AC ∥ DF, m∠F = 40°
1 answer:
If m∠F=40° then m∠D=40°
m∠F, m∠D and m∠G have to be 180° together in order to form a triangle
So m∠G = 180° - 2×40° = 100°
One line is cutting m∠G in half and we get m∠EGF and m∠EGD
We want to know how much m∠EGF is so...
m∠EGF=100°÷2=50°
Now we have m∠F which we can name m∠EFG and we have m∠EGF
Together with m∠FEG they form a triangle so that means together they have the value of 180°
m∠FEG=180°-40°-50°=90°
And because you have parralel lines m∠FEG=m∠CBE
And m∠ABE=180°-m∠CBE=90°
That is if I understand this correctly
m∠F, m∠D and m∠G have to be 180° together in order to form a triangle
So m∠G = 180° - 2×40° = 100°
One line is cutting m∠G in half and we get m∠EGF and m∠EGD
We want to know how much m∠EGF is so...
m∠EGF=100°÷2=50°
Now we have m∠F which we can name m∠EFG and we have m∠EGF
Together with m∠FEG they form a triangle so that means together they have the value of 180°
m∠FEG=180°-40°-50°=90°
And because you have parralel lines m∠FEG=m∠CBE
And m∠ABE=180°-m∠CBE=90°
That is if I understand this correctly
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Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
=
n = 9
r = 3
= ⁹P₃
=
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 ×
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111