10000 digits can be used for 4 digit A.T.M code.
<u>Solution:</u>
Given that A.T.M required 4 digit codes using the digits 0 to 9.
Need to determine how many four digit code can be used.
We are assuming that number starting with 0 are also valid ATM codes that means 0789 , 0089 , 0006 and 0000 are also valid A.T.M codes.
Now we have four places to be filled by 0 to 9 that is 10 numbers
Also need to keep in mind that repetition is allowed in this case means if 9 is selected at thousands place than also it is available for hundreds, ones or tens place .
First digit can be selected in 10 ways that is from 0 to 9.
After selecting first digit, second digit can be selected in 10 ways that is 0 to 9 and same holds true for third and fourth digit.
So number of ways in which four digit number is created = 10 x 10 x 10 x 10 = 10000 ways
Hence 10000 digits can be used for 4 digit A.T.M code.
Answer:
1. x = {1.5, 0.2}
2. x = 1
Step-by-step explanation:
Using the <em>system of equation</em> created, Emily will catch up Lucy after 30 seconds
Given the Parameters :
- Lucy's distance = 2t
- Emily's distance = 5t
<u>We can set up an equation to represent the required scenario thus</u> :
Emily's distance = Lucy's distance + 90
5t = 2t + 90
We solve for t
<em>Collect like terms</em> :
5t - 2t = 90
3t = 90
Divide both sides by 3 to isolate t
t = 90/3
t = 30
Therefore, Emily will catch up with Lucy after 30 seconds
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2 and 3 are prime numbers, so it means that the greatest common factor is:
G.C.M(2;3)=2*3=6
The expression can be simplified to a polynomial of degree 2.
<h3>
How to simplify the expression?</h3>
Here we have the expression:
We can directly simplify this by taking the variable as common factor:
This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.
If you want to learn more about polynomials:
brainly.com/question/4142886
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