Answer:
The probability 
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.90
The sample size is n = 30
Generally mean of the sampling distribution is 
Generally the standard deviation is mathematically represented as

=> 
=> 
Generally the he probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places is mathematically represented as

Generally 
So

From the z-table 
So

Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
Taking square root on both sides

x=±4
2. t^2=81
Taking square root on both sides

t=±9
3. r^2-100=0

r=±10
4. x²-144=0
x²=144
Taking square root on both sides

x=±12
5. 2s²=50

s=±5 ..
Answer:
y = 22.5 - 0.2t
Step-by-step explanation:
Given;
total number of candle, n = 22.5 ounce
Rate of candle burn, R = 1 ounce per 5 hours 
The amount of candle left = total initial value - amount burnt
let the amount let = y
y = 22.5 - 0.2t
where;
t is the time in which the candle is burnt
Thus, the equation for the amount of candle left is given by;
y = 22.5 - 0.2t
First, we need to solve the differential equation.

This a separable ODE. We can rewrite it like this:

Now we integrate both sides.

We get:

When we solve for y we get our solution:

To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:

When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.