Answer:
(D) 
Step-by-step explanation:
Given: In triangle ABC, a=9, c=5 and ∠B=120°.
To find: The value of 
.
solution: It is given that In triangle ABC, a=9, c=5 and ∠B=120°.
Now, using the law of cosines, we get
Substituting the given values, we get
which is the required value of .
Therefore, option D is correct.
Answer:
After 4 movies it will be equal
Step-by-step explanation:
10x + 160 = 50x
160 = 40x
4 = x
Check:
10x + 160 =
10(4) + 160 =
40 + 160 = 200
50x =
50 x 4 = 200
200 = 200
Number of square numbers under 25= 1, 4, 9, 16 and 25
= 5 numbers
number of factors of 8 under 25 = 8, 16 and 24
= 3 numbers
number of good outcomes = 5 + 3
= 8 good outcomes
total outcomes = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 and 25.
= 25 outcomes
probability = good outcomes ÷ total outcomes
= 8/25
The probability that they number chosen is a square number or a factor of 8 is 8/25.
4 hundreds 13 tens 5 ones = 4*100+13*10+5*1=400+130+5= \boxed {535}
Step-by-step explanation:
We let A be the set of those who owned an iPhone, B be the set of those who owned a Blackberry,
and C those that owned an Android. Therefore we have |A| = 60, |B| = 75, and |C| = 30. Also,
we know that |A ∩ B| = 40, |A ∩ C| = 12 and |B ∩ C| = 8. Finally, |A ∩ B ∩ C| = 3. Therefore,
by the principle of inclusion/exclusion, we have
|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|
= 60 + 75 + 30 − 40 − 12 − 8 + 4
= 109
(a) Since there are 300 total people, there are 191 without one of the types of phone.
(b) Since |A ∩ B| = 40 and |B| = 75, there are 35 people with a Blackberry that don’t own
an iPhone.
(c) Since |B ∩ C| = 8 and |B| = 75, there are 67 people with a Blackberry that don’t own
an Android.
It is also helpful to draw Venn diagrams for this problem.
