Answer:
n(n+1)(n+5)/3
Step-by-step explanation:
there is no value, as we don't know n.
but we can create a summary formula/ function definition :
this is the sum for k = 1 to n of k×(k+3)
k×(k+3) = k² + 3k
so, the overall sum splits into the sum of k² for k=1 to n, and the sum of 3k for k=1 to n.
and the sum of 3k is 3 times the sum of k for k=1 to n.
Σk² for k=1 to n = [n(n+1)(2n+1)]/6
Σk for k=1 to n = n(n+1)/2
3×Σk for k=1 to n = 3×n(n+1)/2
so, we have a function formula
n(n+1)(2n+1)/6 + 3n(n+1)/2 = n(n+1)(2n+1)/6 + 9n(n+1)/6 =
= n(n+1)(2n+1+9)/6 = n(n+1)(2n+10)/6 = n(n+1)(n+5)/3
Answer:
See explanation
Step-by-step explanation:
<u>Definition of parallelogram:</u> Parallelogram is a quadrilateral with two pairs of parallel sides.
<u>Definition of transversal (diagonal):</u> A line that cuts across two or more (usually parallel) lines.
<u>Definition of the same side interior angles:</u> These angles are located exactly as their name describes. They are "interior" (between the parallel lines), and they are on the same side of the transversal (diagonal).
<u>The same-side interior angles theorem</u> states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary
Statement Reason
1. ABCD is a parallelogram - Given
2. 
- Definition of parallelogram
3. 
is a diagonal of 
and 
- Definition of diagonal
4. 
and 
are the same side interior angles - Definition of same-side interior angles
5. is supplementary to - Same-Side Interior Angles Theorem
the choices are below
the predicted mean of the population will be less than 200.
The predicted mean of the population will be less than 245.
The predicted mean of the population will be more than 275.
The predicted mean of the population will be more than 250.
b is the answer
