Question

9) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed? A) 256 four-digit numbers B) 8999 four-digit numbers C) 10,000 four-digit numbers D) 9000 four-digit numbers 10) If $4100 earned simple interest of $233.02 in 11 months what was the simple interest rate? A) 7.2% B) 6.2% C) 8.2% D) 5.2% 11) How long will it take for prices in the economy to double at a 6% annual inflation rate? Round answer to the nearest year. 12 years B) 8 years D) 4 years A) 15 years 4./

please I wanted answered step by step

Answer 1

(9) There are 4 digits Also, repetitions are allowed. In 1st place, we have 9 choices In 2nd place, we have 10 choices In 3rd place, we have 10 choices In 4th place, we have 10 choices (1 to 9, 0 cannot be used at first place) (0 to 9) (0 to 9) (0 to 9) Thus, total 4 digit numbers Choices in 1st place Choices in 2nd place Choices in 3rd place Choices in 4th place 10 10 10 =9 =9000 four-digit numbers $ 4100 $ 233.02 (10) Principal Amount (P) Interest earned (I) 11 Period in years (n) years 11 months 12 Let 'r' be rate of interest Simple interest earned is given as Pnr = 100 233.02 100 I*100 Thus, r 6.2 % 11 P*n 4100 12 Simple Interest Rate = 6.2 % r

(11) Inflation Rate (r) = 6 % Let current price be p Thus, Final price after doubling Let n be number of years 2 p We need to use compound inte rest formula here. Compound Interest formula is given as: Current Price * (1 +: Final Price 100 (1+1 Final Price Current Price 100 On taking natutal log on both side s Final Price In( Current Price n In(1 100 n In(1 100 In(2) n In(1.06) n (2) Thus, n 11.89 years 12 years In (1.06) Years to double 12 years