<span>U.S. schools teach the following subsets of the real number system: Natural numbers: {1,2,3,4,...} Integers: {...-4,-3,-2,-1,1,2,3,4,...} Irrationals: Numbers that cannot be expressed as the ratio of two integers, such as nonrepeating, nonterminating decimals.</span>
Yes they can just think of numbers with opposite signs
I-5I=I+5I the absoulte value is 5
Answer:
Option D is the correct choice.
Step-by-step explanation:
We have been given a data set representing the total number of pencils each student in a class needs to sharpen as:
0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9
Let us find median of our given data set. As our data set has 11 data points, so median will be the value of 6th data point, that is 3.
Since first quartile is the median of the lower half of the data. Let us find our lower quartile. Since there are 5 data points below median, so our lower quartile will be the value of 3rd data point, that is 1.
Upper or 3rd quartile is the median of the upper half of the data. Since there are 5 data points above median, so our upper quartile will be the value of 9th data point, that is 6.
We can see that box plot represented by option D is the correct choice as middle line of box is at 3, which represents median of our data set. Lower quartile is at 1 and upper quartile is at 6.
Therefore, box plot shown in option D correctly represents the data.
Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.
Here's another way to look at it:
When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.
For any tangent on g(x), its slope is m = (dy)/(dx)
The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here.
So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.