Answer:
30% is the correct answer.
Step-by-step explanation:
Total number of boys = 2
Total number of girls = 3
Total number of students = 5
To find:
Probability that the pianist will be a boy and the alternate will be a girl?
Solution:
Here we have to make 2 choices.
1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).
Formula for probability of an event E is given as:
For 
, number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So, is:
For 
, number of favorable cases are 3 (total number of girls).
Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4
So, the required probability is:
So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is 
</u>
The answer is 3.16 ft
The surface area (SA) of the rectangular prism is:
SA = 2lw + 2ld + 2wd
However, the pool is without the top side, so the area of the top side should be excluded from the surface area of the pool. The surface area of the rectangular pool is:
SA = lw + 2ld + 2wd
We know:
SA = 210 ft²
l = 9 ft
w = 10 ft
d = ?
210 = 9 * 10 + 2 * 9 * d + 2 * 10 * d
210 = 90 + 18d + 20d
210 - 90 = 38d
120 = 38d
d = 120/38
d = 3.16 ft
Answer:
I think this is a pretty good question of law of indices
Step-by-step explanation:
Given that
a) express n in terms of p and q ,
b) hence if p = 1 and q = 2 find the value of n
Solution to part a)
Simplify the equation and how do we do that? As we can see that 9 can also be written as 3^2 and 27 can be written as 3^3 we can rewrite the following equation like this,
now we multiply p with 2 and
multiply q with 3 respectively,
now since the bases are same and are multiplying the exponents will add themselves like this, in this equation the number 3 is the base
now since the bases on the left hand side and on the right hand side are equal the exponents will also be equal so now,
hence n is expressed in terms of p and q
Solution to part b)
if p = 1 and q = 2 we plug in these values in the above equation we found for n
n = 2p + 3q
n = 2(1) + 3(2)
n = 2 + 6
n = 7
