Answer:
P( sum is prime )= 73/216
Step-by-step explanation:
The minimum value of the sum will be 3 and maximum value will be 18. So the prime numbers in this range are 3 , 5, 7, 11, 13, 17.
P(sum=3)=1/216, P(sum=5)=6/216, P(sum=7)=15/216, P(sum=11)=27/216, P(sum=13)=21/216, P(sum=17)=3/216.
The final probability will be sum of the above given probabilities.
Hence P( sum is prime )= 73/216
Answer:
48x² + 24x + 3
Step-by-step explanation:
Width = (4x + 1) in
Length = 3 *width = 3*(4x + 1) = 3*4x + 3*1
= (12x + 3) in
Area of rectangle = length * width
= (12x + 3) (4x + 1)
= 12x *4x + 12x *1 + 3*4x + 3*1
= 48x² + 12x + 12x + 3
= 48x² + 24x + 3
Answer:
Step 2 contains error in the given problem.
Step-by-step explanation:
Given expression is:

Step 1: identifying the LCM.
The LCM identified is 6.
This step is correct.
In the next step, we multiply the LCM with each term of the equation.
Step 2:

However,
In the given solution, the LCM is not multiplied with each term.
Hence,
Step 2 contains error in the given problem.
$1,365 is the answer, (the third choice)
Let's start from what we know.

Note that:

(sign of last term will be + when n is even and - when n is odd).
Sum is finite so we can split it into two sums, first

with only positive trems (squares of even numbers) and second

with negative (squares of odd numbers). So:

And now the proof.
1) n is even.
In this case, both

and

have

terms. For example if n=8 then:

Generally, there will be:

Now, calculate our sum:



So in this case we prove, that:

2) n is odd.
Here,

has more terms than

. For example if n=7 then:

So there is

terms in

,

terms in

and:

Now, we can calculate our sum:




We consider all possible n so we prove that: