Question Solved1 Answer The reduced row-echelon form of the augmented matrix for a system of linear equations with variables x1, ... , x5 is given below. Determine the solutions for the system and enter them below. 1 0 0 5 0 4 0 1 -3 -4 0-4 0 0 0 0 1-2 If the system has infinitely many solutions, select "The system has at least one solution". Your answer may use expressions involving the parameters r, s, and t. The system has at least one solution X1 = 0 X2 = 0 X3 = 0 X4 = 0 15= 0

At a county fair, adults' tickets sold for $\$5.50$, senior citizens' tickets for $\$4.00$, and children's tickets for $\$1.50$. On the opening day, the number of children's and senior's tickets sold was 30 more than half the number of adults' tickets sold. The number of senior citizens' tickets sold was $5$ more than four times the number of children's tickets. How many of each type of ticket were sold if the total receipts from the ticket sales were $\$14,970$? This is how I solved it, but I did something wrong and don't know what. $$c+s=\frac 12a+30$$ $$s=4c+5$$ $$5.5a+4s+1.5c=14970$$ $$5.5a+16c+20+1.5c=14970$$ $$5.5a+1.75a+87.5+20=14970$$ $$7.25a=1486.25$$ $$a=205$$ $$c=25.5, s=107$$

Find conditions on \( a, b, c \) so that \( v=(a, b, c) \) in \( \mathbf{R}^{3} \) belongs to \( W=\operatorname{span}\left(u_{1}, u_{2}, u_{3}\right) \). where \[ u_{1}=(1,2,0), u_{2}=(-1,1,2), u_{3}=(3,0,-4) \]

Perform the following operations: 10. Z = V(100)2 + (40)2 = 11. Z = V(4 x 10-82 + (50 x 10-22 = 12. Z = V(453)2 + (0.08E5)2 = 14. O = cos-11 X 10-3 50 X 10-4 - V4² +6² omplex Numbers Most scientific calculators provide a sequence of steps for performing required with complex numbers, but few are as direct as the T1-86 and 1 approach is so direct that it is Perform the following operations: 10. Z = V(100)2 + (40)2 = 11. Z = V(4 x 10-82 + (50 x 10-22 = 12. Z = V(453)2 + (0.08E5)2 = 14. O = cos-11 X 10-3 50 X 10-4 - V4² +6² omplex Numbers Most scientific calculators provide a sequence of steps for performing required with complex numbers, but few are as direct as the T1-86 and 1 approach is so direct that it is essentially a duplication of the basic operat

Note: I need help to implement this solution using R Studio Predicting Boston Housing Prices. The file BostonHousing.csv contains information collected by the US Bureau of the Census concerning housing in the area of Boston, Massachusetts. The dataset includes information on 506 census housing tracts in the Boston area. The goal is to predict the median house price in new tracts based on information such as crime rate, pollution, and number of rooms. The dataset contains 13 predictors, and the response is the median house price (MEDV). Table 6.9 describes each of the predictors and the response. a. Why should the data be partitioned into training and validation sets? What will the training set be used for? What will the validation set be used for? b. Fit a multiple linear regression model to the median house price (MEDV) as a function of CRIM, CHAS, and RM. Write the equation for predicting the median house price from the predictors in the model. c. Using the estimated regression model, what median house price is predicted for a tract in the Boston area that does not bound the Charles River, has a crime rate of 0.1, and where the average number of rooms per house is 6? What is the prediction error? d. Reduce the number of predictors: i. Which predictors are likely to be measuring the same thing among the 13 predictors? Discuss the relationships among INDUS, NOX, and TAX. ii. Compute the correlation table for the 12 numerical predictors and search for highly correlated pairs. These have potential redundancy and can cause multicollinearity. Choose which ones to remove based on this table. iii. Use stepwise regression with the three options (backward, forward, both) to reduce the remaining predictors as follows: Run stepwise on the training set. Choose the top model from each stepwise run. Then use each of these models separately to predict the validation set. Compare RMSE, MAPE, and mean error, as well as lift charts. Finally, describe the best model. PROBLEMS 169 PROBLEMS 6.1 Predicting Boston Housing Prices. The file Boston Housing.csv contains informa- tion collected by the US Bureau of the Census concerning housing in the area of Boston, Massachusetts. The dataset includes information on 506 census housing tracts in the Boston area. The goal is to predict the median house price in new tracts based on information such as crime rate, pollution, and number of rooms. The dataset con- tains 13 predictors, and the response is the median house price (MEDV). Table 6.9 describes each of the predictors and the response. TABLE 6.9 DESCRIPTION OF VARIABLES FOR BOSTON HOUSING EXAMPLE CRIM ZN INDUS CHAS NOX RM AGE DIS Per capita crime rate by town Proportion of residential land zoned for lots over 25,000 ft Proportion of nonretail business acres per town Charles River dummy variable (= 1 if tract bounds river; = 0 otherwise) Nitric oxide concentration (parts per 10 million) Average number of rooms per dwelling Proportion of owner-occupied units built prior to 1940 Weighted distances to five Boston employment centers Index of accessibility to radial highways Full-value property-tax rate per $10,000 Pupil/teacher ratio by town Percentage lower status of the population Median value of owner-occupied homes in $1000s RAD TAX PTRATIO LSTAT MEDV a. Why should the data be partitioned into training and validation sets? What will the training set be used for? What will the validation set be used for? b. Fit a multiple linear regression model to the median house price (MEDV) as a function of CRIM, CHAS, and RM. Write the equation for predicting the median house price from the predictors in the model. c. Using the estimated regression model, what median house price is predicted for a tract in the Boston area that does not bound the Charles River, has a crime rate of 0.1, and where the average number of rooms per house is 6? What is the prediction error? d. Reduce the number of predictors: i. Which predictors are likely to be measuring the same thing among the 13 predictors? Discuss the relationships among INDUS, NOX, and TAX. ii. Compute the correlation table for the 12 numerical predictors and search for highly correlated pairs. These have potential redundancy and can cause multi- collinearity. Choose which ones to remove based on this table. iii. Use stepwise regression with the three options (backward, forward, both) to reduce the remaining predictors as follows: Run stepwise on the training set. Choose the top model from each stepwise run. Then use each of these models separately to predict the validation set. Compare RMSE, MAPE, and mean error, as well as lift charts. Finally, describe the best model.

Perform the following operations: 10. Z = V(100)2 + (40) 11. Z = V(4 x 10-8)2 + (50 x 10-92 12. Z = V(453)2 + (0.08E5)2 4 13. 0 = sin 10 14. 0 = cos 1 X 10-3 50 X 10-4 4 15. X = V42 +6² y Numbers S Perform the following operations: 16. 62-120° to rectangular form 17.-5.8 + 19.6 to polar form 18. 6x 10-4 + j50 x 10-to polar form 19. 12 x 10-2102° to rectangular form 20. (6.8 mAZ-30°)(2.2 kN20°) = (polar form) 21. (6.8 k12 20°)(120 V 20°) 6.8 k22 - j3.6 k 2 (rectangular form) 22. 5230° + (6 - j6) - 2.22-90º = (polar form) 23. 6 + j8 (2Z80°)2 – (6 - j8) (rectangular form)

If $s2 = OxABCD 9ABC branch to Label A which includes an instruction to divide the contents of Ssl by 16 else shift left arithmetic the contents of Ss1 2 bit if there is a need use Stl to save the intermediate value