What value of x makes the equation -4x – (-3 − 5x) = -3(2x − 8) true?

The number of flaws in a fiber optic cable follows a Poisson distribution. It is known that the mean number of flaws in 50m of c

boyakko [2]

Answer:

(a) The probability of exactly three flaws in 150 m of cable is 0.21246

(b) The probability of at least two flaws in 100m of cable is 0.69155

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is 0.13063

Step-by-step explanation:

A random variable X has a Poisson distribution and it is referred to as Poisson random variable if and only if its probability distribution is given by

$p(x;\lambda)=\frac{\lambda e^{-\lambda}}{x!}$ for x = 0, 1, 2, ...

where $\lambda$ , the mean number of successes.

(a) To find the probability of exactly three flaws in 150 m of cable, we first need to find the mean number of flaws in 150 m, we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 150 m of cable is $1.2 \cdot 3 =3.6$

The probability of exactly three flaws in 150 m of cable is

$P(X=3)=p(3;3.6)=\frac{3.6^3e^{-3.6}}{3!} \approx 0.21246$

(b) The probability of at least two flaws in 100m of cable is,

we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 100 m of cable is $1.2 \cdot 2 =2.4$

$P(X\geq 2)=1-P(X$

$P(X\geq 2)=1-p(0;2.4)-p(1;2.4)\\\\P(X\geq 2)=1-\frac{2.4^0e^{-2.4}}{0!}-\frac{2.4^1e^{-2.4}}{1!}\\\\P(X\geq 2)\approx 0.69155$

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is

$P(X=1)=p(1;1.2)=\frac{1.2^1e^{-1.2}}{1!}\\P(X=1)\approx 0.36143$

The occurrence of flaws in the first and second 50 m of cable are independent events. Therefore the probability of exactly one flaw in the first 50 m and exactly one flaw in the second 50 m is

$(0.36143)(0.36143) = 0.13063$

4 0

2 years ago

To go on the class trip, chang needs at least $125. he has saved $45, and he makes $7 an hour at his job. what is the minimum nu

Murljashka [212]

The total amount that Chang will received from his wages is the product of his hourly wage times the number of hours he has worked (n). His total savings should not be less than $125. The equation that best describes the situation is,
45 + 7n ≥ 125
Solving for n in the inequality gives an answer of n≥11.42 hours. Thus, he needs to work for at least 12 hours.

6 0

2 years ago

Read 2 more answers

State, with an explanation, whether the mean, median, or mode gives the best description of the following average. The average

erma4kov [3.2K]

Answer:

The mean is the better method.

Step-by-step explanation:

The best way to meassure the average height is throught mean. The mean of a sample is the average of that sample's height, and it will be a good estimate for the population's average height.

The mode just finds the most frequent height. Even tough the most frequent height will influence the average height, knowing only what height is the most frequent one doesnt give you enough informtation about how the height is centrally distributed.

As for the median, it is fine to use the median of a sample to estimate the median of the population, but if you use the median to estimate the average height you may have a few issues. For example, if you include babies in your population, the babies will push the average height down a lot and they are far below te median height. This, as a result, will give you a median height of a sample way above the average height of the population, becuase median just weights every person's height the same, while average will weight extreme values more, in the sense that a small proportion of extreme values can push the average far from the median.

8 0

2 years ago

X=a-2by(2) make y the subject

sladkih [1.3K]

Answer:

y = √{(a - x)/2b}

Step-by-step explanation:

x=a-2by²

2by² = a - x

divide through by 2b

y² = (a - x)/2b

y = √{(a - x)/2b}

3 0

2 years ago

If the pointer in the figure is spun twice, find the probability that the pointer lands on red (R) both spins.

r-ruslan [8.4K]

The probability of the pointer lands on red(R) both spin = $\frac{1}{36}$

Step-by-step explanation:

Given,

The number of parts = 6

The pointer is spun twice.

To find the probability of the pointer lands on red(R) both spin.

Formula

Probability of an event = number of required outcomes ÷ the total number of outcomes.

P(A and B) = P(A)×P(B)

Now,

For one spin,

A = RED comes.

For second spin,

B = RED comes

So,

P(A) = $\frac{1}{6}$ and P(B) = $\frac{1}{6}$

Then,

P(A and B) = $\frac{1}{6}$ × $\frac{1}{6}$ = $\frac{1}{36}$

Hence, the probability of the pointer lands on red(R) both spin = $\frac{1}{36}$

4 0

2 years ago