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maria [59]
3 years ago
7

Phil has 19 other students in his math class. During class one day, the teacher asks for a volunteer to come up to the board. If

no one volunteered, one would be chosen randomly. If everyone was in the class that day, and the teacher did pick someone at random, what is the probability that the teacher will choose Phil.
Select one:

1/19

19/20

20/1

1/20
Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Answer:

1/19

Since there are 19 students in the class, and this is a question of Phil.

Since there is only 1 Phil, it will be 1/19.

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A right circular cone is undergoing a transformation in such a way that the radius of the cone is increasing at a rate of 1/2 in
Ivenika [448]

Answer:

The volume is decreasing at the rate of 1.396 cubic inches per minute

Step-by-step explanation:

Given

Shape: Cone

\frac{dr}{dt} =\frac{1}{2} --- rate of the radius

\frac{dh}{dt} =-\frac{1}{3} --- rate of the height

r = 2

h = \frac{1}{3}

Required

Determine the rate of change of the cone volume

The volume of a cone is:

V = \frac{\pi}{3}r^2h

Differentiate with respect to time (t)

\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})

Substitute values for the known variables

\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)

\frac{dV}{dt} = -\frac{\pi}{3}*\frac{4}{3}

\frac{dV}{dt} = -\frac{22}{7*3}*\frac{4}{3}

\frac{dV}{dt} = -\frac{22}{21}*\frac{4}{3}

\frac{dV}{dt} = -\frac{88}{63}

\frac{dV}{dt} =-1.396in^3/min

The volume is decreasing at the rate of 1.396 cubic inches per minute

3 0
3 years ago
6. You are given a sheet of cardboard that is 8.0 in. x 11.0 in. How many full circles with a diameter of 3.0 inches can you cut
larisa86 [58]
In order to answer this, it would be useful to calculate the area of the cardboard and the circles. We do as follows:

Total area of cardboard = <span> 8.0 in. x 11.0 in = 88 in^2

Area of one circle = pi(r^2) = pi(0.5)^2 = 0.7854 in^2

Number of full circles = 88 / 0.7854 = 112.0451

Therefore, there will be 112 number of full circles. The percentage of waste is equal to:

% waste = (88 - 0.7854(112) / 88) x 100= 0.04%</span>
4 0
4 years ago
The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is 65 yd2. Find the dimensions of the
Law Incorporation [45]

Answer: lenght = 13 yd, width = 8 yd.

Step-by-step explanation: The decision on a photo

7 0
3 years ago
√45 * √96<br> Please show your work on how you got the answer!
zysi [14]

Answer:

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Step-by-step explanation:

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5 0
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hjlf

Answer:

the answer is 41.5

Step-by-step explanation:

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41.5=x

8 0
4 years ago
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