Answer:
B. f(g(x)) = 7x + 27
Step-by-step explanation:
We have, f(x) = 7x+13 and g(x) = x+2.
So, the function f(g(x)) is obtained by substituting the function g(x) = x+2 in f(x) = 7x+13,
i.e. f(g(x)) = f(x+2)
i.e. f(g(x)) = 7 × (x+2) + 13
i.e. f(g(x)) = 7x + 14 + 13
i.e. f(g(x)) = 7x + 27
Thus, f(g(x)) = 7x + 27
Hence, option B is correct.
58% is about equal to 60%, 10% of 121 is 12.1.
12.1 * 6 = 72.6
To take this further, 58% is 2% less than 60%, or 2 times 1%. 1% of 121 is 1.21.
72.6 - (1.21 * 2) = 72.6 - 2.42 = 70.18
B/C = K/L because they are similar
I know you got this from Khan Academy, and so the answer is $9.81. You probably don't care about how it is done, and you probably just want to put the answer and be done, but I will show you. You have to take the original price of $9 and multiply it with 9%, or 0.09, to get the amount of your tip. add the 9%, or $81. You can also just do 9*109%, or 9*1.09, to put these two steps together and add the original price and the tip.
Answer:
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- <em><u>positive correlation, likely causal </u></em>
Explanation:
Correlation and causation are different.
Correlation means that the variables are related, meaning that when one changes the other also change. A positive correlation means that the variables change in the same way: when one increases the other also increases, and when one decreases the other also decreases. A negative correlation means that the variables change in opposite directions, i.e. when one increases the other decreases.
The correlations may be strong, moderated or weak. The correlation coefficient tells how strong the correlation is. The correlation coefficient may take values from - 1 to + 1.
A negative 1 correlation coefficient means a perfect negative correlation. A positive 1 correlation coefficient means a perfect positive correlation. Thus, in this case Brett's teacher found that the correlation coefficent was r = 0.97. That is pretty close to 1, and means that this is a strong positive correlation.
About causation, you only may feature a relationship as causal if one variable is the reason why the other variable changed in the way it did it. In this case, it is very reasonable to attribute a causation relationship between the minutes Brett stayed on task in class and the grade he earned on the homework that night, because the more Brett worked in class the better prepared he should be to do his homework, and that idea is reinforced by the high positive correlation coefficient r = 0.97. That is why you can assert that the teacher must have discored a positive correlation, likely causal.
