Step-by-step explanation:
I think A is the answer to your question
The correct answer is B. For sure it is. It took a while to solve in my head
Let f(x) = ax³ + 9x² + 4x – 10
g(x) = 0⇒x - 3 = 0
⇒ x = 0 + 3
⇒ x = 3
On dividing f(x) by x - 3, it leaves a remainder 5.
Now keeping, f(3) = 5
⇒a(3)³ + 9(3)² + 4(3) - 10 = 5
⇒ a × 27 + 9 × 9 + 4 × 3 - 10 = 5
⇒ 27a + 81 + 12 - 10 = 5
⇒ 81 + 12 - 10 - 5 = 27a
⇒ 81 + 12 - 15 = 27a
⇒ 93 - 15 = 27a
⇒ 78 = 27a
⇒ a = 27/78
⇒ a = 0.3461
Easy way, visual
50---68---80%
Difference 18 12
Invert order to give ratio of 50% and 80%
Ratio 12 18 = 2:3
So by simple proportion:
volume of 50% needed = 100*2/(2+3)=40 mL
volume of 80% needed = 100*3/(2+3)=60 mL
Algebra way
Let x=volume of 50% needed.
Then
0.50*x+0.80*(100-x) = 0.68(100)
Expand and solve for x
0.5x+80-0.8x = 68
0.8x-0.5x = 80-68
0.3x = 12
x=12/0.3 = 40 mL (volume of 50%)
100-x=100-40=60 mL (volume of 80%)
Answer: B. Being around cigarette smokers and developing heart disease .
C. Independent. Being around cigarette smokers does not cause heart disease.
Step-by-step explanation:
Given : A study found that there is no relationship between being around cigarette smokers and developing heart disease.
i.e. The two events here are Being around cigarette smokers and developing heart disease .
Since there is no relationship between the above two events.
Being around cigarette smokers does not cause heart disease.
It means that the two events are not dependent on each other i.e. they are independent.
