Answer:
Step-by-step explanation:
Given that twenty-three percent of automobiles are not covered by insurance (CNN, February 23,2006).
considering the total number of vehicles, probability for a randomly drawn vehicle not covered by insurance = 0.23
Each vehicle can be treated as independent of the other
Hence X no of vehicles not covered by insurance is Binom with n = 35 and p - 0.23
a) the expected number of these automobiles that are not covered by insurance=E(x) =
![np = 35(0.23)\\= 8.05](https://tex.z-dn.net/?f=np%20%3D%2035%280.23%29%5C%5C%3D%208.05)
b) the variance
=![npq = 8.05(0.77) \\=6.1985](https://tex.z-dn.net/?f=npq%20%3D%208.05%280.77%29%20%5C%5C%3D6.1985)
Std dev = square root of variance = 2.4897
Exact form is 469/12 decimal form is 39.083 repeating and mixed number form is 39/1/12
Answer:
![1372\: \mathrm{inches}](https://tex.z-dn.net/?f=1372%5C%3A%20%5Cmathrm%7Binches%7D)
Step-by-step explanation:
Since the ant travels at a constant speed, we can set up the following proportion:
, where
is the distance the ant can travel in 7 minutes.
Solving for
, we get:
.
![\frac{3x-12}{x-4} \\ \boxed{x-4 \neq 0 \to \ \ x \neq 4} \\ \\ \frac{3x-12}{x-4} = \frac{3(x-4)}{(x-4)}= 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B3x-12%7D%7Bx-4%7D%20%5C%5C%20%5Cboxed%7Bx-4%20%5Cneq%200%20%5Cto%20%5C%20%5C%20x%20%5Cneq%204%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B3x-12%7D%7Bx-4%7D%20%3D%20%20%5Cfrac%7B3%28x-4%29%7D%7B%28x-4%29%7D%3D%203)
Answer: <span>B:3;where x does not equal 4</span>
![\bf \cfrac{5}{3x-12}+\cfrac{3x+1}{x^2-x-12}-\cfrac{2}{3}\implies \cfrac{5}{3(x-4)}+\cfrac{3x+1}{(x-4)(x+3)}-\cfrac{2}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B5%7D%7B3x-12%7D%2B%5Ccfrac%7B3x%2B1%7D%7Bx%5E2-x-12%7D-%5Ccfrac%7B2%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B5%7D%7B3%28x-4%29%7D%2B%5Ccfrac%7B3x%2B1%7D%7B%28x-4%29%28x%2B3%29%7D-%5Ccfrac%7B2%7D%7B3%7D)
now, let's take a peek at the denominators, so we have "3" and "x-4" repeated, so we'll use them only once in our LCD, so using those repeated factors once, our LCD boils down to 3(x-4)(x+3).
![\bf \stackrel{\textit{using an LCD of }3(x-4)(x+3)}{\cfrac{(x+3)5~~~~+~~~~(3)(3x+1)~~~ ~-~~~~[(x-4)(x+3)]2}{3(x-4)(x+3)}} \\\\\\ \cfrac{5x+15~~+~~9x+3~~-~~[x^2-x-12]2}{3(x-4)(x+3)} \\\\\\ \cfrac{5x+15~~+~~9x+3~~-~~(2x^2-2x-24)}{3(x-4)(x+3)} \\\\\\ \cfrac{5x+15~~+~~9x+3~~-~~2x^2+2x+24}{3(x-4)(x+3)} \\\\\\ \cfrac{42+16x-2x^2}{3(x-4)(x+3)}\implies \cfrac{2(21+8x-x^2)}{3(x-4)(x+3)}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Busing%20an%20LCD%20of%20%7D3%28x-4%29%28x%2B3%29%7D%7B%5Ccfrac%7B%28x%2B3%295~~~~%2B~~~~%283%29%283x%2B1%29~~~%20~-~~~~%5B%28x-4%29%28x%2B3%29%5D2%7D%7B3%28x-4%29%28x%2B3%29%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B5x%2B15~~%2B~~9x%2B3~~-~~%5Bx%5E2-x-12%5D2%7D%7B3%28x-4%29%28x%2B3%29%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B5x%2B15~~%2B~~9x%2B3~~-~~%282x%5E2-2x-24%29%7D%7B3%28x-4%29%28x%2B3%29%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B5x%2B15~~%2B~~9x%2B3~~-~~2x%5E2%2B2x%2B24%7D%7B3%28x-4%29%28x%2B3%29%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B42%2B16x-2x%5E2%7D%7B3%28x-4%29%28x%2B3%29%7D%5Cimplies%20%5Ccfrac%7B2%2821%2B8x-x%5E2%29%7D%7B3%28x-4%29%28x%2B3%29%7D)