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Shtirlitz [24]
3 years ago
7

a street that is 116 M long is covered in snow. City workers are using a snow plow to clear the street. A tire on the snow plow

house to turn 29 x and traveling the length of the street. What is the diameter of the tire. Use the value 314 for pie
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
8 0
Let diameter of the tire be D.
It turned 29 times and travelled 116 m in distance.

Using the circumference formula,
116=29(2 π r) = 29*(π D) = 29(3.14 D)
Solve for D
D=116/(3.14*29) =  1.274 m.

Answer: The diameter of the tire is 1.27 m (to three significant figures)
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4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ
galben [10]

Answer:

\\ \mu = 118\;grams\;and\;\sigma=30\;grams

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find \\ \mu\;and\;\sigma.

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

<h3>Solving a system of equations for values of the mean and standard deviation</h3>

Having equations (1) and (2), we can form a system of two equations and two unknowns values:

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

Rearranging these two equations:

\\ -0.6*\sigma = 100-\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

\\ 0.6*\sigma = -100+\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

Summing both equations, we obtain the following equation:

\\ 3.0*\sigma = 90

Then

\\ \sigma = \frac{90}{3.0} = 30

To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):

\\ 2.4*30 = 190-\mu (2)

\\ 2.4*30 - 190 = -\mu

\\ -2.4*30 + 190 = \mu

\\ \mu = 118

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romanna [79]
If you divide 36 by 4, it equals 9, so each side is 9. Then you multiply 9 to 9, which equals 81 in^2.
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Solve ln 2 + ln x = 5. Round to the nearest thousandth, if possible.
azamat

Answer:

The  value of x nearest to thousandths is, 74.207

Step-by-step explanation:

Solve :  \ln 2 + \ln x = 5

\ln represents the logarithmic function with base e.

Using logarithmic properties:

  • \ln (mn) = \ln m + \ln n
  • \ln x = a , then x = e^a

\ln 2 + \ln x = 5

Apply the logarithmic properties; we have

\ln 2x = 5

then;

2x = e^5

or

2x=148.41315910258

Divide both sides by 2 we get;

x = 74.2065796

Therefore, the value of x nearest to thousandths is, 74.207

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Answer:

Lauren

Step-by-step explanation:

1/2 is Erin

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