Explain why systems of measurement are defined and provide an example to support your answer.

Mathematics

1 answer:

sasho [114]2 years ago

3 0

Answer:

A unit of measurement is a specific magnitude of a certain quantity that is specified and recognized by convention or legislation and is commonly used as a standard for measuring the same kind of quantity. We would randomly confuse the computations if the unit system was not given to the measurements.

Step-by-step explanation:

Example: If someone wrote 200 as a response to a question on a piece of paper. But You neglected to mention the measuring units. Anyone can mistake it because there are no units written apart from the number (unit less). Complications multiply. It's impossible to say whether it's 200 m or 200 g. 200 milliliters? 200 kilometers, 200 seconds, or 200 meters? It's possible to guess anything. We should always utilize units to be specific about the answer to any problem. This will assist in narrowing down the approach to any challenge and providing a measurable linked quantity regarding the topic in question.

You might be interested in

The Coast Starlight Amtrak train runs from Seattle to Los Angeles. The mean travel time from one stop to the next on the Coast S

Goshia [24]

Solution :

a).

Given :

R = 0.636, $S_x = 99$ , $S_y=113, M_x=108, M_y=129$

Here R = correlation between the two variables

$S_x , S_y$ = sample standard deviations of the distance and travel time between the two train stops, respectively.

$M_x, M_y$ = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, $b_1$ $=R \times \left(\frac{S_y}{S_x}\right)$

$=0.636 \times \left(\frac{113}{99}\right)$

= 0.726

Therefore, the slope of the regression line $b_1$ is 0.726

The equation of the regression line is given by :

$\overline {y} = b_0+b_1 \overline x$

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line $b_0$ is given by :

$b_0=M_y-(b_1 \times M_x)$

= 129 - (0.726 x 108)

= 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b). $\text{ The slope of the line predicts that it will require 0.726 minutes}$ for each additional mile travelled.

The intercept of the line, $b_0$ = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because it seems we have travelled zero distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). $R^2=0.404$