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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 ?

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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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>

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

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2 years ago

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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

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