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3 years ago

6

Mr. John Doe was figuring out his federal income tax. His income was $26,800, but he was able to subtract $5,500 in deductions.

He paid 15% of the remaining income tax. How much did he pay?

1 answer:

kumpel [21]3 years ago

7 0

The answer is
5.70

Mr. John Doe was figuring out his federal income tax. His income was $26,800, but he was able to subtract $5,500 in deductions. He paid 15% of the remaining income tax. How much did he pay?

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What is the surface area of the triangular prism?

horrorfan [7]

C)132
All you do is find the area of each flat surface and add them together.
(rectangle) A=w×h
(triangle) A=w×h/2

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4 years ago

The results of a national survey showed that on average, adults sleep 6.3 hours per night. Suppose that the standard deviation i

alekssr [168]

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by $100(1 - \frac{1}{k^{2}})$ .

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

$k = \frac{4}{1.6} = 2.5$

The minimum percentage is:

$100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%$

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

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3 years ago

Have a wonderful day and here are free pts to make your day better <3 lvu and be safe

rjkz [21]

Answer:

80

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What method would be best to use 53=4(x-3)^2-11

Veronika [31]

Answer:

x = 7 , -1

Step-by-step explanation:

<u>SOLUTION :-</u>

$4(x-3)^2-11 = 53$

Add 11 to both the sides.

$=> 4(x-3)^2-11+11=53+11$

$=> 4(x-3)^2 = 64$

Divide both the sides by 4.

$=> \frac{4(x-3)^2}{4} = \frac{64}{4}$

$=> (x-3)^2 = 16$

Root square both the sides.

$=> \sqrt{(x-3)^2} = \sqrt{16}$

$=> x-3 = +4 \; or -4$

Here , x will have two values -

1) $x-3 = 4$

$=> x = 4 + 3 = 7$

2) $x - 3 = -4$

$=> x = -4 + 3 = -1$

<u>VERIFICATION :-</u>

When x = 7 ,

$4(x-3)^2 - 11 = 4(7 - 3)^2 - 11$

$= 4 \times 4^2 - 11$

$= 4 \times 16 - 11$

$= 64 - 11$

$= 53$

When x = -1 ,

$4(x-3)^2 - 11 = 4(-1 - 3)^2 - 11$

$= 4 \times (-4)^2 - 11$

$= 4 \times 16 - 11$

$= 64 - 11$

$= 53$

7 0

3 years ago

The function f(x) = -(x-3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of

pashok25 [27]

Answer:

Maximum area = 9 sq units

Step-by-step explanation:

$f(x)=-(x-3)^2+9$

which represents the area . As it is a quadratic equation it represents the parabola . And the vertex of the parabola will maximum area of for some value of x

let f(x) = y

$y=-(x-3)^2+9$

$(x-3)^2=-(y-9)$

Comparing it with the standard equation of parabola

$y=(x-h)^2+k$

we get h=3 and y=9

where (h,k) is the vertex (3,9)

Hence the maximum area of the rectangle will be 9

6 0

3 years ago