The table shows the number of students in a school's beginning and advanced orchestra classes. The student pay a fee for instruction books: $5 for brass, $5 for woodwinds, and $8 for strings. Find the amount each class will spend on books.
The table shows the number of students in a school's beginning and advanced orchestra classes. The student pay a fee for instruction books: $5 for brass, $5 for woodwinds, and $8 for strings. Find the amount each class will spend on books.
1a.
Show from first principles, i.e., by using the definition of linear independence,
that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix
A with associated eigenvector v = u + iw, then the two real solutions
Y(t) = eat(u cos bt − wsin bt)
and
Z(t) = eat(u sin bt + wcos bt)
are linearly independent solutions of ˙X = AX.
1b.
Use (a) to solve the system (see image)
Identify each of the following statements as true or false in relation to confidence intervals (CIs).
Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.
True | False | |
---|---|---|
A 95% CI is a numerical interval within which we are 95% confident that the true mean μ lies. | ||
A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯ lies. | ||
The true mean μ is always inside the corresponding confidence interval. | ||
For a sample size n=29, the number of degrees of freedom is n=30. | ||
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not contain the true mean 𝜇. |
Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function
a. Plot the graph of f in the viewing window [0,15]
b. Prove that f is increasing on the interval [0, 15].
As of October, 2016 the world`s largest pumpkin weighed 1190 kilograms. In order to grow a record-setting pumpkin, the fruits mass must increase by an average of
Give your answer with two decimal places, and ensure that you include unots.
Note: Equations for the volume and surface area of a sphere are on D2L in several places.