50 Points!!!

Mathematics

1 answer:

OLEGan [10]3 years ago

5 0

Step-by-step explanation:

(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain

For this case what we see is that we have a scatter diagram, which we can model using a linear trend defining the following variables:

x: number of hours studied.

y: test scores.

The linear relationship would be of the form:

y = mx + b

(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?

y = 8x + 40

For three hours of study we have that the note would be approximate:

y = 8 * (3) + 40

y = 64

The number 40 means that if you do not devote any study time, then you expect the test score to be 40.

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3 years ago

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want

Zanzabum

To solve a system of inequalities we graph both of them.
The inequality representing their combined pay would be
$12.50x+10.00y \geq 750$ . 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
$x+y \leq 65$ , since they do not want their combined hours to be over 65. In both of these inequalities, x represents the number of hours Jane works and y represent the number of hours Jack works.
To graph these, we solve both of them for y:
$x+y \leq 65
\\ x+y-x \leq 65-x
\\ y \leq 65-x$
$12.50x+10.00y \geq750
\\12.50x+10.00y-12.50x \geq 750-12.50x
\\10.00y \geq 750-12.50x
\\ \frac{10.00y}{10.00} \geq \frac{750}{10.00} - \frac{12.50x}{10.00}
\\y \geq 75-1.25x$
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.