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3 years ago

Find an equation of a line parallel to the line y = 3x – 3 that contains the point (6,4).

Mathematics

1 answer:

Sonbull [250]3 years ago

3 0

#First u find the gradient first, remember that the formula of equation of the line is y=mx + c

y = 3x - 3

so the gradient (m) is 3

#Now u find the equation of the line

y - y1 = m(x - x1)

y - 4 = 3(x - 6)

y - 4 = 3x - 18

y = 3x - 18 + 4

y = 3x - 14

<h2>Answer : y = 3x - 14</h2>

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4 years ago

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Natasha2012 [34]

Answer:

a) The probability is the p-value of $Z = \frac{X - 22.6}{5.2}$ , in which X is the gas mileage of the 2020 Honda Civic.

b) Your dad's truck is 1.65 standard deviations below the mean.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.

This means that $\mu = 22.6, \sigma = 5.2$

a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?

This is the p-value of Z, given by:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{X - 22.6}{5.2}$

In which X is the gas mileage of the 2020 Honda Civic.

b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?

This is Z when X = 14. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{14 - 22.6}{5.2}$

$Z = -1.65$

Your dad's truck is 1.65 standard deviations below the mean.

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