Answer:
c.) aₙ = 5 × 4ⁿ⁻¹
Explanation:
Geometric sequence: aₙ = a(r)ⁿ⁻¹
where 'a' resembles first term of a sequence, 'r' is the common difference.
Here sequence: 5, 20, 80, 320,...
First term (a) = 5
Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4
Hence putting into equation: aₙ = 5(4)ⁿ⁻¹
if the diameter is 20, the its radius must be half that or 10.
![\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20sector%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B%5Ctheta%20%5Cpi%20r%5E2%7D%7B360%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20%5Ctheta%20%3D%5Cstackrel%7Bdegrees%7D%7Bangle%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20A%3D5%5Cpi%20%5C%5C%20r%3D10%20%5Cend%7Bcases%7D%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%205%5Cpi%20%3D%5Ccfrac%7B%5Ctheta%20%5Cpi%20%2810%29%5E2%7D%7B360%7D%5Cimplies%205%5Cpi%20%3D%5Ccfrac%7B5%5Cpi%20%5Ctheta%20%7D%7B18%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B5%5Cpi%20%7D%7B5%5Cpi%20%7D%3D%5Ccfrac%7B%5Ctheta%20%7D%7B18%7D%5Cimplies%201%3D%5Ccfrac%7B%5Ctheta%20%7D%7B18%7D%5Cimplies%2018%3D%5Ctheta%20%5Cend%7Barray%7D)
The first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132
<h3>Highest common factors</h3>
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
According to the question, we are to find two numbers between 100 and
150 that have a HCF of 22.
In order to do that we will<u> multiply 22 by the values 5 and 6</u>
First number = 22 * 5 = 10
Second number = 22 * 6 = 132
Hence the first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132
Learn more on HCF here; brainly.com/question/21504246
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Step-by-step explanation:
You need to find the total number of students the pie chart will represent:
17 + 35 + 38 = 90
So you know, 360° represents 90 people
You can then find out the angle for each person: 360 ÷ 90 = 4
Each person is 4°
a)
1. 17 people took French so you would do 4° × 17 = 68°
2. 35 people took German so you would do 4° × 35 = 140°
3. 38 people took Italian so you would do 4° × 38 = 152°
b)
17 out of 90 people chose french so the probability would be 17/90
Answer:
The selections are dependent.
Yes, they can be treated as independent (less than 5% of the population).
Step-by-step explanation:
Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.
Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:

Thus the selections can be treated as independent for the purposes of calculations.