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Q166 Simultaneous equations View

The supply and demand curves of a product represent, respectively, the quantities that sellers and consumers are willing to trade as a function of the product's price. In some cases, these curves can be represented by straight lines. Suppose that the quantities of supply and demand of a product are, respectively, represented by the equations: $$Q_{0} = -20 + 4P$$ $$Q_{D} = 46 - 2P$$ where $Q_{o}$ is the quantity supplied, $Q_{D}$ is the quantity demanded, and P is the price of the product.
From these supply and demand equations, economists find the market equilibrium price, that is, when $\mathrm{Q}_{\circ}$ and $\mathrm{Q}_{\mathrm{D}}$ are equal.
For the situation described, what is the value of the equilibrium price?

Q168 Indices and Surds Evaluating Expressions Using Index Laws View

Among other research objects, Allometry studies the relationship between measurements of different parts of the human body. For example, according to Allometry, the area A of the body surface of a person relates to their mass $m$ by the formula $A = k \cdot \mathrm{~m}^{\frac{2}{3}}$, where $k$ is a positive constant.
If during the period from childhood to adulthood of an individual their mass is multiplied by 8, by how much will the area of body surface be multiplied?
(A) $\sqrt[3]{16}$
(B) 4
(C) $\sqrt{24}$
(D) 8
(E) 64

Q169 Matrices Matrix Algebra and Product Properties View

A student recorded the bimonthly grades of some of his subjects in a table. He observed that the numerical entries in the table formed a $4 \times 4$ matrix, and that he could calculate the annual averages of these subjects using matrix multiplication. All tests had the same weight, and the table he obtained is shown below.

	$1^{st}$ bimonth	$2^{nd}$ bimonth	$3^{rd}$ bimonth	$4^{th}$ bimonth
Mathematics	5.9	6.2	4.5	5.5
Portuguese	6.6	7.1	6.5	8.4
Geography	8.6	6.8	7.8	9.0
History	6.2	5.6	5.9	7.7

To obtain these averages, he multiplied the matrix obtained from the table by
(A) $\left[\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\right]$

Q174 Measures of Location and Spread View

The table below shows the evolution of annual gross revenue in the last three years of five microenterprises (ME) that are for sale.

ME	2009 (in thousands of reais)	2010 (in thousands of reais)	2011 (in thousands of reais)
Pins V	200	220	240
Candies W	200	230	200
Chocolates X	250	210	215
Pizzeria Y	230	230	230
Textiles Z	160	210	245

An investor wants to buy two of the companies listed in the table. To do so, he calculates the average of the annual gross revenue of the last three years (from 2009 to 2011) and chooses the two companies with the highest annual average.
The companies that this investor chooses to buy are
(A) Candies W and Pizzeria Y.
(B) Chocolates X and Textiles Z.
(C) Pizzeria Y and Pins V.
(D) Pizzeria Y and Chocolates X.
(E) Textiles Z and Pins V.

Q176 Measures of Location and Spread View

An irrigated coffee producer in Minas Gerais received a statistical consulting report, containing, among other information, the standard deviation of the productions from one harvest of the plots on his property. The plots have the same area of $30000\mathrm{~m}^{2}$ and the value obtained for the standard deviation was $90\mathrm{~kg}/\mathrm{plot}$. The producer must present information about the production and the variance of these productions in bags of 60 kg per hectare ($10000\mathrm{~m}^{2}$).
The variance of the productions of the plots expressed in (bags/hectare)$^{2}$ is
(A) 20.25.
(B) 4.50.
(C) 0.71.
(D) 0.50.
(E) 0.25.

Q178 Probability Definitions Finite Equally-Likely Probability Computation View

José, Paulo, and Antônio are playing fair dice, on which, on each of the six faces, there is a number from 1 to 6. Each of them will roll two dice simultaneously. José believes that, after rolling his dice, the numbers on the faces facing up will give him a sum equal to 7. Paulo believes that his sum will be equal to 4, and Antônio believes that his sum will be equal to 8.
With this choice, who has the greatest probability of getting their respective sum correct is
(A) Antônio, since his sum is the largest of all the chosen ones.
(B) José and Antônio, since there are 6 possibilities for both José's choice and Antônio's choice, and there are only 4 possibilities for Paulo's choice.
(C) José and Antônio, since there are 3 possibilities for both José's choice and Antônio's choice, and there are only 2 possibilities for Paulo's choice.
(D) José, since there are 6 possibilities to form his sum, 5 possibilities to form Antônio's sum, and only 3 possibilities to form Paulo's sum.
(E) Paulo, since his sum is the smallest of all.

Q179 Measures of Location and Spread View

The graph presents the behavior of formal employment created, according to CAGED, in the period from January 2010 to October 2010.
Based on the graph, the value of the integer part of the median of formal employment created in the period is
(A) 212952.
(B) 229913.
(C) 240621.
(D) 255496.
(E) 298041.

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2012 enem__day2