For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get
x^2-12x+45
___ ________________________
x+1 | x^3-11x^2+33x+45
- (x^3+x^2)
_________________________
-12x^2+33x+45
- (-12x^2-12x)
______________
45x+45
-(45x+45)
___________
0
Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
Answer:
See below...
Step-by-step explanation:
Theoretical probability is the probability that something should happen based on the beginning conditions. Such as having a jar of 30 marbles with 5 being blue. The probability of pulling out a blue marble when selecting 1 marble is
5/30, or 1/6. Theoretically you should pull one blue marble out every 6 times you pull a marble out.
This isn't guaranteed to happen though, that's where experimental probability comes form.
Experimental probability is the number of desired outcomes achieved, divided by the total number of outcomes. This is based on what actually happened. Say you selected a marble, and put it back 10 times, recording the color each time and you got 2 blue marbles. Your experimental probability is
2/10, or 1/5, which doesn't match the theoretical probability. The more times this experiment is conducted, the closer your result will be to the theoretical probability
Answer:
111.4 degrees
Step-by-step explanation:
Let's write cos x = -0.3646. Or, look up the symbols chart at the bottom of your page and click on Ф to obtain this character: cos Ф = -0.3646.
If Ф is in Quadrant III, then the adjacent side is negative and the hypotenuse is positive.
-1
Type this into your calculator: cos -0.3646. Result: 1.934 (radians)
This converts to degrees as follows:
1.934 rad 180 degr
--------------- * --------------- = 111.4 degrees. Note that this angle is in QIII.
1 π rad
23/50 you want the denominator to be 100 so you multiply both by 2
then you get
46/100 or you can divide and get .46
to turn it to a percentage multiple by 100
.46 and 46%
21/2 or 10 1/2
Explanation:
8 3/4 is the same as 35/4
so Darcy harvests 35/4 per 5/6 hours
to figure out how much is harvested in one hour, you divide the amount harvested by the amount of hours taken to harvest it.
35/4 ÷ 5/6 =35/4 × 6/5
35/4 × 6/5 = 7/2 × 3/1 = 21/2
so the answer is 21/2 or 10 1/2
