Answer:
FD≈25.94.. rounded = 26
Step-by-step explanation:
FD²=12²+(4x+11)²
FD²=144+16x²+88x+121
FD²=265+16x²+88x
also
FD²=12²+(13x-16)²
FD²=144+169x²-416x+256
FD²=400+169x²-416x
thus
265+16x²+88x = 400+169x²-416x
16x²-169x²+88x+416x+265-400 = 0
-153x²+504x-135 = 0
we will solve this quadratic equation by suing the quadratic formula to find x
x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)
x=(-504±
)/2(-153)
x=(-504±
)/-306
x=(-504±
)/-306
x=(-504±414)/-306
x=(-504+414)/-306 and x=(-504-414)/-306
x=-90/-306 and x=-918/-306
x= 5/17 , 3
substituting x by the roots we found
check for 5/17:
4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..
13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..
check for 3:
4x+11 = 4×3+11 = 12+11 = 23
13x-16 = 13×3-16 = 23
thus 3 is the right root
therfore
ED=23 and CD=23
FD²=FE²+ED² or FD²=FC²+CD²
FD²=12²+23²
FD²=144+529
FD²=673
FD=√673
FD≈25.94.. rounded = 26
For this, we use simultaneous equations. Let George's page be g, Charlie's be c and Bill's page be b.
First, <span>George's page contains twice as many type words as Bill's.
Thus, g = 2b.
</span><span>Second, Bill's page contains 50 fewer words than Charlie's page.
Thus, b = c - 50.
</span>If each person can type 60 words per minute, after one minute (i.e. when 60 more words have been typed) <span>the difference between twice the number of words on bills page and the number of words on Charlie's page is 210.
We can express that as 2b - c = 210.
Now we need to find b, since it represents Bill's page.
We can substitute b for (c - 50) since b = c - 50, into the equation 2b - c = 210. This makes it 2(c - 50) - c = 210.
We can expand this to 2c - 100 - c = 210.
We can simplify this to c - 100 = 210.
Add 100 to both sides.
c - 100 + 100 = 210 + 100
Then simplify: c = 210 + 100 = 310.
Now that we know c, we can use the first equation to find b.
b = c - 50 = 310 - 50 = 260.
260 is your answer. I don't know where George comes into it. Maybe it's a red herring!</span>
Answer: The answer is the yellow square.
Options :
a mean - 40, median - 50, mode - 60
b. mean-60, median - 50, mode - 40
c. mean - 40, median-60, mode - 50
d. mean - 50, median - 50, mode - 50
Answer: mean - 40, median - 50, mode - 60
Step-by-step explanation: A negatively skewed distribution is characterized by it long tail being positioned to the left(negative direction) with its peak positioned to the right (positive direction) of the distribution. On a general note, the mean is always positioned towards the left or negative side if the peak, with the median coming next and usually positioned to the right of the mean and the mode positioned to the right side of the median.
Hence, for a negatively skewed distribution, the mean has the least value followed by the median, with the mode boasting the highest.
That is : mean < median < mode
Answer:
Proved
Step-by-step explanation:
Given
![(2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=%282%20%2A%2010%5E2%29%20%2A%20%283%20%2A%2010%5E5%29%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Required
Prove
On the right hand side, we have:
![2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=2%20%2A%2010%5E2%20%2A%203%20%2A%2010%5E5%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Rewrite:
![2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=2%20%2A%203%2A%2010%5E2%20%20%2A%2010%5E5%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
![6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=6%2A%2010%5E2%20%20%2A%2010%5E5%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Apply law of indices
![6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=6%2A%2010%5E%7B2%2B5%7D%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
![6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=6%2A%2010%5E7%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Express 6 as 3.5 + 2.5
![(3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=%283.5%20%2B%202.5%29%2A%2010%5E7%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Open bracket
![3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7](https://tex.z-dn.net/?f=3.5%20%2A10%5E7%2B%202.5%2A10%5E7%20%3D%203.5%20%2A%2010%5E7%20%2B%202.5%20%2A%2010%5E7)
Proved