Mathematics: Astudent repeatedly measures the mass of an object using a mechanical balance and gets the following values: 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g calculate the standard deviation of his measurements

Astudent repeatedly measures the mass of an object

Ответ:

fernandaretanaoxwln0

02.01.2022

Mathematics

2.76 g

Step-by-step explanation:

The formula to find the standard deviation:-

$\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{n}}$

The given data values : 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g.

Then, $\overline{x}=\dfrac{\sum_{i=1}^{10} x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{560+562+556+558+560+556+559+561+565+563}{10}\\\\\Rightarrow\ \overline{x}=\dfrac{5600}{10}=560$

Now, $\sum_{i=1}^{10}(x_i-\overline{x})^2=0^2+2^2+(-4)^2+(-2)^2+0^2+(-4)^2+(-1)^2+1^2+5^2+3^2\\\\\Rightarrow\ \sum_{i=1}^{10}(x_i-\overline{x})^2=76$

Then, $\sigma=\sqrt{\dfrac{76}{10}}=\sqrt{7.6}=2.76$

Hence, the standard deviation of his measurements = 2.76 g

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Ответ:

chavez0

22.01.2021

Mathematics

$12^{\circ}$ $1\ feet\ and$ $94.28\ ft^2$

Step-by-step explanation:

Data provided in the question

The radius of a wheel = 30 feet

Number of cars attached = 30 cars

Based on the above information

The computation is shown below:

The center angle is

$= \frac{360}{30}$

$= 12^{\circ}$

The arc length is

$= \frac{12}{360}(30)$

= 1 feet

And, the area of a sector between two cars is

$= \frac{12}{360}(\pi (30)^2)$

= $94.28\ ft^2$

We simply do the above calculations so that each item could be find out

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Astudent repeatedly measures the mass of an object using a mechanical balance and gets the following values: 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g calculate the standard deviation of his measurements

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