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3 years ago

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Solve for p and simplify

2 answers:

nadezda [96]3 years ago

7 0

Answer:

8

Step-by-step explanation:

$-\dfrac{1}{2} + p = \dfrac{5}{8}$

Add 1/2 to both sides.

$-\dfrac{1}{2} + p + \dfrac{1}{2} = \dfrac{5}{8} + \dfrac{1}{2}$

$p = \dfrac{5}{8} + \dfrac{4}{8}$

$p = \dfrac{9}{8}$

dedylja [7]3 years ago

3 0

$Given : \dfrac{-1}{2} + p = \dfrac{5}{8}$

$\implies p = \dfrac{1}{2} + \dfrac{5}{8}$

$\implies p = \dfrac{4 + 5}{8}$

$\implies p = \dfrac{9}{8}$

The Question Mark should be Replaced with 8

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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:

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

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

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

$P_{75} = 28 + 1.5$

$P_{75} = 29.5$

7 0

3 years ago

Please HELP ME ON THIS MATH WRITTEN RESPONSE QUESTION.. THANK YOU

sergij07 [2.7K]

Answer:

Quadrilateral ABCD is not a square. The product of slopes of its diagonals is not -1.

Step-by-step explanation:

Point A is (-4,6)

Point B is (-12,-12)

Point C is (6,-18)

Point D is (13,-1)

Given that the diagonals of a square are perpendicular to each other;

We know that the product of slopes of two perpendicular lines is -1.

So, slope(m) of AC × slope(m) of BD should be equal to -1.

Slope of AC = (Change in y-axis) ÷ (Change in x-axis) = (-18 - 6) ÷ (6 - -4) = -24/10 = -2.4

Slope of BD = (Change in y-axis) ÷ (Change in x-axis) = (-1 - -12) ÷ (13 - -12) = 11/25 = 0.44

The product of slope of AC and slope of BD = -2.4 × 0.44 = -1.056

Since the product of slope of AC and slope of BD is not -1 hence AC is not perpendicular to BD thus quadrilateral ABCD is not a square.

4 0

3 years ago

Larry deposits $15 a week into a savings account. His balance in his savings account grows by a constant percent rate.

dimaraw [331]

Answer:

The answer is true

Step-by-step explanation:

3 0

3 years ago

How to solve <img src="https://tex.z-dn.net/?f=log_%7By%7D%285y%29%20%3D%202" id="TexFormula1" title="log_{y}(5y) = 2" alt="log_

Natalija [7]

Answer:

y = 5

Step-by-step explanation:

Expand the logarithm:

$\log_y{(5)}+\log_y{(y)}=2\\\\\dfrac{\log{(5)}}{\log{(y)}}+1=2 \quad\text{change of base formula}\\\\\dfrac{\log{(5)}}{\log{(y)}}=1 \quad\text{subtract 1}\\\\\log{(5)}=\log{(y)} \quad\text{multiply by log(y)}\\\\5=y \quad\text{take the anti-log}$

_____

You can also take the antilog first:

5y = y²

y(y -5) = 0 . . . . . subtract 5y, factor

y = 0 or 5 . . . . . y=0 is not a viable solution, so y=5.

5 0

3 years ago

PLEASE HELP HELP HELP HELP

Rus_ich [418]

You write nite so I will help

6 0

3 years ago