07.24.14
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SAT – counting and ordering

Q: You are 18th in line and your friend is 34th in line. How many people are in line between you and your friend?

Answer:  15

No, not 16! Do 34-18=16, but then subtract one. Why? The 16 includes either the person you started with (you) or the person you ended with (your friend), and you don’t want to include either person in the count.

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07.22.14
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Algebra 2 – solving quadratic equations

Q: The length of a rectangle is 4 cm longer than the width. If the rectangle’s area is 45 cm², what is the width?

Answer: 5 cm

Explanation:  Call the width x.  Then, the length is x+4.

Area of a rectangle = (length)(width).

45 = x(x+4)

45 = x² + 4x

0 = x² + 4x – 45

Now, factor:

0 = (x + 9)(x – 5)

x = -9 or x = 5

Since a length can’t be negative, discard x = -9.  The only solution is x = 5.  Since ‘x’ is what we called the width, it is the answer to the question.  Just put the appropriate unit on it: 5 cm.

 

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07.20.14
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SAT – Probability

Using a standard pair of dice, what is the probability of rolling two numbers with a sum of 8?

Answer:

5/36

Explanation:  6 x 6 = 36 ways you can roll two dice.  Now, find the ways you can get a sum of 8:

2+6, 6+2, 3+5, 5+3, 4+4

That’s 5 ways.  So, the probability is 5/36.

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07.19.14
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SAT – Venn Diagrams

Q: Of the 20 students in the classroom, 14 are taking Calculus, 12 are taking Physics, and 4 are taking neither Calculus nor Physics. How many students are taking both Calculus and Physics?
 
Answer: 10
Use a Venn Diagram.  Assume for a moment that there is no overlap between Calculus and Physics.  Then, there would be 14 + 12 = 26 students taking either Calculus or Physics.  Add the 4 students taking neither, and that would be a total of 30 students.  The question states that there are only 20 students in the class.  So there must be some overlap after all.  How much?  30 – 20 = 10 students taking both Calculus and Physics.  Put 10 in the overlapping region.  To fill out the rest of the diagram: 14 – 10 = 4 students in Calculus but not Physics.  12 – 10 = 2 students in Physics but not Calculus.
venn
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07.18.14
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Geometry – Triangles

Q: In triangle ABC below, what is sin C ?
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Answer: 4/5
Explanation:  Use the Pythagorean Theorem or the 3-4-5 Pythagorean triple to find out that the hypotenuse is 10.
Then, sin C = (opposite)/(hypotenuse) = 8/10 = 4/5.
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07.16.14
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Hello, and Welcome!

Hi Everyone!  I’m starting a blog with all the questions I’ve answered on my Facebook page.  Please ‘like’ me at www.facebook.com/mathprotutoring!  There, you may submit problems to me by sending a private message to that page.

My website is www.mathprotutoring.com.  Please find info there about my math tutoring services, both in person in Cooper City, Florida, or online for anyone in the US and Canada.

 

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