Answer: the interest rate is 6%
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
A = $4482
P = 1000
t = 25 years
Therefore,
4482 = 1000 x 2.7183^(r x 25)
4482/1000 = 2.7183^25r
4.482 = 2.7183^25r
Taking ln of both sides, it becomes
Ln 4.482 = 25rLn2.7183
1.5 = 25r
r = 1.5/25 = 0.06
r = 0.06 × 100 = 6%
Answer:
1815 pi cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the diameter =22
so the radius is d/2 = 22/2 =11
V = pi (11)^2 (15)
V = pi1815
V = 1815 pi cm^3
Answer:
22
Step-by-step explanation:
Given:
An art teacher has the total number of buttons = 
1. In order to give each in the class 6 buttons, she will need 18 more buttons.
2. If she gives each child 5 buttons, she will have 4 left over.
Question asked:
How many children are in the class ?
Solution:
<u>Let total number of children in the class = </u>
<u><em>As given that, 18 more buttons will be needed to give 6 buttons to each.</em></u>
The equation will be:-

<em><u>Also given that, If she gives 5 buttons to each, she will have 4 left over.</u></em>
The equation will be:-

Subtraction equation 2 from 1

Hence, total number of children are 22.
Answer:

Step-by-step explanation:
8^2+5^2=c^2
64+25=c^2
89=c^2
c=
<-- this is the length of the rectangle at the bottom
2^2+(
)^2=c^2
4+89=c^2
c=
<-- length of dotted line (diagonal)
Answer:
P(x > 10) = 0.6981.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
In this question:

P(x>10)

In which






So P(x > 10) = 0.6981.