20% of 1000 gal = 200 gal of premium gasoline
80% of 1000 gal = 800 gal of regular gasoline
x = volume of premium gasoline that you need to add to the current mixture
60% of the new mixture is supposed to be premium gasoline. The new mixture would have a total volume of (1000 + x) gal, and in this total, you'd have (200 + x) gal of premium gasoline. So
You'd need to add 1000 gal of premium gasoline to get a mixture of 60% premium.
Answer:
p = - 5, p = - 1
Step-by-step explanation:
Given
-
=
Multiply through by the LCM of (p - 5)(p + 3)
3p(p + 3) - 2(p - 5) = p(p - 5) ← distribute parenthesis
3p² + 9p - 2p + 10 = p² - 5p
3p² + 7p + 10 = p² - 5p ( subtract p² - 5p from both sides )
2p² + 12p + 10 = 0 ← divide through by 2
p² + 6p + 5 = 0 ← in standard form
(p + 1)(p + 5) = 0 ← in factored form
Equate each factor to zero and solve for p
p + 1 = 0 ⇒ p = - 1
p + 5 = 0 ⇒ p = - 5
Answer:
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case
Step-by-step explanation:
For this case we can define the random variable X as the amount of time it takes her to arrive to work and we know that the distribution for X is given by:
And we want to use the empirical rule to estimate the middle 95% of her commute times. And the empirical rule states that we have 68% of the values within one deviation from the mean, 95% of the values within two deviations from the mean and 99.7 % of the values within 3 deviations from the mean. And we can find the limits on this way:
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case