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3 years ago

ZE and ZF are vertical angles with mZE= 9x + 12 and mZF= 3x + 24. What is the value of x?

Mathematics

1 answer:

gogolik [260]3 years ago

5 0

Answer:

x=2

Step-by-step explanation:

Vertical angles are equal

m ZE = m ZF

9x+12 = 3x+24

Subtract 3x from each side

9x -3x +12 = 3x-3x+24

6x+12 = 24

Subtract 12 from each side

6x+12 -12 = 24-12

6x = 12

Divide each side by 6

6x/6 =12/6

x = 2

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3 years ago

I roll a fair die twice and obtain two numbers X1= result of the first roll and X2= result of the second roll. Given that I know

azamat

By definition of conditional probability,

$P(X_1=4\text{ or }X_2=4\mid X_1+X_2=7)=\dfrac{P((X_1=4\text{ or }X_2=4)\text{ and }X_1+X_2=7)}{P(X_1+X_2=7)}$

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Assuming a standard 6-sided fair die,

if $X_1=4$ , then $X_1+X_2=7$ means $X_2=3$ ; otherwise,
if $X_2=4$ , then $X_1=3$ .

Both outcomes are mutually exclusive with probability $\frac1{36}$ each, hence total probability $\frac2{36}=\frac1{18}$ .

Of the 36 possible outcomes, there are 6 ways to sum the integers 1-6 to get 7:

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and so a sum of 7 occurs $\frac6{36}=\frac16$ of the time.

Then the probability we want is

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3 years ago