Answer: x>_3.2 OR x<_ -0.75
Step-by-step explanation: first break down your compound inequality. 5x-4>_12
You first cancel out your constants by adding 4 to both sides. Now you’re left with 5x>_16 then to cancel five you have to divide on both sides by five which equals to 3.2. Then, x>_ 3.2.
Next you do your second part, 12x+5<_-4
So first cancel out the constant of 5 by subtracting 5 on both sides, making the equation 12x<_-9. Now, you divide by 12 on both sides, making it -9/12. Which effectively is -0.75. Therefor, the answer being x<_ -0.75. Add the two together x>_3.2 OR x<_0.75
Since its to the tenth power and the exponent is negative all you have to do is move the decimal point two positions back and your new answer is 0.382
In this question, we made a license that does not allow repeated digit and letter. That means the probability count of letter and digit will be decreased by 1 for every roll.
There is 10 kinds of digits (0-9) and 26 kinds of letters (a to z). So, 2 digits and 5 letter would be:
(10 * 9) * (26 * 25 * 24 * 23 * 22)= 710424000 kinds of license plates
Answer:
a) the probability is P(G∩C) =0.0035 (0.35%)
b) the probability is P(C) =0.008 (0.8%)
c) the probability is P(G/C) = 0.4375 (43.75%)
Step-by-step explanation:
defining the event G= the customer is a good risk , C= the customer fills a claim then using the theorem of Bayes for conditional probability
a) P(G∩C) = P(G)*P(C/G)
where
P(G∩C) = probability that the customer is a good risk and has filed a claim
P(C/G) = probability to fill a claim given that the customer is a good risk
replacing values
P(G∩C) = P(G)*P(C/G) = 0.70 * 0.005 = 0.0035 (0.35%)
b) for P(C)
P(C) = probability that the customer is a good risk * probability to fill a claim given that the customer is a good risk + probability that the customer is a medium risk * probability to fill a claim given that the customer is a medium risk +probability that the customer is a low risk * probability to fill a claim given that the customer is a low risk = 0.70 * 0.005 + 0.2* 0.01 + 0.1 * 0.025
= 0.008 (0.8%)
therefore
P(C) =0.008 (0.8%)
c) using the theorem of Bayes:
P(G/C) = P(G∩C) / P(C)
P(C/G) = probability that the customer is a good risk given that the customer has filled a claim
replacing values
P(G/C) = P(G∩C) / P(C) = 0.0035 /0.008 = 0.4375 (43.75%)
Answer: C) 25
Step-by-step explanation:
x²+10x+ __=16+ __
Only the square of 5, 5², which is 25, can make the two factors plus equal to 10x, so we need to add 25.
