Answer:
Gerri spends 1/7 (A).
Step-by-step explanation:
If Gerri spends 1/21 of her money on pencils and 2/21 of her money on paper, adding these two fractions together will give us the total fraction of her money that she spent. Since 1/21 and 2/21 have the same denominator, we can add the numerators to get 3/21. However, fractions must always be in simplest form, meaning if the numerator (top number) and denominator (bottom number) can both be divided evenly by the same factor, then the fraction can be simplied to lower numbers. In this case the number 3 and the number 21 can both be divided evenly by 3: (3÷3)/21÷3) = 1/7.
Answer:
(a) See attachment for tree diagram
(b) 24 possible outcomes
Step-by-step explanation:
Given


Solving (a): A possibility tree
If urn 1 is selected, the following selection exists:
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
If urn 2 is selected, the following selection exists:
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
<em>See attachment for possibility tree</em>
Solving (b): The total number of outcome
<u>For urn 1</u>
There are 4 balls in urn 1

Each of the balls has 3 subsets. i.e.
![B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]](https://tex.z-dn.net/?f=B_1%20%5Cto%20%5BR_1%2C%20R_2%2C%20R_3%5D%3B%20R_1%20%5Cto%20%5BB_1%2C%20R_2%2C%20R_3%5D%3B%20R_2%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_3%5D%3B%20R_3%20%5Cto%20%5BB_1%2C%20R_1%2C%20R_2%5D)
So, the selection is:


<u>For urn 2</u>
There are 4 balls in urn 2

Each of the balls has 3 subsets. i.e.
![B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]](https://tex.z-dn.net/?f=B_2%20%5Cto%20%5BB_3%2C%20R_4%2C%20R_5%5D%3B%20B_3%20%5Cto%20%5BB_2%2C%20R_4%2C%20R_5%5D%3B%20R_4%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_5%5D%3B%20R_5%20%5Cto%20%5BB_2%2C%20B_3%2C%20R_4%5D)
So, the selection is:


Total number of outcomes is:



Using the formula of P(1 + r)^n = x where p represents the initial value, r represents the rate and n represents the number of years and x is our final output. We want to find P so we have to make it the subject of the equation.
1 + 0.04 = 1.04
1.04^18 = 2.025816515
Then divide the total amount by this to get 185,110.5454
Therefore the answer is $185,110.55
Hope this helps! :)
Answer:
x = 3, y = - 2
Step-by-step explanation:
By substitution method,
4x + y = 10 -------> equation 1.
7x + 2y = 17 -------> equation 2.
From equation 1,
y = 10 - 4x ------> equation 3.
Substitute equation 3 in 2,
7x + 2 ( 10 - 4x ) = 17
7x + 20 - 8x = 17
7x - 8x = 17 - 20
- x = - 3
x = 3
Substitute x = 3 in equation 1,
4 ( 3 ) + y = 10
12 + y = 10
y = 10 - 12
y = - 2
Hence,
x = 3
y = - 2