Let S be the sum,
S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n
Reverse the order of terms:
S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2
Add up terms in the same positions, so that twice the sum is
2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)
or
2S = n (2n + 2)
Divide both sides by 2 to solve for S :
S = n (n + 1)
Answer:
4
Step-by-step explanation:
Graph 4
Yes that is true, all opposite sides would be parallel, and all the corners are 90 degrees, then yes it is true
Answer:
Approximately 45% students signed up for neither canoeing or trekking.
Step-by-step explanation:
First we subtract the number of the students who signed up from the number of the total students to find the number of the students who did not signed up for either.
But there are 13 students who signed up canoeing and also for trekking.
Hence the number of students they signed up for activity is
72 + 23 - 13 = 82
And the number of students they not signed up for any activity is
150 - 82 = 68
so 68 students signed up neither for trekking nor canoeing. The percentage of those students are :
× 100 = 45.3333%
Approximately 45% students signed up for neither canoeing or trekking.
Answer: a) The figure can be reasonably divided into two geometries:
• a rectangular prism
• a hemisphere.
b) The volume of the rectangular prism is given by
V = lwh
V = (10 cm)(5 cm)(4 cm) = 200 cm³
The volume of the hemisphere is given by
V = (2π/3)r³
V = (2π/3)(3 cm)³ = 18π cm³
c) The total volume of the figure is
total volume = (prism volume) + (hemisphere volume)
V = 200 cm³ + 18π cm³
V ≈ 256.549 cm³
Step-by-step explanation:
