Given that the point B is (1,1) is rotate 90° counterclockwise around the origin.
We need to determine the coordinates of the resulting point B'.
<u>Coordinates of the point B':</u>
The general rule to rotate the point 90° counterclockwise around the origin is given by
The new coordinate can be determined by interchanging the coordinates of x and y and changing the sign of y.
Now, we shall determine the coordinates of the point B' by substituting (1,1) in the general rule.
Thus, we have;
Coordinates of B' = 
Thus, the coordinates of the resulting point B' is (-1,1)
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:
#7 is x = 51
#8 is x = 9
Step-by-step explanation:
#7 walk-through
35 + 2x + 16 + 4x + 3 = 360
35 + 16 + 3 + 2x + 4x = 360
54 + 6x = 360
6x = 306
x = 51
#8 walk-through
6x + 2 = 56
6x = 54
x = 9
I want to say 81°
Here's how I found that:
The angle 105° is on a straight line showing the outer obtuse angle. A straight line is 180°.
180-105=75.
Therefore that inner angle of the 105° is 75°.
We are also given the top angle of 24°.
All 3 angles of a triangle should add up to 180. So, we get the 75+24=99
180-99=81
Last angle should be 81°
