Psychology
<span>z =(48-87)/14 </span>
<span>z = -2.796 </span>
<span>Economics </span>
<span>z =(52-53)/8 </span>
<span>z = -0.125 </span>
<span>The score of Economics is better.</span>
Answer:
The first one cannot be simplified
reason: usually when simplifying an expression you combine like terms but in the given expression there are no like terms
An example of like terms would be 6a and 9a
Essentially what i am saying is that the variables have to be the same in order for them to be combined
The second one is 36r
This is the answer because they tried to combine like terms that aren't similar
r and f are not the same variable therefore they cannot be combined
Hope this helps :)
First we find the mean (average)
(17 + 18 + 19 + 20 + 21) / 5 = 95/5 = 19
now subtract 19 from all values...then square it
17 - 19 = -2...-2^2 = 4
18 - 19 = -1...-1^2 = 1
19 - 19 = 0...0^2 = 0
20 - 19 = 1....1^2 = 1
21 - 19 = 2...2^2 = 4
now take the mean (average) of those
(4 + 1 + 0 + 1 + 4) / 5 = 10/5 = 2 <== this is ur variance
standard deviation is the square root of the variance...
sq rt 2 = 1.414
As given by the question
There are given that the vector:
Now,
From the formula to find the unit vector in same direction is:
Then,
![\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7Bv%7D%7D%7B%5Clvert%5Cvec%7Bv%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%5Crvert%7D%20%5Cend%7Bgathered%7D)
Then,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B4%2B9%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5Cend%7Bgathered%7D)
Then,
Rationalize the denominator:
So,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B13%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B%5Csqrt%5B%5D%7B13%7D%282i%7D%2B%5Cvec%7B3j%7D%29%7D%7B13%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B2%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Di%2B%5Cfrac%7B3%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Dj%20%5Cend%7Bgathered%7D)
Hence, the unit vector is shown below:
![\vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j](https://tex.z-dn.net/?f=%5Cvec%7Bu%7D%3D%5Cfrac%7B2%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Di%2B%5Cfrac%7B3%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Dj)
Sum of interior angles = (n-2) × 180<span> = (5-2) x 180 = 3 x 180 = 540
so
x + 90 + 107 + 144 + 138 = 540
x + 479 = 540
x = 540 - 479
x = 61</span>
