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A table shows the number of packages purchased from a store. (i) Copy and complete the table. (ii) Calculate the mean number of packages purchased. (iii) Find the total number of customers. (iv) What

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6 parts
c(ii)
2.58
c(iii)
19
c(iv)
49
c(v)

GHe 2131.50\text{GHe 2131.50}

d(i)

9.429228×1029.429228 \times 10^2

d(ii)

2(2a - 1)(3b + 2)

Step-by-step solution

12 steps

Here are the solutions to the questions you sent.

Part c(i)

Copy and complete the table.

The table shows the number of packages purchased from a store.

The completed table is:
$$
\begin{array}{|c|c|c|} \hline \text{Packages (x)} & \text{Customers (f)} & \text{fx} \\ \hline 0 & 0 & 0 \\ 1 & 4 & 4 \\ 2 & 4 & 8 \\ 3 & 8 & 24 \\ 4 & 2 & 8 \\ 5 & 1 & 5 \\ \hline \end{array}
$$

Part c(ii)2.58

Calculate the mean number of packages purchased.

  1. Calculate the sum of customers (∑f\sum f).

    $$
\sum f = 0 + 4 + 4 + 8 + 2 + 1 = 19
$$

  2. Calculate the sum of fxfx (∑fx\sum fx).

    $$
\sum fx = 0 + 4 + 8 + 24 + 8 + 5 = 49
$$

  3. Calculate the mean using the formula Mean=∑fx∑f\text{Mean} = \frac{\sum fx}{\sum f}.

    $$
\text{Mean} = \frac{49}{19} \approx 2.5789
$$
The mean number of packages purchased is $\boxed{2.58}$ (rounded to 2 decimal places).

Part c(iii)19

Find the total number of customers.

The total number of customers is the sum of the frequencies ($\sum f$).
$$
\text{Total customers} = 0 + 4 + 4 + 8 + 2 + 1 = 19
$$
The total number of customers is $\boxed{19}$.

Part c(iv)49

What is the total number of packages purchased?

The total number of packages purchased is the sum of $fx$ ($\sum fx$).
$$
\text{Total packages} = 0 + 4 + 8 + 24 + 8 + 5 = 49
$$
The total number of packages purchased is $\boxed{49}$.

Part c(v)

GHe 2131.50\text{GHe 2131.50}

If a package costs GHe 43.50, how much did the store make?

  1. Use the total number of packages purchased from part (iv).

    Total packages = 49.

  2. Multiply the total packages by the cost per package.

    $$
\text{Total earnings} = 49 \times \text{GHe } 43.50
$$
$$
\text{Total earnings} = \text{GHe } 2131.50
$$
The store made $\boxed{\text{GHe 2131.50}}$.

Part d(i)

9.429228×1029.429228 \times 10^2

Find the sum of 16.702, 923.5 and 2.7208, leaving your answer in standard form.

  1. Add the numbers.

    $$
16.702 + 923.5 + 2.7208 = 942.9228
$$

  2. Convert the sum to standard form (A×10nA \times 10^n, where 1≤∣A∣<101 \le |A| < 10).

    $$
942.9228 = 9.429228 \times 10^2
$$
The sum in standard form is $\boxed{9.429228 \times 10^2}$.

Part d(ii)2(2a - 1)(3b + 2)

Factorize completely: 12ab−6b+8a−412ab - 6b + 8a - 4.

  1. Group the terms.

    $$
(12ab - 6b) + (8a - 4)
$$

  2. Factor out the common factor from each group.

    $$
6b(2a - 1) + 4(2a - 1)
$$

  3. Factor out the common binomial (2a−1)(2a - 1).

    $$
(2a - 1)(6b + 4)
$$

  4. Factor out the common factor from the second binomial.

    $$
(2a - 1)2(3b + 2)
$$

  5. Rearrange for the final factored form.

    $$
2(2a - 1)(3b + 2)
$$
The completely factorized expression is $\boxed{2(2a - 1)(3b + 2)}$.
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