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professor190 [17]
1 year ago
14

a password system uses four digits from 0 to 9. how many different four-digit passwords with no digit repeated are possible?

Mathematics
1 answer:
JulijaS [17]1 year ago
3 0

Total 5040 passwords can be generated when no digits are repeated

• Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.

• Permutation is classified into four types :

1) where repetition is not allowed

2) where repetition is allowed

3) objects that are non distinct  

4) circular permutation

• The formula for calculating permutation is n!/(n-r)!

As we are given that the password uses four digits from 0-9 and repetition is not allowed.

So, n = 10 and r = 4

Using the formula for permutation we get

= 10! / (10-4)!

= 10!/6!

= 10 * 9 * 8 * 7 * 6! / 6!

= 10 * 9 * 8 * 7

= 5040

Therefore, 5040 four digit passwords are possible when no digit is repeated.

Learn more about permutaion here

brainly.com/question/12468032

#SPJ4

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1. what is the period of the function f(x) shown in the graph?
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Problem 1)

Answer: pi/2

-------------------------------

Place your pencil at (0,3) which is a good starting point, since x = 0 is often a good starting point. Trace along the curve until you reach back up at y = 3 again. So you'll go down and then back up until you reach (pi/2, 3). The difference in x values is pi/2-0 = pi/2. Every pi/2 units, the graph curve repeats itself over and over infinitely. 

Note: this is not the only way to determine the period. You can start at any point really. It helps to start at a min or max value, or at x = 0. In this case, it happened to be both. 

===========================================================
Problem 2)

Answer: See figure 2 (attached image)

-------------------------------

Point A is at (0,0)
Point B is at approximately (1.57,-2) which is exactly (pi/2,-2)

===========================================================
Problem 3)

Answer: See figure 3 (attached image)

===========================================================
Problem 4)

Answer: Choice B
The graph is horizontally compressed by a factor of 2 and shifts up 1 unit

-------------------------------

The jump from x to 2x will have the period go from 2pi to pi. The graph curve repeats itself more and more often (twice as often). Therefore we have an accordion squeeze effect going on, or think of it like a spring being pressed down. We have horizontal compression along the x axis.

Adding 1 to the end shifts every point upward 1 unit. Overall, this gives the visual the entire curve itself is shifted up 1 unit.

===========================================================
Problem 5)

Answer: f(x) = 5.05*sin((pi/12)x)+5.15

-------------------------------

max = 10.2
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d = 5.15 is the midline, which is the starting height at x = 0

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===========================================================
Problem 6)

Answers are:
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B) The radius of the Ferris wheel is 30 ft

-------------------------------

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C is false because the height at t = 0 is 34 ft, but the lowest point is at height h = 4

D is false because the period is actually 10 seconds. Eg: going from t = 7.5 to t = 17.5 is a time of 10 seconds. During this time, the heights are 4, 34, 64, 34, 4 telling us that a full cycle has taken place.

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