Answer:
They are not independent
Step-by-step explanation:
Given
E = Occurrence of 1 on first die
F = Sum of the uppermost occurrence in both die is 5
Required
Are E and F independent
First, we need to list the sample space of a roll of a die

Next, we list out the sample space of F


In (1): the sample space of E is:

So:


In (2): the sample space of F is:

So:



For E and F to be independent:

Substitute values for P(E) and P(F)
This gives:


However, the actual value of P(E and F) is 0.
This is so because
and
have 0 common elements:
So:

Compare
and
.
These values are not equal.
Hence: the two events are not independent
Answer:

Step-by-step explanation:
The equation is ,
- Here e is the Euler's Number . The log which are defined on the base e are called Natural logarithms.
Say if we have a expoteintial equation ,
In logarithmic form it is ,

Similarly our required answer will be ,

Answer:
x = 13
y = 15
Step-by-step explanation:
ST = DT ( Reason : from given )
5x = 65
x = 65 / 5
x = 13
TY = TU ( Reason : from given )
3y + 5 = 50
3y = 50 - 5
3y = 45
y = 45 / 3
y = 15
<h3>
Answer: (n-1)^2</h3>
This is because we have a list of perfect squares 0,1,4,9,...
We use n-1 in place of n because we're shifting things one spot to the left, since we start at 0 instead of 1.
In other words, if the answer was n^2, then the first term would be 1^2 = 1, the second term would be 2^2 = 4, and so on. But again, we started with 0^2 = 0, so that's why we need the n-1 shift.
You can confirm this is the case by plugging n = 1 into (n-1)^2 and you should find the result is 0^2 = 0. Similarly, if you tried n = 2, you should get 1^2 = 1, and so on. It appears you already wrote the answer when you wrote "Mark Scheme".
All of this only applies to sequence A.
side note: n is some positive whole number.
Well number one is an acute angle number two is obtuse and number three is obtuse