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yaroslaw [1]
3 years ago
10

Evaluate the expression

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
3 0

Answer:

-5

Step-by-step explanation:

\tt \log_3\cfrac{1}{243}=\log_3\cfrac{1}{3^5}=\log_33^{-5}=-5\log_33=-5\cdot1=-5

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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
Determine the value of that makes the equati
arsen [322]

Answer:

x = 5.5

Step-by-step explanation:

  1. 6-(2x-4)+x = 6-2x+4+x = 10-x
  2. 3(x-4) = 3x-12
  3. Based on the 1st and the 2nd steps, 10-x=3x-12 --> 10+12=3x+x --> 22 = 4x --> x =22/4 = 5.5
3 0
3 years ago
plzzz finish 4, 5, 6, 9, 10, 11, 12, 14, and 15 you dont have to answer all but atleast anwer like 2 or 3 \( i scratched out the
nika2105 [10]

Answer:

4. -4

5. -2

6. -3

Step-by-step explanation:

4. -12 = 5r + 8

Subtract 8 from both sides;

-20 = 5r

Divide both sides by 5;

-4 = r OR r = -4

5. -6p - 3 = 9

Add 3 to both sides;

-6p = 12

Divide both sides by -6

p = -2

6. -14 = 4x - 2

Add 2 to both sides;

-12 = 4x

Divide both sides by 4;

-3 = x OR x = -3

8 0
3 years ago
lea invests 3,466 in a savings account with a fixed annual interest rate of 7% compound continuously what will the account balan
arlik [135]
The account balance after 10 years will be 5,892.2
5 0
3 years ago
Three machines A, B, and C produce 55%, 25% and 20% respectively. The percentages of defective output are 3.5%, 4.5% and 5.5%. I
pishuonlain [190]

We are given the following information concerning the three production machines;

\begin{gathered} Of\text{ the total production;} \\ A=55\text{ \%}=0.55 \\ B=25\text{ \%}=0.25 \\ C=20\text{ \%}=0.20 \end{gathered}

Also, we are given the percentage of defective output as follows;

\begin{gathered} A=3.5\text{ \%}=0.035 \\ B=4.5\text{ \%}=0.045 \\ C=5.5\text{ \%}=0.055 \end{gathered}

Therefore, if an item is selected randomly, the probability that the item is defective would be;

\begin{gathered} P\lbrack defective\rbrack=(0.55\times0.035)+(0.25\times0.045)+(0.20\times0.055) \\ P\lbrack\text{defective\rbrack}=0.01925+0.01125+0.011 \\ P\lbrack\text{defective\rbrack}=0.0415 \end{gathered}

ANSWER:

The probability that the item is defective would be 0.0415

6 0
1 year ago
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