Answer:
![-7ab\sqrt[3]{3ab^2}](https://tex.z-dn.net/?f=-7ab%5Csqrt%5B3%5D%7B3ab%5E2%7D)
Step-by-step explanation:
Remove perfect cubes from under the radical and combine like terms.
![2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }](https://tex.z-dn.net/?f=2ab%5Csqrt%5B3%5D%7B192ab%5E2%7D-5%5Csqrt%5B3%5D%7B81a%5E4b%5E5%7D%3D2ab%5Csqrt%5B3%5D%7B4%5E3%5Ccdot%203ab%5E2%7D-5%5Csqrt%5B3%5D%7B%283ab%29%5E3%5Ccdot%203ab%5E2%7D%5C%5C%5C%5C%3D%288ab%20-15ab%29%5Csqrt%5B3%5D%7B3ab%5E2%7D%3D%5Cboxed%7B-7ab%5Csqrt%5B3%5D%7B3ab%5E2%7D%20%7D)
The angle θ that the field e⃗ makes with the surface of the slab, which is perpendicular to the x direction is <span>θ = -1.57 <span>rad
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Answer:
Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.
Step-by-step explanation:
We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.
A random sample of 70 users was selected.
Let
= <u><em>sample proportion of users who used Internet Explorer as their browser.</em></u>
The z score probability distribution for sample proportion is given by;
Z =
~ N(0,1)
where, p = population proportion of users who use internet explorer = 53.4%
= sample proportion =
= 0.457
n = sample of users = 70
Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P(
0.457)
P(
0.457) = P(
) = P(Z
-1.29)
= P(Z
1.29) = <u>0.9015</u>
The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.
Males that watched action movies : 13
males that watched drama movies : 5
so there are (13 - 5) = 8 more that watched action then drama