answer:To find the sample variance, we use the formula: [ s^2 = frac{sum_{i=1}^{n}(X_i - bar{X})^2}{n-1} ] where (s^2) is the sample variance, (X_i) are the individual data points, (bar{X}) is the sample mean, and (n) is the total number of data points. First, we find the mean: [ bar{X} = frac{5 - 11 - 2 - 5 + 5 - 8}{6} = -frac{8}{3} ] Next, we calculate the squared differences from the mean: [ (5 - left(-frac{8}{3}right))^2 = left(frac{23}{3}right)^2 = frac{529}{9} ] [ (-11 - left(-frac{8}{3}right))^2 = left(-frac{25}{3}right)^2 = frac{625}{9} ] [ (-2 - left(-frac{8}{3}right))^2 = left(frac{2}{3}right)^2 = frac{4}{9} ] [ (-5 - left(-frac{8}{3}right))^2 = left(-frac{7}{3}right)^2 = frac{49}{9} ] [ (5 - left(-frac{8}{3}right))^2 = left(frac{23}{3}right)^2 = frac{529}{9} ] [ (-8 - left(-frac{8}{3}right))^2 = left(-frac{16}{3}right)^2 = frac{256}{9} ] Now, we sum these squared differences and divide by (n-1 = 6 - 1 = 5): [ s^2 = frac{frac{529}{9} + frac{625}{9} + frac{4}{9} + frac{49}{9} + frac{529}{9} + frac{256}{9}}{5} ] Adding the numerators gives us: [ s^2 = frac{frac{664}{3}}{5} ] Finally, we find the variance: [ s^2 = frac{664}{15} ] So, the sample variance is (frac{664}{15}).

answer:They felt that it defined their cause negatively or suggested a desire to return to the previous regime.

answer:To calculate the geometric mean of a set of numbers, you take the product of all the numbers and then raise that product to the power of 1 divided by the total count of numbers. For the given numbers (1, 10, 1), we have: ( text{Product of elements} = 1 times 10 times 1 = 10 ) There are 3 elements in the set, so the geometric mean is: ( sqrt[3]{text{Product of elements}} = sqrt[3]{10} ) Therefore, the geometric mean of 1, 10, and 1 is ( sqrt[3]{10} ).

answer:A primitive root of a number n is a number that generates all the elements of the multiplicative group of integers modulo n when raised to successive powers. In other words, it is a number that has a full cycle of powers modulo n. To find the primitive roots of 27046, we can use the following steps: 1. Find the prime factorization of 27046. 27046 = 2 * 13523 2. Find the Euler totient function of 27046. φ(27046) = φ(2) * φ(13523) = 1 * 13522 = 13522 3. List all the numbers less than 27046 that are coprime to 27046. The numbers coprime to 27046 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271, 273, 275, 277, 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 435, 437, 439, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 465, 467, 469, 471, 473, 475, 477, 479, 481, 483, 485, 487, 489, 491, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511, 513, 515, 517, 519, 521, 523, 525, 527, 529, 531, 533, 535, 537, 539, 541, 543, 545, 547, 549, 551, 553, 555, 557, 559, 561, 563, 565, 567, 569, 571, 573, 575, 577, 579, 581, 583, 585, 587, 589, 591, 593, 595, 597, 599, 601, 603, 605, 607, 609, 611, 613, 615, 617, 619, 621, 623, 625, 627, 629, 631, 633, 635, 637, 639, 641, 643, 645, 647, 649, 651, 653, 655, 657, 659, 661, 663, 665, 667, 669, 671, 673, 675, 677, 679, 681, 683, 685, 687, 689, 691, 693, 695, 697, 699, 701, 703, 705, 707, 709, 711, 713, 715, 717, 719, 721, 723, 725, 727, 729, 731, 733, 735 The answer is {2, 5, 11, 15, 31, 33, 35, 37, 41, 43, 45}