Suppose that Carol has x 10p coins in her purse. Since she has three times as many 20p coins as 10p coins, then she has 3x 20p coins in her purse.
x coins of 10p value $0.10x and 3x coins of 20p value $0.60x.
In total this amount of money is $(0.10x+0.60x)=$0.70x that is exactly $4.20. Thus, you get the equation
0.70x=4.20.
Solve it:
Carol has 6 coins of 10p and 3·6=18 coins of 20p.
By knowing that p and 2/3 are additive inverses, we will see that p = -2/3
So two numbers A and B are additive inverses if:
A + B = 0
Here the two numbers are p and 2/3, so we have:
2/3 + p = 0
Solving this for p gives:
p = -2/3
Then the value of p is just -2/3.
Now, I can't "drag and drop" the labels in the given image, so I will post a little graph of where each point should be:
If you want to learn more about additive inverses, you can read:
Answer:
(a) 4/9
(b) 19/27
Step-by-step explanation:
The probability of each die turning up red or not turning red are:
(a). Exactly one face up is red.
The odds of only the first die being red are:
The same odds are valid for only the second or only the third die being red. Therefore, the probability that exactly one die turns up red is:
(b). At least one face up is red.
The probability that at least one die turns up red is the sum of the probabilities of exactly one (found in the previous item), two or all dice turning up red.
Following the same logic as in the previous item, the probability that exactly two dice turn up red is:
The probability that all die turn up red is:
Thus, the probability that at least one die turns up red is: