Tutor profile: Lizzie C.
Subject: SAT II Mathematics Level 2
If f(x) = (5x - 3)/(2x + 4), what value does f(x) approach as x gets infinitely larger?
As x gets infinitely larger, the subtraction and addition values will become decreasingly important. If x is 1,000,000, 5x will be 5,000,000. At these high values, subtracting three will hardly make a difference. The same goes for the 2x+4. As 2x becomes increasingly large, adding four will make little difference to the value of 2x+4. If we can effectively ignore the -3 and +4 in this equation, then we have f(x) = 5x/2x. Since x/x = 1, we can cancel out the x's. Thus, f(x) would approach 5/2 as x got increasingly larger.
Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights? John is at a restaurant and has spent $35.50 so far. He plans to purchase a slice of cake for dessert that costs $4.50, and then pay his bill. A tax of 6% will be applied to his total purchase, and he'll leave a tip on the total, pre-taxes. How would you represents John's total cost, in dollars, if he leaves a tip of x%?
John's total bill, pre-taxes and pre-tip, would be $35.50 + $4.50, or $40. He would have to pay 6% in taxes on the $40, which would be 0.06*$40 =$2.40, bring his total to $42.40. In addition, he has to pay a tip of x% on his pre-tax total. Thus, his total cost would be $42.40 + (x/100)*40, or $42.40 + 0.4x
How is mRNA created in eukaryotic cells, and what role does it play in protein synthesis?
mRNA is created through a process called transcription, in which RNA polymerase utilizes the coding in the DNA to generate corresponding mRNA. The mRNA is then processed and transported to the cytoplasm, where a ribosome attaches to the mRNA. This ribosome translates the mRNA by creating a chain of amino acids, or a protein, that corresponds to the coding of the mRNA.
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