Answer: 12 students
Step-by-step explanation:
Let X and Y stand for the number of students in each respective class.
We know:
X/Y = 2/5, and
Y = X+24
We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:
(Y-x)/(X+x) = 1
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We can rearrange X/Y = 2/5 to:
X = 2Y/5
The use this value of X in the second equation:
Y = X+24
Y =2Y/5+24
5Y = 2Y + 120
3Y = 120
Y = 40
Since Y = X+24
40 = X + 24
X = 16
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Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:
(Y-x)=(X+x)
(40-x)=(16+x)
24 = 2x
x = 12
12 students must transfer to the more difficult, very early morning, class.
Answer:
a) P(B'|A) = 0.042
b) P(B|A') = 0.625
Step-by-step explanation:
Given that:
80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered
Of the aircraft that are discovered, 63% have an emergency locator,
whereas 89% of the aircraft not discovered do not have such a locator.
From the given information; it is suitable we define the events in order to calculate the probabilities.
So, Let :
A = Locator
B = Discovered
A' = No Locator
B' = No Discovered
So; P(B) = 0.8
P(B') = 1 - P(B)
P(B') = 1- 0.8
P(B') = 0.2
P(A|B) = 0.63
P(A'|B) = 1 - P(A|B)
P(A'|B) = 1- 0.63
P(A'|B) = 0.37
P(A'|B') = 0.89
P(A|B') = 1 - P(A'|B')
P(A|B') = 1 - 0.89
P(A|B') = 0.11
Also;
P(B ∩ A) = P(A|B) P(B)
P(B ∩ A) = 0.63 × 0.8
P(B ∩ A) = 0.504
P(B ∩ A') = P(A'|B) P(B)
P(B ∩ A') = 0.37 × 0.8
P(B ∩ A') = 0.296
P(B' ∩ A) = P(A|B') P(B')
P(B' ∩ A) = 0.11 × 0.2
P(B' ∩ A) = 0.022
P(B' ∩ A') = P(A'|B') P(B')
P(B' ∩ A') = 0.89 × 0.2
P(B' ∩ A') = 0.178
Similarly:
P(A) = P(B ∩ A ) + P(B' ∩ A)
P(A) = 0.504 + 0.022
P(A) = 0.526
P(A') = 1 - P(A)
P(A') = 1 - 0.526
P(A') = 0.474
The probability that it will not be discovered given that it has an emergency locator is,
P(B'|A) = P(B' ∩ A)/P(A)
P(B'|A) = 0.022/0.526
P(B'|A) = 0.042
(b) If it does not have an emergency locator, what is the probability that it will be discovered?
The probability that it will be discovered given that it does not have an emergency locator is:
P(B|A') = P(B ∩ A')/P(A')
P(B|A') = 0.296/0.474
P(B|A') = 0.625
Answer:
d, e
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
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In this case, it means the product is ...
(6^1)(6^0)(6^-3) = 6^(1+0-3) = 6^-2 = 1/6^2 = 1/36
__
The 6 without an exponent is equivalent to 6^1, an exponent of 1.
The sum of the exponents is -2.
Add the exponents to simplify the expression.
The value of the expression is 1/36.
An equivalent is any expression that results in 6^-2. One such is (6^5)(6^-7).
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Only the last two choices, d and e, apply.
Answer:
4
Step-by-step explanation
because 256 is root of 4 raised to 4
so 4 root 4 is to 4 which is = to 4
hope it helped u i am new on brainly so counldnt write properly
if it helped u plzzz mark as brainliest
To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership. So set the no-membership cost equal to the yearly membership cost and solve.
no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day. So if we let d = number of days, our cost can be calculated by "7d"
a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"
Set them equal to each other and solve:
7d = 200 + 3d
4d = 200
d = 50
So you would need to attend the classes for at least 50 days to justify a yearly membership. I hope that helps!
