Answer:
Step-by-step explanation:
![[(6^{2}+8^{2})^{\frac{1}{2}}]^{3} = [(36+64)^{\frac{1}{2}}]^{3}\\\\= [(100)^{\frac{1}{2}}]^{3}\\\\= 10^{3}\\\\= 1000](https://tex.z-dn.net/?f=%5B%286%5E%7B2%7D%2B8%5E%7B2%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E%7B3%7D%20%3D%20%5B%2836%2B64%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E%7B3%7D%5C%5C%5C%5C%3D%20%5B%28100%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E%7B3%7D%5C%5C%5C%5C%3D%2010%5E%7B3%7D%5C%5C%5C%5C%3D%201000)
Answer:
Step-by-step explanation:
- Initial number = 17
- Final number = 10
<u>Decrease in number:</u>
<u>Percent decrease:</u>
- 7/17*100% = 41.18% (rounded)
Answer:
111
t + 11
x
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>Taylor series</u> expansions of f(x) at the point x = a
This expansion is valid only if 
exists and is finite for all 
, and for values of x for which the infinite series converges.
Substituting the values in the series expansion gives:
Factoring out e⁴:
![e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]](https://tex.z-dn.net/?f=e%5E%7B4x%7D%3De%5E4%5Cleft%5B1%2B4%28x-1%29%2B8%7D%28x-1%29%5E2%2B...%5Cright%5D)
<u>Taylor Series summation notation</u>:
Therefore:
Answer:
1/4
Step-by-step explanation:
Let's denote the probabilities as following:
Probability that a teenager has a sister:
P(A) = 12/28
Probability that a teenager has a brother:
P(B) = 7/28
Probability that a teenager has both a sister and a brother:
P(A⋂B) = 3/28
Probability that a selected teenager has a sister also has a brother, or in other words, he/she has a brother, given he/she had a sister:
P(B|A)
Let's apply the formula of conditional probability to work out P(B|A)
P(B|A) = P(A⋂B)/P(A) = (3/28)/(12/28) = (3*28)/(12*28) = 3/12 = 1/4
=> Option C is correct
Hope this helps!
