Answer: The first and second angles measure 54 degrees each. The third angle measures 72 degrees.
Step-by-step explanation:
First, I transcribed the sentences into equations.
The first part of the sentence says that "two angles of a triangle have equal measures", and we can use the konwledge that the interioir angle sum of all triangles in 180 degrees to solve this.
Lets call the first and second angles x and the third angle y. Then we can get the equation that 2x + y = 180. You might be asking "where did the 2x come from?", well, we know that if we add all of the angles up we get 180 degrees, and since two of the angles are equal, they can be simplified to 2x.
The second part of the sentence says that "the third angles measure is 36 degrees less than the sum of the other two", which translates to:
y = 2x - 36
Then we can substitute the second equation into the first and solve!
2x + (2x - 36) = 180
4x - 36 = 180
4x = 216
x = 54
Knowing that x = 54, we can substitute back into the first equation to solve for y. 2(54) + y = 180, 108 + y = 180, y = 72.
1) In this study, the control group is the first group of 310 subjects that were instructed to take only 600 mg daily of vitamin C. (Option C; that is, group 1).
2) The study is not Blind (Option C).
In an experimental setup to test a theory, A control group is the set of experimental participants that the theory to be tested isn't applied upon.
In the case of testing a new treatment, the control group is the group that the new treatment isn't administered.
For this question, the experiment was set up to test the effectiveness of a combination of vitamin A and vitamin E in treating flu cases rather than using vitamin C alone. Group A is the only group that only the old treatment alone is applied to; group 1 participants received no dosage of the new combination of treatments to be tested involving vitamins A and E, unlike the two other groups.
It is obvious now why the experimental participants of group 1 are the control group.
2) A blind experiment/study is one in which the participants don't know which group they belong to, whether they are in the control group or the other experimental group. Like in this case, if this was a blind study, the participants wouldn't know which group they belonged to or which treatment is administered to them.
A double-blind experiment/study is one in which both the conductors of the experiment and the participants in the experiment wouldn't know which group any participant is in. The conductors wouldn't know which participants were in the control or treatment group and the participants too wouldn't have an idea whether they are in the control or treatment group.
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Answer:
1) 0.487,0.0436
2) 56.3 cm
Step-by-step explanation:
Let X be the scores ranging from 0 to 20 of the Psychology students at Wittenberg University completed the Dental Anxiety Scale questionnaire.
X is N(11,3.5)
a) the probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale.
=
b)
c) Y is N(50, 20) where Y is tree diameter at breast height 110 years after the fire.
P(X>d) = 0.30
Corresponding Z value = 0.525
d = 56.3 cm
Answer:
Step-by-step explanation:
The given system is:
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
We could solve the first equation for and replace the second with that.
Let's do that.
Subtract on both sides:
So we are replacing the second in the second equation with which gives us:
Now recall the first equation we arranged so that was the subject. I'm referring to .
We can now find given that using the equation .
Let's do that.
with :
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with :
is a true equation so the "solution" looks promising still.
with :
is also true so the solution has been verified since both equations render true for that point.