# Recent questions in Post Secondary

First order differential equations

Derivatives

Derivatives

Random variables

### Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was \$1570. Assume $$\sigma\ math=250$$. Find 0.90 and 0.99 confidence intervals for the mean claim payment.

Vectors and spaces

### An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. In a study of post-traumatic stress disorder, soldiers who have been in combat are given biannual physical and psychological tests for five years after they return from active duty.

Differential equations

### $$\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}$$

Confidence intervals

Derivatives

Derivatives

### Find derivatives of the functions defined as follows. $$\displaystyle{y}=-{4}{e}^{{-{0.3}{x}}}$$

Confidence intervals

Random variables

### Mutually exclusive versus independent. The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male, and event B: student has blue eyes. $$\text{Gender}\ \text{Eye color}\begin{array}{l|c|c|c} & \text { Male } & \text { Female } & \text { Total } \\ \hline \text { Blue } & & & 10 \\ \hline \text { Brown } & & & 40 \\ \hline \text { Total } & 20 & 30 & 50 \end{array}$$ Copy and complete the two-way table so that events A and B are mutually exclusive.

Transformations of functions

### The two linear equations shown below are said to be dependent and consistent: $$2x−5y=3$$ $$6x−15y=9$$ Explain in algebraic and graphical terms what happens when two linear equations are dependent and consistent.

Forms of linear equations

### Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the system. Assume that the variables are named $$x_1, x_2,...x,...$$ ,… from left to right.

Forms of linear equations

### Let $$AX = B$$ be a system of linear equations, where A is an $$m\times nm\times n$$ matrix, X is an n-vector, and $$BB$$ is an m-vector. Assume that there is one solution $$X=X0$$. Show that every solution is of the form $$X0+Y$$, where Y is a solution of the homogeneous system $$AY = 0$$, and conversely any vector of the form $$X0+Y$$ is a solution.

Transformations of functions

Scatterplots

Study design

Two-way tables

### Describe how you can use a two -way table to organize data you collect from a survey.

Analyzing categorical data