# Determine which of the following are linear inequalities and linear equations.Write LI if the sentence is linear inequality and LE if it is linear equation 1.2x+y>1 2.y=3x-6 3.y-5<7x 4.3s >= t+1 5.x+5y=10

Question
Equations and inequalities
Determine which of the following are linear inequalities and linear equations.Write LI if the sentence is linear inequality and LE if it is linear equation
1.2x+y>1
2.y=3x-6
3.y-5
4.$$3s >= t+1$$
5.x+5y=10

2020-12-23
As per bartleby guidelines only the first three subparts are to be solved. Please upload other parts separately.
Given:
The objective is to find which of the equations are linear inequality and linear equations.
2x+y>1
y=3x−6
y−5
An equation which contains the symbols <,>,$$>=,<=$$</span> are called linear inequality.
Similarly, an equation which contains the symbol = is called linear equation.
Consider the first equation, 2x+y>1.
As the first equation contains the symbol >, it is a linear inequality.
Consider the third equation, y=3x−6.
As the second third equation contains the symbol =, it is a linear equation.
Consider the second equation, y−5
As the second equation contains the symbol
Hence, option (1) and option (3) are LI and option (2) is LE.

### Relevant Questions

Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
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6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
For each problem below, either prove that the mapping is linear or explain why it cannot be linear.
$$\displaystyle{1}.{f{{\left({x}_{{1}},{x}_{{2}}\right)}}}={\left({2}{x}_{{1}}-{x}_{{2}},{3}{x}_{{1}}+{x}_{{2}}\right)}$$
$$\displaystyle{2}.{L}{\left({x},{y},{z}\right)}={\left({x}+{y},{y}+{z},{z}+{5}\right)}$$
$$\displaystyle{3}.{L}{\left({x},{y}\right)}={\left({x}+{y},{0},{x}-{2}{y}\right)}$$
$$\displaystyle{4}.{f{{\left({x},{y}\right)}}}={\left({2}{x}+{y},-{3}{x}+{5}{y}\right)}$$
$$\displaystyle{5}.{f{{\left({x},{y}\right)}}}={\left({x}^{{2}},{x}+{y}\right)}$$
$$\displaystyle{6}.{L}{\left({x},{y}\right)}={\left({x},{x}+{y},-{y}\right)}$$
Solve the equations for x and simplify the answer if possible. Indicate which solving technique is used, Linear, Factor, SRP ZPR, QF.
$$1/6(3/4x-2)=(-1)/5$$
Solve the equations and inequalities below, if possible. $$\displaystyle{a}.\sqrt{{{x}−{1}}}+{13}={13}$$
$$\displaystyle{b}.{6}{\left|{x}\right|}{>}{18}$$
$$\displaystyle{c}.{\left|{3}{x}-{2}\right|}\le{2}$$
$$\displaystyle{d}.{\frac{{{4}}}{{{5}}}}-{\frac{{{2}{x}}}{{{3}}}}={\frac{{{3}}}{{{10}}}}$$
$$\displaystyle{e}.{\left({4}{x}-{2}\right)}^{{{2}}}\le{100}$$
$$\displaystyle{f}.{\left({x}-{1}\right)}^{{{3}}}={8}$$
Consider a capital budgeting problem with six projects represented by $$0-1\ \text{variables}\ x1,\ x2,\ x3,\ x4,\ x5,\ \text{and}\ x6.$$
a. Write a constraint modeling a situation in which two of the projects 1, 3, and 6 must be undertaken.
b. In which situation the constraint "$$x3\ -\ x5 = 0$$" is used, explain clearly:
c. Write a constraint modeling a situation in which roject 2 or 4 must be undertaken, but not both.
d. Write constraints modeling a situation where project 1 cannot be undertaken IF projects 3. also is NOT undertaken.
e. Explain clearly the situation in which the following 3 constraints are used simulataneously (together):
$$\displaystyle{x}{4}\le{x}{1}$$
$$\displaystyle{x}{4}\le{x}{3}$$
$$\displaystyle{x}{4}\ge{x}{1}+{x}{3}-{1}$$
A linear regression was performed on a bivariate data set with variables x and y. Analysis by a computer software package included the following outputs:
Sample Size: $$n=15$$
Regression Equation: $$y\hat{e} =0.359 - 1.264x$$
Coefficient of Determination: r square = 0.915
Sums of Squares :$$SSy = 35.617. SSex = 32.589, SSresid = 3.028$$
a. Calculate the standard error Se.
b. write a sentence interpreting the value of rsquare.
c.What is the value of Pearson's correlation coefficient?
d. Determine whether the variables x and y are significant using a $$5\%$$ significance level. You may assume a simple random sample from a bivariate normal populaton.
Celine, Devon, and another friend want to purchase some snacks that cost a total of $7.50. They will share the cost of the snacks. Which of these statements is true? A. An equation that can be used to find x, the amount of money each person will pay is x+3=7.5. The solution to the equation is 4.5, so each person will pay$4.50.
B. An equation that can be used to find x, the amount of money each person will pay is x+3=7.5. The solution to the equation is 10.5, so each person will pay $10.50. C. An equation that can be used to find x, the amount of money each person will pay is x⋅3=7.5. The solution to the equation is 2.5, so each person will pay$2.50.
D. B. An equation that can be used to find x, the amount of money each person will pay is x⋅3=7.5. The solution to the equation is 22.5, so each person will pay \$22.50.
Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \\ \hline \end{array}$$ b) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \\ \hline \end{array}$$
c) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \\ \hline \end{array}$$
d) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \\ \hline \end{array}$$