Answer:
a₁ = 6
Step-by-step explanation:
The sum to n terms of a geometric sequence is
= ![\frac{a_{1}(r^{n}-1) }{r-1}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%28r%5E%7Bn%7D-1%29%20%20%7D%7Br-1%7D)
where a₁ is the first term and r the common ratio
Here
= 1530 and r = 2, thus
= 1530 , that is
a₁ (256 - 1) = 1530
255a₁ = 1530 ( divide both sides by 255 )
a₁ = 6
Answer:
15cm
Step-by-step explanation:
a^2+b^2=c^2
12^2+9^2=c^2
144+81=c^2
c^2=225
c=15
Answer:
![Probability = \frac{2}{35}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B2%7D%7B35%7D)
Step-by-step explanation:
Given
![Total = 70](https://tex.z-dn.net/?f=Total%20%3D%2070)
First, we need to list the multiples of 5
![M_5 = \{5,10,15,20,25,30,35,40,45,50,55,60,65,70\}](https://tex.z-dn.net/?f=M_5%20%3D%20%5C%7B5%2C10%2C15%2C20%2C25%2C30%2C35%2C40%2C45%2C50%2C55%2C60%2C65%2C70%5C%7D)
Then, multiples of 3![M_3 = \{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69\}](https://tex.z-dn.net/?f=M_3%20%3D%20%5C%7B3%2C6%2C9%2C12%2C15%2C18%2C21%2C24%2C27%2C30%2C33%2C36%2C39%2C42%2C45%2C48%2C51%2C54%2C57%2C60%2C63%2C66%2C69%5C%7D)
Next, is to list out the common elements in both
![M_3\ n\ M_5 = \{15,30,45,60\}](https://tex.z-dn.net/?f=M_3%5C%20n%5C%20M_5%20%3D%20%5C%7B15%2C30%2C45%2C60%5C%7D)
![n(M_3\ n\ M_5) = 4](https://tex.z-dn.net/?f=n%28M_3%5C%20n%5C%20M_5%29%20%3D%204)
The required probability is then calculated as thus:
![Probability = \frac{n(M_3\ n\ M_5)}{Total}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7Bn%28M_3%5C%20n%5C%20M_5%29%7D%7BTotal%7D)
![Probability = \frac{4}{70}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B4%7D%7B70%7D)
![Probability = \frac{2}{35}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B2%7D%7B35%7D)
Answer = 10=21
When you’re multiplying numbers with exponents with the same base (10 is the base) all you have to do is add the exponents
18 and 3 are the exponents we’re dealing with, so we add them and get 21. The base stays the same
10^18 x 10^3 = 10^21
Answer = 10=21