Answer:
I think you are right
Step-by-step explanation:
Answer:
Step-by-step explanation:
Writing the description in algebraic translation
![\frac{b^{-2}}{ab^{-3}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D)
so we have to find the expression which will be equal to
.
Considering the expression
![\frac{b^{-2}}{ab^{-3}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D)
![\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Bx%5Ea%7D%7Bx%5Eb%7D%3Dx%5E%7Ba-b%7D)
![\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%7D%7Bb%5E%7B-3%7D%7D%3Db%5E%7B-2-%5Cleft%28-3%5Cright%29%7D)
so the expression becomes
∵ ![\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%7D%7Bb%5E%7B-3%7D%7D%3Db%5E%7B-2-%5Cleft%28-3%5Cright%29%7D)
![\mathrm{Subtract\:the\:numbers:}\:-2-\left(-3\right)=1](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A-2-%5Cleft%28-3%5Cright%29%3D1)
![=\frac{b}{a}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bb%7D%7Ba%7D)
Therefore,
![\frac{b^{-2}}{ab^{-3}}=\frac{b}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D%3D%5Cfrac%7Bb%7D%7Ba%7D)
Answer:
6/5
Step-by-step explanation:
The scale factor can be obtained by simply finding the ratio of the lenght of the side of one shape to the length of the same side of the other shape.
Thus, we can obtain the scale factor that will take us from △ABC to △MNO as illustrated below:
Original Length BC = 15 in
New Length NO = 18 in
Scale factor =?
Scale factor = New lenght NO / Original length BC
Scale factor = 18 / 15
Scale factor = 6/5
Therefore, the scale factor that will take us from △ABC to △MNO is 6/5.
Answer:
1. 24
2.
where n denotes number of days.
3. 70
Step-by-step explanation:
1.
Consider the sequence: ![12,14,16,18,...](https://tex.z-dn.net/?f=12%2C14%2C16%2C18%2C...)
Here,
![14-12=2\\16-14=2\\18-16=2](https://tex.z-dn.net/?f=14-12%3D2%5C%5C16-14%3D2%5C%5C18-16%3D2)
Take the common difference as d = 2 and the first term as a = 12
Use the formula: ![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
To find expected gain at the end of the week, find ![a_7](https://tex.z-dn.net/?f=a_7)
![a_7=12+(7-1)2\\=12+6(2)\\=12+12\\=24](https://tex.z-dn.net/?f=a_7%3D12%2B%287-1%292%5C%5C%3D12%2B6%282%29%5C%5C%3D12%2B12%5C%5C%3D24)
2.
Yes, the gain shows the pattern.
Put
in ![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
![a_n=12+(n-1)2\\=12+2n-2\\=10+2n](https://tex.z-dn.net/?f=a_n%3D12%2B%28n-1%292%5C%5C%3D12%2B2n-2%5C%5C%3D10%2B2n)
Here, n denotes number of days.
3.
To find expected gain at the end of 30 days, put
in ![a_n=10+2n](https://tex.z-dn.net/?f=a_n%3D10%2B2n)
![a_{30}=10+2(30)\\ =10+60\\=70](https://tex.z-dn.net/?f=a_%7B30%7D%3D10%2B2%2830%29%5C%5C%20%3D10%2B60%5C%5C%3D70)