Answer:
$9,840
Step-by-step explanation:
Let the money earned from college be 'x'.
Given:
Total money earned from the two jobs = $50,450
Money earned at the store = 1250 + 4(Money earned at college)
∴ Money earned at the store =
Now, total money earned by Erica is the sum of money earned at store and college. Therefore,
Total money = Money at store + Money at college
Therefore, the money earned by Erica from her job at the college is $9,840.
The third coordinate of the equilateral triangle is . Ir can be obtained by distance formula.
What is distance formula?
It gives the distance between two coordinates.
Distance formula is given by the following expression:
Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.
Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).
Now, caculate the distance between (0,-a) and (0, a).
Now, distance between (x,0) and (0, a) should be 2a.
Now, square on both the sides.
and
But the negative value of x is not possible because the coordinate lies on the right side.
Hence, the third coordinate of equilateral triangle is .
Learn more about distance formula from the following link:
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Answer:
The proportion of the chocolate bars produced that have mass within one standard deviation of the mean is 0.6826 = 68.26%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A consumer organization finds that the mass of the chocolate bar is normally distributed with a mean of 200.4 g and a standard deviation of 0.05 g.
This means that
a) Find the proportion of the chocolate bars produced that have mass within one standard deviation of the mean.
pvalue of Z when X = 200.4 + 0.05 = 200.9 subtracted by the pvalue of Z when X = 200.4 - 0.05 = 199.9.
X = 200.9
has a pvalue of 0.8413
X = 199.9
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
The proportion of the chocolate bars produced that have mass within one standard deviation of the mean is 0.6826 = 68.26%.