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galina1969 [7]
3 years ago
11

The number of dollars per month it costs you to own a car is a function of the number of kilometers per month you drive it. Base

d on the information in an issue of Time magazine, the cost varies linearly with the distance, and is $366 per month for 300 kilometers per month, and 510 per month for 1500 kilometers per month. Write the particular equation expressing cast (c) in terms of distance (d)
Mathematics
1 answer:
klasskru [66]3 years ago
7 0
Y=1.22x
y is the cost and x is kilometers driven. I got 1.22 by dividing 366 by 300 to find how it costs per kilometer.
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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

7 0
3 years ago
Assume that random guesses are made for nine multiple choice questions on an SAT​ test, so that there are nequals9 ​trials, each
Marina86 [1]

Answer:  Find the probability that the number x of correct answers is fewer than 4 = 0.6087

Step-by-step explanation: Please find the attached files for the solution

6 0
3 years ago
If f(x) = 2x^4, then f'(3) =
valkas [14]

To find f'(3) (f prime of 3), you must find f' first.  f' is the derivative of the function f(x).

Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.

The power rule for derivatives is \frac{d}{dx} [x^{n} ] =nx^{n-1}.  In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.

f'(x) = \frac{d}{dx}(2x⁴)

f'(x) = 2(4)x³

f'(x) = 8x³

Now, to find f'(3), plug 3 into your derivative.

f'(3) = 8(3)³

f'(3) = 216

<h3>Answer:</h3>

f'(3) = 216

6 0
3 years ago
What is the value of x ?????
Rasek [7]

what............there’s no pic

3 0
3 years ago
Read 2 more answers
Find and interpret the mean absolute deviation of the data. Round your answers to the nearest tenth. If necessary 101.5 98.7 95.
lesya692 [45]

Answer:

\bar X = 100.4

And we can calculate the deviations from each value like this:

|101.5-100.4 |=1.1

|98.7-100.4 |=1.7

|95.4-100.4 |=5.0

|92.3-100.4 |=8.1

|109.8-100.4 |=9.4

|104.7-100.4|=4.3

And the mean absolute deviation would be:

MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93

Step-by-step explanation:

For this case we have the following dataset given:

101.5 98.7 95.4 92.3 109.8 104.7

We can calculate the mean with the following formula:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

And replacing we got:

\bar X = 100.4

And we can calculate the deviations from each value like this:

|101.5-100.4 |=1.1

|98.7-100.4 |=1.7

|95.4-100.4 |=5.0

|92.3-100.4 |=8.1

|109.8-100.4 |=9.4

|104.7-100.4|=4.3

And the mean absolute deviation would be:

MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93

8 0
3 years ago
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