Given that Nicholas has a 115 fantasy and science fiction books which is 46% of his collection.
Now we have to find what is total number of books in his collection.
Let number of books in Nicholas collection = x
then number of fantasy and science fiction books = 46% of x = 0.46x
We already know that he has 115 fantasy and science fiction books, so both values will be equal and give equation:
0.46x=115
now we can solve this equation to find the answer.
x= 250
Hence final answer is:
Nicholas has 250 books in his collection.
If the area of the paper is 625 sq in, the length of one side of this square is sqrt(625 sq in), or 25 inches. That's the min. side length of an easel that is to support the whole sheet of paper along its lowest side.
Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
Answer:
<em>Choice: B.</em>
Step-by-step explanation:
<u>Operations With Functions</u>
Given the functions:
![f(x)=\sqrt[3]{12x+1}+4](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7B12x%2B1%7D%2B4)
The function (g-f)(x) can be obtained by replacing both functions and subtracting them as follows:
![(g-f)(x)= \log(x-3)+6 - (\sqrt[3]{12x+1}+4)](https://tex.z-dn.net/?f=%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%2B6%20-%20%28%5Csqrt%5B3%5D%7B12x%2B1%7D%2B4%29)
Operating:
![(g-f)(x)= \log(x-3)+6 - \sqrt[3]{12x+1}-4](https://tex.z-dn.net/?f=%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%2B6%20-%20%5Csqrt%5B3%5D%7B12x%2B1%7D-4)
Joining like terms:
![\boxed{(g-f)(x)= \log(x-3) - \sqrt[3]{12x+1}+2}](https://tex.z-dn.net/?f=%5Cboxed%7B%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%20-%20%5Csqrt%5B3%5D%7B12x%2B1%7D%2B2%7D)
Choice: B.
