$$ \left. \begin{array} { l } { b = \frac { n ( \sum x y ) - ( \sum x ) ( \sum y ) } { n ( \sum x ^ { 2 } ) - ( \sum x ) ^ { 2 } } } \ { a = \frac { ( 673 ) ( 669 ) - ( 73 ) ( 5,715 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } = } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { b = \frac { n ( \sum x y ) - ( \sum x ) ( \sum y ) } { n ( \sum x ^ { 2 } ) - ( \sum x ) ^ { 2 } } } \ { a = \frac { ( 673 ) ( 669 ) - ( 73 ) ( 5,715 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } = } \end{array} ight. $$

UpStudy AI · Accepted Answer

We start with the expression for $$ a $$:

$$
a = \frac{(673)(669) - (73)(5\,715)}{10(669) - (73)^2}.
$$

**Step 1. Compute the numerator**

Calculate the two parts separately:

1. $$673 \times 669$$:

$$
673 \times 669 = 673 \times (670 - 1) = 673 \times 670 - 673.
$$

First, compute $$673 \times 670$$:

$$
673 \times 670 = 673 \times 600 + 673 \times 70 = 403800 + 47110 = 450910.
$$

Then subtract $$673$$:

$$
450910 - 673 = 450237.
$$

2. $$73 \times 5\,715$$:

$$
73 \times 5\,715 = 73 \times (5\,700 + 15) = 73 \times 5\,700 + 73 \times 15.
$$

Calculate each part:

$$
73 \times 5\,700 = 416\,100 \quad \text{(Note: } 73 \times 5\,700 = 70 \times 5\,700 + 3 \times 5\,700 = 399\,000 + 17\,100\text{)}
$$

$$
73 \times 15 = 1\,095.
$$

Thus:

$$
73 \times 5\,715 = 416\,100 + 1\,095 = 417\,195.
$$

Now find the numerator:

$$
450237 - 417195 = 33042.
$$

**Step 2. Compute the denominator**

The denominator is given by:

$$
10 \times 669 - (73)^2.
$$

Compute each part:

1. $$10 \times 669 = 6690.$$

2. $$73^2 = 5329.$$

Thus, the denominator is:

$$
6690 - 5329 = 1361.
$$

**Step 3. Write the final expression**

Substitute the computed values into the expression for $$a$$:

$$
a = \frac{33042}{1361}.
$$

**Step 4. (Optional) Decimal approximation**

Performing the division:

$$
\frac{33042}{1361} \approx 24.28.
$$

Thus, the final result is:

$$
a = \frac{33042}{1361} \approx 24.28.
$$
$$ a = \frac{33042}{1361} \approx 24.28 $$

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