Answer: a) N(t) = 950e^0.0475t b) 1020
Step-by-step explanation:
a)
N(t) = 950e^0.0475t.
N/B — Base is e (exponential) because growth is continuous.
b)
N = {36/24} =(approximately) 1020
Answer:
1) The probability that ten students in a class have different birthdays is 0.883.
2) The probability that among ten students in a class, at least two of them share a birthday is 0.002.
Step-by-step explanation:
Given : Assume there are 365 days in a year.
To find : 1) What is the probability that ten students in a class have different birthdays?
2) What is the probability that among ten students in a class, at least two of them share a birthday?
Solution :

Total outcome = 365
1) Probability that ten students in a class have different birthdays is
The first student can have the birthday on any of the 365 days, the second one only 364/365 and so on...

The probability that ten students in a class have different birthdays is 0.883.
2) The probability that among ten students in a class, at least two of them share a birthday
P(2 born on same day) = 1- P( 2 not born on same day)
![\text{P(2 born on same day) }=1-[\frac{365}{365}\times \frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B365%7D%7B365%7D%5Ctimes%20%5Cfrac%7B364%7D%7B365%7D%5D)
![\text{P(2 born on same day) }=1-[\frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B364%7D%7B365%7D%5D)

The probability that among ten students in a class, at least two of them share a birthday is 0.002.
Answer:
Step-by-step explanation: 54in
Let the arc is ABC with angle 324 degree, to find the length of that arc follow the steps;
The circumference of the circle E is :C = 2 r π
C = 2 * 40 π = 80 π cm.
Also 324° / 360° = 0.9m Arc (ABC ) = 0.9 * 80 π = 72 π cm
There is also formula for calculating the measure of an arc:
m Arc = r π α / 180°
m Arc = 40 π * 324 / 180
= 40π * 1.8 = 72 π
Now we have to find the exact length ( π ≈ 3.14 )
m Arc ( ABC ) = 72 * 3.14 = 226.08 cm
Answer:

5 StartRoot 10 EndRoot
Step-by-step explanation:
we know that
The legs of a 45°-45°-90° triangle are congruent
Let
x ----> the length of one leg of the triangle
Applying the Pythagorean Theorem

where
c is the hypotenuse
a and b are the legs
we have


substitute


Simplify

5 StartRoot 10 EndRoot