Answer:
Four raised to the one-sixth power
Step-by-step explanation:
We want to simplify: ![\dfrac{\sqrt{4} }{\sqrt[3]{4} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D)
First, we apply the fractional law of indices to each term.
![\text{If } a^{1/x}=\sqrt[x]{a},$ then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}](https://tex.z-dn.net/?f=%5Ctext%7BIf%20%20%7D%20a%5E%7B1%2Fx%7D%3D%5Csqrt%5Bx%5D%7Ba%7D%2C%24%20then%3A%5C%5C%5Csqrt%7B4%7D%3D4%5E%7B1%2F2%7D%5C%5C%5Csqrt%5B3%5D%7B4%7D%3D4%5E%7B1%2F3%7D)
We then have:
![\dfrac{\sqrt{4} }{\sqrt[3]{4} }=\dfrac{4^{1/2} }{4^{1/3} }\\$Applying the division law of indices: \dfrac{a^m }{a^n }=a^{m-n}\\\dfrac{4^{1/2} }{4^{1/3} }=4^{1/2-1/3}\\\\=4^{1/6}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D%3D%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%5C%5C%24Applying%20the%20division%20law%20of%20indices%3A%20%5Cdfrac%7Ba%5Em%20%7D%7Ba%5En%20%7D%3Da%5E%7Bm-n%7D%5C%5C%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%3D4%5E%7B1%2F2-1%2F3%7D%5C%5C%5C%5C%3D4%5E%7B1%2F6%7D)
The correct option is B.
To Find :
Net worth of Rachel.
Solution :
Net worth is given by the (sum of all the assets she owns) -( total amount of loans she have ).
Therefore, net worth of Rachel is $ 363587.
Hence, this is the required solution.
First we need to find out what kind
of logarithm rule is given, the given is logarithm product rule which states
that a log of a product is equal to the sum of the log of the first base and
the log of the second base.
By:
= log (1.37 x 10⁹) =
log (1.37) + log (10⁹)
= log (1.37) + 9
= 9 + log (1.37)
In the meantime, 1.37 is between
1 and 10 its logarithm will be between 0 and 1. Thus, the value of log (1.37 x 10⁹)
falls between 9 and 10 because when you compose a scientific notation you will
always have a number among 1 and 10 by 10 to some power. That power tells you
the integer part of the logarithm.
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The total amount that Chang will received from his wages is the product of his hourly wage times the number of hours he has worked (n). His total savings should not be less than $125. The equation that best describes the situation is,
45 + 7n ≥ 125
Solving for n in the inequality gives an answer of n≥11.42 hours. Thus, he needs to work for at least 12 hours.
In your problem:
p = 18.3% = 0.183
n = 130
The standard error can be calculated by the formula:
SE = √[p · (1 - p) / n]
= √[0.183 · (1 - 0.183) / 130]
= 0.0339
The standard error of the proportion is 0.034.
