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belka [17]
2 years ago
11

If m∠EBD= 4x - 8 and m∠EBC= 5x + 20, find the value of x and m∠EBC.

Mathematics
1 answer:
coldgirl [10]2 years ago
4 0

Answer:

-28 = x

Step-by-step explanation

[5x + 20] + [4x - 8] = 180

9x + 12 = 180

- 12 -12

______________

9x = 168

18⅔ = x

m∠EBC = 5[18⅔] + 20 = 113⅓

93⅓

You will get a negative answer if you set them equal to each other, which is not allowed when you are talking about <em>length</em><em>.</em>

I hope this is correct, and as always, I am joyous to assist anyone at any time.

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A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 7
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Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 \times 10^{-6} .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = <u><em>times for service calls.</em></u>

So, X ~ Normal(\mu=75,\sigma^{2} =15^{2})

The z-score probability distribution for the normal distribution is given by;

                              Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = mean time = 75 minutes

           \sigma = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

       P(X > 93.6 min) = P( \frac{X-\mu}{\sigma} > \frac{93.6-75}{15} ) = P(Z > 1.24) = 1 - P(Z \leq 1.24)

                                                                = 1 - 0.8925 = <u>0.1075</u>

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........

where, n = number of trials (samples) taken = 12 service calls

            r = number of success = exactly 8

            p = probability of success which in our question is probability that

                   it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = <u><em>Number of service calls which takes more than 93.6 minutes</em></u>

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

               P(Y = 8)  =  \binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}

                             =  495 \times 0.1075^{8} \times 0.8925^{4}

                             =  5.6015 \times 10^{-6} .

6 0
3 years ago
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