Answer:
(a) 34.
(b) Yes.
Step-by-step explanation:
The first term is 3(1)^2 + 1 = 4 ( where k = 1).
The sum of 2 terms = 3(2)^2 + 2 = 14.
The sum of 3 terms = 3(3)^2 + 3 = 30.
The sum of 4 terms = 3(4)^2 + 4 = 52.
So the first 4 terms are 4, 10, 16 and 22 . - increasing by 6.
The common difference is 6 so it is an arithmetic sequence.
The 6th term = a1 + d(n - 1)
= 4 + 6(6-1)
= 34.
Answer:
0.1 or 1/10
Step-by-step explanation:
The digits 4, 5, 6, 7 and 8 are randomly arranged to form a three digit number, where the digits are not repeated.
This is question of permutation.
Imagine this sum as; there are 3 boxes(blank spaces for digits) and 5 different fruits(digits) are to be put in these boxes, where a box can hold a maximum of only 1 fruit. The number of such permutations are: ⁵P₃
By formula (a! is factorial a):
ᵃPₙ
⁵P₃
⁵P₃
⁵P₃
⁵P₃= 60
This is the total count of possible numbers that can be formed.
Now, for a number to be greater than 800 and even; first digit should necessarily be 8. Last digit can be 4 or 6. Using these conditions, there are 6 possibilities. 854, 864, 874, 846, 856, 876 are the numbers.
The probability that number is even and greater than 800 is:
<h3>
Answer: 37</h3>
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Work Shown:
We have a triangle with sides a,b,c such that
The third side c can be represented by this inequality
b-a < c < b+a
which is a modified form of the triangle inequality theorem.
Plug in the given values to get
b-a < c < b+a
20-17 < c < 20+17
3 < c < 37
The third side length is between 3 and 37; it cannot equal 3, and it cannot equal 37. So we exclude both endpoints.
Of the answer choices, the values {7,20, 12} are in the range 3 < c < 37.
The value c = 37 is not in the range 3 < c < 37 because we can't have the third side equal to either endpoint. Otherwise, we get a straight line instead of a triangle forming.
So that's why 37 is the only possible answer here.
Answer:
6+6=12
Step-by-step explanation:
Answer: First answer: hexagon
second answer: triangle
Step-by-step explanation: right on edge 2020