This problem is a combination of the Poisson distribution and binomial distribution.
First, we need to find the probability of a single student sending less than 6 messages in a day, i.e.
P(X<6)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)
=0.006738+0.033690+0.084224+0.140374+0.175467+0.175467
= 0.615961
For ALL 20 students to send less than 6 messages, the probability is
P=C(20,20)*0.615961^20*(1-0.615961)^0
=6.18101*10^(-5) or approximately
=0.00006181
Answer:

Step-by-step explanation:
- Height of cone (h) = 7 cm
- Formula for Volume of cone is given as:
- Plugging the values of h and r in the above formula, we find:
Answer:
Volume of right rectangular prism = 3.75 in³
Step-by-step explanation:
Given:
First side of rectangular prism = 2 inches
Second side of rectangular prism = 1
= 1.5 inches
Third side of rectangular prism = 1
= 1.25 inches
Find:
Volume of right rectangular prism:
Computation:

Average rate of change: r=[f(b)-f(a)]/(b-a)
r=-60→[f(b)-f(a)]/(b-a)=-60
b=5; f(b)=-213; a=1; f(a)=27
(-213-27)/(5-1)=(-240)/4=-60
Answer: The <span>two points in the table which create an interval with an average rate of change of -60 are:
x f(x)
1 27
5 -213</span>
Answer:
The surface area of the cylinder is about 954.56 square inches.
Step-by-step explanation:
The total surface area of a cylinder is given by the formula:

Here, we are given that the radius is 8 inches and that the height is 11 inches. We are also using 3.14 for π. So, substitute:

Use a calculator:

The surface area of the cylinder is about 954.56 square inches.