Answer:
The angle F of the triangle DEF measures 105 degrees.
Step-by-step explanation:
Given that triangle DEF has an angle D measuring 25 degrees and an angle E measuring 50 degrees, to determine what is the measure of angle F in degrees, knowing that the sum of the internal angles of every triangle gives a total of 180 degrees, we must perform the following calculation:
180 - 50 - 25 = F
130 - 25 = F
105 = F
Therefore, the angle F of the triangle DEF measures 105 degrees.
<span>Linear relations are not functions when they appear graphically as:
Vertical lines
One x not one y</span>
Answer: Option D is correct. The function equation y= -16x^2 + 9x + 4
is non-linear.
Step-by-step explanation:
It is not linear because it is a quadratic function.
You can see this on the graph in the photo below:
, Hope this helps :)
Have a great day!!
Answer:
a). The mean = 1000
The variance = 999,000
The standard deviation = 999.4999
b). 1000 times , loss
Step-by-step explanation:
The mean of geometric distribution is given as , ![$\mu = \frac{1}{p}$](https://tex.z-dn.net/?f=%24%5Cmu%20%3D%20%5Cfrac%7B1%7D%7Bp%7D%24)
And the variance is given by, ![$\sigma ^2=\frac{q}{p^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%5E2%3D%5Cfrac%7Bq%7D%7Bp%5E2%7D%24)
Given : ![$p=\frac{1}{1000}$](https://tex.z-dn.net/?f=%24p%3D%5Cfrac%7B1%7D%7B1000%7D%24)
= 0.001
The formulae of mean and variance are :
![$\mu = \frac{1}{p}$](https://tex.z-dn.net/?f=%24%5Cmu%20%3D%20%5Cfrac%7B1%7D%7Bp%7D%24)
![$\sigma ^2=\frac{q}{p^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%5E2%3D%5Cfrac%7Bq%7D%7Bp%5E2%7D%24)
![$\sigma ^2=\frac{1-p}{p^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%5E2%3D%5Cfrac%7B1-p%7D%7Bp%5E2%7D%24)
a). Mean = ![$\mu = \frac{1}{p}$](https://tex.z-dn.net/?f=%24%5Cmu%20%3D%20%5Cfrac%7B1%7D%7Bp%7D%24)
=
= 1000
Variance = ![$\sigma ^2=\frac{1-p}{p^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%5E2%3D%5Cfrac%7B1-p%7D%7Bp%5E2%7D%24)
= ![$\sigma ^2=\frac{1-0.001}{0.001^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%5E2%3D%5Cfrac%7B1-0.001%7D%7B0.001%5E2%7D%24)
= 999,000
The standard deviation is determined by the root of the variance.
![$\sigma = \sqrt{\sigma^2}$](https://tex.z-dn.net/?f=%24%5Csigma%20%3D%20%5Csqrt%7B%5Csigma%5E2%7D%24)
=
= 999.4999
b). We expect to have play lottery 1000 times to win, because the mean in part (a) is 1000.
When we win the profit is 500 - 1 = 499
When we lose, the profit is -1
Expected value of the mean μ is the summation of a product of each of the possibility x with the probability P(x).
![$\mu=\Sigma\ x\ P(x)= 499 \times 0.001+(-1) \times (1-0.001)$](https://tex.z-dn.net/?f=%24%5Cmu%3D%5CSigma%5C%20x%5C%20P%28x%29%3D%20499%20%5Ctimes%200.001%2B%28-1%29%20%5Ctimes%20%281-0.001%29%24)
= $ 0.50
Since the answer is negative, we are expected to make a loss.