Tutor profile: Karen C.
Subject: SAT II Mathematics Level 2
In a garment factory, 4 workers can knit 40 sweaters in 4 days. How long would it take for 10 workers to knit 200 sweaters? Assume that each of these workers work at same pace.
Given that it is assumed that each of the workers work at the same pace, it is important to first find the pace at which the workers can knit. 4 workers can knit 40 sweaters in 4 days, meaning that 4 workers can knit 10 sweaters in 1 day, meaning each worker can knit 2.5 sweaters in 1 day. You can find this number by first dividing the 40 sweaters by the number of days to find the total number of sweaters knitted per day and then dividing the total number of sweaters by the total number of workers to find the number of sweaters knitted per day per worker. Now that we know that each worker can knit 2.5 sweaters a day, we can find out how many sweaters 10 workers can knit for a day by multiplying 2.5 sweaters by 10 workers, which equals 25 sweaters a day. The question asks to find out how many days it would take to knit 200 sweaters. Since we know that 10 workers can knit 25 sweaters a day, we can divide the total number of sweaters, 200, by 25 sweaters a day, to find out how many days it would take the 10 workers. Here, we find that 200 sweaters divided by 25 sweaters per day equals 8 days. So, it would take the 10 workers 8 days to finish 200 sweaters.
Find the x intercept of the graph of the equation: 3x-5y = 15.
To review, the x intercept is where the line crosses the X-axis, which also means what x is equal to when the y-coordinate is 0. To find the x intercept, we are solving for x in this equation. Since we are looking for the x intercept, we can set the y variable to 0. By doing so, you are left with the equation 3x - 5(0) = 15 or 3x = 15. If you divide both sides by 3 and isolate x, you find that x = 5.
In the current debate over environmental policy, there is a lot of discussion of having carbon taxes or caps in order to curb carbon emissions into the environment. If I were trying to draft a policy to limit carbon emissions, would it be more effective to implement a carbon tax or a carbon cap?
Economically, the effectiveness would be the same. To explain, first imagine a supply-demand graph, with the downward sloping demand representing the demand for carbon and the upward-sloping supply line representing the supply for carbon. Price of carbon is on the Y-axis and quantity of carbon used (or emitted) is on the X-axis. Currently, carbon usage is at equilibrium, Q0 and P0. Let's say that through your policy, you want Q0 to shift to the left, to Q1 (representing a decrease in carbon emissions). You can do this in two ways - through a carbon tax or a carbon cap. With a carbon tax, you are essentially making the price of producing carbon more expensive by putting the tax on the supplier (e.g. a factory emitting carbon). This makes the supplier's cost of producing carbon equal to the original P0 + the tax. This shifts supply to the left, and ideally, you will establish a tax that will shift supply far enough to the left that it forms an equilibrium with demand at Q1. This will also put the new price at P1, higher than the original P0. With a carbon cap, you are essentially making the supply of carbon a fixed value. Graphically, this means that the supply curve goes from being upward sloping to a vertical line at your desired carbon emission amount, Q1. No matter the price of carbon, the cap forces the equilibrium to always be at Q1. Therefore, economically, there is no difference in effectiveness with either policy. However, there are other differences. WIth a carbon tax, the government is able to gain revenue from the tax to spend on other purposes whereas the carbon cap does not generate that kind of revenue. Also, the selection mechanisms for who gets to emit carbon are different for these two policies that have real-world implications. For the carbon tax, the tax weeds out companies that cannot afford to pay the tax but may be important businesses for the economy. For the carbon cap, the policy that is created would have to create a way to allocate carbon emissions to various companies, which could have its own flaws and biases.
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