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Caroline B.

Tutor for K-12 level English, math, and science

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Linear Algebra

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Question:

Rearrange the equation 6x+5=12+8x and solve for x.

Caroline B.

Answer:

First, subtract 5 from both sides of the equation 6x+5=12+8x: You are then left with 6x=7+8x. Then, combine the like terms 6x and 8x by subtracting 8x from both sides, leaving you with: -2x=7. Now, divide both sides by -2 to isolate x. Therefore: 7/-2=x

Basic Chemistry

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Question:

The molar mass of calcium chloride (CaCl2) is 110.98 g/mol. How many moles of calcium chloride are there in 50 g of CaCl2?

Caroline B.

Answer:

The molar mass of any compound expresses the weight in grams of that compound per mole of the compound. For the problem above, we are given that one mole of CaCl2 is 110.98 grams, and the question asks for the number of moles in 50 grams of CaCl2. So, when expressed mathematically, the question looks like this: 50 g CaCl2/1 * 1 mole CaCl2/110.98 g CaCl2. Then, we check that the grams cancel out of the expression and leave us with an answer in moles, as the question called for. Grams of CaCl2 will cancel out. Perform the remaining calculation after canceling units where appropriate: 50/1 *1 mole CaCl2/110.98= .450 moles CaCl2 Therefore, the answer is .450 moles CaCl2 are in 50 g of CaCl2.

English

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Question:

Identify the independent and dependent clauses in the sentence: When I went shopping on Tuesday, I bought two pairs of shoes and one shirt.

Caroline B.

Answer:

The independent clause in the sentence is, "...I bought two pairs of shoes and one shirt." This phrase qualifies as the independent clause because it has both a subject (I) and a verb (bought), ergo the clause can stand alone as a complete sentence with a subject and action word (verb.) The dependent clause would be, "When I went shopping on Tuesday..." because the clause cannot stand by itself as a complete sentence, as it does not express a complete thought.

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