What is the volume of the figure?

A bulb can either be on or off. A board contains 20 bulbs connected to a randomization circuit that lights up a random sequence

Step2247 [10]

The chance that any given bulb is on is equal to 1/2. The chance that all twenty bulbs are on at the same time is $(\frac{1}{2}) ^{20} = \frac{1^{20}}{2^{20}} = \frac{1}{1048576}$

8 0

3 years ago

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Simplify the expression by combining like terms. 22+5m−4m+7n−8

rewona [7]

Answer: The simplified form by combining like terms is given by

$14+m+7n$

Step-by-step explanation:

Since we have given that

$22+5m-4m+7n-8$

Now, we combine the like terms :

1) First we collect m terms :

$22+5m-4m+7n-8\\\\=22+m+7n-8\\\\$

2) Combine n terms and constant terms :

$=22-8+m+7n\\\\=14+m+7n$

Hence, the simplified form by combining like terms is given by

$14+m+7n$

6 0

3 years ago

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Solve the following equation <br><br> 1/x-1+1/x+2=3

disa [49]

Answer:

x = 1

Step-by-step explanation:

Solve for x over the real numbers:

-1 + 2 + 1/x + 1/x = 3

-1 + 2 + 1/x + 1/x = 1 + 2/x:

1 + 2/x = 3

Bring 1 + 2/x together using the common denominator x:

(x + 2)/x = 3

Multiply both sides by x:

x + 2 = 3 x

Subtract 3 x + 2 from both sides:

-2 x = -2

Divide both sides by -2:

Answer: x = 1

6 0

4 years ago

Whats the input value of f(x)=2x+5

Juli2301 [7.4K]

Answer:

x

Step-by-step explanation:

f(x)=2x+5

Input: x

Output: f(x)

For i.e:

Input: 1

Output: f(1) = 2(1) + 5 = 2 + 5 = 7

8 0

3 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

3 years ago