Outside a home, there is a 7-key keypad numbered 1 through 7. The correct five-digit code will open the garage door. The numbers can be repeated in the code. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?

(a) How many codes are possible is 16,807

(b) The probability of entering the correct code on the first  is 5.95%

(a) How many codes are possible

Since we have 7 number that can placed in 5 places which means the possible code will be calculated as:

Possible Code =7×7×7×7×7 or 7^5

Possible Code =16,807

(b) The probability of entering the correct code on the first  try will be:

Since only 1 correct code is correct

Hence:

Probability=1/16,807

Probability=5.949%

Probability=5.95% (Approximately)

Inconclusion (a) How many codes are possible is 16,807

(b) The probability of entering the correct code on the first  is 5.95%

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a: 16807

b: 0.0000595

Step-by-step explanation:

(a): We have 7 possibilities of numbers, and we need to choose 5 numbers that can repeat. So, for each of the 5 numbers, we have 7 possibilities. To determine how many codes are possible, we just need to multiply the number of possibilities of each of the 5 numbers, so we have 7x7x7x7x7, or 7^5, which is 16807 possibilities.

(b): to put the correct code in the first try, we need to find the exact combination (just one combination) among these 16807 possibilities, so the probability is 1/16807, which is 0.0000595, or 0.00595%.

a

b

d

step-by-step explanation:

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: