sheilaaguilar2014

21.03.2021 •

Mathematics

37% of visitors to a museum make voluntary donations. On a certain day the
museum has 175 visitors. What is the
probability that at least 50 visitors make a
donation? What is the probability that
between 55 and 65 (inclusive) visitors will
make a donation?

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Ответ:

leekkk

06.07.2022

Mathematics

a) $t = 1\,s$ , $\dot A \approx 22619.467\,\frac{cm^{2}}{s}$ , b) $t = 3\,s$ , $\dot A \approx 67858.401\,\frac{cm^{2}}{s}$ , c) $t = 5\,s$ , $\dot A \approx 113097.336\,\frac{cm^{2}}{s}$ . The rate at which the area within the circle is increasing linearly inasmuch as time passes by.

Step-by-step explanation:

The area of a circle is described by the following formula:

$A = \pi \cdot r^{2}$

Where:

- Area, measured in square centimeters.

- Radius, measured in centimeters.

Since circular ripple is travelling outward at constant speed, radius can be described by the following equation of motion:

$r (t) = \dot r \cdot t$

Where:

$\dot r$ - Speed of the circular ripple, measured in centimeters per second.

- Time, measured in seconds.

The rate of change of the circle is determined by deriving the equation of area and replacing radius with the function in terms of the speed of the circular ripple and time. That is to say:

$\dot A = 2\cdot \pi \cdot r \cdot \dot r$

$\dot A = 2 \cdot \pi \cdot \dot r^{2}\cdot t$

Where:

$\dot A$ - Rate of change of the circular area, measured in square centimeters per second.

$\dot r$ - Speed of the circular ripple, measured in centimeters per second.

- Time, measured in seconds.

If $\dot r = 60\,\frac{cm}{s}$ , then:

a) $t = 1\,s$

$\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (1\,s)$

$\dot A \approx 22619.467\,\frac{cm^{2}}{s}$

b) $t = 3\,s$

$\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (3\,s)$

$\dot A \approx 67858.401\,\frac{cm^{2}}{s}$

c) $t = 5\,s$

$\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (5\,s)$

$\dot A \approx 113097.336\,\frac{cm^{2}}{s}$

The rate at which the area within the circle is increasing linearly inasmuch as time passes by.

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37% of visitors to a museum make voluntary donations. On a certain day the museum has 175 visitors. What is the probability that at least 50 visitors make a donation? What is the probability that between 55 and 65 (inclusive) visitors will make a donation?

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37% of visitors to a museum make voluntary donations. On a certain day the
museum has 175 visitors. What is the
probability that at least 50 visitors make a
donation? What is the probability that
between 55 and 65 (inclusive) visitors will
make a donation?