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nata0808 [166]
2 years ago
6

I need help with 15,19,17 Negative exponents

Mathematics
1 answer:
Hoochie [10]2 years ago
6 0
15) 4m^2
17)9n^6
198a^2 (^ = power of)
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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

 standard deviation of 45 minutes

∵ 1 hour = 60 minutes

∴ 45 minutes = 45/60 = 0.75 hour

∴ The standard deviation is 0.75 hour

i)

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

 form in more than 5 hours

* Lets use z-score to find the probability

∵ z-score = (x - μ)/σ , where

# x is the score

# μ is the mean

# 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

 of z-score -1.33

∵ The corresponding area of -1.33 = 0.09176

∵ P(x > 5) = 1 - P(z > -1.33)

∴ 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%

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

ii)

- A sample of 20 taxpayers are selected

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

 than 6.5 hours

- The sample means is called M

- The standard deviation of the distribution of sample means is

  called σM  where σM = σ/√n , where σ is the standard deviation and

  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

 of z-score 2.98

∵ 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%)

6 0
3 years ago
What is the solution to the following system? (3, –1, 4) (4, 1, 3) (4, –1, 3) (3, 1, 4)
lbvjy [14]

Answer:

(4, –1, 3)

What is the solution to the following system? (3, –1, 4) (4, 1, 3) (4, –1, 3) (3, 1, 4

8 0
3 years ago
The sum of the reciprocals of two consecutive integers is -9/20. Find the two integers
mr_godi [17]
Suppose the first integer is x, the second one is then x+1
reciprocals are 1/x and 1/(x+1)
1/x +1/(x+1)=-9/20
make the denominators the same:
1(x+1)/x(x+1) + 1x/x(x+1)=-9/20
simplify the demonstrator and add up the numerators: (2x+1)/(x^2+x)=-9/20
20(2x+1)=-9(x^2+x)
40x+20=-9x^2-9x
9x^2 +49x+20=0
factor: (1+5)(9x+4)=0
x=-5 or x=-4/9 (this one doesn't work because it is not an integer)
so the first integer is -5, the second integer is -4

5 0
3 years ago
Solve the equation, using the inverse operation. b − 14 = 5
Nikolay [14]

Answer:

b=19

Explanation:

5 0
3 years ago
Read 2 more answers
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100
julsineya [31]

Answer:

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

V = \frac{4\pi r^3}{3}

How fast is the volume increasing:

To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

The radius of a sphere is increasing at a rate of 2 mm/s.

This means that \frac{dr}{dt} = 2

How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?

Radius is half the diameter, so r = \frac{100}{2} = 50

Then

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt} = 4\pi (50)^2(2) = 62832

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

6 0
2 years ago
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