 hours bacteria population will be
(c) Time to reach population as 21
By the explicit formula
Now we take log on both the sides of the equation
6t log2 = log 7
6t(0.301) = 0.845
t(1.806) = 0.845
t = 
hours
Or t = 0.468×60 = 28.07 minutes
Therefore, after 28.07 minutes bacterial population will be 21
