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Algebra Integers Test

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Subject
Algebra
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Answers
1) P (9) = 0.125
2) b + c
3) 21/(4x-8)
1. Let and let . Find P (9)
Solution
If we let P(x) = P (9), then x = 9. The "e" represents the Euler's constant which is ≈ 2.718.
The "!" in the denominator represents "factorial" or the product of the integer and all the
integers below it.
P(x) = (µ
x
e
-µ
)/9!
P (9) = (10
9
e
-10
)/9!
P (9) = (10
9
2.718
-10
)/ (9*8*7*6*5*4*3*2*1)
P (9) = (10
9
2.718
-10
)/ (9*8*7*6*5*4*3*2*1)
P (9) = 45447.03/362880
P (9) = 0.125
2. Perform all indicated operations and write the answer with positive integer
exponents.
Solution
The rule for negative exponent states that "negative exponent that is in the
numerator get moved to the denominator and become positive exponent. Negative
exponent that is in the denominator get moved to the numerator and become
positive exponents". Such that,
x
-n
can be transformed into 1/(x
n
)
Let us work first on the numerator b
-1
+ c
-1
can be transformed into 1/(b
1
) + 1/(c
1
) or
(1/b) + (1/c). It can be simplified as (c + b)/bc
b
-1
+ c
-1
= 1/(b
1
) + 1/(c
1
)
b
-1
+ c
-1
= (1/b) + (1/c)
b
-1
+ c
-1
= (c + b)/(bc) ----> this will be the simplified numerator
For the denominator (bc)
-1
can be transformed into 1/bc. Therefore, the fraction will
be:
= numerator/denominator
= [(c + b)/(bc)]/(1/bc)
= bc(c+b)/(bc) ----> fraction as a denominator will be multiplied to the numerator as
its reciprocal
= c + b = b + c

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1 Answers 1) P (9) = 0.125 2) b + c 3) 21/(4x-8) 1. Let and let . Find P (9) Solution If we let P(x) = P (9), then x = 9. The "e" represents the Euler's constant which is ≈ 2.718. The "!" in the denominator represents "factorial" or the product of the integer and all the integers below it. P(x) = (µxe-µ)/9! P (9) = (109e-10)/9! P (9) = (1092.718-10)/ (9*8*7*6*5*4*3*2*1) P (9) = (1092.718-10)/ (9*8*7*6*5*4*3*2*1) P (9) = 45447.03/362880 P (9) = 0.125 2. Perform all indicated operations and write the answer with positive integer exponents. Solution The rule for negative exponent state ...
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