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3 years ago

Please help with this math question

Mathematics

1 answer:

blagie [28]3 years ago

8 0

Answer:

Mirandah added 5x and 9y, which she shouldn't do because one is y and the other is x, meaning they don't match.

There is no simplifying the equation. It should stay 5x + 9y - 4

If wrong, I apologize, but this should be correct.

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Let x represent the measurment of an acute angle in degrees. the ratio of the complement of x to the supplement of x is 2: 5. gu

Nadusha1986 [10]

Ratio of complement of x : supplement of x
2 : 5
⇒ 2 times the supplement of x will be equal to 5 times the complement of x

5(90 - x) = 2 (180 - x)
450 - 5x = 360 - 2x
5x - 2x = 450 - 360
3x = 90
x = 30°

Complement of x = 90 - x = 90 - 30 = 60
Supplement of x = 180 - x = 180 - 30 = 150
Ratio:
60 : 150
60 ÷ 30 : 150 ÷ 30
2 : 5 (checked)

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3 years ago

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.

Ulleksa [173]

Answer:

0.52763 is the probability that the time between the next two calls will be 54 seconds or less.

0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.

Step-by-step explanation:

We are given the following information in the question:

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.2 minutes.

The distribution function can be written as:

$f(x) = \lambda e^{-\lambda x}\\\text{where lambda is the parameter}\\\\\text{Mean} = \mu = \displaystyle\frac{1}{\lambda}\\\\\Rightarrow 1.2 = \frac{1}{\lambda}\\\\\lambda = 0.84 \\f(x) = 0.84 e^{0.84 x}$

The probability for exponential distribution is given as:

$P( x \leq a) = 1 - e^{\frac{-a}{\mu}}\\\\P(a \leq x \leq b) = e^{\frac{-a}{\mu} -\frac{-b}{\mu}}$

a) P( time between the next two calls will be 54 seconds or less)

$P( x \leq 0.9)\\= 1 - e^{\frac{\frac{-54}{60}}{1.2}} = 0.52763$

0.52763 is the probability that the time between the next two calls will be 54 seconds or less.

b) P(time between the next two calls will be greater than 118.5 seconds)

$p( x > \frac{118.5}{60}) = P(x > 1.975)\\\\ = 1 - P(x \leq 1.975) \\\\= 1 -1+ e^{\frac{-1.975}{1.2}}\\\\= 0.19285$

0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.

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