Step-by-step explanation:
The zeroes of f(x) are -2, -3 and 2.
Hence f(x) = (x + 2)(x + 3)(x - 2) = (x + 3)(x² - 4) = x³ + 3x² - 4x - 12.
Answer:
C, 40 degrees
Step-by-step explanation:
All the angles of a triangle add to 180 degrees according to the Triangle Sum Theorem.
Since all angles sum to 180, we can set all the values to add to 180.
We have:
![2y+y+10+50=180](https://tex.z-dn.net/?f=2y%2By%2B10%2B50%3D180)
Combining like terms, we have:
![3y+60=180](https://tex.z-dn.net/?f=3y%2B60%3D180)
Subtracting 60 from both sides gets us
![3y=120](https://tex.z-dn.net/?f=3y%3D120)
Dividing by 3 from both sides equals
![y=40](https://tex.z-dn.net/?f=y%3D40)
it equals <span>(−<span>12</span>)</span> because <span><span>cos<span>(<span>60∘</span>)</span></span>=<span>12</span></span>
Explanation:
The reference angle for <span>240∘</span> is <span>60∘</span> (since <span><span>240∘</span>=<span>180∘</span>+<span>60∘</span></span>)
<span>60∘</span> is an angle of one of the standard triangles with
<span><span>cos<span>(<span>60∘</span>)</span></span>=<span>12</span></span>
<span>240∘</span> is in the 3rd quadrant so (either by CAST or noting that the "x-side" of the associate triangle is negative)
<span><span>cos<span>(<span>240∘</span>)</span></span>=−<span>cos<span>(<span>60∘</span>)</span></span></span>
<span><span>cos<span>(<span>240∘</span>)</span></span>=−<span><span>12</span></span></span>
Answer:
The mean is 561.40 ppm. The standard deviation is 29.15 ppm.
Step-by-step explanation:
We can calculate the mean and the standard deviation using the proportions of the population that are subjected to the different levels.
The mean can be calculated as
![\mu=\sum p_i*L_i\\\\\mu=0.06*370+0.13*470+0.46*560+0.35*630\\\\\mu=561.40 \,ppm](https://tex.z-dn.net/?f=%5Cmu%3D%5Csum%20p_i%2AL_i%5C%5C%5C%5C%5Cmu%3D0.06%2A370%2B0.13%2A470%2B0.46%2A560%2B0.35%2A630%5C%5C%5C%5C%5Cmu%3D561.40%20%5C%2Cppm)
The standard deviation of the mean can be calculated in a similar way
![\sigma=\sqrt{\sum p_i(L_i-\mu)^2}\\\\\sigma=\sqrt{0.06(370-561.4)^2+0.13(470-561.4)^2+0.46(560-561.4)^2+0.35(630-561.4)^2}\\\\\sigma=\sqrt{0.06(36634)+0.13(8354)+0.46(2)+0.35(4706)}\\\\\sigma=\sqrt{2198.04+1086.01+0.90+1647.09}=\sqrt{4932.04}=29.15](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Csum%20p_i%28L_i-%5Cmu%29%5E2%7D%5C%5C%5C%5C%5Csigma%3D%5Csqrt%7B0.06%28370-561.4%29%5E2%2B0.13%28470-561.4%29%5E2%2B0.46%28560-561.4%29%5E2%2B0.35%28630-561.4%29%5E2%7D%5C%5C%5C%5C%5Csigma%3D%5Csqrt%7B0.06%2836634%29%2B0.13%288354%29%2B0.46%282%29%2B0.35%284706%29%7D%5C%5C%5C%5C%5Csigma%3D%5Csqrt%7B2198.04%2B1086.01%2B0.90%2B1647.09%7D%3D%5Csqrt%7B4932.04%7D%3D29.15)
The mean is 561.40 ppm. The standard deviation is 29.15 ppm.