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3 years ago

If the measure of angle AOB = 2x + 4 and the measure of angle COD = 4x - 10, write an equation for solve for x

Mathematics

2 answers:

rosijanka [135]3 years ago

5 0

Answer:

$x=7$

Step-by-step explanation:

We know that ∠AOB is (2x+4) and ∠COD is (4x-10).

Note that ∠AOB and ∠COD both have one arc mark.

In other words, they are congruent. Therefore, their angle measures are the same.

So, we can set the two equations equal to each other:

$2x+4=4x-10$

Now, we can solve for x. Let's add 10 to both sides. This yields:

$2x+14=4x$

Now, let's subtract 2x from both sides. This yields:

$14=2x$

Finally, divide both sides by 2. Therefore, the value of x is:

$x=7$

And we're done!

poizon [28]3 years ago

3 0

Answer:

2x+4=4x-10

Step-by-step explanation:

AOB and COD are same

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2 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

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$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

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Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

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This means that,

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5 0

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3 years ago

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cupoosta [38]

Answer:

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