In this question, we have to write the set of points from -6 to 3 but excluding -2 and 3 as a union of intervals .
For union, we use U.
For the points that we have to exclude , we put parenthesis on there side that is ().
Therefore the required interval form is
As we see that () are used with -2 and 3 . And that's the required interval form .
Y=1/x solve for x
x=1/y now reverse lables...
y=1/x
Yes that is the same equation you started with. What that means is the the inverse function in this case produces the same exact graph :)
Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.
We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II
We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)
We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III
Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml
Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml
Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
Answer: 99% decrease
Step-by-step explanation: Since the number changes from 6,000 to 60, we know that it's decreasing. Now to find the percent decrease, we divide the amount of change by the original number.
The amount of change is the difference between 6,000 and 60 and the original number is 6,000.
6,000 - 60 is 5,940 so we are left with 
and dividing 6,000 into 5,940 gives us 0<em>.</em>99.
Finally, since the problem is asking us for the <em>percent</em>, we write 0.999 as a percent by moving the decimal point 2 places to the right to get 99%.
So when a number changes from 6,000 to 60, it has decreased by 99%.
