The first table is proportional. Y is 4 times X. The second table is 1.25 times X
We have an arithmetic progression:
an=number of item at row n
an=a₁+(n-1)d
d=common difference=an-a(n-1)=a₂-a₁=2-1=1
n=number of row
In this case:
an=1+(n-1)*1=n
The sum of an arithmetic serie is:
Sn=(a₁+an)n / 2
In this case:
a₁=1 (number of itms in the first row)
an=n (we have to calculate this before)
Sn=(1+n)n /2=(n+n²)/2
Therefore:
f(n)=Sn=number of items when we have n number of rows
f(n)=(n+n²)/2
Answer: f(n)=(n+n²)/2
To chek:
f(1)=(1+1²)/2=1
f(2)=(2+2²)/2=6/2=3
f(3)=(3+3²)/2=(3+9)/2=12/2=6
....
We know that 12² = 144 and 13² = 169 , then :
12² < 152 < 13²
Send the question sentences.
The number of combinations of 2 health care providers of different types possible are 47.
<u>Explanation:</u>
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Doctors = 4
Dentists = 3
Nurses = 5
combinations of two different health care providers = ?
Combination would be = ⁴C₁ X ³C₁ + ³C₁ X ⁵C₁ + ⁴C₁ X ⁵C₁
ⁿCₐ = n! / ( n - a )! X a!
So on calculating the combination we get,
= 4 X 3 + 3 X 5 + 4 X 5
= 12 + 15 + 20
= 47
Therefore, the number of combinations of 2 health care providers of different types possible are 47.