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3 years ago

10

There are 5 girls and 5 boys in a chess club. The club holds a round-robin tournament in which every player plays against every

other player exactly once.
What fraction of the games are boy-versus-boy

1 answer:

umka21 [38]3 years ago

5 0

The answer would be 18.9%

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Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

3 years ago

What is the congruence theorem used to prove that the two triangles are congruent?

natka813 [3]

Answer:

AAS, the two equal angles, the two right triangles, and the shared side

Step-by-step explanation:

8 0

2 years ago

What’s 150 divided by 180 step by step?

liubo4ka [24]

150 can't go into 180 equally, so the answer is 1.2

8 0

3 years ago

Find the correct linear equation: y is the quotient of thrice a number and ten.

Anarel [89]

Answer:

y = (3x)/10

Step-by-step explanation:

quotient = divide

7 0

2 years ago

Please help me on this!!<br> 5n+17≥n–3≥–15+5n

DENIUS [597]

Answer:

-5 ≤ n ≤ 3

Step-by-step explanation:

Firstly we solve the equation two at a time;

5n + 17 ≥ n - 3

5n - n ≥ -3 - 17

4n ≥ -20

n ≥ -5

-5 ≤ n

n - 3 ≥ -15 + 5n

n - 5n ≥ -15 + 3

-4n ≥ -12

-n ≥ -3

n ≤ 3

Therefore,

5n+17 ≥ n–3 ≥ –15+5n, becomes

-5 ≤ n ≤ 3

6 0

3 years ago