Can someone show me how to do the following problem...? 5x^2-5x-30=0
2 answers:
Ooh, quadratic equations!
alright, you see that zero at the end right?
that means you are trying to find the two factors
I'll write out the equation on paper to show you
take note of the signs in b and c
(ax²+bx+c)
because 5x is a negative (-5x), when you factor it out, the two, when multiplied together, should be negative. and because 30 is negative, the numbers will have two different signs. in other words, one will be positive and one will be negative.
now that that's cleared, we need to find all of the multiples of 30
there is:
30×1
15×2
10×3
and 6×5
of all of them, 10 and 3 would give you the -5 needed in -5× since one of them are going to be multiplied times 5
now let's factor it:
(5x+10)(x-3)
finally, divide everything
I wrote everything down for you to see
alright, you see that zero at the end right?
that means you are trying to find the two factors
I'll write out the equation on paper to show you
take note of the signs in b and c
(ax²+bx+c)
because 5x is a negative (-5x), when you factor it out, the two, when multiplied together, should be negative. and because 30 is negative, the numbers will have two different signs. in other words, one will be positive and one will be negative.
now that that's cleared, we need to find all of the multiples of 30
there is:
30×1
15×2
10×3
and 6×5
of all of them, 10 and 3 would give you the -5 needed in -5× since one of them are going to be multiplied times 5
now let's factor it:
(5x+10)(x-3)
finally, divide everything
I wrote everything down for you to see
You might be interested in
Answer:
a) 75%.
b) 84%
c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Chebyshev Theorem:
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by .
In this question:
Mean: 6.3 hours
Standard deviation: 1.6 hours
(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.
3.1 = 6.3 - 2*1.6
9.5 = 6.3 + 2*1.6
Within 2 standard deviations, so the minimum percentage is 75%.
(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.
How many standard deviations from the mean?
One standard deviation is 1.6
These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which
The minimum percentage is:
So 84%.
(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.
Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.