Answer: A = k =250
B= y,x=0.5
Step-by-step explanation: Find the constant of variation.
35 times, because you add 4+3+6 which gives you 13. Then you find the probability of getting bananas which is 0.35. Then you muliply by 100 which gives you 35.
Answer:
$46.50
Step-by-step explanation:
From the question we are given;
gross weekly pay= $750
Tax rate= 6.2%
Find 6.2% of the gross weekly pay
6.2/100 × $750 = $46.50
Answer:
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668
Step-by-step explanation:
mean, μ = 80 mg/mi
Standard deviation, ![\sigma = 4 mg/mi](https://tex.z-dn.net/?f=%5Csigma%20%3D%204%20mg%2Fmi)
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG
![P(X > x ) = P(z > \frac{x - \mu}{\sigma})](https://tex.z-dn.net/?f=P%28X%20%3E%20x%20%29%20%3D%20P%28z%20%3E%20%5Cfrac%7Bx%20-%20%5Cmu%7D%7B%5Csigma%7D%29)
![P(X > x ) =1 - P(z < \frac{x - \mu}{\sigma})](https://tex.z-dn.net/?f=P%28X%20%3E%20x%20%29%20%3D1%20-%20%20P%28z%20%3C%20%5Cfrac%7Bx%20-%20%5Cmu%7D%7B%5Csigma%7D%29)
![P(X > 86 ) =1 - P(z < \frac{86 - 80}{4})](https://tex.z-dn.net/?f=P%28X%20%3E%2086%20%29%20%3D1%20-%20%20P%28z%20%3C%20%5Cfrac%7B86%20-%2080%7D%7B4%7D%29)
P(X > 86) = 1 - P(z < 1.5)
From the standard normal table, P(z < 1.5) = 0.9332
P(X > 86) = 1 - 0.9332
P(X > 86) = 0.0668
Answer:
![tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%3Dtan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29)
Option A is correct.
Step-by-step explanation:
We need to find equivalent of ![tan\:\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
First we solve ![tan\:\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
We get ![-\frac{1}{\sqrt{3} }](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D)
Now checking all the options.
Option A: ![tan\:(-\frac{\pi}{6} )](https://tex.z-dn.net/?f=tan%5C%3A%28-%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29)
Solving ![tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3A%20we%5C%3A%20get%5C%3A%20%5Cmathbf%7B%20-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%7D)
Option B: ![tan\left(\frac{7\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5Cleft%28%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}](https://tex.z-dn.net/?f=tan%5Cleft%28%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3A%20we%5C%3A%20get%5C%3A%20%5Cmathbf%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%7D)
Option C: ![cot\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=cot%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }](https://tex.z-dn.net/?f=cot%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3Awe%5C%3Aget%5C%3A%5Cmathbf%7B-%5Csqrt%7B3%7D%20%7D)
Option D : ![tan\left(-\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%20%5C%3Awe%5C%3Aget%3A%5Cmathbf%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20%7D)
So, looking at the options, only Option A has the same result as given question
So, ![tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%3Dtan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29)
Option A is correct.