If we have 2 dices rolling, we have all 6x6=36 different ways.
But for the sum of the two being 4, we have (1;3), (3;1) and (2;2), only 3 ways.
And we calculate the probability : 3:36= 1/12
Have fun
The sales tax is 2.88 because 6% of 48 is 2.88 so the original price before tax was applied was 45.12
What we know:
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil.
What we need to find:
If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
Set up a proportion to find how much natural oil is used.
7L natural oil/5L synthetic oil = x/355 synthetic oil where x=natural oil
7/5=x/355
(5)(x)=(7)(355) cross multiplied
5x=2485 simplified
5/5x=2485/5 multiplicative inverse
x=497L
Now, add both synthetic oil and natural oil to find amount of petrolyn oil.
355 L synthetic oil + 497 L natural oil= 852 L of petrolyn oil
Answer:
f'(x) = 5 x<4
= 2x 4<x<6
= 4 x>6
Domain is all real numbers except 4 and 6
Step-by-step explanation:
We need to find the derivative of the piecewise function
f'(x) = 5 x<4
= 2x 4≤x≤6
= 4 x>6
Is the function continuous at 4
f(4-) = 5(4) - 6 = 20-6 = 14
f(4+) = 4^2 -2 = 16-2 = 14
this is continuous, so there is no problem with the continuity here
Is the function continuous at
f(6-) = 6^2 -2 = 36-2 = 34
f(6+) = 4(6)+10 = 24+10 = 34
this is continuous, so there is no problem with the continuity here
Now we need to check the derivatives
f'(4-) = 5
f'(4+) = 8
This is not continuous, so we get a piecewise definition for the derivative excluding 4
f'(6-) =12
f'(6+) =4
This is not continuous, so we get a piecewise definition for the derivative excluding 6
