The first 3 terms are a, ar and ar^2
so a + ar + ar^2 = 7a
a + ar + ar^2 + ar^3 = 45
7a + ar^3 = 45
a(7 + r^3) = 45
a = 45/(7 + r^3)
Because we know the sequence are positive integers r must be a natural number.
(7 + r^3) is a factor of 45 [ie 1, 3, 5, 9, 15, 45]
so r = 2 because 7 + 2^3 = 15 is the only factor possible
a = 45/15 = 3
I believe the answer should be C
Triangle LMN has two sides that are of the same size, therefore, triangle LMN is described as: isosceles triangle.
<h3>What is an Isosceles Triangle?</h3>
A triangle with two equal sides and two equal base angles is described as an isosceles triangle.
<h3>What is the Distance Formula?</h3>
The formula for finding the distance between two coordinate points is called the distance formula, and it is expressed as:
.
Given the vertices of the angles of triangle LMN as:
- L(-2, 4),
- M(3, 2),
- N(1,-3)
Use the distance formula to find the length of each side of the triangle.
LM = √[(3−(−2))² + (2−4)²]
LM = √[(5)² + (−2)²]
LM = √29 units
MN = √[(3−1)² + (2−(−3))]²
MN = √29 units
LN = √[(−2−1)² + (4−(−3))²]
LN = √(−3)² + (7)²]
LN = √(9 + 49)
LN = √58 units
Isosceles triangles have two equal sides. Triangle LMN has two sides that are of the same size, therefore, triangle LMN is described as: isosceles triangle.
Learn more about isosceles triangle on:
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Answer:
10, 11 , 16, 18 &19
Step-by-step explanation:
Answer:
The smallest sample size to satisfy the conditions is n=500.
Step-by-step explanation:
The condition for performing the inference related to the sample size is that, for all the categories, the expected success and failures in the sample are at least 10:

The largest sample size required will be for the minimum p or (1-p).
This happens to be the proportion that can play other instruments: 2%.
Then, we can calculate the minimum sample size as:
