1. For each expression, use the distributive property to write an equivalent expression.
1 answer:
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Given that mean of quiz scores = 6.4 and standard deviation = 0.7
And we need to use Chebyshev's theorem to find the range in which 88.9% of data will reside.
Chebyshev's theorem states that "Specifically, no more than of the distribution's values can be more than k standard deviations away from the mean".
That is
k = 3
So, we want the range of values within 3 standard deviations of mean.
Hence range is [mean -3*standard deviation, mean +3*standard deviation]
= [6.4 - 3*0.7 , 6.4+3*0.7]
= [6.4 - 2.1 , 6.4+2.1] = [4.3,8.5]
Answer:
i)x=0,x=1
ii)
Step-by-step explanation:
so I did not use the graphs actually.
for the answer to question i), i wrote out the equation as given:
3x^2-3x+2=2
then, i subtracted the two from the right side of the equation to make the equation set equal to 0, and I got:
3x^2-3x+2-2=+2-2, which becomes 3x^2-3x=0
then, I used the quadratic method of taking out the greatest common factor, which in this case is 3x, and the equation becomes:
3x(x-1)=0
finally, for this equation, I set 3x=0 and x-1 =0 to get the solutions to this equation, as shown below
3x=0(divide both sides by 3 to get)x=0
x-1=0(add 1 to both sides to get)x=1
now for the second equation, I had no other choice but to use the quadratic formula to find the solutions.
so I set up the quadratic formula as shown:
from there the equation gets simplified down to:
simplifying the formula even further gives us:
if we simplify the equation one last time, we get:
therefore, the solutions to this equation are: