Answer:
The length of the pole to the nearest feet = 36 ft
Step-by-step explanation:
Let the length of the pole be L
The image of this question is attached to this solution.
From the image,
The two other angles in the triangle formed by the stick, its shadow and the line of angle of elevation can be found.
The first angle to the right of angle of elevation = 90° - 8° = 82°
And the third angle can be found, using the sum of angles in a triangle.
Sum of angles in a triangle = 180°
The third angle = 180° - (70° + 82°) = 28°
Using the sine rule, we can then obtain the length of the pole.
Sine rule
(a/sin A) = (b/sin B) = (c/sin C)
For our question
(L/sin 70°) = (18/sin 28°)
L = (18 × sin 70°)/(sin 28°)
L = 36.03 ft = 36 ft
Answer:
"0.0125" is the right solution.
Step-by-step explanation:
The given values are:
Random sample,
n = 90
Claims,
p = 20%
or,
= 0.20
By using normal approximation, we get
⇒ 
On substituting the values, we get
⇒ 
⇒ 
Now,
The standard deviation will be:
⇒ 
On putting the above given values, we get
⇒ 
⇒ 
⇒ 
⇒ 
hence,
By using the continuity correction or the z-table, we get
⇒ 
⇒ 
⇒ 
From table,
⇒ 
Expectation = Sum of (item * Probability)
Expectation in this case:
$0*0.70 + $20000*0.16 + $40000*0.07 + $60000*0.05 + $80000*0.01 + $100000*0.01 = $ 10800
The fractions in this equation are 3/4 and 5/6. The denominators of those fractions are 4 and 6. The lowest common multiple (LCM) of the numbers 4 and 6 is 12. The LCM is 12 because this is the smallest multiple 4 and 6 have in common
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ....
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ....
The LCM has been highlighted in bold to make it easier to spot
Therefore, the LCD (lowest common denominator) of the fractions is 12. If we were to multiply both sides of this equation by the LCD, then we will clear out the fractions entirely to have whole numbers only left over.
Check out the attached image below for the steps of this process.
Final Answer: 9x + 36 = 10
Bigger piece =
4 * 5 * 7 = 140 inches squared
"Piece you do not care about" (lol) =
2 * 2 * 5 = 20 inches squared
(Edit):
Oops forgot the last part:
140 + 20 = 160 inches squared
