Answer:
(a) 3.8
Step-by-step explanation:
The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.
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<h3>compare angles</h3>
The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.
<h3>compare sides</h3>
Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.
EF > DE
EF > 3
Only one answer choice satisfies this inequality.
EF = 3.8
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<em>Additional comment</em>
If you want to do the actual computation, we have ...
EF/sin(D) = DE/sin(F)
EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828
EF ≈ 3.8
-5.5x+0.56= -1.64
-0.56 -0.56
-5.5x= -2.2
/5.5 /5.5
x= -0.4 is the answer
Answer:
x<1/3
Step-by-step explanation:
Answer:
The coordinates of A' are (6,6).
Step-by-step explanation:
It is given that in triangle ABC, A = (-1, 3), B = (1, - 1) and C = (2, 2).
If a point is rotated 90 ° clockwise about the point ( a,b ), then
It is given that the triangle is rotated 90 ° clockwise about the point ( 4, 1 ). So, a=4 and b=1.
The coordinates of A are (-1,3), So, the coordinates of A' are
Therefore the coordinates of A' are (6,6).
Answer
a. True
Step-by-step explanation:
Based on this survey we estimate that about 
of the college students smokes. And a 
confidence interval is ![[15.1\% ; 21.6\%]](https://tex.z-dn.net/?f=%5B15.1%5C%25%20%3B%2021.6%5C%25%5D)
. So we know that 
our estimative for the smoking rate is in the confidence interval with certainty. We also know the estimative for the smoking rate in the general population is 
. So we can write the two possible hypothesis:
Smoking rate is equal to .
Smoking rate is not equal to .
We will reject the null hypothesis 
if the estimate doesn't fall into the confidence interval for the college students smoking rate.
Since this condition holds we reject the null hypothesis. So with certainty we say that the smoking rate for the general population is different than the smoking rate for the college students.
