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3 years ago

6

Can someone please help me ASAP

1 answer:

charle [14.2K]3 years ago

4 0

Answer:

(4,12)

(-1,-3)

Step-by-step explanation:

x^2 - y = 4

y = 3x

Use substitution. Substitute 3x for y in the first equation

x^2 - (3x) = 4

x^2 -3x =4

Subtract 4 from each side

x^2 -3x -4 = 4-4

x^2 -3x-4 =0

Factor

(x-4) (x+1) =0

Using the zero product property

x-4 =0 x+1 =0

x=4 x=-1

Now to find y for each x solution

x=4

y =3x = 3(4) =12

(4,12)

x=-1

y =3x = 3(-1) =-3

(-1,-3)

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Consider a sample with data values of 27, 24, 21, 16, 30, 33, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles. 20

densk [106]

Answer:

$P_{20} = 20$ --- 20th percentile

$P_{25} = 21.75$ --- 25th percentile

$P_{65} = 27.85$ --- 65th percentile

$P_{75} = 29.5$ --- 75th percentile

Step-by-step explanation:

Given

27, 24, 21, 16, 30, 33, 28, and 24.

N = 8

First, arrange the data in ascending order:

Arranged data: 16, 21, 24, 24, 27, 28, 30, 33

Solving (a): The 20th percentile

This is calculated as:

$P_{20} = 20 * \frac{N +1}{100}$

$P_{20} = 20 * \frac{8 +1}{100}$

$P_{20} = 20 * \frac{9}{100}$

$P_{20} = \frac{20 * 9}{100}$

$P_{20} = \frac{180}{100}$

$P_{20} = 1.8th\ item$

This is then calculated as:

$P_{20} = 1st\ Item +0.8(2nd\ Item - 1st\ Item)$

$P_{20} = 16 + 0.8*(21 - 16)$

$P_{20} = 16 + 0.8*5$

$P_{20} = 16 + 4$

$P_{20} = 20$

Solving (b): The 25th percentile

This is calculated as:

$P_{25} = 25 * \frac{N +1}{100}$

$P_{25} = 25 * \frac{8 +1}{100}$

$P_{25} = 25 * \frac{9}{100}$

$P_{25} = \frac{25 * 9}{100}$

$P_{25} = \frac{225}{100}$

$P_{25} = 2.25\ th$

This is then calculated as:

$P_{25} = 2nd\ item + 0.25(3rd\ item-2nd\ item)$

$P_{25} = 21 + 0.25(24-21)$

$P_{25} = 21 + 0.25(3)$

$P_{25} = 21 + 0.75$

$P_{25} = 21.75$

Solving (c): The 65th percentile

This is calculated as:

$P_{65} = 65 * \frac{N +1}{100}$

$P_{65} = 65 * \frac{8 +1}{100}$

$P_{65} = 65 * \frac{9}{100}$

$P_{65} = \frac{65 * 9}{100}$

$P_{65} = \frac{585}{100}$

$P_{65} = 5.85\th$

This is then calculated as:

$P_{65} = 5th + 0.85(6th - 5th)$

$P_{65} = 27 + 0.85(28 - 27)$

$P_{65} = 27 + 0.85(1)$

$P_{65} = 27 + 0.85$

$P_{65} = 27.85$

Solving (d): The 75th percentile

This is calculated as:

$P_{75} = 75 * \frac{N +1}{100}$

$P_{75} = 75 * \frac{8 +1}{100}$

$P_{75} = 75 * \frac{9}{100}$

$P_{75} = \frac{75 * 9}{100}$

$P_{75} = \frac{675}{100}$

$P_{75} = 6.75th$

This is then calculated as:

$P_{75} = 6th + 0.75(7th - 6th)$

$P_{75} = 28 + 0.75(30- 28)$

$P_{75} = 28 + 0.75(2)$

$P_{75} = 28 + 1.5$

$P_{75} = 29.5$

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3 years ago

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devlian [24]

Step-by-step explanation:

Taking any two points through which the line passes;(-10,-3) and (-5,-1)

The equation of the line is given by

$\frac{y2 - y1}{x2 - x1} = \frac{y - y1}{x - x1}$

$=> \frac{ - 1 - ( - 3)}{ - 5 - ( - 10)} = \frac{y - ( - 3)}{x - ( - 10)} = \frac{y + 3}{x + 10}$

$=> \frac{ - 1 + 3}{ - 5 + 10} = \frac{y + 3}{x + 10}$

$=> \frac{2}{5} = \frac{y + 3}{x + 10}$

$=> 5(y + 3) = 2(x + 10)$

=> 5y+15 = 2x+20

=> 5y =2x+5

$=> y= \frac{2}{5} x + 1$

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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