Answer:
a) 63°
b) 127°
Step-by-step explanation:
Complements are 90° while supplements are 180°.
So you need to find the complement of 27°. So, 90-27=63
To find the supplement, it is 180-53=127
Answer:
a. correlation
b. inverse linear correlation exists If the higher the population of students lead to a decrease in test score,
c. yes
Step-by-step explanation:
a. Correlation is a measure of the amount of association existing between two variables.
b. For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists,
Similarly,when a straight line having a negative gradient can reasonably be drawn through points on a graph, negative or inverse linear correlation exists,
The results of this determination give values of r lying between +1 and −1, where +1 indicates perfect direct Positive linear correlation and −1 indicates perfect inverse correlation or Negative linear correlation and 0 indicates that no correlation exists.
If the higher the population of students lead to a decrease in test score, there will definitely be a negative correlation between class size and test score. i.e low class size result in high test score which consequently lead to high performance.
c. YES
A negative correlation means low class size result in high test score which consequently lead to better performance.
An easier way to think of this problem is just keep adding for each additional hour:
0.5 hours --> $2
1.5 hrs --> $3.75
2.5 hrs --> $5.50
3.5 hrs --> $7.25
and since you can only spend $7, the maximum time is 2.5 hours
Answer: choice A. 40 liters
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Explanation:
x = number of liters of the 50% alcohol solution
If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).
So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below
0.50*x + 36 = 0.70*(40+x)
0.50*x + 36 = 0.70*(40)+0.70*(x)
0.50*x + 36 = 28+0.70*x
36 - 28 = 0.70*x - 0.50x
8 = 0.20x
0.20x = 8
x = 8/0.20
x = 40
So that is why the answer is choice A. 40 liters
