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2 years ago

Is Triangle UVW cong Triangle XYZ? If so, name the postulate that applies

Mathematics

1 answer:

rosijanka [135]2 years ago

3 0

Answer:

Might not be congruent

Step-by-step explanation:

Because look carefully and use the measurment and you can compare my answer to yours

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Evaluate log3 (8), given log3 (2) ≈ 0.631

IRINA_888 [86]

Answer: 1.893 Welcome

Step-by-step explanation:

7 0

2 years ago

Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (E

krok68 [10]

Answer:

Here both probabilities are not equal.

Therefore the die is not fair and biased.

Step-by-step explanation:

Now n= 1200 times and x = 419 times.

a) Empirical Probability:

$=\frac{x}{n} \\\\= \frac{419}{1200}\\ \\=0.349$

Probability = 0.349

b) Theoretical Probability:

$=\frac{1}{6}$

Here both probabilities are not equal.

Therefore the die is not fair and biased.

3 0

2 years ago

Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .