Answer:
4/23
Step-by-step explanation:
Probability of choosing a red marble = # of red marbles / total # of marbles
We are told that there are 4 red marbles and 19 blue marbles
So the # of red marbles = 4
And the total # of marbles = 4 + 19
4 + 19 = 23
So there are a total of 23 marbles
Recall that probability of choosing a red marble is equal to # of red marbles / total # of marbles
Hence, the probability of choosing a red marble is 4/23
Note: 4/23 is already in it's simplest form so no simplifying has to be done.
Answer:
Volume of the cone is increasing at the rate 
.
Step-by-step explanation:
Given: The radius of a right circular cone is increasing at a rate of 
in/s while its height is decreasing at a rate of 
in/s.
To find: The rate at which volume of the cone changing when the radius is 
in. and the height is 
in.
Solution:
We have,
, 
, 
, 
Now, let 
be the volume of the cone.
So, 
Differentiate with respect to 
.
![\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Cleft%20%5B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%2Bh%5Cleft%20%28%202r%20%5Cright%20%29%5Cfrac%7Bdr%7D%7Bdt%7D%20%5Cright%20%5D)
Now, on substituting the values, we get
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%20%5Cleft%20%28%20134%20%5Cright%20%29%5E2%5Cleft%20%28%20-2.2%20%5Cright%20%29%2B%5Cleft%20%28%20%20136%5Cright%20%29%5Cleft%20%28%202%20%5Cright%20%29%5Cleft%20%28%20134%20%5Cright%20%29%5Cleft%20%28%201.9%20%5Cright%20%29%20%5Cright%20%5D)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ -39503.2+69251.2 \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%20%20-39503.2%2B69251.2%20%5Cright%20%5D)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ 29748 \right ]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cleft%20%5B%2029748%20%5Cright%20%5D)
Hence, the volume of the cone is increasing at the rate .
Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are not factors of 42
Blizzard [7]
Answer:
5, 25, 28, 35, 56, 75 80 are not the factors of 42
I'm going with 10. Let me know.
Let x be the length of the train.
On the basis of the observer;
Speed of the train = x/6
On the basis of the bridge;
Total distance covered by any point of the train= 350+x
Speed = (350+x)/20
Equating the two expressions of speed;
x/6 = (350+x)/20
20(x) = 6(350+x)
20x = 2100+6x
(20-6)x = 2100
14x = 2100
x= 2100/14 = 150 m
Speed = x/6 = (350+x)/20 = 150/6 = 500/20 = 25 m/s.
Therefore,
Length of train = 150 m
Speed of train = 25 m/s
