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Nikitich [7]
3 years ago
8

Rearrange the equation so m is the independent variable. -2m-5n=7m-3n n=___

Mathematics
1 answer:
Aneli [31]3 years ago
3 0
<h2>Answer:</h2>

The equation is given by:

        n=\dfrac{-9}{2}m

<h2>Step-by-step explanation:</h2>

We are given a equation in terms of the variable m and variable n as follows:

-2m-5n=7m-3n

Now, we are asked to find the equation in terms of m i.e. we have to consider m as independent variable and n as dependent variable since it's value is to be expressed in terms of m.

Now, we add 5n on both the sides of the equation to get:

-2m=7m-3n+5n\\\\i.e.\\\\-2m=7m+2n

Now, we subtract 7m from both the sides of the equation to get:

-2m-7n=2n\\\\i.e.\\\\2n=-9m\\\\n=\dfrac{-9}{2}m

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One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analyst
grandymaker [24]

Answer:

(a) P (X = 0) = 0.0498.

(b) P (X > 5) = 0.084.

(c) P (X = 3) = 0.09.

(d) P (X ≤ 1) = 0.5578

Step-by-step explanation:

Let <em>X</em> = number of telephone calls.

The average number of calls per minute is, <em>λ</em> = 3.0.

The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 3.0.

The probability mass function of a Poisson distribution is:

P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...

(a)

Compute the probability of <em>X</em> = 0 as follows:

P(X=0)=\frac{e^{-3}3^{0}}{0!}=\frac{0.0498\times1}{1}=0.0498

Thus, the  probability that there will be no calls during a one-minute interval is 0.0498.

(b)

If the operator is unable to handle the calls in any given minute, then this implies that the operator receives more than 5 calls in a minute.

Compute the probability of <em>X</em> > 5  as follows:

P (X > 5) = 1 - P (X ≤ 5)

              =1-\sum\limits^{5}_{x=0} { \frac{e^{-3}3^{x}}{x!}} \,\\=1-(0.0498+0.1494+0.2240+0.2240+0.1680+0.1008)\\=1-0.9160\\=0.084

Thus, the probability that the operator will be unable to handle the calls in any one-minute period is 0.084.

(c)

The average number of calls in two minutes is, 2 × 3 = 6.

Compute the value of <em>X</em> = 3 as follows:

<em> </em>P(X=3)=\frac{e^{-6}6^{3}}{3!}=\frac{0.0025\times216}{6}=0.09<em />

Thus, the probability that exactly three calls will arrive in a two-minute interval is 0.09.

(d)

The average number of calls in 30 seconds is, 3 ÷ 2 = 1.5.

Compute the probability of <em>X</em> ≤ 1 as follows:

P (X ≤ 1 ) = P (X = 0) + P (X = 1)

             =\frac{e^{-1.5}1.5^{0}}{0!}+\frac{e^{-1.5}1.5^{1}}{1!}\\=0.2231+0.3347\\=0.5578

Thus, the probability that one or fewer calls will arrive in a 30-second interval is 0.5578.

5 0
3 years ago
Natalia is making a pizza. The radius of the pizza is 25 inches. What is
aniked [119]

(b)(b)=25 cm2

b2=25 cm2

√(b2)=√(25 cm2)

b= 5 cm

Please note the square root of 25 was taken, as well as the square root of cm2.

Perimeter=4b

Perimeter=4(5 cm)

Perimeter=20 cm

Step:

A circle of radius = 12.5 or diameter = 25 or circumference = 78.54 cm has an area of: 4.909 × 10-8 square kilometers (km²) 0.04909 square meters (m²)

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omeli [17]

Answer:

C

Step-by-step explanation:

It would take 90 degree to rotate clockwise so it will take 360-90=270 degree to rotate counterclockwise

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3 years ago
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