Hello! The error that Clara made was that she didn't combine the r's together. For questions like these, we would combine like terms. The 6b part is correct, because 8b - 2b is 6b. But, the other r needs to be combined with the -4r, and in this case we would add, because subtracting a negative number turns the problem from subtracting to adding. -4r - (-r) is -3r. The correct result is really 6b - 3r.
Answer:
7 more boys
Step-by-step explanation:
Given
![Total = 70](https://tex.z-dn.net/?f=Total%20%3D%2070)
![Boys = 37](https://tex.z-dn.net/?f=Boys%20%3D%2037)
![Girls = 33](https://tex.z-dn.net/?f=Girls%20%3D%2033)
![Group\ 1 = 40](https://tex.z-dn.net/?f=Group%5C%201%20%3D%2040)
![Group\ 2 = 30](https://tex.z-dn.net/?f=Group%5C%202%20%3D%2030)
Required
Number of more boys than girls in group 2
Represent the number of boys in group 1 with B and the number of girls with G.
So:
![B + G = 40](https://tex.z-dn.net/?f=B%20%2B%20G%20%3D%2040)
Make G the subject
![G = 40 - B](https://tex.z-dn.net/?f=G%20%3D%2040%20-%20B)
The number of girls in group 2 will be:
Total number of girls (33) - number of girls in group 1(40 - B)
So, we have:
![Group\ B\ Girls = 33 -(40 - B)](https://tex.z-dn.net/?f=Group%5C%20B%5C%20Girls%20%3D%2033%20%20-%2840%20-%20B%29)
![Group\ B\ Girls = 33 -40 + B](https://tex.z-dn.net/?f=Group%5C%20B%5C%20Girls%20%3D%2033%20%20-40%20%2B%20B)
![Group\ B\ Girls = -7 + B](https://tex.z-dn.net/?f=Group%5C%20B%5C%20Girls%20%3D%20-7%20%2B%20B)
![Group\ B\ Girls = B-7](https://tex.z-dn.net/?f=Group%5C%20B%5C%20Girls%20%3D%20B-7)
<em>This means that there are 7 more boys than girls</em>
Answer:
7.56
Step-by-step explanation:
Just multiply
20.16 times 0.375
7.56
0.5 is not equivalent to 2 <span />
Answer:
![a_6_3=371](https://tex.z-dn.net/?f=a_6_3%3D371)
Step-by-step explanation:
we know that
In an <u><em>Arithmetic Sequence</em></u> the difference between one term and the next is a constant and this constant is called the common difference
we have
![-1,5,11,...](https://tex.z-dn.net/?f=-1%2C5%2C11%2C...)
Let
![a_1=-1\\a_2=5\\a_3=11](https://tex.z-dn.net/?f=a_1%3D-1%5C%5Ca_2%3D5%5C%5Ca_3%3D11)
![a_2-a_1=5-(-1)=5+1=6](https://tex.z-dn.net/?f=a_2-a_1%3D5-%28-1%29%3D5%2B1%3D6)
![a_3-a_2=11-5=6](https://tex.z-dn.net/?f=a_3-a_2%3D11-5%3D6)
The common difference is ![d=6](https://tex.z-dn.net/?f=d%3D6)
We can write an Arithmetic Sequence as a rule
![a_n=a_1+d(n-1)](https://tex.z-dn.net/?f=a_n%3Da_1%2Bd%28n-1%29)
where
a_n is the nth term
d is the common difference
a_1 is the first term
n is the number of terms
Find the 63rd term of the arithmetic sequence
we have
![n=63\\d=6\\a_1=-1](https://tex.z-dn.net/?f=n%3D63%5C%5Cd%3D6%5C%5Ca_1%3D-1)
substitute
![a_6_3=-1+6(63-1)](https://tex.z-dn.net/?f=a_6_3%3D-1%2B6%2863-1%29)
![a_6_3=-1+6(62)](https://tex.z-dn.net/?f=a_6_3%3D-1%2B6%2862%29)
![a_6_3=-1+372](https://tex.z-dn.net/?f=a_6_3%3D-1%2B372)
![a_6_3=371](https://tex.z-dn.net/?f=a_6_3%3D371)