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ipn [44]
3 years ago
7

A padlock has the digits 0 through 9 arranged in a circle on its face. A combination for 0 1 2 3 4 6 5 7 8 9 this padlock is fou

r digits long. Because of the internal mechanics of the lock, no pair of consecutive numbers in the combination can be the same or one place apart on the face. For example 0-2-7-1 is a valid combination, but neither 0-4-4-7 (repeated digit 4) nor 3-0-9-5 (adjacent digits 0-9) are permitted. How many combinations are possible?
Mathematics
1 answer:
stepan [7]3 years ago
8 0

Answer:

The total numbers of possible combinations are 3430.

Step-by-step explanation:

Consider the provided information.

A combination for 0 1 2 3 4 6 5 7 8 9 this padlock is four digits long. Because of the internal mechanics of the lock, no pair of consecutive numbers in the combination can be the same or one place apart on the face.

Here, for the first digit we have 10 choices.

For the second digit we have 7 choices, as the digit can't be the same nor adjacent to the first digit.

For the third digit we have 7 choices, as the digit can't be the same nor adjacent to the second digit.

For the fourth digit we have 7 choices, as the digit can't be the same nor adjacent to the third digit.

So the number of choices are:

10\times 7\times 7\times 7=10\times 7^3\\10\times 343=3430

Hence, the total numbers of possible combinations are 3430.

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To approach the runway, a pilot of a small plane must begin a 10 degrees descent starting from a height of 1983 feet above the g
ddd [48]
<h3>Answer:</h3>

2.2 miles

<h3>Explanation:</h3>

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

We are given an angle (10°) and its opposite side length (1983 ft), and we are asked to find the hypotenuse (the straight-line distance from the plane to the runway).

... sin(10°) = (1983 ft)/distance

Multiplying by distance and dividing by sin(10°), we have ...

... distance = (1983 ft)/sin(10°) ≈ 11419.6 ft

We want to express this in miles, so we have ...

... 11419.6 ft = (m mi)×(5280 ft/mi)

... (11419.6 ft)/(5280 ft/mi) = m mi ≈ 2.163 mi

Rounding to tenths, the distance is ...

2.2 miles

_____

<em>Comment on the question</em>

The distance from the plane to the airport is different than the horizontal distance from the airport at which the descent must start. The latter distance is the "adjacent" leg of the triangle, so must be found using the tangent function. Rounded to tenths, it is 2.1 miles.

8 0
3 years ago
20 red marbles to 40 blue marbles (ratio as a fraction)
Tanya [424]

Answer:

20/40 = 10/20 = 1/2, 1:2

Step-by-step explanation:

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3 0
2 years ago
Read 2 more answers
NEED HELP ASAP PLEASE !!
Alexxandr [17]

Answer:

A, C, E

Step-by-step explanation:

The square root of 10 is approximately 3.16, which is greater than pi which is equal to about 3.14, which shows that C is correct as well. The square root of 11 is 3.31, and the square root of 5 added to the square root of 6 is equal to about 3.69, which is greater than the square root of 11.

6 0
3 years ago
The difference between two numbers is 10 and their sum is 20. Find the biggest number.
marysya [2.9K]

Answer:

15

Step-by-step explanation:

x - y = 10, then x = 10 + y

x + y = 20

substitute for x:

10 + y + y = 20

2y = 10

y = 5

x = 10 + 5 = 15

8 0
3 years ago
Mr. Soto plans to open a savings account. Four banks offer the annual interest rates shown. Which list shows these interest rate
Delvig [45]
Ok, so IDK if I'm about to do this problem right, but here we go;


so first, lets change these all to decimals (I more of a decimal gal)

3 1/2 = 3.5
3 2/3 = 3.6666 (repeating)
3 3/5 = 3.6
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So now, just order them from greatest to least.  

3.66666, 3.6, 3.5, 3.375.  

Now, change them back to fractions.  
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So, if I'm correct, the answer is 3 2/3%, 3 3/5%, 3 1/2%, 3 3/8%
Hopefully I solved your problem! 
6 0
3 years ago
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