Stan took 25 classes during college. The Venn diagram below shows classes Stan studied for, classes Stan
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So for this, we will be doing a system of equations, with one equation representing the total invested and the other equation representing the total gained from the investments. But first, we have to do calculations:
firstly, to represent a percentage gain (in this case 12% gain) you are to add 0.12 (12% in decimal form) to 1 to get 1.12. <em>Keep 1.12 in mind, as it will be used for the equations.</em>
Next, to represent a percentage loss (in this case 11%), you are to subtract 0.11 (11% in decimal form) from 1 to get 0.89. <em>Keep 0.89 in mind, as it will be used in the equations.</em>
Next, we need to find the total amount of money after the investments. To do this, add 21,000 and 1,715 together to get 22,715. <u>$22,715 is the total amount of money gained in 1 year.</u>
Now that we have all of our information, we can form our equations as such:
- Let x = $ invested into the account with 12% gain and y = $ invested into the account with 11% loss
Now with these system of equations, I will be using the substitution method. So firstly, with the first equation subtract x on both sides of that equation:
Now that we know that y = 21000 - x, replace y for (21000 - x) in the second equation and solve for x as such:
Now that we have the value of x, substitute it into either equation to solve for y:
<u>In short, $17500 was invested into the account that gained 12% and $3500 was invested into the account that had lossed 11%.</u>
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
<h3>What is the line of best fit?</h3>A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
Learn more about the line of best fit here:
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