Part 2!
2 answers:
Math is about number sense and matching patterns. You get number sense by playing with numbers: counting, arranging. Most people do not find it difficult to match patterns, as our brains are wired to see them--sometimes even when they aren't there.
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
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Answer:
A person can select 3 coins from a box containing 6 different coins in 120 different ways.
Step-by-step explanation:
Total choices = n = 6
no. of selections to be made = r = 3
The order of selection of coins matter so we will use permutation here.
Using the formula of Permutation:
nPr =
We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.
Order of coin is important means that if we select 3 coins in these two orders:
--> nickel - dime - quarter
--> dime - quarter - nickel
They will count as two different cases.
Calculating the no. of ways 3 coins can be selected from 6 coins.
nPr = =
nPr = 120
Answer:
NR = 12
Step-by-step explanation:
Given that both trjangles are similar, therefore, it follows that their corresponding side lengths would be proportional to each other. Thus:
Cross multiply
(addition property of equality)
Divide both sides by 10
x = 7
✔️NR = 2x - 2
Plug in the value of x
NR = 2(7) - 2 = 14 - 2
NR = 12