Answer:
PQ = 34.4
Step-by-step explanation:
First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74
Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)
This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.
We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that
NO/QR = MN/PQ
Thus,
11/27 = 14/PQ
multiply both sides by PQ to remove a denominator
PQ * 11/27 = 14
multiply both sides by 27 to remove the other denominator
PQ * 11 = 14 * 27
divide both sides by 11 to isolate the PQ
PQ = 14 * 27 /11
PQ = 34.4
Simply it as follows:
1 + 39 = 40
2 + 38 = 40 etc
18 + 22 = 40
19 + 21 = 40
There are 19 of these plus 40 itself . . .therefore 20 of them
20 x 40 = 800
And finally the last number not used, 20
Therefore 800 + 20 = 820
Answer:
14.54
Step-by-step explanation:
In a <em>weighted average</em> a “weight” is associated to each value.
The weighted mean is computed the following way:
Suppose you want to calculate the weighted mean of the values
a1, a1, …, an
with weights
w1, w2,..., wn
Then
<em>Weighted mean</em> =(w1*a1+w2*a2+... +wn*an)/(w1+w2+...+wn)
In this case we have
a1= 12, w1 = 8
a2 = 13, w2 = 6
a3 = 17, w3 = 12
<u>Weighted mean </u>
(12*8+13*6+17*12)/(8+6+12) = 14.54 rounded to 2 decimal places.
If Julian works 40 hours per week and you would like to know what are his earnings after taxes, you can calculate this using the following steps:
per one hour: 0.77 * (13.50 * 1h) = 0.77 * 13.50 = $10.395
per 40 hours: 0.77 * (13.50 * 40h) = 0.77 * 13.50 * 40 = $415.8
Result: His earnings after taxes will be $415.8.
