x = c – b + a – b + c – a = 2c – 2 b . pg. 17. Correct answer is A.

Let's combine a and b to single element that we call *. Then our set will become A={0,1,2,3,*}. Since this set has 5 elements it has 32 subsets (2⁵=32). Out of these 32 sets, there are 16 sets that doesn't contain *. (If we delete *, there remains a set containing 4 elements which has 2⁴=16 subsets). A subset will either contain * or it will not contain *. Thus 32-16=16 sets contain *, namely a and b.

2⁷=128

The correct answer is D.

x = max {2 / 5, 1 / 4, 3 / 8, 3 / 10, 7 / 16} = max {32, 20, 30, 24, 35} / 80 = 7 / 16. pg. 12. Correct answer is E.

we can calculate that: 4²=16, 4³=64, 4⁴=256, 4⁵=1024, 4⁶=4096 Then the power of 4, which lies between 4000 and 4100, is 6.

From the graph we see that f(5/2)=-6 and f(-3)=8, so 2f (5/2)–f (-3)=(2.-6)-8=-20

Note that one can rewrite;

5^2x+3=1/25=5^2x+3=5^-2

Since the exponential function 5^x is one-to one, we have

2x+3=-2 then x=-5/2

5⁰=1

The correct answer is B.

Since 20 percent is lost, 80 percent is remaining at the end of 10 years. Thus we can write:

0.8Q=Q.e^10k

ln0.8/10=k=-0.0223

So we can find the half life by:

0.5Q=Q.e-^0.0223t

ln0.5=-0.0223t, then t=31.06 years

3x-6=0, x=2. Therefore the answer is C.

(x – 2) (x + 1) = 0 ; x = 2, x = -1 . pg. 55 . Correct answer is C.

The answer is A.

-2 ln(x – 1) = -4 ; ln(x – 1) = 2 = ln e² ; x – 1 = e² ; x = e² + 1. Correct answer is A.

Correct answer is A.

For the first earthquake, the intensity is; M = log₁₀I› 7.1=log₁₀I› I=10^7.1

For the second earthquake, the intensity is; M = log₁₀I› 5.2=log₁₀I› I=10^5.2

on the Richter scale yields an intensity change by a factor of

10^7.1_{/10^{5.2 =}10^1.9=79.43} 

^{Strictly speaking; the fist earthquake had a magnitude about 80 times greater than second earthquake.}

Denote by M and S the set of all students who are members of the Mathematics and Sports clubs, respectively. Then, s(M ? S) = 250-17 = 233. Using the formula (M ? S) = s(M) + s(S) – s(M ? S), we have s(M ? T) = 233 = 153 + 110 - x, where x is the required number. Then we find that x = 153 + 110 - 233. Thus, x equals to 30. 

Total value at the end=10.000(1.2)⁴=2.0736*10000=20736

x + x^-1 + 1 ; -1 is not natural number ; all powers of the variable x must be natural numbers. pg. 50. Correct answer is D.

• a⁰ = 1 for all nonzero numbers a.
• If a = 0, a⁰ is called indeterminate.
• ? (infinity) is not a number. It represents an infinitely large quantity.
• The whole real line is an interval denoted by (–?, ?).
• Powers are used when we multiply a real number by itself repeatedly.

As also understood from the information given, the correct answer is C. The statements in the options I a⁰ = 1 for all nonzero numbers a.”, III “? (infinity) is not a number. It represents an infinitely large quantity.”, IV “The whole real line is an interval denoted by (–?, ?).” and V “Powers are used when we multiply a real number by itself repeatedly.” are correct. The statement in the option II “If a = 0, a⁰ is called power of a.” is not correct because of the fact that if a = 0, a⁰ is called indeterminate.