To find the number of tails, subtract 225 from 500, yielding 275. So, we establish a ratio of 225 to 500, which needs to be simplified. Dividing both by 25 gives us 9 and 20 respectively. Therefore, the simplified ratio is 9:20.
Regarding the logarithmic equation, option c is correct: x=6 is a valid solution, while x=-6 is considered an extraneous solution. Explanation: The equation requires dividing both sides by 2, simplifying further until each step can be logically followed based on logarithmic definitions, from which we affirm that both sides equal when substituting back the values, confirming that x=6 is the true solution.
Answer: 0.5507
Step-by-step explanation:
Given: The time between sightings of speeders by a radar system is represented by the continuous random variable X, which follows a cumulative distribution function
If we convert 12 minutes into hours, it equals 
hours or 0.2 hours.
To find the probability of waiting less than 12 minutes:
Thus, the probability we are looking for is: 0.5507
When regrouping, you're essentially simplifying the problem into smaller parts. For instance, you would calculate 60 + 40=? and then solve 4 + 3=? The final answer would be 107.
(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.
