Bài 34. Áp dụng phân tích đa thức thành nhân tử để chứng minh chia hết:
1) a2-a chia hết cho 2 ; 2) a3-a chia hết cho 3
3) a5-a chia hết cho 5 ; 4) a7-a chia hết cho 7
5)a3+3a2+2a chia hết cho
6)(n2+n-1)2-1 chia hết cho 24;
7) n3+6n+8n chia hết cho 48 với mọi n chẵn
8) n4-10n2+9 chia hết cho 384 với mọi n lẻ
9) n6+n4-2n2 chia hết cho 72;
10) 32n - 9 chia hết cho 72
11) n3 – n chia hết cho 6 với mọi số nguyên n

If the speed of an electromagnetic wave is 100,000 cm/s and its wavelength is 100 cm, what is its frequency? a) 100,000 cycles per second (hz) b) 1 × 10-3 cycles per second (hz) c) 10,000,000 cycles per second (hz) d) 1,000 cycles per second (hz)

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x,y,z) = (1,-x,z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)