Answer:
Sqrt 29
Step-by-step explanation:
Answer:
(a) 283 days
(b) 248 days
Step-by-step explanation:
The complete question is:
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. (a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths?
Solution:
The random variable <em>X</em> can be defined as the pregnancy length in days.
Then, from the provided information
.
(a)
The minimum pregnancy length that can be in the top 11% of pregnancy lengths implies that:
P (X > x) = 0.11
⇒ P (Z > z) = 0.11
⇒ <em>z</em> = 1.23
Compute the value of <em>x</em> as follows:

Thus, the minimum pregnancy length that can be in the top 11% of pregnancy lengths is 283 days.
(b)
The maximum pregnancy length that can be in the bottom 5% of pregnancy lengths implies that:
P (X < x) = 0.05
⇒ P (Z < z) = 0.05
⇒ <em>z</em> = -1.645
Compute the value of <em>x</em> as follows:

Thus, the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths is 248 days.
Answer:
the volume of the cylinder is 904.32 m³
Step-by-step explanation:
Volume of a cylinder is 
π = 3.14
r = 6 units
h - 8 units
Substitute for the values in the volume equation
V = 904.32
Answer:
Step-by-step explanation:
Recall the following formula:
Given a triangle with side lengths a, b, and c. Let the measure of the angle between sides of length a and c be B.
Then, the area of the triangle is given by :

.
In our example we have: Area=10 square cm, a=8 cm, c=5 cm, and we want to find the measure of the angle between the 2 sides a and c.
Substituting in the formula we have:

Thus,

, which means

.

is the sine of

, but also

.
Answer: both 30, and 150 degrees are possible