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nydimaria [60]
3 years ago
10

Write an equation of the line that passes through (1,2) and is parallel to the line y=−5x+4

Mathematics
2 answers:
liq [111]3 years ago
4 0

We know that the slope is -5, so:

y = -5x + b

Input (1, 2)

2 = -5 + b

b = 7

So:

y = -5x + 7

lukranit [14]3 years ago
3 0

You are using the equation:

y = mx + b

You need to find "m" and "b".

"m" is the slope, "b" is your y-intercept(when x = 0)

For the equation of the line to be parallel to the given equation, the slopes have to be the SAME. The slope of the given line is -5, so the parallel line's slope is also -5. (m = -5)

y = mx + b

y = -5x + b

To find b, you plug in the point (1,2) into the equation

y = -5x + b

2 = -5(1) + b

2 = -5 + b Add 5 on both sides to get "b" by itself

2 + 5 = -5 + b + 5

7 = b


Your equation is:

y = -5x + 7

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Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question, we have that:

\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when X = 260. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{260 - 270}{21.2}

Z = -0.47

Z = -0.47 has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

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3 years ago
A special discount was offered to the employees of Ryan's, a lead ing men's store. Employees were given their employee discount
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Answer: a) $2155, b) $1763.03.

Step-by-step explanation:

Since we have given that

Number of cable knit sweaters = 15

Cost per sweaters = $65.00

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Cost of each pair = $50.00

Number of casual jackets = 18

Cost of each jackets = $62.00

total sale volume would be

15\times 65+22\times 50+18\times 62\\\\=\$3191

Employee discount = 35%

Additional discount = 15%

So, Total markdown dollars taken is given by

3191\times \dfrac{100-35}{100}\times \dfrac{100-15}{100}\\\\=3191\times \dfrac{65}{100}\times \dfrac{85}{100}\\\\=3191\times 0.65\times 0.85\\\\=\$1763.0275

Hence, a) $2155, b) $1763.03.

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