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3 years ago

If y varies directly with x, find the missing value below. (-9, -45) and (11, y)

Mathematics

2 answers:

Ainat [17]3 years ago

6 0

Answer:

-45×11÷-9

=5×11

=55

so y=55

Deffense [45]3 years ago

4 0

Y=55

Explanation:

If you’re looking to see how 11 and y would match -9 and -45 you would find the unit rate of -9 and -45.

-9/-9=1
-45/-9=5

So if the y is going up by 5’s it would be 55.

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The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second. Use the central limi

Mila [183]

Answer:

0.048 is the probability that more than 950 message arrive in one minute.

Step-by-step explanation:

We are given the following information in the question:

The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second.

Let X be the number of messages arriving at a multiplexer.

Mean = 15

For poison distribution,

Mean = Variance = 15

$\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{15} = 3.872$

From central limit theorem, we have:

$z = \displaystyle\frac{x-n\mu}{\sigma\sqrt{n}}$

where n is the sample size.

Here, n = 1 minute = 60 seconds

P(x > 950)

$P( x > 950) = P( z > \displaystyle\frac{950 - (60)(15)}{\sqrt{(15)(60)}}) = P(z > 1.667)$

$= 1 - P(z \leq 1.667)$

Calculation the value from standard normal z table, we have,

$P(x > 950) = 1 - 0.952 = 0.048$

0.048 is the probability that more than 950 message arrive in one minute.

3 0

3 years ago

Round to the nearest tenth.

laila [671]

Answer:

8.2 units

Step-by-step explanation:

Given that the only information for our triangle are 2 sides and 1 angle, we must use the Law of Cosines to find side BC

Recall the Law of Cosines

$a^2=b^2+c^2-2bc\cdot cos(A)$

Identify angles and sides

$m\angle A=23^\circ\\a=BC=?\\b=AC=14\\c=AB=6$

Solve for side "a"

$a^2=b^2+c^2-2bc\cdot cos(A)\\\\a^2=14^2+6^2-2(14)(6)\cdot cos(23^\circ)\\\\a^2=196+36-168cos(23^\circ)\\\\a^2=222-168cos(23^\circ)\\\\a=\sqrt{222-168cos(23^\circ)}\\ \\a\approx8.2$