Answer:
y'(t) = k(700,000-y(t)) k>0 is the constant of proportionality
y(0) =0
Step-by-step explanation:
(a.) Formulate a differential equation and initial condition for y(t) = the number of people who have heard the news t days after it has happened.
If we suppose that news spreads through a city of fixed size of 700,000 people at a time rate proportional to the number of people who have not heard the news that means
<em>dy/dt = k(700,000-y(t)) </em>where k is some constant of proportionality.
Since no one has heard the news at first, we have
<em>y(0) = 0 (initial condition)
</em>
We can then state the initial value problem as
y'(t) = k(700,000-y(t))
y(0) =0
Answer:
Explained below.
Step-by-step explanation:
(1)
The hypothesis can be defined as follows:
<em>H</em>₀: The Speedy Oil Change will change the oil in customers’ cars in more than 30 minutes on average, i.e. <em>μ</em> > 30.
<em>H</em>ₐ: The Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average, i.e. <em>μ</em> ≤ 30.
(2)
Use Excel to compute the sample mean and standard deviation as follows:
Compute the test statistic as follows:
The degrees of freedom is:
df = n - 1
= 36 - 1
= 35
Compute the p-value as follows:
(3)
The <em>p</em>-value = 0.0006 is very small.
The null hypothesis will be rejected at any of the commonly used significance level.
(4)
There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average.
Answer:
45
Step-by-step explanation:
Let the original number be xy where y is unit and x is tens hence original number is 10x+y When reversed, the new number is yz hence 10y+x
We know that the original number plus 9 is the reversed number hence
10x+y+9=10y+x
9y-9x=9 which when simplified we obtain that
y-x=1 equation 1
Originally, we are told that the sum of x and y is 9 hence
y+x=9 equation 2
Solving equation 1, it means y=x+1
Substituting the above into equation 2
x+1+x=9
2x=9-1
2x=8
x=8/2=4
Since y=x+1 then y=4+1=5
Therefore, the original number, xy is 45
Answer:3^2
Step-by-step explanation:
