1. The prism below measures 6 inches x 3 inches x 10 inches. A diagonal
1 answer:
9514 1404 393
Answer:
√145 ≈ 12.04
Step-by-step explanation:
The length of the space diagonal is the root of the sum of the squares of the prism edge lengths:
d² = a² +b² +c² = 6² +3² +10² = 145
d = √145 ≈ 12.04 . . . inches
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The face diagonal is found using the Pythagorean theorem in the usual way:
f² = a² + b²
The space diagonal is the hypotenuse of the right triangle whose sides are the face diagonal and the remaining edge:
d² = f² +c²
d² = a² +b² +c²
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Here is a diagram.
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Answer:
b ≈ 9.5, c ≈ 14.7
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
=
, substitute values
=
( cross- multiply )
b × sin23° = 7 × sin32° ( divide both sides by sin23° )
b = ≈ 9.5 ( to the nearest tenth )
Also
=
=
( cross- multiply )
c × sin23° = 7 × sin125° ( divide both sides by sin23° )
c = ≈ 14.7 ( to the nearest tenth )
Answer:
26 years
Step-by-step explanation:
Given:
The mean age of 9 women = 27 years old
The mean age of 7 men = 25 years old
Question asked:
What is the mean age (nearest year) of all the people in the office?
solution:
By using, mean = sum of observations divided by number of entities
The mean age of 9 women = 27 years old
=
The mean age of 7 men = 25 years old
=
Total sum of ages of men and women in the office = 243 + 175
= 418 years
Total number of people in the office = 9 women + 7 men = 16
The mean age of all the people in the office = Total sum of ages of men and women in the office divided by Total number of people in the office
=
Therefore, the mean age (nearest year) of all the people in the office = 26 years