$$ \left. \begin{array} { l } { b = \frac { n ( \Sigma x y ) - ( \Sigma x ) ( \Sigma y ) } { n ( \Sigma x ^ { 2 } ) - ( \Sigma x ) ^ { 2 } } } \ { a = \frac { ( 673 ) ( 669 ) - ( 73 ) ( 5,715 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } = 2428 } \ { b = \frac { 10 ( 5,715 ) - ( 73 ) ( 673 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { b = \frac { n ( \Sigma x y ) - ( \Sigma x ) ( \Sigma y ) } { n ( \Sigma x ^ { 2 } ) - ( \Sigma x ) ^ { 2 } } } \ { a = \frac { ( 673 ) ( 669 ) - ( 73 ) ( 5,715 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } = 2428 } \ { b = \frac { 10 ( 5,715 ) - ( 73 ) ( 673 ) } { 10 ( 669 ) - ( 73 ) ^ { 2 } } } \end{array} ight. $$

UpStudy AI · Accepted Answer

Let's solve for $$ b $$ using the provided formula:

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

We will calculate the numerator and the denominator separately before finding $$ b $$.

1. **Calculate the numerator:**
   $$
   10 ( 5,715 ) - ( 73 ) ( 673 )
   $$

2. **Calculate the denominator:**
   $$
   10 ( 669 ) - ( 73 ) ^ { 2 }
   $$

Let's compute these values step by step.
Calculate the value by following steps:
- step0: Calculate:
  $$10\times 5715-73\times 673$$
- step1: Multiply the numbers:
  $$57150-73\times 673$$
- step2: Multiply the numbers:
  $$57150-49129$$
- step3: Subtract the numbers:
  $$8021$$
Calculate or simplify the expression $$ 10 * 669 - 73^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10\times 669-73^{2}$$
- step1: Multiply the numbers:
  $$6690-73^{2}$$
- step2: Evaluate the power:
  $$6690-5329$$
- step3: Subtract the numbers:
  $$1361$$
Now we have the results for both the numerator and the denominator:

1. **Numerator:**
   $$
   10 ( 5,715 ) - ( 73 ) ( 673 ) = 8021
   $$

2. **Denominator:**
   $$
   10 ( 669 ) - ( 73 ) ^ { 2 } = 1361
   $$

Now we can substitute these values into the formula for $$ b $$:

$$
b = \frac{8021}{1361}
$$

Let's calculate $$ b $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{8021}{1361}$$
The value of $$ b $$ can be expressed as:

$$
b = \frac{8021}{1361} \quad \text{or} \quad b = 5 \frac{1216}{1361}
$$

Thus, the final result for $$ b $$ is approximately $$ 5.89 $$ when expressed as a decimal.
$$ b = \frac{8021}{1361} $$ or approximately $$ 5.89 $$.

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