(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.
You will achieve this in 15 days. Both 5 and 3 have a least common multiple of 15.
A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour
e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
The expression m over 5 indicates the miles traveled by the cyclist in a span of 5 minutes. This represents a value corresponding to speed. It describes the magnitude of velocity, reflecting the total distance covered within a specific time frame. As it lacks direction, it is classified as a scalar quantity. The dimensions include distance per time with SI units being meters per second. Alternative measurements can include kilometers per hour and miles per hour. In contrast, the vector equivalent known as velocity incorporates both speed and direction, signified through positive and negative indicators.
Answer:
The standard ticket price was $12.
Step-by-step explanation:
Let’s denote 
the normal ticket price, which would total
if she had purchased tickets for that amount.
However, since Holly received a $4 discount on each ticket, her cost for one ticket became
and with 23 tickets, her total cost was
amounting to $184; thus, we conclude
we will solve this equation as follows:
Therefore, the regular price amounted to $12.
