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faltersainse
1 month ago
12

Which ratio would allow you to convert from 45 cm into feet? A. 1 inch/2.54 cm...because feet would cancel out B. 2.54cm/1 becau

se cm would cancel out C. 2.54cm/1 inch...because in would cancel out D. 1 inch/2.54 cm...because cm would cancel out ​
Mathematics
1 answer:
Svet_ta [12.7K]1 month ago
6 0

Answer:

The appropriate ratio to convert 45 cm into feet is 1 foot / 2.54 cm since the centimeters will cancel out.

Step-by-step explanation:

We aim to find the ratio that will allow us to convert from centimeters to feet for 45 cm.

The right ratio here is 1 foot / 2.54 cm, as the cm unit will be eliminated, resulting only in feet.

This works as follows;

1 foot / 2.54 cm * 45 cm.

This simplifies to;

(45 cm * 1 foot) / 2.54 cm.

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At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with
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Answer:

a) Slope: \hat \beta_1 =\frac{7625.9}{1248.9}=6.106

Intercept: \hat \beta_o = 157.955 -6.106 (69.686)=-267.548

b) r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657

Additionally, the coefficient of determination is r^2 = 0.657^2 =0.432

Step-by-step explanation:

Definitions and data provided

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n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9, sum y^2_i=\sum(y-\bar y)^2 =94228.8

\sum Y_i =17375, \sum X_i = 7665.5

Part a

The slope can be calculated using this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

Following the substitutions, we have:

\hat \beta_1 =\frac{7625.9}{1248.9}=6.106

The intercept can be determined with this formula:

\hat \beta_o = \bar y -\hat \beta_1 \bar x

Average values for x and y can be calculated this way:

\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955

Replacing yields:

\hat \beta_o = 157.955 -6.106 (69.686)=-267.548

Part b

The correlation coefficient can be calculated using the following formula:

r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}

In our situation:

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9, sum y^2_i=\sum(y-\bar y)^2 =94228.8

We can compute the correlation coefficient by substituting values:

r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657

The coefficient of determination is r^2 = 0.657^2 =0.432

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