Using the angle relationships, the sizes of the angles are:
a = 21°
b = 70°
c = 89°
<h3>What are Angle Relationships?</h3>
- Vertical angles are equal in measure.
- Two angles on a straight line are linear pair and are supplementary.
- All angles in a triangle will add up to the sum of 180 degrees.
Thus:
a = 21° (vertical angles).
b = 180 - 110 = 70° (linear pair).
c = 180 - (70 + 21) = 89° (triangle sum)
Therefore, using the angle relationships, the sizes of the angles are:
a = 21°
b = 70°
c = 89°
Learn more about angle relationships on:
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Answer:
-14y -154
Step-by-step explanation:
Multiply -14 and y = -14y
Multiply -14 and 11 = -154
X=29
There is always a total of 180 degrees in a triangle. Let’s represent this mathematically.
180=35+52+3(x+2)
We can subtract the 35 and the 52 from both sides.
93=3(x+2)
Now, distribute.
93=3x+6
And subtract the 6.
87=3x
Finally, divide both sides by 3.
29=x
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Answer:
The hippocampus volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm³
Step-by-step explanation:
Let x= the hippocampus volumes in the alcoholic adolescents
We'll conduct a hypothesis test at the 0.01 significance level with
Null hypothesis: x = 9.02 cm³
Alternate hypothesis: x < 9.02 cm³
A sample of 13 alcoholic adolescents gives the parameters
size=N= 13
mean=M= 8.12 cm³
standard deviation= s= 0.8 cm³
According to the sample, with 99% confidence, t statistic for the value X=9.02 can be found using the formula:
t=
where
- M is the sample mean (8.12)
- s is the standard deviation of the sample (0.8)
- N is the sample size (13)
If we put these numbers in the formula:
t=
=4.056
One tailed critical value for the sample with 12 degrees of freedom (sample size-1) in 99% confidence level is 2.681.
Since t value (4.056) is bigger than the critical value, we fail to reject the alternate hypothesis, therefore reject the null hypothesis and accept alternate hypothesis.
Answer:
a) Qualitative
b) Qualitative
c) Quantitative
d) Quantitative
Step-by-step explanation:
A variable is quantitative if it assumes numerical values, for example 1,2,3.
If it assumes "labels", for example good or bad, it is qualitative.
(a) The occupation of your neighbors. Answer:
Labels. Teacher, trainer, athlete, ...
So it is qualitative
(b) The martial status of your coworkers. Answer:
Labels: Married, single,..
So it is qualitative
(c) Your college GPA. Answer:
Numeric, 2,3,...
So it is quantitative
(d) The amount of bacteria on a piece of moldy bread
Numeric, 0.5mm, etc
So it is quantitative