1a) if all the angles are perpendicular, they all =90°
Answer:
True
Step-by-step explanation:
64x³ + 125
64x³ = (4x)³ ← a perfect cube
125 = 5³ ← a perfect cube
Thus 64x³ + 125 ← is a sum of cubes
The question requires stating the Null and Alternative hypothesis for the scenario described :
Answer:
H0 : μ = 24
H1 : μ < 24
Step-by-step explanation:
The claim or hypothesis to be tested in a statistical problem or analysis is the alternative hypothesis. This is usually the opposite of the Null hypothesis which is the usually the initial truth until there is significant evidence provided using statistical test to prove otherwise.
The null hypothesis, H0 in the scenario above is :
H0 : μ = 24 ( average battery life is 24 hours)
The alternative hypothesis is the claim, that is. The mean battery life not up to 24 hours ;
H1 : μ < 24
Answer:
First Question: <u>63 coins are not nickels.</u>
Second Question: <u>63+n=91</u>
Step-by-step explanation:
For your first question: 29+21=50 and 50+13=63. 63 coins are not nickels.
For your second question: You can do 29+21+13+n=91, I just simplified and said 63+n=91. You can choose.
Hope that this helps! Good luck with what you're working on!
Answer:

Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of
and the hypotenuse of
.
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is
. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

Now use this value in the Law of Sines to find AD:

Recall that
and
:

Now that we have the length of AD, we can find the length of AB. The right triangle
is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio
, where
is the side opposite to the 30 degree angle and
is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent
in this ratio and since AB is the side opposite to the 30 degree angle, it must represent
in this ratio (Derive from basic trig for a right triangle and
).
Therefore, AB must be exactly half of AD:
