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SECTION B ESSAY TEST PART 1. (a) Simplify: w2 x w x w⁻². (b) What is 21 1/2% of Le 80,000.00. (c) At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?

Mathematics

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Answers

3 parts
a

w\mathbf{w}

b

Le 17,200.00\mathbf{Le \ 17,200.00}

c

0.8%\mathbf{0.8\%}

Step-by-step solution

10 steps

Part a· 2 steps

Simplify: w2×w×w−2w^2 \times w \times w^{-2}.

  1. Apply the rule of exponents am×an=am+na^m \times a^n = a^{m+n}.

    w2×w1×w−2=w2+1+(−2)w^2 \times w^1 \times w^{-2} = w^{2+1+(-2)}

  2. Add the exponents.

    w2+1−2=w1w^{2+1-2} = w^1

    The simplified expression is ww.

    w\boxed{\mathbf{w}}

Part b

Le 17,200.00\mathbf{Le \ 17,200.00}

What is 2112%21\frac{1}{2}\% of Le 80,000.00.

  1. Convert the percentage to a decimal or fraction.

    2112%=21.5%=21.510021\frac{1}{2}\% = 21.5\% = \frac{21.5}{100}

  2. Multiply the decimal/fraction by the amount.

    21.5100×80,000.00=0.215×80,000.00\frac{21.5}{100} \times 80,000.00 = 0.215 \times 80,000.00

  3. Calculate the value.

    0.215×80,000.00=17,200.000.215 \times 80,000.00 = 17,200.00

    The amount is Le 17,200.00.

    Le 17,200.00\boxed{\mathbf{Le \ 17,200.00}}

Part c

0.8%\mathbf{0.8\%}

At what rate will Le 10,000.00 earn an interest of Le 400.00 in 5 years?

  1. Identify the given values for simple interest.

    Principal (P)=Le 10,000.00(P) = \text{Le } 10,000.00
    Interest (I)=Le 400.00(I) = \text{Le } 400.00
    Time (T)=5 years(T) = 5 \text{ years}

  2. Use the simple interest formula I=P×R×TI = P \times R \times T to find the rate (R)(R).

    Rearrange the formula to solve for RR:

    R=IP×TR = \frac{I}{P \times T}

  3. Substitute the values into the formula.

    R=40010,000×5R = \frac{400}{10,000 \times 5}

  4. Calculate the rate.

    R=40050,000R = \frac{400}{50,000} R=0.008R = 0.008

  5. Convert the rate to a percentage.

    R=0.008×100%=0.8%R = 0.008 \times 100\% = 0.8\%

    The interest rate is 0.8%0.8\%.

    0.8%\boxed{\mathbf{0.8\%}}
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