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3 years ago

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,.to find the following:

1 answer:

6 0

$a)\\\\
a_{n+1}-a_n=d\\
for\ n=1\\
a_2-a_1=d\\
d=3-1=2\ - difference\ between\ two\ consecutive\ terms\\\\
b)\\
a_n=a_1+(n-1)d\\
n=101\\
a_{101}=1+(101-1)*2\\
a_{101}=1+100*2=200+1=201\\\\
c)\\
Sn=\frac{a_1+a_n}{2}*n\\
n=20\\
a_n=a_{20}=1+(20-1)*2=1+38=39\\
Sn=\frac{1+39}{2}*20=400\ \ Sum\ of\ the\ first\ 20 \ numbers.$

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Vladimir [108]

Answer:

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Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

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Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as $\mathbb{Z}_{\ge 0}$

Whole numbers less than or equal to 20: $A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$

A. Prime numbers

From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.

Once we have 21 numbers in total and 8 prime numbers, the probability is:

$P=\frac{8}{21} \approx 40\%$

B. Composite numbers

From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Once we have 21 numbers in total and 11 composite numbers, the probability is:

$P=\frac{11}{21} \approx 52\%$

C. Divisible by three

From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.

Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:

$P=\frac{6}{21} \approx 30\%$

D. Square of 2

From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.

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$\sqrt{4} =2$

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$\sqrt{16} =4$

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Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

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$x\in \left(\frac{3}{4},\infty \right)$

Q4. if three fourth of a number is one tenths, what is the number?

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If two points are together, then you subtract the numbers to get the distance

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