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If 3n + 2 = 8, find the value of n. Arrange (3)/(4), 0.8, (5)/(8), 0.65 in descending order. Mr Mensah left his house at 9:45 am and reached his village at 4:15 pm. Find the time spent.

Mathematics

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Answer

D

Step-by-step solution

13 steps

Here are the solutions to the questions:

Part 1· 2 steps

If 3n+2=83n + 2 = 8, find the value of nn.

  1. Subtract 2 from both sides of the equation.

    3n+2−2=8−23n + 2 - 2 = 8 - 2 3n=63n = 6

  2. Divide both sides by 3.

    3n3=63\frac{3n}{3} = \frac{6}{3} n=2n = 2

    The correct option is D.

    D. 2\boxed{\text{D. } 2}

Part 2· 3 steps

Arrange the following: 34,0.8,58,0.65\frac{3}{4}, 0.8, \frac{5}{8}, 0.65 in descending order.

  1. Convert all numbers to decimal form for easy comparison.

    34=0.75\frac{3}{4} = 0.75 0.8=0.800.8 = 0.80 58=0.625\frac{5}{8} = 0.625 0.65=0.6500.65 = 0.650

  2. Arrange the decimal values in descending order (from largest to smallest).

    0.80,0.75,0.650,0.6250.80, 0.75, 0.650, 0.625

  3. Write the numbers back in their original form.

    0.8,34,0.65,580.8, \frac{3}{4}, 0.65, \frac{5}{8}

    The correct option is A.

    A. 0.8,34,0.65,58\boxed{\text{A. } 0.8, \frac{3}{4}, 0.65, \frac{5}{8}}

Part 3· 3 steps

Mr Mensah left his house at 9:45 am and reached his village at 4:15 pm. Find the time spent.

  1. Calculate the time from 9:45 am to 12:00 pm.

    From 9:45 am to 10:00 am = 15 minutes.
    From 10:00 am to 12:00 pm = 2 hours.
    Total time from 9:45 am to 12:00 pm = 2 hours 15 minutes.

  2. Calculate the time from 12:00 pm to 4:15 pm.

    This is 4 hours 15 minutes.

  3. Add the two time durations.

    Total time spent = (2 hours 15 minutes) + (4 hours 15 minutes)
    Total time spent = 6 hours 30 minutes.
    The correct option is C.

    C. 6 hours 30 minutes\boxed{\text{C. } 6 \text{ hours } 30 \text{ minutes}}

Part 4· 3 steps

In a test, 23\frac{2}{3} of the learners passed. If the number of learners who failed was 69, how many passed?

  1. Determine the fraction of learners who failed.

    If 23\frac{2}{3} of the learners passed, then the fraction who failed is 1−231 - \frac{2}{3}.

    1−23=33−23=131 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}

    So, 13\frac{1}{3} of the learners failed.

  2. Use the number of failed learners to find the total number of learners.

    If 13\frac{1}{3} of the total learners is 69, then the total number of learners is 3×693 \times 69.

    Total learners=3×69=207\text{Total learners} = 3 \times 69 = 207

  3. Calculate the number of learners who passed.

    The number of learners who passed is 23\frac{2}{3} of the total learners.

    Number passed=23×207\text{Number passed} = \frac{2}{3} \times 207 Number passed=2×2073\text{Number passed} = 2 \times \frac{207}{3} Number passed=2×69=138\text{Number passed} = 2 \times 69 = 138

    The correct option is B.

    B. 138\boxed{\text{B. } 138}

Part 5· 2 steps

Factorize: 3a2b−9ab23a^2b - 9ab^2.

  1. Identify the greatest common factor (GCF) for the terms 3a2b3a^2b and 9ab29ab^2.

    The GCF of the numerical coefficients (3 and 9) is 3.
    The GCF of the variable a2a^2 and aa is aa.
    The GCF of the variable bb and b2b^2 is bb.
    So, the overall GCF is 3ab3ab.

  2. Factor out the GCF from each term.

    3a2b−9ab2=3ab(a)−3ab(3b)3a^2b - 9ab^2 = 3ab(a) - 3ab(3b) 3a2b−9ab2=3ab(a−3b)3a^2b - 9ab^2 = 3ab(a - 3b)

    The correct option is A.

    A. 3ab(a−3b)\boxed{\text{A. } 3ab(a - 3b)}
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