If you use the SAS theorem, you can prove the triangles are congruent. Due to vertical angles, we have one angle, and we know one side is congruent. In order to prove these triangles are simillar, we need another side

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2 years ago

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What is the least common multiple of 24, 16, and 32?

notsponge [240]

Answer: the LCM is 96

Step-by-step explanation: looked it up

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3 years ago

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A bag contains 42 red marbles, 6 white marbles, and 8 gray marbles. You randomly pick out a marble, record its color, and put it

Elanso [62]

For any single draw,

$\mathbb P(\text{white})=\dfrac6{42+6+8}=\dfrac6{56}$
$\mathbb P(\text{gray})=\dfrac8{42+6+8}=\dfrac8{56}$

Drawing a white marble or a gray marble are disjoint events; only one of them can happen. So

$\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0$
$\mathbb P(\text{white or gray})=\dfrac6{56}+\dfrac8{56}=\dfrac{14}{56}$

Out of 224 draws, you should expect $\dfrac{14}{56}\times224=56$ of the marbles to be either white or gray.

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3 years ago

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