Question

The ordered pairs show amounts y​ (in inches) of rainfall equivalent to x​ inches of snow.(16, 1.5), (12, 1.3), (18, 1.8), (15, 1.5), (20, 2.1),(23, 2.4)​ About how many inches of rainfall are equivalent to 6 inches of snow? Round your answer to the nearest hundredth, if necessary.

Answer 1

Approximately 0.554 inches of rainfall are equivalent to 6 inches of snow.

Step-by-step explanation:

To find the approximate amount of rainfall that is equivalent to 6 inches of snow, we can use the given ordered pairs. The first number in each ordered pair represents the amount of snow (x) and the second number represents the equivalent amount of rainfall (y) in inches. We can create a ratio using the snow amounts and rainfall amounts:

Ratio = rainfall / snow

Using the ordered pairs, we can calculate the average ratio:

Average Ratio = (1.5 + 1.3 + 1.8 + 1.5 + 2.1 + 2.4) / (16 + 12 + 18 + 15 + 20 + 23)

Average Ratio ≈ 9.6 / 104 ≈ 0.0923

To find the amount of rainfall equivalent to 6 inches of snow, we multiply the snow amount by the average ratio:

Equivalent Rainfall = 6 * 0.0923 ≈ 0.554

Therefore, approximately 0.554 inches of rainfall are equivalent to 6 inches of snow.

Answer 2

0.57 inches of rainfall is equivalent to 6 inches of snow

Step-by-step explanation:

The given data are presented here as follows;

`\begin{array}{cc}x&y\\16&1.5\\12&1.3\\18&1.8\\15&1.5\\20&2.1\\23&2.4\\\end{array}`

The data points are approximately linear

From the the trend line of the plotted points of the graph, created with Microsoft Excel, with Forecasting, when there is 6 inches of snow the rainfall is 0.575 inches

By linear regression, we have;

Y = a + b·X

Where;

`b = (n \cdot \sum XY - \left (\sum X \right ) \cdot \left (\sum Y \right ))/(n \cdot \sum X^(2) - \left (\sum X \right )^(2))`

`a = (\sum Y - b \cdot \sum X)/(n)`

∑x = 104

∑y = 10.6

∑(x·y) = 191.7

(∑x)·(∑y) = 1102.4

(∑x)² = 10816

n = 6

SigX^2 = 1878

Plugging in the values, gives;

`b = (6 *191.7 - 1102.4)/(6 * 1878 - 10816) \approx 0.10575`

`a = (10.6 - 0.10575 * 104)/(6) \approx -0.06637`

Therefore;

Y = 0.10575·x - 0.06637

When x = 6 inches, we have;

Y = 0.10575 × 6 - 0.06637 = 0.56813

Y = 0.56813 inches ≈ 0.57 inches of rainfall

Therefore;

0.57 inches of rainfall is equivalent to 6 inches of snow