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3 years ago

A What is the median number for the numbers 4, 8, 10, 5, 9?*

1 answer:

4 0

First we need to sort from the smallest number to the largest number.

4, 5, 8, 9, 10

Median is the middle number.

Your answer is 8.

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I need help.. i really want to go sleep.. thank you so much...

Effectus [21]

Answer:

1) True 2) False

Step-by-step explanation:

1) Given $\sum\limits_{k=0}^8\frac{1}{k+3}=\sum\limits_{i=3}^{11}\frac{1}{i}$

To verify that the above equality is true or false:

Now find $\sum\limits_{k=0}^8\frac{1}{k+3}$

Expanding the summation we get

$\sum\limits_{k=0}^8\frac{1}{k+3}=\frac{1}{0+3}+\frac{1}{1+3}+\frac{1}{2+3}+\frac{1}{3+3}+\frac{1}{4+3}+\frac{1}{5+3}+\frac{1}{6+3}+\frac{1}{7+3}+\frac{1}{8+3}$ $\sum\limits_{k=0}^8\frac{1}{k+3}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Now find $\sum\limits_{i=3}^{11}\frac{1}{i}$

Expanding the summation we get

$\sum\limits_{i=3}^{11}\frac{1}{i}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Comparing the two series we get,

$\sum\limits_{k=0}^8\frac{1}{k+3}=\sum\limits_{i=3}^{11}\frac{1}{i}$ so the given equality is true.

2) Given $\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\sum\limits_{i=1}^3\frac{3i}{i+5}$

Verify the above equality is true or false

Now find $\sum\limits_{k=0}^4\frac{3k+3}{k+6}$

Expanding the summation we get

$\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\frac{3(0)+3}{0+6}+\frac{3(1)+3}{1+6}+\frac{3(2)+3}{2+6}+\frac{3(3)+4}{3+6}+\frac{3(4)+3}{4+6}$

$\sum\limits_{k=0}^4\frac{3k+3}{k+6}=\frac{3}{6}+\frac{6}{7}+\frac{9}{8}+\frac{12}{8}+\frac{15}{10}$

now find $\sum\limits_{i=1}^3\frac{3i}{i+5}$

Expanding the summation we get

$\sum\limits_{i=1}^3\frac{3i}{i+5}=\frac{3(0)}{0+5}+\frac{3(1)}{1+5}+\frac{3(2)}{2+5}+\frac{3(3)}{3+5}$

$\sum\limits_{i=1}^3\frac{3i}{i+5}=\frac{3}{6}+\frac{6}{7}+\frac{9}{8}$

Comparing the series we get that the given equality is false.

ie, $\sum\limits_{k=0}^4\frac{3k+3}{k+6}\neq\sum\limits_{i=1}^3\frac{3i}{i+5}$

6 0

4 years ago

what is the value of x in the diagram below? if necessary round your answer to the nearest tenth of a until

VladimirAG [237]

Answer:

Step-by-step explanation:

Calculate AC using Pythagoras' identity in ΔABC

AC² = 20² - 12² = 400 - 144 = 256, hence

AC = $\sqrt{256}$ = 16

Now find AD² from ΔACD and ΔABD

ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²

ΔABD → AD² = 12² - x² = 144 - x²

Equate both equations for AD², hence

256 - 400 + 40x - x² = 144 - x²

-144 + 40x - x² = 144 - x² ( add x² to both sides )

- 144 + 40x = 144 ( add 144 to both sides )

40x = 288 ( divide both sides by 40 )

x = 7.2 → C

6 0

3 years ago

Read 2 more answers

7. The following numerical ordered sequence of numbers has a mean of 13 and a median of 14. 4. a. 8. 10. 13.b. 16. 18. 20:21 Gve

Montano1993 [528]

Answer:

a = 9

b = 19

Step-by-step explanation:

DO B FIRST

The mean is the average of all the terms (numbers) in the sequence

To find the average you find the sum of the terms and divided the sum by the number of terms there are.

The mean times the number of terms equals the sum of all the terms subtract the terms that you know from the sum to get A

a = 17(10)-7-12-15-17-19-20-22-24-25

a = 170-161

a = 9

The median is found by taking the average of the two middle terms

Our middle terms are 17 and B

the median times 2 equals the sum of the two terms and then subtract the term you know from the sum

b = 18(2)-17

b = 36-17

b = 19

4 0

3 years ago

Diane goes to pay for her car parking. she arrives at the car park at 2.15 but leaves at 4:45 on thursday. how much does Diane p

Alecsey [184]

4,50 pounds because 2:15-4:40 is 2 hours and 30 minutes, which is from 2-4 hours. I believe this answers your question, and if it doesn't, please clarify so I can help you! I'd love to help!

5 0

3 years ago

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.Which graph represents g(x)?

Vitek1552 [10]

The graph of $f(x)=x^2$ and the graph of $g(x)=(x-5)^2+1$ . These two graphs are illustrated in the Figure bellow. So, let's explain what this means:

For a function f(x), a new function g(x) = f(x - c) represents to shift the graph c units to the right.
For a function f(x), a new function g(x) = f(x) + k represents to shift the graph k units upward.

Since in our problem the function g(x) = f(x - c) + k, we have shifted the function f(x) c units to the right and k units upward, that is, we have shifted the function f(x) 5 units to the right and 1 unit upward as indicated in the Figure bellow.

8 0

3 years ago

Read 2 more answers