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3 years ago

What is the area of the sector of a circle with radius r=2 cm, and the measure of its intercepted arc of 150 degrees ?

Mathematics

1 answer:

AURORKA [14]3 years ago

6 0

There are is 160 metres squared is the answer to this question

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The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a m

castortr0y [4]

Answer:

a) 50.34% probability that the arrival time between customers will be 7 minutes or less.

b) 24.42% probability that the arrival time between customers will be between 3 and 7 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Mean of 10 minutes:

This means that $m = 10, \mu = \frac{1}{10} = 0.1$

A. What is the probability that the arrival time between customers will be 7 minutes or less?

$P(X \leq x) = 1 - e^{-\mu x}$

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

50.34% probability that the arrival time between customers will be 7 minutes or less.

B. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3)$

$P(X \leq x) = 1 - e^{-\mu x}$

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

$P(X \leq 3) = 1 - e^{-0.1*3} = 0.2592$

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3) = 0.5034 - 0.2592 = 0.2442$

24.42% probability that the arrival time between customers will be between 3 and 7 minutes

3 0

3 years ago

Deremine the slope and y-intercept y=x+5

const2013 [10]

Slope:1
Y intercept:5

8 0

3 years ago

R2+2r-33=0 solve by completing the square

-BARSIC- [3]

R^2+2r-33=0 move constant to other side by adding 33 to both sides

r^2+2r=33 halve the linear coefficient, square it and add to both sides, in this case it is just one

r^2+2r+1=34 now the left side is a perfect square...

(r+1)^2=34 take the square root of both sides...

r+1=34^(1/2) subtract 1 from both sides

r=-1+34^(1/2) and -1-34^(1/2)

8 0

3 years ago

The area of a rectangle is 77ft, and the length of the rectangle is 3 more than twice the width. Find the dimensions of the rect

Alexeev081 [22]

Answer:

W = 11/2, L = 14 sq ft

Step-by-step explanation:

Area = 77ft

L = length, W = width

L = 3 + 2W

L * W = 77

Plug W in to find the L

5 0

3 years ago

The variables are higher or lower

Marina CMI [18]

Answer:

Higher

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers