Answer: 6 hours
Step-by-step explanation:
Given, Tim and Jim are working on a school project together.
Tim takes 10 hours to complete the school project.
If Jim worked alone, it would take him 15 hours
Let t be the time they both take if they work together.
Then,
So, it will take<u> 6 hours</u> to complete the school project together .
Answer:
Step-by-step explanation:
I solved this using initial conditions and calculus, so I hope that's what you are doing in math. It's actually NOT calculus, just a concept that is taught in calculus.
The initial condition formula we need is
Filling in our formula with the 2 conditions we are given:
and
With those 2 equations, we have 2 unknowns, the C (initial value) and the k (the constant). We know that the initial value (or starting temp) for both conditions is the same, so we solve for C in one equation, sub it into the other equation and solve for k. If
then
which, by exponential rules is the same as
Since that value of C is the same as the value of C in the other equation, we sub it in:
Divide both sides by 65 and use the rules of exponents again to get
which simplifies down to
Take the natural log of both sides to get
Do the log thing on your calculator to get
.2682639866 = 5k and divide both sides by 5 to find k:
k = .0536527973
Now that we have k, we sub THAT value in to one of the original equations to find C:
which simplifies down to
Raise e to that power on your calculator to get
65 = C(1.710059171) and divide to solve for C:
C = 38.01038064
Now sub in k and C to the final problem when t = 23:
which simplifies a bit to
Raise e to that power on your calculator to get
y = 38.01038064(3.434991111) and
finally, the temp at 23 minutes is
130.565
Answer:
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.
Step-by-step explanation:
We are in posession of the sample's standard deviation, so we use the student's t-distribution to find the confidence interval.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 35 degrees of freedom(y-axis) and a confidence level of ). So we have T = 2.9467
The margin of error is:
M = T*s = 2.9467*0.058 = 0.171
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.053 - 0.171 = 0.882kg
The upper end of the interval is the sample mean added to M. So it is 1.053 + 0.171 = 1.224 kg.
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.