The Spotlight on Teaching and Learning at the beginning of this chapter discusses the emphasis in the Common Core State Standard
1 answer:
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To solve a system of inequalities we graph both of them.
The inequality representing their combined pay would be
. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
, since they do not want their combined hours to be over 65. In both of these inequalities, <em>x</em> represents the number of hours Jane works and <em>y</em> represent the number of hours Jack works.
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
The inequality representing their combined pay would be
The inequality representing their combined hours working would be
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
a) Mean: 13.25
Variance: 11.02
b)
0 if x below than 7.5
is x in between 7.5 and 19
1 if x higher than 19.
Step-by-step explanation:
This is a problem in which we use the uniform probability distribution.
(a) What are the mean and variance of depth?
The mean is the midpoint of 7.5 and 19. So
The mean is 13.25
The variance is given by the following formula:
In which b and a are the limits of the interval. So
So
The variance is 11.02.
(b) What is the cdf of depth?
The uniform probability distribution has a cummulative distribution function, of 0 if is below a, for x in between a and b and 1 is x is greater than b.
So:
0 if x below than 7.5
is x in between 7.5 and 19
1 if x higher than 19.