Statistics Projects for High School Students

Call centers are booming in a country as multinational companies increasingly outsource these operations. The annual revenue for call centers in the country from 2006-2010, in billions of dollars can be modeled by R(x)=0.922x-3.82, where x is the number of years after 2000
A. According to the mode, the rate of change of revenue for call center in the country was $... billion per year.
B. According to the model, the revenue for call centers in the country in 2010 was $...billion
C. Would this model be valid to estimate the revenue of 2000? Why or why not. Choose from the correct option.
1. The model would be valid for 2000 because it would give a positive revenue
2. The model would not be valid for 2000 because it would give a negative revenue.
3. The model would not be valid for 2000 because it would give a positive revenue.
4. The model would be valid for 2000 because it would give a negative revenue

Reference for Book Design Theory
First, when i studied group action, i found out about design theory, then i got interested in it. But is there any good book to study design theory? especially for introduction and undergraduate student level. I knew about Design Theory book athor by Thomas Beth, D. Jungnickel, H. Lenz.
But i find it too way long and i thought it is not introduction level. Pleas inform me if you know anything about it, thank You so Much!

Should I combine the negative part of the spectrum with the positive one?
When filtering sound I currently analyse only the positive part of the spectrum. From the mathematical point of view, will discarding the negative half of the spectrum impact significantly on my analysis?
Please consider only samples that I will actually encounter, not computer generate signals that are designed to thwart my analysis.
I know this question involves physics, biology and even music theory. But I guess the required understanding of mathematics is deeper than of those other fields of study.

National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $50 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?
(x,y):
what is the optimal profit?

Computing the fixed point for cos x
While studying about Compiler Design I came with the term 'fixed point'.I looked in wikipedia and got the definition of fixed point but couldn't get how fixed point is computed for cos x as said in fixed point.
It says that the fixed point for cos x=x using Intermediate Value Theorem.But I couldn't get how they computed the fixed point for cos x.Do anyone know how they computed this?

Solve. m=3, b=1

Mathematical Epidemiology Reference Request
I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book.

Multiple Choice: What is the design for this experiment?
The prompt is the following: A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn.
This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.
The answer choices are as follows:
A. observational study
B. matched pairs design
C. randomized block design
D. completely randomized design
My solution: My guess is C. In this case, the matched pair is when each experimental unit receives both treatments in random order, and the participants were separated into the yoga or meditation group by a flip of the coin. In A, I do not think that it is a matched pair because each person was asked their stress level. I rule out D as well, because I do think this is a matched pairs design.

Including a local tax of 5%, a watch costs $26.25. What was the marked price (in dollars) of the watch?

Maximum possible city block distance
Anya participated in a study comparing two blood glucose monitors. A total of 20 persons with diabetes participated. Ten participants used Monitor A for two days and then used Monitor B for two days. The other ten participants (including Anya) used Monitor B for two days and then used Monitor A for two days. On the 5th day, participants rated the two monitors on the basis of four features. The four features were rated on a 5 point scale that ranged from −2 (poorly designed) to 2 (well designed). The distance between Anya’s ratings of the two monitors was 4 city blocks. What is the maximum possible city block distance between the two blood glucose monitors?

Experiment design parameters.
I have a doubt identifying the elements of the following experiment design:
A study wants to determine whether users perceive the difference while playing a game at 30 fps or 60 fps. In the game the player has to destroy objects that traverse the screen. All subjects played a first part at 30 fps, a second part half of them played at 30 fps and the other half at 60 fps and finally the two halves interchanged roles.
Here I understand that fps is an independent variable of the experiment and that the experiment is a "within subjects" one.
After the game, we ask them if they perceived a difference between the equality of the three parts and in affirmative case we ask which image was the best. We register their score at the end of each part and their responses to which was the best image. In each condition, half of the subjects used a standard resolution screen and the other half used a high resolution screen.
From here I deduce that the score is a dependent variable and I hope that the perceived quality of the image is another dependent variable (later on response time appears as a third dependent variable?). I have doubts whether the resolution of the screens is a second independent variable.
We verify that visual accuracy doesn't change between the two groups. We register each action of the subjects during the game. The results show that globally the subjects aren't capable of telling what part of the game had higher fps but the scores were higher at 60 fps.
So this part states that the visual accuracy is a controlled variable and that the principal effect of the experiment was that score was better when using higher fps.
The response time (duration between the apparition of an object and first action of the subject) were shorter after 60 fps, but only for players with a high screen resolution.
This should be an interaction effect between but there is no dependent variable stated.
Therefore my explanation of the experiment doesn't fit the solution expected. Could you please point me what I'm missing here? I should be able to state:
Two independent variables
Two dependent variables
An intermediate variable.
A controlled variable.
A principal effect.
An interaction effect.

In a simple linear regression $Y=X\mathrm{\beta <!--\; \beta \; -->}+\mathrm{\epsilon <!--\; \epsilon \; -->}$, residuals are given by $\stackrel{^<!--\; ^\; -->}{\mathrm{\epsilon <!--\; \epsilon \; -->}}=M\mathrm{\epsilon <!--\; \epsilon \; -->}$, where $M=I_n-<!--\; -\; -->P$ is the annihilator matrix, and $P=X(X^{T}X{)}^{-1}{X}^T$ is the projection matrix, and $X$ is the design matrix. Assuing that the errors $\mathrm{\epsilon <!--\; \epsilon \; -->}$ are iid normal with mean $0$ and standard deviation$\mathrm{\sigma <!--\; \sigma \; -->}$, what is the joint (conditional on $X$) distribution of the residuals $\stackrel{^<!--\; ^\; -->}{\mathrm{\epsilon <!--\; \epsilon \; -->}}$?

Consider the dataset below.
$\begin{array}{|ccccc|}\hline 44& 72& 74& 78& 102\\ \hline\end{array}$
Find the percentile rank of 44.

Model:
$y_i=B_0+\underset{i=0}{\overset{p}{\sum <!--\; \sum \; -->}}{B}_k{X}_{ik}+e_i$
show the sum of squared residuals is zero if $p=(n-<!--\; -\; -->1)$

What can covariance be used for?

How do you find the standard deviation for the numbers 4, 4, 5, 5, 6, 6?

Use the following data set: 13, 8, 10, 7, 13, 9, 7, 11, 12, 10, 13 to answer questions
The data is said to be
Select one:
a. bimodal
b. multimodal
c. Unimodal

Please, tell whether the statement is TRUE or FALSE.
1) The F distribution is symmetric, and its mean is close to 1.
2) A small P-value indicates that the two variables in a two-way table are associated.
3) If the null hypothesis of an ANOVA F-test is true, the F statistic is greater than 1.
4) The more similar the conditional distributions in a two-way table are, the smaller the P-value of the chi-square test becomes.
5) In a two-way table, if the expected counts are about the same as the observed counts, we reject the null hypothesis.
6) The larger the chi-square statistic, the stronger the evidence against the null hypothesis.
7) In a two-way table, if the expected counts are about the same as the observed counts, we reject the null hypothesis.