Step-by-step explanation:
Answer above
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Stanley drove a race car an average speed of 120 miles per hour for 3 minutes. How far did Stanley drive the race car?
1 answer:
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Answer:
Consider the system of equations,
and
As we know that,
'The intersection points of the graphs of the system of equations are the solutions of the system of equations'.
So, after plotting the given graphs, we see that,
The only intersection point is (0.714,-2.857).
Thus, the solution of the system is x= 0.714 and y= -2.857.
Answer:
a) 30.85% of people earn less than $40,000
b) 37.21% of people earn between $45,000 and $65,000.
c) 15.87% of people earn more than $70,000
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this problem, we have that:
a.What percent of people earn less than $40,000?
This is the pvalue of Z when X = 40000. So
has a pvalue of 0.3085.
30.85% of people earn less than $40,000
b.What percent of people earn between $45,000 and $65,000?
This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 45000. So
X = 65000
has a pvalue of 0.7734.
X = 45000
has a pvalue of 0.4013.
0.7734 - 0.4013 = 0.3721
37.21% of people earn between $45,000 and $65,000.
c.What percent of people earn more than $70,000?
This is 1 subtracted by the pvalue of Z when X = 70000. So
has a pvalue of 0.8413.
1 - 0.8413 = 0.1587
15.87% of people earn more than $70,000
For this case we must solve the following equations:
We subtract 3x on both sides of the equation:
We subtract 7 on both sides of the equation:
We divide between 2 on both sides of the equation:
The second equation is:
We apply distributive property to the terms of parentheses:
We add common terms:
We add 10 to both sides of the equation:
We divide between 5 on both sides of the equation:
Third equation:
We apply distributive property to the terms within parentheses:
We add similar terms:
We subtract 6x on both sides of the equation:
We subtract 5 on both sides of the equation:
Answer: