Solve for x 3 (x – 4) = 12x
1 answer:
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Keywords:
<em>System of equations, variables, hardcover version, paperback version, books </em>
For this case we must construct a system of two equations with two variables. Let "h" be the number of hardcover version books, and let "p" be the number of paperback version books. If the hardcover version of a book weighs 7 ounces and the paperback version weighs 5 ounces, to reach a total of 249 ounces we have:
(1)
On the other hand, if there are Forty-five copies of the book then:
(2)
If from (2) we clear the number of books paperback version we have:
As each paperback version book weighs 5 ounces, to obtain the total weight of the paperback version books, represented by "x" in the table shown, we multiply
So,
Answer:
Option D
Answer:
The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424
Step-by-step explanation:
The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.
Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.
The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.
We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words
The values of the cummulative function of the standard normal variable W, which we will denote are tabulated and they can be found in the attached file.
Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.
Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.