Answer:
![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
Step-by-step explanation:
Using the rules of exponents
×
=
,
=
,
= ![a^{mn}](https://tex.z-dn.net/?f=a%5E%7Bmn%7D)
Simplifying the product of the first 2 terms
× ![\frac{a^{q^2+qr} }{a^{qr+r^2} }](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7Bq%5E2%2Bqr%7D%20%7D%7Ba%5E%7Bqr%2Br%5E2%7D%20%7D)
=
× ![a^{q^2-r^2}](https://tex.z-dn.net/?f=a%5E%7Bq%5E2-r%5E2%7D)
= ![a^{p^2-r^2}](https://tex.z-dn.net/?f=a%5E%7Bp%5E2-r%5E2%7D)
Simplifying the third term
5(![(a^p+r)^{p-r}](https://tex.z-dn.net/?f=%28a%5Ep%2Br%29%5E%7Bp-r%7D)
= 5
= 5![a^{(p^2-r^2)}](https://tex.z-dn.net/?f=a%5E%7B%28p%5E2-r%5E2%29%7D)
Performing the division, that is
← cancel
on numerator/ denominator leaves
= ![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
Answer:
1![\frac{7}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B20%7D)
Step-by-step explanation:
1. Convert the mixed number to an improper fraction to match the rest of the problem (this just makes it easier for now, the answer will still be a mixed number)
-1
becomes ![\frac{9}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B5%7D)
2. Re-write the new equation. When there is a "+" in front of a set of parentheses the expression doesn't change aside from removing the plus signs.
The new equation becomes
![\frac{9}{5} - \frac{1}{4} -\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B5%7D%20-%20%5Cfrac%7B1%7D%7B4%7D%20-%5Cfrac%7B1%7D%7B5%7D)
3. Calculate. Just work out the new expression.
The answer is ![\frac{27}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B20%7D)
4. Convert to a simplified mixed decimal.
27 goes into 20 once with seven left over, making the answer 1![\frac{7}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B20%7D)
The probability of an event cannot be less than 0 because 0 means it's impossible. The probability of an event cannot be more than 1 because 1 means that it's certain that it will happen. That's why the probability must be between 0 and 1.
Answer:
Where's the rest of this question??