3m²n + 12mn²
3mn(m) + 3mn(4n)
3mn(m + 4n)
The GCF of this expression is 3mn.
Answer:
∠ Y = 45°, ∠ X = 135°
Step-by-step explanation:
Since the 2 angles are supplementary, then
X + Y = 180 ← substitute X = 3Y
3Y + Y = 180, that is
4Y = 180 ( divide both sides by 4 )
Y = 45
and
X + Y = 180, so
X + 45 = 180 ( subtract 45 from both sides )
X = 135
Thus
∠ X = 135° and ∠ Y = 45°
Given:
Diameter of the hole = 30 cm
To find:
The area of the hole.
Solution:
The radius of a circle is always half of the diameter. It is given that the diameter of the hole is 30 cm. So, the radius of the hole is:


Area of a circle is:

Putting
and
in the above formula, we get



Therefore, the area of the hold is 706.5 square cm.
Answer:
The expected participation rate is 0.637.
The standard error is 0.04397
Step-by-step explanation:
For each working age people asked, there are only two possible outcomes. Either they are in the labor force, or they are not. This means that we can solve this problem using binomial distribution probability concepts.
Binomial probability:
Expected value for the participation rate: The expected value is the probability of a success. In this problem, a success is a working age people being in the labor force. 63.7% of them are. So
. This means that the expected participation rate is 0.637.
Standard error for the participation rate:
The standard error is given by the following formula:
.
In this problem, 120 people are asked, so 
.
So the standard error is 0.04397