k = 13 is the value of k in quartic equation.
What does the term "quartic equation" mean?
An equation of the fourth degree, often known as a quartic equation, is one that reduces a quartic polynomial to zero. in which a 0. A quartic function's derivative is a cubic function.
Let α = 7x
β = 6x
α + β = 7x + 6x = k/3 ............1
13x = k/3
αβ = 7x × 6x = 14/3
42x² = 14/3
x² = 14/3 × 42
x² = 1/9
x = 1/3
now putting value of x in 1
7/3 + 6/3 = k/3
1/3( 7 + 6 )= k/3
k = 13
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3 hours
On the way there, 1.5x12 = 18
On the way back, 1.5x10 = 15
Using proportions, it is found that the farmer has planted 258 acres.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He plants 413 acres during the entire year, hence, considering he plants an equal amount daily, and the year is 5/8 over, the amount he has planted is:
A = (5/8) x 413 = 258 acres.
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Answer:
Step-by-step explanation:
There are 8 Jonathan (red), 4 Granny Smith (green), and 5 Golden Delicious (yellow) apples in the bag.
a) Select 3 apples with replacement. Find the probability that all there are green.
- Given that we are taking all apples with replacement, the probability of getting a green apples remains the same in all 3 trials. Therefore the probability here is computed as:
- = (Number of green apples/Total apples)
Therefore 0.0130 is the required probability here.
b) Select 3 apples with replacement. Find the probability that none are red
Probability that none are red is computed here as:
- = (Number of non red apples/Total apples)
Therefore 0.14838 is the required probability here
c) Select 4 apples with replacement. Find the probability that you get at least 2 red apples
- Probability that we get at least 2 red apples when 4 apples are drawn is computed here as:
- = 1 - (Probability that no red apple is taken out when 4 apples are taken out + Probability that 1 red apple is taken out when 4 apples are taken out)
- = 1 - 8C0 x 9C4 + 8C1 x 9C3 / 17C4
Therefore 0.6647 is the required probability here
d) Select 2 apples with replacement. Find the probability that the second apple is yellow given that the first apple is red.
- Given that the first apple is red, we are left with 16 apples out of which 5 are yellow. Therefore the required probability here is computed as:
Therefore 0.3125 is the required probability here
You can find percentages like this by taking the total number of questions dividing it by 100 to find out how much each question was worth, then multiplying by the number correct.
So, 85 ÷ 100 ≈ 1.18
1.18 x 68 ≈ 80
So, the score was 80%.
