Answer:
a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170
Step-by-step explanation:
(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:
Marginal cost (MC) = change in total cost/change in quantity
Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:
Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k
where k is a constant.
The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k
C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k
Thus:
C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH
(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170
The variable is Quantitative, has Interval level of measurement.
Variables which can be quantified & expressed numerically are Quantitative variables. Eg : as given , price
Variables which cant be qualified & expressed numerically are Qualitative variables. Eg : level of honesty, loyalty etc
Nominal & Ordinal are qualitative variables : signifying yes or no to a category (like men or women) , or ranks (x better than y) respectively. So price level is not such categorical & ordinal ratio.
Quantitative ratio variables are with reference to time , or are in forms of rate (like speed , growth per year). So, price level is not such ratio variable also.
Price is a quantitative variable, in which the ranking, its difference can be calculated. This is characteristic of a <u>Quantitative Interval Variable</u>.
Answer:
<em><u /></em>
- <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.
