Answer:
Third choice from the top is the one you want
Step-by-step explanation:
This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out. For example:
![\sqrt[6]{x^6} =x](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7Bx%5E6%7D%20%3Dx)
and another example:
![\sqrt[12]{2^{12}}=2](https://tex.z-dn.net/?f=%5Csqrt%5B12%5D%7B2%5E%7B12%7D%7D%3D2)
Let's take this step by step. First we will rewrite both the numerator and the denominator in rational exponential equivalencies:
![\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B4%5D%7B6%7D%20%7D%7B%5Csqrt%5B3%5D%7B2%7D%20%7D%3D%5Cfrac%7B6%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%7D%7B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%7D)
In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number. The LCM of 3 and 4 is 12. So we rewrite as
Now we will put it back into radical form so we can rationalize the denominator:
![\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B12%5D%7B6%5E3%7D%20%7D%7B%5Csqrt%5B12%5D%7B2%5E4%7D%20%7D)
In order to rationalize the denominator, we need the power on the 2 to be a 12. Right now it's a 4, so we are "missing" 8. The rule for multiplying like bases is that you add the exponents. Therefore,
We will rationalize by multiplying in a unit multiplier equal to 1 in the form of
![\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B12%5D%7B2%5E8%7D%20%7D%7B%5Csqrt%5B12%5D%7B2%5E8%7D%20%7D)
That looks like this:
![\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B12%5D%7B6%5E3%7D%20%7D%7B%5Csqrt%5B12%5D%7B2%5E4%7D%20%7D%2A%5Cfrac%7B%5Csqrt%5B12%5D%7B2%5E8%7D%20%7D%7B%5Csqrt%5B12%5D%7B2%5E8%7D%20%7D)
This simplifies down to
![\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B12%5D%7B216%2A256%7D%20%7D%7B%5Csqrt%5B12%5D%7B2%5E%7B12%7D%7D%20%7D)
Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2! Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:
![\frac{\sqrt[12]{55296} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B12%5D%7B55296%7D%20%7D%7B2%7D)
Phew!!!
Answer:
R = 0.862
Strong positive relationship
Step-by-step explanation:
Given the data:
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12
Score,x = 65 50 55 65 55 70 65 70 55 70 50 55
Grade, y = 85 74 76 90 85 87 94 98 81 91 76 74
Using technology :
The CORREL function in excel, calculators will give accurate value of the correlation Coefficient between two variables, x and y. The correlation Coefficient obtained using technology is : 0.862
The correlation Coefficient value ranges between (-1 and 1) with values closer to either - 1 or 1 reflecting stronger relationship. A value of 0 means there is no relationship between the variables. Negative values indicate negative relationships while positive indicates positive association between the variables.
Therefore. With a correlation Coefficient of 0.862, the correlation Coefficient can be interpreted as meaning that ; there is a strong positive relationship between score and grade.
The answers to the blanks are
1. 600,
2. 120,
3. 120,
4. 180.
Explanation:
- The fence means perimeter around the court. So a tennis court's perimeter is 600 feet fence. The perimeter of a rectangle is 2 times the sum of the rectangle's length and the rectangle's width.
- It is given that length equals 60 more than width i.e. l = w + 60, where l is the length of the court and w is the width of the court.
- The perimeter of a court = 600 = 2 (l + w) = 2l + 2w = 2 (w +60) + 2w, this becomes, 2w + 120 + 2w = 600; 4w = 480, w = 120.
- Since l = w + 60, l = 120 + 60 = 180. So length of a court is 180 feet and the width of a court is 120 feet.
