<u>Solution</u><u>:</u>


- Now, square root and square gets cancel out in the LHS. And in the RHS, apply the identity: (a + b)² = a² + 2ab + b².

- Now, transpose 4x and 4 to LHS.

- Now, do the addition and subtraction.

<u>Answer</u><u>:</u>
<u>x </u><u>=</u><u> </u><u>±</u><u> </u><u>3</u>
Hope you could understand.
If you have any query, feel free to ask.
Step-by-step explanation:
I am not allowed to answer more than 3 questions. So I will do the first 3.
15a. i) (2/3) = 4/9
ii) (2/3) = 8/27
iii) (2/3) = 16/81
b. The product is small because you are finding the fraction of a fraction.
16. Compared to the factors, the product is less than each fraction. This is because, as stated above, you are trying to find a fraction (a part of the whole) of another fraction. When you multiply a whole number by a fraction, the whole number decreases. The same applies to a fraction.
17a. 0.4 × 0.3 = 0.12
b. 0.4 = 4/10 = 2/5
0.3 = 3/10
3/10 × 2/5 = 6/50
Answer:

Step-by-step explanation:
Lets use the compound interest formula provided to solve this:

<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
First, change 6% into a decimal:
6% ->
-> 0.06
Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:

Answer:
16/52, or 4/13.
Step-by-step explanation:
First, since we know that the question is asking for the probability of a club <u>or</u> a jack, we know that we have to add the two probabilities. The first probability is that of picking a club, which is 13/52. The probability of picking a jack (be sure not to overlap; don't double count the jack of clubs) is 3/52. Adding these two gives us 13/52+3/52=16/52, which simplifies to 4/13.
Answer: We should expect its actual return in any particular year to be between<u> -40%</u> and<u> 80%</u>.
Step-by-step explanation:
Given : The continuously compounded annual return on a stock is normally distributed with a mean 20% and standard deviation of 30%.
From normal z-table, the z-value corresponds to 95.44 confidence is 2.
Therefore , the interval limits for 95.44 confidence level will be :
Lower limit = Mean -2(Standard deviation) = 20% -2(30%)= 20%-60%=-40%
Upper limit = Mean +2(Standard deviation)=20% +2(30%)= 20%+60%=80%
Hence, we should expect its actual return in any particular year to be between<u> -40%</u> and<u> 80%</u>.