Total number of ways to make a pair:
The first player can be any one of 7 . For each of those . . .
The opponent can be any one of the remaining 6 .
Total ways to make a pair = 7 x 6 = 42 ways .
BUT ... every pair can be made in two ways ... A vs B or B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.
If every pair plays 2 matches, then (21 x 2) = <em><u>42 total matches</u></em> will be played.
Now, is that an elegant solution or what !
Answer:
Quartz, Cups
Step-by-step explanation:
1 gallon = 16 cups
1 quartz = 4 cups
1 pint = 2 cups
1 fluid ounce = 1/8 cups
Answer:
5 cm
Step-by-step explanation:
We khow that the altitude of this triangle is 1cm shorter than the base
- Let H be our altitude and B our base and A the area of the triangle
- A= (B*H)/2 ⇒ 15=(B*H)/2
- H is 1cm shorter than B ⇒ B=H+1
- H*(H+1)/2=15 ⇒ H*(H+1)=30⇒ H²+H=30⇒H²+H-30+0
that's a quadratic equation . Let's calculate the dicriminant .
Let Δ be the dicriminant
- a=1
- b=1
- c= -30
- Δ=b²-4*a*c = 1²-4*1*(-30)=1+4*30=121≥0
- Δ≥0⇔ that we have two solutions x and y
- x= (-1-
)/2= (-1-11)/2= -6 - y= (-1+)/2= 10/2 = 5
We have a negative value and a positive one
The altitude is a distance so it can't be negative
H= 5cm
The next number would be 8+13 = 21
Answer:
The profit of the company will be $224.85
Step-by-step explanation:
Let the equation of profit be termed as E(x)
we are given
amount of purchasing the policy (let a)= $1000
probability that women will live for at least 1 year (let b) = 0.9581
amount lost by insurance company if the women dies (let c) = 18,500-1000 = 17,500
the probability woman dies within one year (let d) = 1-0.9581=0.0419
the equation will be
E(x) of profit= a*b - c*d = 1000*0.9581 - 17500*0.0419
= 958.1 - 733.25
= 224.85
