Process information：練習問題

A simple encryption rule shifts every letter in the alphabet forward by \(3\) places (e.g., A becomes D, B becomes E). If the resulting letter is a vowel (A, E, I, O, or U), it is then replaced by its numerical position in the vowel sequence (A=1, E=2, I=3, O=4, U=5). Using this rule, what does the word CAB become?

A floor area measuring \(10 \times 10\) tiles is covered by a repeating pattern of \(2 \times 2\) tile blocks. Each \(2 \times 2\) block contains exactly one black tile and three white tiles. How many black tiles are used to cover the entire floor?

A mechanical clock is slightly broken and loses exactly \(4\) minutes every hour. If the clock is set to the correct time of \(08:00\) in the morning, what time will the clock show when the actual time is \(13:00\) on the same day?

A sequence of automated traffic lights follows a specific cycle: Red for \(30\text{s}\), Green for \(45\text{s}\), and then Yellow for \(10\text{s}\). The light just turned Red at exactly \(12:00:00\). What color will the light be at \(12:14:50\)?

A shipping company assigns codes to packages based on three criteria: Weight Class, Region Code, and Security Level.
- Weight Classes: A (less than \(5\text{kg}\)), B (\(5\text{kg}\) to \(10\text{kg}\)), C (more than \(10\text{kg}\)).
- Region Codes: 1 (North), 2 (South).
- Security Level: The sum of the digits of the package's weight (rounded up to the nearest whole kilogram) plus the Region Code.

What is the code for a package weighing \(12.4\text{kg}\) being sent to the North region?

A factory produces 120 units every hour. A quality check finds that 5% of units are defective. If the factory runs for 5 hours, calculate the total number of non-defective units produced.<\/p>

A manufacturing machine produces 3 units every 5 minutes. However, the machine requires a 10-minute cooling period after every 12 units produced. Calculate the minimum time required, in minutes, to complete an order of 30 units starting from when the machine is first turned on.

A security code consists of four digits. The first digit is a prime number and is greater than the second digit. The sum of the first and second digits is 10. The third digit is exactly half of the fourth digit. If the sum of all four digits is 19, determine the 4-digit code.

A baker produces loaves of bread. The cost of ingredients for each loaf is \$0.80. The baker also has fixed costs (rent and electricity) of \$50.00 per day. Each loaf is sold for \$2.50.

a) Write an expression for the daily profit \(P\) if the baker sells \(n\) loaves.
b) What is the minimum number of loaves the baker must sell in a day to ensure they do not make a loss?

A library uses a specific coding system for its books. Each code consists of a genre letter followed by three digits. The sum of the three digits must be exactly 12, and the first digit must be at least twice the value of the last digit.

a) List all possible 3-digit combinations where the first digit is 7.
b) A student finds a book with the digits 6, 4, and 2. Does this combination satisfy both criteria? Explain your answer.