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3 years ago

Is the relation a function? {(4, 10), (7,6), (3,8), (11, 10), (7,15)}

Mathematics

1 answer:

astraxan [27]3 years ago

8 0

Answer:

Step-by-step explanation:

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If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

======================================================

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

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Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

3 0

4 years ago

1. Write the solution set in interval notation: 3x-2 > x-4 or 7x-5 < 3x+3

Yakvenalex [24]

$3x-2>x-4\ \ | subtract\ x\ \ \ \ \textbf{or}\ \ \ \ 7x-5-4\ \ | add\ 2\ \ \ \ \ \textbf{or}\ \ \ \ 4x-5-2\ \ \ \ \ \textbf{or}\ \ \ \ \ 4x-1\ \ \ \ or\ \ \ \ x$

5 0

4 years ago

Read 2 more answers

How much pure acid should be mixed with 55 gallons of a 60%acid solution in order to get an 80% acid solution?

horsena [70]

Work in amount of pure acid let x = gallons of pure acid required.
then we have the equation:-

x + 55(0.6) = 0.80(x + 55)

x + 33 = 0.80x + 44
0.20x = 11
x = 11/0.2 = 55 gallons answer

4 0

3 years ago

Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61

Irina-Kira [14]

$ 2772 is paid in state income tax

Solution:

Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income

Federal taxable income = $61,600

To find: Amount paid by Tina in state income tax

Tax rate = 4.5 %

Which means, 4.5 % of $61,600 is paid as tax

$Tax\ Rate = 4.5 \% \text{ of } 61600$

Here, "of" means multiplication or product

$Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772$

Thus $ 2772 is paid in state income tax

7 0

4 years ago

Please write the converse of the statement. If Daphne has flu, then she is ill

Hitman42 [59]

Converse = reversing two statements

If she is ill, then Daphne has the flu.

7 0

3 years ago