Think: 0.99x = 194 implies that x, the sample size, was 196.
The test was incorrect 2 times. Look at "2" in the table and determine for yourself why.
Part C: 2/196 = 0.01 => 1%
This makes sense, since 99% of the time the test is correct.
1% + 99% = 100%
If it is :
![10 - \frac{ (3x - 1)}{2} = \frac{(6x + 3)}{11} \\](https://tex.z-dn.net/?f=10%20-%20%20%5Cfrac%7B%20%283x%20-%201%29%7D%7B2%7D%20%3D%20%20%5Cfrac%7B%286x%20%2B%203%29%7D%7B11%7D%20%5C%5C%20%20%20)
Multiply both sides by 22
![(22 \times 10) - 11 \times (3x - 1) = 2 \times (6x + 3) \\](https://tex.z-dn.net/?f=%2822%20%5Ctimes%20%2010%29%20-%2011%20%5Ctimes%20%283x%20-%201%29%20%3D%202%20%5Ctimes%20%286x%20%2B%203%29%20%5C%5C%20)
![220 - 33x + 11 = 12x + 6](https://tex.z-dn.net/?f=220%20%20%20-%20%2033x%20%20%2B%20%2011%20%3D%2012x%20%2B%206)
![- 33x + 231 = 12x + 6](https://tex.z-dn.net/?f=%20-%2033x%20%2B%20231%20%3D%2012x%20%2B%206)
Plus both sides <em>3</em><em>3</em><em>x</em>
![231 = 33x + 12x + 6](https://tex.z-dn.net/?f=231%20%3D%2033x%20%2B%2012x%20%2B%206)
![231 = 45x + 6](https://tex.z-dn.net/?f=231%20%3D%2045x%20%2B%206)
Subtract sides minus 6
![231 - 6 = 45x](https://tex.z-dn.net/?f=231%20-%206%20%3D%2045x)
![45x = 225](https://tex.z-dn.net/?f=45x%20%3D%20225)
Divided sides by 45
![x = \frac{225}{45} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B225%7D%7B45%7D%20%5C%5C%20%20)
![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
_________________________________
If it is :
![\frac{10 - (3x - 1)}{2} = \frac{6x + 3}{11} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%20-%20%283x%20-%201%29%7D%7B2%7D%20%3D%20%20%5Cfrac%7B6x%20%2B%203%7D%7B11%7D%20%5C%5C%20%20%20)
Multiply sides by 22
![(11 \times 10) - 11 \times (3x - 1) = 2 \times (6x + 3) \\](https://tex.z-dn.net/?f=%2811%20%5Ctimes%2010%29%20-%2011%20%5Ctimes%20%283x%20-%201%29%20%3D%202%20%5Ctimes%20%286x%20%2B%203%29%20%5C%5C%20)
![110 - 33x + 11 = 12x + 6](https://tex.z-dn.net/?f=110%20-%2033x%20%2B%2011%20%3D%2012x%20%2B%206)
![- 33x + 121 = 12x + 6](https://tex.z-dn.net/?f=%20-%2033x%20%2B%20121%20%3D%2012x%20%2B%206)
Plus sides <em>3</em><em>3</em><em>x</em>
![121 = 12x + 33x + 6](https://tex.z-dn.net/?f=121%20%3D%2012x%20%2B%2033x%20%2B%206)
![121 = 45x + 6](https://tex.z-dn.net/?f=121%20%3D%2045x%20%2B%206)
Subtract sides minus 6
![121 - 6 = 45x](https://tex.z-dn.net/?f=121%20-%206%20%3D%2045x)
![45x = 115](https://tex.z-dn.net/?f=45x%20%3D%20115)
![x = \frac{115}{45} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B115%7D%7B45%7D%20%5C%5C%20%20)
![x = \frac{23}{9} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B23%7D%7B9%7D%20%5C%5C%20%20)
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
7)
8/14 = x/7
14x = 56
x = 56/14
x = 4
answer
GH = 4
8)
24/56 = 36/x
24x = 2016
x = 2016/24
x = 84
answer
PR = 84
Answer:
(-24, -8)
Step-by-step explanation:
Let us recall that when we have a function f
![\large f:\mathbb{R}^2\rightarrow \mathbb{R}\\f(x,y)=z](https://tex.z-dn.net/?f=%5Clarge%20f%3A%5Cmathbb%7BR%7D%5E2%5Crightarrow%20%5Cmathbb%7BR%7D%5C%5Cf%28x%2Cy%29%3Dz)
<em>if the gradient of f at a given point (x,y) exists, then the gradient of f at this point (x,y) gives the direction of maximum rate of increasing and minus the gradient of f at this point gives the direction of maximum rate of decreasing</em>. That is
![\large \nabla f=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})](https://tex.z-dn.net/?f=%5Clarge%20%5Cnabla%20f%3D%28%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%2C%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%29)
at the point (x,y) gives the direction of maximum rate of increasing
![\large -\nabla f](https://tex.z-dn.net/?f=%5Clarge%20-%5Cnabla%20f)
at the point (x,y) gives the direction of maximum rate of decreasing
In this case we have
![\large f(x,y)=100-4x^2-2y^2](https://tex.z-dn.net/?f=%5Clarge%20f%28x%2Cy%29%3D100-4x%5E2-2y%5E2)
and we want to find the direction of fastest speed of decreasing at the point (-3,-2)
![\large \nabla f(x,y)=(-8x,-4y) \Rightarrow -\nabla f=(8x,4y)](https://tex.z-dn.net/?f=%5Clarge%20%5Cnabla%20f%28x%2Cy%29%3D%28-8x%2C-4y%29%20%5CRightarrow%20-%5Cnabla%20f%3D%288x%2C4y%29)
at the point (-3,-2) minus the gradient equals
![\large -\nabla f(-3,-2)=(-24,-8)](https://tex.z-dn.net/?f=%5Clarge%20-%5Cnabla%20f%28-3%2C-2%29%3D%28-24%2C-8%29)
hence the vector (-24,-8) points in the direction with the greatest rate of decreasing, and they should start their descent in that direction.
Hi, I'm happy to help!
To solve this, we need to multiply the 60% by the amount of students.
75×60%
Percentages are always out of 100, so we can write 60% like this:
75×60%
75×0.60, or 75×0.6
Now, we just multiply these together.
75×0.6
45
So, 45 of the students are girls.
I hope this was helpful, keep learning! :D