Answer:
Step-by-step explanation:
Let us assume that if possible in the group of 101, each had a different number of friends. Then the no of friends 101 persons have 0,1,2,....100 only since number of friends are integers and non negative.
Say P has 100 friends then P has all other persons as friends. In this case, there cannot be any one who has 0 friend. So a contradiction. Hence proved
Part ii: EVen if instead of 101, say n people are there same proof follows as
if different number of friends then they would be 0,1,2...n-1
If one person has n-1 friends then there cannot be any one who does not have any friend.
Thus same proof follows.
Answer:
- interest: $144
- principal plus interest: $944
Step-by-step explanation:
The amount of interest is found using the simple interest formula. That is added to the principal to find the total account balance.
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<h3>Interest</h3>
I = Prt . . . . . P = principal, r = annual rate, t = number of years
I = $800·0.06·3 = $144
The simple interest earned in 3 years is $144.
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<h3>Principal plus interest</h3>
Adding that to the principal gives ...
$800 +144 = $944
The total principal plus interest is $944.
Answer:
x^2 +4x = 18
Step-by-step explanation:
The variable y is isolated in the first equation by dividing both sides by the coefficient of y:
3y = 12x . . . . . . given
3y/3 = 12x/3 . . . . . divide by the coefficient of y
y = 4x . . . . . . . simplify
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This expression (4x) is put in place of y when substitution is used.
x^2 +y = 18 . . . . given
x^2 +4x = 18 . . . . . with 4x substituted for y
Answer:
1. x = 27
2. h = 35
Step-by-step explanation:
From the question given above, the following data were obtained:
<ABD = 52°
Angle C = 43°
Line BC = 29
x =..?
h =...?
1. Determination of the value of x.
Angle C = 43°
Line BC = 29
x =..?
Using Tan ratio, the value of x can be obtained as follow:
Opposite = x
Adjacent = Line BC = 29
Angle C = 43°
Tan C = Opposite /Adjacent
Tan 43° = x/29
Cross multiply
x = 29 × Tan 43°
x = 29 × 0.9325
x = 27.0425 ≈ 27
x = 27
2. Determination of the value of h.
<ABD = 52°
x = 27
h =...?
Using Tan ratio, the value of h can be obtained as follow:
<ABD = 52°
Adjacent = x = 27
Opposite = h
Tan <ABD = Opposite /Adjacent
Tan 52° = h/27
Cross multiply
h = 27 × Tan 52
h = 27 × 1.2799
h = 34.5573 ≈ 35
h = 35