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docker41 [41]
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
Mathematics
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
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