Answer:
Sample size should be atleast 55320
Step-by-step explanation:
Given that a group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week.
population standard deviation ![\sigma = 6 hrs](https://tex.z-dn.net/?f=%5Csigma%20%3D%206%20hrs)
Std error = ![\frac{6}{\sqrt{n} }](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B%5Csqrt%7Bn%7D%20%7D)
Margin of error for 95%
= ![1.96*\frac{6}{\sqrt{n} } 235.2\\n \geq 55319.04](https://tex.z-dn.net/?f=1.96%2A%5Cfrac%7B6%7D%7B%5Csqrt%7Bn%7D%20%7D%20%3C0.5%5C%5C%5Csqrt%7Bn%7D%20%3E235.2%5C%5Cn%20%5Cgeq%2055319.04)
Since sample size is number of items it cannot be indecimal.
So we can round off to the next high integer on a safer side.
The line integral is the path of the function along a line having a continuous value.
The integral solved gives the value 111.
The given question is
![\int\limits^c {z}^2 \, dx+ {x}^2 \, dy+ {y} ^2\, dz](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ec%20%7Bz%7D%5E2%20%5C%2C%20dx%2B%20%7Bx%7D%5E2%20%5C%2C%20dy%2B%20%7By%7D%20%5E2%5C%2C%20dz)
where C is the line from (1, 0, 0) to (4, 1, 3)
Here
x→ 1⇒ 4
y→ 0⇒1
z→ 0⇒ 3
Let t be defined be the range 0≤ t ≤ 1
Then x= 4t+1 : dx= 4dt
y= t ": dy= dt
z= 3t : dz= 3dt
Putting the values
![\int\limits^1_0{9t^2} \, 4dt + \int\limits^1_0 {16t^2+1+8t} \, 3dt +\int\limits^1_0 {t^2} \,3dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%7B9t%5E2%7D%20%5C%2C%204dt%20%2B%20%5Cint%5Climits%5E1_0%20%7B16t%5E2%2B1%2B8t%7D%20%5C%2C%203dt%20%2B%5Cint%5Climits%5E1_0%20%7Bt%5E2%7D%20%5C%2C3dt)
= [36(1)²- 36(0)²]+ 3 [16(1)² +1+8(1)] - 3 [16(0)² +1+8(0)] + [3(1)²- 3(0)² ]
= 36 +75-3+3
= 111
brainly.com/question/16571667
brainly.com/question/18762649
Answer:
![\Large{\bold{\frac{4x\:+\:1}{x\:+\:6}}}](https://tex.z-dn.net/?f=%5CLarge%7B%5Cbold%7B%5Cfrac%7B4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D%7D%7D)
Step-by-step explanation:
![(8x\:-\:4x\:+\:1) ÷ (x\:+\:6)](https://tex.z-dn.net/?f=%288x%5C%3A-%5C%3A4x%5C%3A%2B%5C%3A1%29%20%C3%B7%20%28x%5C%3A%2B%5C%3A6%29)
![\frac{8x\:-\:4x\:+\:1}{x\:+\:6}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%5C%3A-%5C%3A4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D)
![\frac{4x\:+\:1}{x\:+\:6}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5C%3A%2B%5C%3A1%7D%7Bx%5C%3A%2B%5C%3A6%7D)
Answer:
b= 7 times the square root of 2
Step-by-step explanation: In a 45-45-90 degree triangle the base and the height both equal x and the hypotenuse is equal to x times the square root of 2.
Hope this helps