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Rom4ik [11]
3 years ago
14

Auto pistons at Wemming​ Chung's plant in Shanghai are produced in a forging​ process, and the diameter is a critical factor tha

t must be controlled. From sample sizes of 10 pistons produced each​ day, the mean and the range of this diameter have been as​ follows:
Day Mean Bold x overbar ​(mm) Range R ​(mm)
1 158.9 4.0
2 151.2 4.6
3 155.6 4.3
4 155.5 5.0
5 154.6 4.3

a) What is the value of x ?
Mathematics
1 answer:
oee [108]3 years ago
6 0

Missing part of the question

b)What is the value of R?

Answer:

a. X = 155.2

b. R = 4.4

Step-by-step explanation:

a. Calculating the value of x.

The value of x is the mean of the mean observation; i.e. the mean column

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 158.9 + 151.2 + 155.6 + 155.5 + 154.6

Summation of Observation = 775.8

Number of Observations = 5

X = Mean = 775.8/5

X = 155.16

X = 155.2 ----- Approximated to 1 decimal place

b. Calculating the value of R.

The value of R is the mean/average of the Range

Mean is calculated as: the summation of all observation divided by the number of observations.

Summation of Observation = 4.0 + 4.6 + 4.3 + 5.0 + 4.3

Summation of Observation = 22.2

Number of Observations = 5

R = Mean = 22.2/5

R = 4.44

R = 4.4 ----- Approximated to 1 decimal place

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The diameter of cold virus cell is about 3x10-9 meter,and the diameter of a streptoccus bacterium cell is about 9x10-7 meter. Wh
Archy [21]

Here we need to compare the orders of magnitude of two measures.

We will see that the bacteria is<em> 300 times larger than the virus.</em>

We know that:

The diameter of the virus-cell is:

D_v = 3 \cdot 10^{-9} m

The diameter of the bacteria cell is:

D_b = 9 \cdot 10^{-7} m

So, to compare them, first notice that both are in the same units, meters, so we only need to <u>compare the numbers</u>.

Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus <u>the bacteria should be the larger one.</u>

But let's prove this with math, remember the property:

\frac{a^n}{a^m} = a^{n - m}

Let's take the quotient between the diameters and see what we get, I will use the <u>diameter of the bacteria in the numerator</u>, thus <u>if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.</u>

quotient = \frac{ 9 \cdot 10^{-7} m}{ 3 \cdot 10^{-9} m}  = \frac{9}{3} \cdot 10^{-7 + 9}\\\\= 3*10^2

So we can say that the bacteria is 3*10^2 = 3*100 = 300 times larger than the virus.

If you want to learn more, you can read:

brainly.com/question/4953281

8 0
2 years ago
What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?​
s344n2d4d5 [400]

Answer:

The roots are

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Step-by-step explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

<h3>x =  \frac{ - b\pm \sqrt{ {b}^{2}  - 4ac} }{2a}</h3>

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

<h3>x =  \frac{ - 54\pm \sqrt{ {54}^{2}  - 4(9)(82)} }{2(9)}  \\ x =  \frac{ - 54\pm \sqrt{2916 - 2952} }{18}  \\ x =  \frac{ - 54\pm \sqrt{ - 36} }{18}  \\ x =  \frac{ - 54\pm 6i}{18}</h3>

Separate the real and imaginary parts

That's

<h3>x =  -  \frac{54}{18} \pm \frac{6}{18}  \: i \\ x =  - 3\pm \frac{1}{3} i</h3>

We have the final answer as

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Hope this helps you

5 0
3 years ago
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