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Ber [7]
3 years ago
14

The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable

. In fact, the times are exponentially distributed with a mean of 7 minutes. What is the probability that a car can complete the transaction in less than 4 minutes?
Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer:

0.4353 = 43.53%

Step-by-step explanation:

The times are exponentially distributed, so let's call n the mean, and x the time of transaction. The times of the transaction occurs in a certain time is:

e^{-x/n}

So, the probability that a car complete the transaction in less than 4 minutes, is 1 less the times it does it at 4 minutes:

P = 1 - e^{-4/7}

P = 0.4353

P = 43.53%

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

diagonal=\sqrt{10^2+10^2}

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3 years ago
Which graph represents the circle given by the equation x + y - 4x + 9y -7 = 0?
PSYCHO15rus [73]

The graph of the circle equation is graph (d)

<h3>How to determine the circle?</h3>

The equation is given as:

x^2 + y^2 - 4x + 9y -7 = 0

Rewrite as:

x^2 - 4x + y^2 + 9y = 7

Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.

So, we have:

(x - 2)^2 + (y + 3)^2 = 7 + 4 +  20.25

Evaluate the sum

(x - 2)^2 + (y + 3)^2 = 31.25

A circle equation is represented as:

(x - h)^2 + (y - k)^2 = r^2

Where

Center = (h, k)

Radius = r

So, we have:

(h, k) = (2, -3)

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r = 5.5

The circle that has a center of (2, -3) and a radius of 5.5 is graph d

Hence, the graph of the circle equation is graph (d)

Read more about circle equation at:

brainly.com/question/1559324

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5 0
2 years ago
2. A solar lease customer built up an excess of 6,500 kilowatt hours (kwh) during the summer using his solar
tia_tia [17]

9514 1404 393

Answer:

  a)  E = 6500 -50d

  b)  5000 kWh

  c)  the excess will last only 130 days, not enough for 5 months

Step-by-step explanation:

<u>Given</u>:

  starting excess (E): 6500 kWh

  usage: 50 kWh/day (d)

<u>Find</u>:

  a) E(d)

  b) E(30)

  c) E(150)

<u>Solution</u>:

a) The exces is linearly decreasing with the number of days, so we have ...

  E(d) = 6500 -50d

__

b) After 30 days, the excess remaining is ...

  E(30) = 6500 -50(30) = 5000 . . . . kWh after 30 days

__

c) After 150 days, the excess remaining would be ...

  E(150) = 6500 -50(150) = 6500 -7500 = -1000 . . . . 150 days is beyond the capacity of the system

The supply is not enough to last for 5 months.

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2 years ago
What is the measure of the missing exterior angle?
larisa86 [58]

Answer:

the missing angle is 148°

Step-by-step explanation:

the sum of all exterior angles of a triangle are 360°

so, 360-138-74 = 148°

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2 years ago
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