Answer:
<u>x = 60°</u>
Step-by-step explanation:
The rest of the question is the attached figure.
Given: A rhombus inside a regular hexagon, work out the angle x.
As shown
ABCDEF is a regular hexagon.
The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°
So, the measure of one angle of the regular hexagon = 720/6 = 120°
So, ∠F = ∠BAF = 120°
AFEG is a rhombus.
The rhombus have 2 obtuse angles and 2 acute angles.
∠F is one of the obtuse angles of the rhombus = 120°
∠F and ∠FA G are supplementary angles
So, ∠F + ∠FA G = 180°
∴ ∠FA G = 180° - ∠F = 180 - 120 = 60°
∴ x = ∠GAB = ∠BAF - ∠FA G = 120 - 60 = 60°
<u>So, the measure of the angle x = 60°</u>
Answer : His saving in 52 weeks is $ 867.
Step-by-step explanation :
Let the income per week be $100.
Saving = 25%
Saved income = $25
Take home income = $100 - $25 = $75
If he take home $75 a week then his saving = $25
If he take home $50 a week then his saving = 
= 
His saving in 1 week =
His saving in 52 weeks = 
= $ 866.66
≈ $ 867
Therefore, his saving in 52 weeks is $ 867.
If its has to be odd it would most likely be 29 times instead of 28
Answer:
0.4435
Step-by-step explanation:
Given that :
X is normally distributed:
mean(m) = 1,000
standard deviation (s) = 250
probability that X lies between 800 and 1,100?
Using the relation :
X = 800
Zscore = (x - m) / s
Zscore = (800 - 1000) / 250
Zscore = - 200 / 250
Zscore = - 0.8
P(Z ≤ - 0.8) = 0.2119
X = 1100
Zscore = (x - m) / s
Zscore = (1100 - 1000) / 250
Zscore = 100 / 250
Zscore = 0.4
P(Z ≤ 0.4) = 0.6554
P(Z ≤ 0.4) - P(Z ≤ - 0.8)
0.6554 - 0.2119
= 0.4435
5 out of 12 = 5/12
Those are
1 - 106
2 - 137
4 - 120
6 - 195 and
8 - 139
