5.) 12(x - 10)=
1 answer:
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Answer:
x=25
Step-by-step explanation:
we know that "x" is Peter's age
assume that "y" is Phil's age
In the sentence "Phil's age is 7 years more than 1/5 times than Peter's age" are two things: "Phil's age": y and "1/5 times Peter's age": 1/5 x
create equation with these two things
y = 1/5 x
including "7 years more"
many people make a lot of errors with it, they dont know: y+7 = 1/5 x or y=1/5 x + 7 ?
in order to avoid mistakes
read the sentence and point, which: y or 1/5 x is greater and smaller
"Phil's age is 7 years more than ..."
so y is greater, and 1/5 x smaller
y = 1/5 x
greater = smaller
we must add 7 to smaller number to make an equality
greater = smaller + 7
y = 1/5 x + 7
Second sentence:
"4 times Phil's age is 2 years less than twice Peter's age."
Two things: "4 times Phil's age": 4y and "twice Peter's age": 2x
4y = 2x
read the sentence once again
"4 times Phil's age is 2 years less than (...)" , so 4y - smaller, 2x - greater
4y = 2x
smaller = greater
including "2 years less" we add 2 to a smaller number
smaller + 2 = greater
4y + 2 = 2x
Substitute y=1/5 x + 7 to the equation 4y+2 = 2x
Answer:
97.73% of bags weigh more than 14.8 ounces.
Step-by-step explanation:
We are given that the weight of potato chip bags filled by a machine at a packaging plant is normally distributed with a mean of 15.0 ounces and a standard deviation of 0.1 ounces.
<em>Let X = weight of potato chip bags filled by a machine</em>
So, X ~ N()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean weight = 15.0 ounces
= standard deviation = 0.1 ounces
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, percentage of bags that weigh more than 14.8 ounces is given by = P(X > 14.8 ounces)
P(X > 14.8 ounces) = P( >
) = P(Z > -2) = P(Z < 2)
= 0.9773 or 97.73%
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.9773.</em>
Hence, 97.73% of bags weigh more than 14.8 ounces.