(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now we will express 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
This reduces to
1 ≡ -1082 * 1234 (mod 4321)
Thus, the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.
Answer:
1443.36
Step-by-step explanation:
6014 multiplied by.24 equals 1443.36
I hope this is helpful
Answer:
Step-by-step explanation:
We start with the fact that
The formula for simple interest is represented by
where:
I denotes the Final Interest Value
P indicates the Principal amount to be invested
r specifies the interest rate
t refers to the Number of Time Periods
For this scenario, we have
We can substitute these values into the formula mentioned above
Next, we solve for t
Convert to a percentage format
You have two kinds of data $ and %!
Align them properly and perform cross multiplication.
16% corresponds to $38 as
100% corresponds to $x
Following this, x = (38*100)/16 = $237.5, which is the original price before the discount.
