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2 years ago

What is the expanded form of a number mean?

Mathematics

1 answer:

MatroZZZ [7]2 years ago

3 0

Like if the number is 4,359

You write 4 times 1,000+ 3times 100+ 5times 10+ 9 times 1

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The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of si

OverLord2011 [107]

Answer:

a) P(x=3)=0.089

b) P(x≥3)=0.938

c) 1.5 arrivals

Step-by-step explanation:

Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.

The variable X is modeled by a Poisson process with a rate parameter of λ=6.

The probability of exactly k arrivals in a particular hour can be written as:

$P(x=k)=\lambda^{k} \cdot e^{-\lambda}/k!\\\\P(x=k)=6^k\cdot e^{-6}/k!$

a) The probability that exactly 3 arrivals occur during a particular hour is:

$P(x=3)=6^{3} \cdot e^{-6}/3!=216*0.0025/6=0.089\\\\$

b) The probability that <em>at least</em> 3 people arrive during a particular hour is:

$P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938$

c) In this case, t=0.25, so we recalculate the parameter as:

$\lambda =r\cdot t=6\;h^{-1}\cdot 0.25 h=1.5$

The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.

$E(x)=\lambda=1.5$

3 0

2 years ago

What is 4 3/7 written as an improper fraction?

aleksley [76]

31/7
First you multiply the denominator(7) by the whole number(4) then you would add the numerator(3) to get the new numerator place the new numerator(31) I’ve the old denominator(7)
I hope this helps

5 0

2 years ago

Read 2 more answers

What is an outlier mmkay

weeeeeb [17]

In statistics, an outlier is an observation point that is distant from other observations. These extreme values need not necessarily impact the model performance or accuracy, but when they do they are called “Influential” points. Note: An outlier is a data point that diverges from an overall pattern in a sample.

3 0

2 years ago

Read 2 more answers

Please help I might fail math on god I’m not lyy

love history [14]

Answer:in the points given, plot them first than the number in the left of the parentheses is x and the right is y.

Step-by-step explanation:

5 0

2 years ago

Solve the polynomial equation

ExtremeBDS [4]

Hey there!

You can solve this by squaring both sides to first cancel out the square root on the left. Then, you can eliminate each term as your normally would.

$2 \sqrt{x} =x-3$

$(2 \sqrt{x})^{2} = (x-3)^{2}$

$(4x) = (x-3)(x-3)$

$4x = x^{2} -6x+9$

$x^{2} -10x+9$

Now, you're given the opportunity to find your solution using the quadratic formula. That formula is:

$\frac{-b_-^+ \sqrt{b^2-4ac} }{2a}$

You can find out a, b, and c by comparing your new equation to the standard form. Luckily, we just put our equation into standard form:

$ax^{2} + bx + c$

$x^{2} -10x+9$

$a = 1 \\ b = -10 \\ c = 9$

To find your solution, plug these numbers into the quadratic formula and solve.

$\frac{-b_-^+ \sqrt{b^2-4ac} }{2a}$

$\frac{10_-^+ \sqrt{-10^2-4(9)}}{2}$

Remember to use PEMDAS when solving these problems.

$\frac{10_-^+ \sqrt{100-36}}{2}$

$\frac{10_-^+ \sqrt{64}}{2}$

$\frac{10_-^+ 8}{2}$

Now, solve this final bit by adding the top terms then subtracting them for two different answers.

$\frac{10 + 8}{2} = 9$

$\frac{10- 8}{2} = 1$

Don't assume that both of these are correct. The very last step is to plug both of these into the original problem you were given and see if they make the equation true.

$2 \sqrt{9} =9-3$
$2*3=6$
$6=6$

$2 \sqrt{1} =1-3$
$2*1=-2$
$2 \neq -2$

So (finally), your answer will be x = 9.

Hope this helped you out! :-)

7 0

3 years ago