Answer:
1) 19/25 likely
2)5/25 unlikely
3) 2/25 = 8%
I have to go so I cant finish 4 and 5 but I hope this helped
Step-by-step explanation:
1) this is based just on the results so we don't have to do any probability tree or anything. there are 25 groups overall and 19 of those 25 groups contain at least one senior. this is 76% and is over 2 thirds so it is likely
2) again this is based just on the results so we don't have to do any probability tree or anything. there are 25 groups overall and 5 of those 25 groups contain at least 2 freshmen. this is 20% and is under 1 third so it is unlikely
3)again this is based just on the results so we don't have to do any probability tree or anything. there are 25 groups overall and 2 of those 25 groups contain four students from the same grade level. this is 8% and so is unlikely.
Answer: The number of yes votes = 1918.
Step-by-step explanation:
Given : The ratio of yes to no votes = 2:3
Then the ratio of yes to total votes = ![\dfrac{2}{2+3}=\dfrac25](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B2%2B3%7D%3D%5Cdfrac25)
Total votes = 4795
Number of yes votes = (ratio of yes to total votes) x (Total votes )
= ![\dfrac{2}{5}\times4795=1918](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%5Ctimes4795%3D1918)
Hence, the number of yes votes = 1918.
The square 8 units is above the grid for stage. Coordinations was the location
Answer: 993.6
Step-by-step explanation:
height*base*depth=Area
8*6.9= 55.2
55.2*18= 993.6
Sorry if i gave you the wrong answer, I am super sorry
Parameterize each line segment from
to
by
![\vec r(t) = (1-t) (x_0\,\vec\imath + y_0\,\vec\jmath + z_0\,\vec k) + t (x_1\,\vec\imath + y_1\,\vec\jmath + z_1\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%20%3D%20%281-t%29%20%28x_0%5C%2C%5Cvec%5Cimath%20%2B%20y_0%5C%2C%5Cvec%5Cjmath%20%2B%20z_0%5C%2C%5Cvec%20k%29%20%2B%20t%20%28x_1%5C%2C%5Cvec%5Cimath%20%2B%20y_1%5C%2C%5Cvec%5Cjmath%20%2B%20z_1%5C%2C%5Cvec%20k)
with
. The work done by
on the particle along each segment is given the line integral of
with respect to that segment,
![\displaystyle \int_{C_i} \vec F \cdot d\vec r = \int_0^1 \vec F(\vec r_i(t)) \cdot \dfrac{d\vec r_i(t)}{dt} \, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7BC_i%7D%20%5Cvec%20F%20%5Ccdot%20d%5Cvec%20r%20%3D%20%5Cint_0%5E1%20%5Cvec%20F%28%5Cvec%20r_i%28t%29%29%20%5Ccdot%20%5Cdfrac%7Bd%5Cvec%20r_i%28t%29%7D%7Bdt%7D%20%5C%2C%20dt)
• (3, 0, 0) to (3, 5, 1)
![\vec r_1(t) = 3\,\vec\imath + 5t\,\vec\jmath + t\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20r_1%28t%29%20%3D%203%5C%2C%5Cvec%5Cimath%20%2B%205t%5C%2C%5Cvec%5Cjmath%20%2B%20t%5C%2C%5Cvec%20k)
![W_1 = \displaystyle \int_0^1 \left(t^2\,\vec\imath + 75t\,\vec\jmath + 50t^2\,\vec k\right) \cdot \left(5\,\vec\jmath + \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (375t + 50t^2) \, dt = \frac{1225}6](https://tex.z-dn.net/?f=W_1%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%28t%5E2%5C%2C%5Cvec%5Cimath%20%2B%2075t%5C%2C%5Cvec%5Cjmath%20%2B%2050t%5E2%5C%2C%5Cvec%20k%5Cright%29%20%5Ccdot%20%5Cleft%285%5C%2C%5Cvec%5Cjmath%20%2B%20%5Cvec%20k%5Cright%29%20%5C%2C%20dt%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Cint_0%5E1%20%28375t%20%2B%2050t%5E2%29%20%5C%2C%20dt%20%3D%20%5Cfrac%7B1225%7D6)
• (3, 5, 1) to (0, 5, 1)
![\vec r_2(t) = 3(1-t)\,\vec\imath + 5(1-t)\,\vec\jmath + \vec k](https://tex.z-dn.net/?f=%5Cvec%20r_2%28t%29%20%3D%203%281-t%29%5C%2C%5Cvec%5Cimath%20%2B%205%281-t%29%5C%2C%5Cvec%5Cjmath%20%2B%20%5Cvec%20k)
![W_2 = \displaystyle \int_0^1 \left(\vec\imath + 75(1-t)\,\vec\jmath + 50 \,\vec k\right) \cdot \left(-3\,\vec\imath - 5\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -3 \int_0^1 \,dt = -3](https://tex.z-dn.net/?f=W_2%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%28%5Cvec%5Cimath%20%2B%2075%281-t%29%5C%2C%5Cvec%5Cjmath%20%2B%2050%20%5C%2C%5Cvec%20k%5Cright%29%20%5Ccdot%20%5Cleft%28-3%5C%2C%5Cvec%5Cimath%20-%205%5C%2C%5Cvec%5Cjmath%5Cright%29%20%5C%2C%20dt%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20-3%20%5Cint_0%5E1%20%5C%2Cdt%20%3D%20-3)
• (0, 5, 1) to (0, 0, 0)
![\vec r_3(t) = 5(1-t)\,\vec\jmath + (1-t)\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20r_3%28t%29%20%3D%205%281-t%29%5C%2C%5Cvec%5Cjmath%20%2B%20%281-t%29%5C%2C%5Cvec%20k)
![W_3 = \displaystyle \int_0^1 \left((1-t)^2\,\vec\imath + 50(1-t)^2\,\vec k\right) \cdot \left(-5\,\vec\jmath - \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (-50 + 100t - 50t^2) \, dt = -\frac{50}3](https://tex.z-dn.net/?f=W_3%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%28%281-t%29%5E2%5C%2C%5Cvec%5Cimath%20%2B%2050%281-t%29%5E2%5C%2C%5Cvec%20k%5Cright%29%20%5Ccdot%20%5Cleft%28-5%5C%2C%5Cvec%5Cjmath%20-%20%5Cvec%20k%5Cright%29%20%5C%2C%20dt%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Cint_0%5E1%20%28-50%20%2B%20100t%20-%2050t%5E2%29%20%5C%2C%20dt%20%3D%20-%5Cfrac%7B50%7D3)
Then the total work done by
on the particle is
![W = W_1 + W_2 + W_3 = \boxed{\dfrac{369}2}](https://tex.z-dn.net/?f=W%20%3D%20W_1%20%2B%20W_2%20%2B%20W_3%20%3D%20%5Cboxed%7B%5Cdfrac%7B369%7D2%7D)