Answer:
![Average = 38](https://tex.z-dn.net/?f=Average%20%3D%2038)
Step-by-step explanation:
Given
The attached histogram
Required
The average work hours by 20 salespeople
First, we get the total hours worked as follows:
![Hours = 3 * 30 + 5 * 34 + 9 * 40 + 2 * 45 + 1 * 50](https://tex.z-dn.net/?f=Hours%20%3D%203%20%2A%2030%20%2B%205%20%2A%2034%20%2B%209%20%2A%2040%20%2B%202%20%2A%2045%20%2B%201%20%2A%2050)
![Hours = 760](https://tex.z-dn.net/?f=Hours%20%3D%20760)
Divide by number of salespeople
![Average = Hours/n](https://tex.z-dn.net/?f=Average%20%3D%20Hours%2Fn)
![Average = 760/20](https://tex.z-dn.net/?f=Average%20%3D%20760%2F20)
![Average = 38](https://tex.z-dn.net/?f=Average%20%3D%2038)
Answer:
![P(Canada\ or\ Mexico)= 23\%](https://tex.z-dn.net/?f=P%28Canada%5C%20or%5C%20Mexico%29%3D%2023%5C%25)
Step-by-step explanation:
Given
![P(Canada) = 18\%](https://tex.z-dn.net/?f=P%28Canada%29%20%3D%2018%5C%25)
![P(Mexico) = 9\%](https://tex.z-dn.net/?f=P%28Mexico%29%20%3D%209%5C%25)
![P(Both) = 4\%](https://tex.z-dn.net/?f=P%28Both%29%20%3D%204%5C%25)
Required
Determine ![P(Canada\ or\ Mexico)](https://tex.z-dn.net/?f=P%28Canada%5C%20or%5C%20Mexico%29)
In probability:
![P(A\ or\ B) = P(A) + P(B) - P(Both)](https://tex.z-dn.net/?f=P%28A%5C%20or%5C%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28Both%29)
In this case:
![P(Canada\ or\ Mexico)= P(Canada) + P(Mexico) - P(Both)](https://tex.z-dn.net/?f=P%28Canada%5C%20or%5C%20Mexico%29%3D%20P%28Canada%29%20%2B%20P%28Mexico%29%20-%20P%28Both%29)
Substitute values:
![P(Canada\ or\ Mexico)= 18\% + 9\% - 4\%](https://tex.z-dn.net/?f=P%28Canada%5C%20or%5C%20Mexico%29%3D%2018%5C%25%20%2B%209%5C%25%20-%204%5C%25)
![P(Canada\ or\ Mexico)= 23\%](https://tex.z-dn.net/?f=P%28Canada%5C%20or%5C%20Mexico%29%3D%2023%5C%25)
<em></em>
<em>Hence, the required probability is 23%</em>
Answer:
See below.
Step-by-step explanation:
I can do this but it's a pretty long proof. There might be a much easier way of proving this but this is the only way I can think of.
Write tan A as s/c and sec A as 1/c ( where s and c are sin A and cos A respectively).
Then tanA+ secA -1/ tanA - secA+1
= (s/c + 1/c - 1) / ( sc - 1/c + 1)
= (s + 1 - c) / c / (s - 1 + c) / c
= (s - c + 1) / (s + c - 1).
Now we write the right side of the identity ( 1 + sin A) / cos A as (1 + s) / c
So if the identity is true then:
(s - c + 1) / (s + c - 1) = (1 + s) / c.
Cross multiplying:
cs - c^2 + c = s + c - 1 + s^2 + cs - s
Simplifying:
cs - c^2 + c = cs - (1 - s^2) + c + s - s
Now the s will disappear on the right side and 1 - s^2 = c^2 so we have
cs - c^2 + c = cs - c^2 + c.
Which completes the proof.
Answer:
For left circle,
Exact: 4π cm
Approximate: 12.57 cm
For right circle,
Exact: 23π/3 m
Approximate : 24.09 m
Step-by-step explanation:
I've attached the solution
One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Then the lines are parallel
<h3><u>Solution:</u></h3>
Given that, One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle.
We have to prove that the lines are parallel.
If they are parallel, sum of the described angles should be equal to 180 as they are same side exterior angles.
Now, the 1st angle will be 1/6 of right angle is given as:
![\begin{array}{l}{\rightarrow 1^{\text {st }} \text { angle }=\frac{1}{6} \times 90} \\\\ {\rightarrow 1^{\text {st }} \text { angle }=15 \text { degrees }}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Crightarrow%201%5E%7B%5Ctext%20%7Bst%20%7D%7D%20%5Ctext%20%7B%20angle%20%7D%3D%5Cfrac%7B1%7D%7B6%7D%20%5Ctimes%2090%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%201%5E%7B%5Ctext%20%7Bst%20%7D%7D%20%5Ctext%20%7B%20angle%20%7D%3D15%20%5Ctext%20%7B%20degrees%20%7D%7D%5Cend%7Barray%7D)
And now, 15 degrees is 11 times smaller than the other
Then other angle = 11 times of 15 degrees
![\text {Other angle }=11 \times 15=165 \text { degrees }](https://tex.z-dn.net/?f=%5Ctext%20%7BOther%20angle%20%7D%3D11%20%5Ctimes%2015%3D165%20%5Ctext%20%7B%20degrees%20%7D)
Now, sum of angles = 15 + 165 = 180 degrees.
As we expected their sum is 180 degrees. So the lines are parallel.
Hence, the given lines are parallel