1. x <- seq(2,10,by=2)
    y <- c(3,5,7,11,13)
    
    x+y
    ## [1]  5  9 13 19 23
    x-y
    ## [1] -1 -1 -1 -3 -3
    x*y
    ## [1]   6  20  42  88 130
    x/y
    ## [1] 0.6666667 0.8000000 0.8571429 0.7272727 0.7692308
  2. geometric_mean <- function(x) {
      J <- length(x)
      res <- prod(x)^(1/J)
      res
    }
    
    geometric_mean(c(10,8,13))
    ## [1] 10.13159
  3. first_date <- lubridate::mdy("01-01-1981")
    second_date <- lubridate::mdy("01-10-2022")
    second_date - first_date
    ## Time difference of 14984 days
    1. nrow(mtcars)
      ## [1] 32
    2. ncol(mtcars)
      ## [1] 11
    3. colnames(mtcars)
      ##  [1] "mpg"  "cyl"  "disp" "hp"   "drat" "wt"   "qsec" "vs"   "am"   "gear"
      ## [11] "carb"
    4. subset(mtcars, mpg >= 20)
      ##                 mpg cyl  disp  hp drat    wt  qsec vs am gear carb
      ## Mazda RX4      21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
      ## Mazda RX4 Wag  21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
      ## Datsun 710     22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
      ## Hornet 4 Drive 21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
      ## Merc 240D      24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
      ## Merc 230       22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
      ## Fiat 128       32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
      ## Honda Civic    30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
      ## Toyota Corolla 33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
      ## Toyota Corona  21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
      ## Fiat X1-9      27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
      ## Porsche 914-2  26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
      ## Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
      ## Volvo 142E     21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
    5. subset(mtcars, (mpg >= 20) & (hp >= 100))
      ##                 mpg cyl  disp  hp drat    wt  qsec vs am gear carb
      ## Mazda RX4      21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
      ## Mazda RX4 Wag  21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
      ## Hornet 4 Drive 21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
      ## Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
      ## Volvo 142E     21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
    6. subset(mtcars, (cyl >= 6) | (hp >= 100))
      ##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
      ## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
      ## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
      ## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
      ## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
      ## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
      ## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
      ## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
      ## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
      ## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
      ## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
      ## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
      ## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
      ## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
      ## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
      ## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
      ## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
      ## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
      ## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
      ## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
      ## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
      ## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
      ## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
      ## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
    7. mtcars[10,]
      ##           mpg cyl  disp  hp drat   wt qsec vs am gear carb
      ## Merc 280 19.2   6 167.6 123 3.92 3.44 18.3  1  0    4    4
    8. # without reversing the order, we would order from lowest to smallest
      mtcars[rev(order(mtcars$mpg)),]
      ##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
      ## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
      ## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
      ## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
      ## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
      ## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
      ## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
      ## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
      ## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
      ## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
      ## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
      ## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
      ## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
      ## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
      ## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
      ## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
      ## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
      ## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
      ## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
      ## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
      ## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
      ## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
      ## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
      ## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
      ## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
      ## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
      ## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
      ## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
      ## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
      ## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
      ## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
      ## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
      ## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4