Answer:
(x-3)(x-9)
Step-by-step explanation:
first thing you need to do is move the -6 over. so we're going to add 6 to both sides (we add because it's negative 6 and we need 0 on the right side)
so you have: x^2-12x+27
now we need to come up with two numbers that add to -12 and multiply to 27.
the factors of 27 are 9 & 3 and 27 & 1. only 9 & 3 add to 12 so we are going to use those.
since the 12 is negative however, 9 and 3 should both be negative.
therefore we get: (x-3)(x-9)
*it doesn't matter which order you put them in!
Answer:
try find apps about answering this question im not sure about this one :)
Step-by-step explanation:
When the velocity goes from 40km/h to 20 km/h, the kinetic energy decreases by a factor of 4.
<h3>
What happens to the kinetic energy?</h3>
We know that the kinetic energy depends of the square of the velocity. Thus, if we decrease the velocity from 40km/h to 20km/h, then the kinetic energy decreases.
Remember that the kinetic energy is:
K = (m/2)*v²
Where m is the mass.
The initial kinetic energy is:
K = (m/2)*(40km/h)²
The final kinetic energy is:
K' = (m/2)*(20km/h)²
The quotient gives:
K/K' = [ (m/2)*(40km/h)²]/[ (m/2)*(20km/h)²]
K/K' = (40km/h)²/(20km/h)² = 4
So the kinetic energy decreases by a factor of 4.
Learn more about kinetic energy:
brainly.com/question/25959744
#SPJ1
Answer:
(0.4578 , 0.5318)
Step-by-step explanation:
The attached figure shows the formula for calculating confidence intervals for the difference of proportions in large samples.
Let's call
= proportion of married couples, in the first sample, who had two or more personality preferences in common.
= 197/347 = 0.5677
![q_1 = 1-p_1](https://tex.z-dn.net/?f=q_1%20%3D%201-p_1)
= size of the first random sample
![n_1 = 347](https://tex.z-dn.net/?f=n_1%20%3D%20347)
= proportion of married couples, in the second sample, who had no preferences in common.
= 39/535 = 0.0729
![q_2 = 1-p_2](https://tex.z-dn.net/?f=q_2%20%3D%201-p_2)
= size of the second random sample = 535
= confidence%.
= 80%
![(1-\alpha) = 0.8](https://tex.z-dn.net/?f=%281-%5Calpha%29%20%3D%200.8)
![\alpha = 0.2](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.2)
Looking in the normal standard table, we have that
= 1.28.
Substituting this values in the formula we have:
![0.5677-0.0729 + 1.28\sqrt{\frac{0.5677(1-0.5677)}{347}+\frac{0.0729(1-0.0729)}{535}}= 0.4948 + 0.03696\\\\ 0.5677-0.0729 - 1.28\sqrt{\frac{0.5677(1-0.5677)}{347}+\frac{0.0729(1-0.0729)}{535}}= 0.4948 - 0.03696](https://tex.z-dn.net/?f=0.5677-0.0729%20%2B%201.28%5Csqrt%7B%5Cfrac%7B0.5677%281-0.5677%29%7D%7B347%7D%2B%5Cfrac%7B0.0729%281-0.0729%29%7D%7B535%7D%7D%3D%200.4948%20%2B%200.03696%5C%5C%5C%5C%200.5677-0.0729%20-%201.28%5Csqrt%7B%5Cfrac%7B0.5677%281-0.5677%29%7D%7B347%7D%2B%5Cfrac%7B0.0729%281-0.0729%29%7D%7B535%7D%7D%3D%200.4948%20-%200.03696)
![0.4948 + 0.03696 = 0.5318\\\\0.4948 - 0.03696 = 0.4578\\](https://tex.z-dn.net/?f=0.4948%20%2B%200.03696%20%3D%200.5318%5C%5C%5C%5C0.4948%20-%200.03696%20%3D%200.4578%5C%5C)
Then the confidence interval for p1-p2 is: (0.4578 , 0.5318)