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The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the proba

mart [117]

Answer:

The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.

Step-by-step explanation:

The distribution that represents the ocurrence of this events is the Poisson distribution.

The probability of having k events in a ten-minute-period can be expressed as:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}$

being λ the mean number of occurrences in ten minutes.

The probablility that there are 8 occurrences in ten minutes can be calculated as:

$P(x=k)=\frac{ \lambda^ke^{-k}}{k!}\\\\P(x=8)=\frac{5.3^8e^{-8}}{8!}=\frac{(622596*0.000335463)}{40320}=0.00518$

The probablility that there are 8 occurrences in ten minutes is 0.00518 or 0.5%.

5 0

2 years ago

A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China. Find the length and width of a si

dusya [7]

The length and width of the similar rectangular screen are 110 meters and 35 meters respectively.

<u>SOLUTION: </u>

Given, A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China.

We have to find the length and width of a similar rectangular screen

We are also given that the length is 5 meters more than 3 times its width,

Let width of rectangle be "b" meters, the its length will be 5 + 3b meters

And, the viewable area is 3,850 square meters.

$\begin{array}{l}{\text { So, area }=3850} \\\\ {\text { Length } \times \text { width }=3850} \\\\ {(5+3 b) \times b=3850} \\\\ {5 b+3 b^{2}=3850} \\\\ {3 b^{2}+5 b-3850=0}\end{array}$

Now,let us use quadratic formula:

$\begin{array}{l}{\mathrm{x}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}} \\\\ {\text { Then, } \mathrm{b}=\frac{-5 \pm \sqrt{5^{2}-4 \times 3 \times(-3850)}}{2 \times 3}}\end{array}$

$\begin{array}{l}{\mathrm{b}=\frac{-5 \pm \sqrt{25+46200}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm \sqrt{46225}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm 215}{6}} \\\\ {\mathrm{b}=\frac{-5+215}{6} \text { or } \frac{-5-215}{6}} \\\\ {\mathrm{b}=\frac{210}{6} \mathrm{or} \frac{-220}{6}}\end{array}$

Neglect negative values as width can’t be negative

$b=\frac{210}{6}=35$

so, width = 35 meters, then length = 5 + 3(35) = 5 + 105 = 110 meters

hence, the length and width of the similar rectangular screen are 110 meters and 35 meters respectively.

3 0

2 years ago

Kim is making a bouquet for her friend. she used x tulips and some daffodils in the bouquet. the number of daffodils is equal to

mrs_skeptik [129]

There are 16 tulips because the square root of 16 is 4, which means there will be 4 daffodils and 16+4=20. So the answer is 16 tulips.

3 0

2 years ago

Read 2 more answers

I neeeee helppppppppp

kaheart [24]

Answer:

The pin number is 1147

Step-by-step explanation:

We have given that:

Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500.

Pin number is between 1000 and 1500

PIN is the product of two consecutive prime numbers.

Prime numbers are those numbers which are divisible by one or itself only.

So,

prime numbers are 1, 3, 5, 7,………29, 31,37, 41, …..

Multiply 29 x 31 = 899 which does not come in the range of 1000 and 1500.

Next,

31 x 37 = 1147 this is between 1000 and 1500

Thus the pin number is 1147....

7 0

3 years ago

18 of the last 30 cars that passed by you were black. what is the probability the next car will be black. (0.18, 0.6, or 0.30)

Black_prince [1.1K]

18 divided by 30 is 0.6. So I would say that B, or 0.6, is the correct answer.

3 0

2 years ago

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