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Elan Coil [88]
3 years ago
10

Find the slope of the line. ​

Mathematics
2 answers:
mrs_skeptik [129]3 years ago
8 0

Answer:

slope = - \frac{4}{5}

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m = \frac{-2-2}{2+3} = \frac{-4}{5} = - \frac{4}{5}

son4ous [18]3 years ago
3 0

Answer:

-4/5.

Step-by-step explanation:

The 2 marked points are (-3, 2) and (2, -2)

So the slope = (-2-2)/(2- -3)

= -4/5.

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5. The Inland Revenue department claims it takes an average of 6 hours to complete a tax form. Assuming the time to complete the
forsale [732]

Answer:

i) 90.82% of the people can complete the form in more than 5 hours

ii) The probability that the sample mean is less than 6.5 hours is 0.9986 (99.86%)

Step-by-step explanation:

* Lets explain how to sole the problem

- The average time to complete a tax form is 6 hours

- Assuming the time to complete the form is normally distributed with a

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∵ 1 hour = 60 minutes

∴ 45 minutes = 45/60 = 0.75 hour

∴ The standard deviation is 0.75 hour

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- We need to know the percentage of the people who complete the

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* Lets use z-score to find the probability

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# σ is the standard deviation

∵ μ = 6 , σ = 0.75 , x = 5

∴ z=\frac{5-6}{0.75}=-1.33

- Use the normal distribution table to find the corresponding area

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∵ The corresponding area of -1.33 = 0.09176

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∴ P(x > 5) = 1 - 0.09176 = 0.90824

- Change it to percentage by multiply it by 100%

∴ P(x > 5) = 0.90824 × 100% = 90.82%

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ii)

- A sample of 20 taxpayers are selected

- We need to know the probability that the sample mean is less

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- The sample means is called M

- The standard deviation of the distribution of sample means is

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  n is the sample size

- z-score = (M - μ)/σM, where μ is the mean of the population  

∵ μ = 6 , σ = 0.75 , n = 20 ,  M = 6.5 hours

∴ σM = \frac{0.75}{\sqrt{20}}=0.1677

∴ z=\frac{6.5-6}{0.1677}=2.98

- Use the normal distribution table to find the corresponding area

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∵ The corresponding area of 2.98 is 0.99856

∵ P(x < 6.5) = P(z < 2.98)

∴ P(x < 6.5) = 0.99856

∴ The probability that the sample mean is less than 6.5 hours

   is 0.9986 (99.86%)

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