The total number of students in 8th grade will be the sum of number of all students shown in the Venn Diagram, as the students in 8th class are the Universal set in this case.
So, total number of students in grade 8 = 34 + 14 + 44 + 15 = 107
Number of students who are taking either of these subjects as elective are shown in the colored regions and are equal to = 34 + 14 + 44 = 92
Probability of a student chosen at random taking either of these subjects as an elective = Student taking these courses as elective / Total number of students
So,
Probability of a student chosen at random taking either of these subjects as an elective = 92/107
Thus option B gives the correct answer.
Ans: Option A
Explanation:Let's solve it smartly!
Given expression:
--- (A)
Factors: (x+p)(x+q)
Condition: c<0
Now let us expand (x+p)(x+q):
=>
--- (B)
By comparing (B) with (A), we can say that:
pq = c --- (C)
Now, as the condition says,
c<0, it means either p or q is negative. Both cannot be positive or both cannot be negative.
1) If p>0, q>0, it means c>0 since (+p)(+q) = (+c)(according to equation (C)). Condition is not met.
Hence, option B and D are wrong.
2) If p<0, q<0 it means c>=0 since (-p)(-q) = (+c)(according to equation (C)). Condition is not met.
Hence option C is out as well.
We are left with Option A:
p<0, q>0 it means c<0 since (-p)(+q) = (-c)(according to equation (C)). Condition is MET!
Hence,
Ans: Option A: p= -3, q= 7
Answer: =11x−8
Step-by-step explanation:
Distribute:
=(3)(x)+(3)(−2)+(2)(4x)+(2)(−1)
=3x+−6+8x+−2
Combine Like Terms:
=3x+−6+8x+−2
=(3x+8x)+(−6+−2)
=11x+−8
Answer:
42
Step-by-step explanation: