Tutor profile: Taylor P.
Fill in the blanks of the following sentences with the correct conjugated form of the verb given in parentheses: a. Esperamos que ellos (llegar) antes de las nueve. b. Mi mamá quiere ir Chili's para (cenar). c. Ella (estar) en un restaurante porque ella tiene hambre.
a. The correct answer is "lleguen" (they arrive). "Ellos" (they) is the third person plural pronoun. The use of the conjugation "Esperamos" (We hope) followed by the conjunction "que" (that) expresses desire, and therefore elicits the use of the subjunctive mood. Note that "llegar" is irregular in this mood. b. The correct answer is "cenar" (to eat dinner). When preceded by the preposition "para" (meaning "in order to" when followed directly by a verb), the verb remains in its infinitive state. c. The correct answer is "está" (is). The conjugated verb "tiene" indicates that the sentence is in the present tense, therefore the first verb must conjugated to the third person singular form of "estar" (to be).
Subject: Basic Chemistry
Determine the molarity of a solution containing 0.2074g of calcium hydroxide [Ca(OH)2] dissolved in 40.00 mL of solution.
When it comes to problems such as these, I like to break down the solution into steps: Step 0- Review what you are given. Step 1- Determine the molecular weight of the compound. Step 2- Find the number of moles in the compound. Step 3- Using the number of moles, find the molarity of the solution. Step 0: When I solve a chemistry (or any type of science problem, really), I like to begin by writing down what the problem gives me and what it is that we are looking for. In this case, we would note that we are given: -m=0.2074g Ca(OH)2 -v=40.00mL -M=? Step 1: To determine the molecular weight of the compound, we must use the formula of the compound as well as the periodic table. The numbers in the chemical formula tell us how many of each molecule is in the compound. Ca(OH)2, for example, has 1 Ca molecule, 2 O molecules, and 2 H molecules (the parentheses indicate that the number in the subscript is distributed to all elements contained within them). Now, we must find MW of each element: 1 Ca x 40.078= 40.078 2O x 16.00= 32.00 2H x 1.00784 =2.01568 To find the overall MW, we simply add the individual weights together: 40.078 + 32.00 + 2.01568= 74.09368.* This number is important because it provides us with a conversion factor: 74.09368g/mol Ca(OH)2 *REMEMBER- it may be tedious, but while calculating, be sure to keep as many significant figures on your answers as possible to allow for the most accurate calculations. Step 2: To determine the number of moles in the compound, simply multiply the amount of Ca(OH)2 in grams by the conversion factor calculated in Step 1 using dimensional analysis: *0.2074g Ca(OH)2 x 1 mol Ca(OH)2/74.09368g Ca(OH)2*= 0.002799159 mol Ca(OH)2 *When dimensional analysis is used, the "g of Ca(OH)2" on the top and bottom will cancel, leaving you with "mol Ca(OH)2". **REMEMBER- it may be tedious, but while calculating, be sure to keep as many significant figures on your answers as possible to allow for the most accurate calculations. Step 3: To find the molarity of the solution, we must now use all the numbers that we've been given, as well as the numbers that we have determined. Remember that "M" is equivalent to "mol/L", so ultimately, we want moles on top and liters on the bottom. Using the number of moles that we calculated in Step 2 and dimensional analysis: 0.002799159 mol Ca(OH)2 x 1/ 40mL x 1000ml/ 1L*= 0.06998** mol/L OR 0.06998 M *REMEMBER- it is essential to make sure that the units on your final calculations are correct. Be sure to convert mL to L or else your answer will be incorrect! **The final answer is the time to make sure that your significant figures are correct. Because this was ultimately a multiplication problem, the final answer should contain 4 significant figures, for the number with the lowest amount of sig figs has 4.
Factoring Sample Problem: Factor -24x^9y^5 - 64x^7y^8.
We begin by determining what the sets of numbers have in common. I like to first divide the terms like so: -24, -64; x^9, x^7; y^5, y^8 After the terms have been separated accordingly, we determine the GCF (greatest common factor, or the greatest factor that divides two numbers) of each set. In this case, the GCF is -8, x^7, and y^5 respectively. Therefore, one of the factors is -8x^7y^5. But what about the rest of the equation? To determine the other factor(s) of the polynomial, we simply determine what's left after the GCF is divided out of the equation: (This factor goes on the outside of the parentheses because it is shared by both terms in the equation)--> -8x^7y^5(3x^2+8y^3) <--(The numbers inside the parentheses are what's left after the GCF is factored out) So, the final answer is -8x^7y^5(3x^2+8y^3). **Be sure to check your work afterward by multiplying the factors together!
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