Answer:
Step-by-step explanation:
<u>Equations</u>
We have two cases where some variable is required to be found such that some condition is met. The first case is about finding the value of a that complies:
Rearranging
Factoring:
There are two solutions:
The second case requires us to find the value of x such that
Rearranging
This second-degree equation has no real roots. We'll offer the imaginary (complex) solutions:
Answer:
Step-by-step explanation:
In 5 liters, there is 4% salt.
Lets find liters of salt.
First, converting 4% to decimal (dividing by 100):
4% = 4/100 = 0.04
0.04 * 5 = 0.2
So, there is 0.2 liters of salt.
Now, x liters of water is added to total, so total is now:
5 + x
The concentration of salt will be amount of salt divided by amount of salt water solution.
Amount of salt = 0.2 (as seen above)
Amount of new salt water solution = x + 5
So,
Concentration of salt in new solution is
2nd choice is right.
So, the total number of balls is 11. We want to pick 2 red balls and 1 green ball. WLOG (since order doesnt matter here), we can say he picks red, green, red. That means on his first pick, he has a chance of picking the red ball, and he places it back in the bag. The probability of picking a green ball is , and then he places the ball back in the bag. The probability of picking the last red ball is the same as the last red ball example, and we simply multiply the probabilities together as per the multiplication rule to get:
Now, without replacement the order does matter. He picks a red ball, a red ball then a green ball. The probability of picking the first red ball is, and the probability of picking the second red ball is and the probability of picking the green ball is. We want to multiply thm again, as per the multiplication rule like the last problem.
Answer:
Step-by-step explanation:
From the graph, we can conclude that,
is less than 2 and not including as there is a hollow circle at the mark 2.
Also, is greater than or equal to 7 including 7 as there is a solid circle at the mark 7
So, the compound inequality will be
Now, the option that simplifies to the above inequality is the required answer.
Let us check the first option.
Therefore, option 1 simplifies to the above compound inequality.
So, the correct answer is option 1.
Answer:
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Step-by-step explanation: