Answer:
364
Step-by-step explanation:
Hello, you can use the formula which is ![v=lwh/3](https://tex.z-dn.net/?f=v%3Dlwh%2F3)
Answer:
Step-by-step explanation:
i have no idea but i thinkit is A.or D i think the kid is right with a different answer
happy to help
Answer:
The set of all pages in the book:
S={1, 2, 3, ..., 428}
Step-by-step explanation:
The sample space is the set containing all possible outcomes for the experiment. In this problem, the experiment is stopping at a random page of the textbook, and the sample space is the set of all pages in the book:
S={1, 2, 3, ..., 428}.
Answer:
a) ![cos(\alpha)=-\frac{3}{5}\\](https://tex.z-dn.net/?f=cos%28%5Calpha%29%3D-%5Cfrac%7B3%7D%7B5%7D%5C%5C)
b) ![\sin(\beta)= \frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Csin%28%5Cbeta%29%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
c) ![\frac{4+3\sqrt{3} }{10}\\](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B3%5Csqrt%7B3%7D%20%7D%7B10%7D%5C%5C)
d) ![\alpha\approx 53.1^o](https://tex.z-dn.net/?f=%5Calpha%5Capprox%2053.1%5Eo)
Step-by-step explanation:
a) The problem tells us that angle
is in the second quadrant. We know that in that quadrant the cosine is negative.
We can use the Pythagorean identity:
![tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}](https://tex.z-dn.net/?f=tan%5E2%28%5Calpha%29%2B1%3Dsec%5E2%28%5Calpha%29%5C%5C%28-%5Cfrac%7B4%7D%7B3%7D%29%5E2%20%2B1%3Dsec%5E2%28%5Calpha%29%5C%5Csec%5E2%28%5Calpha%29%3D%5Cfrac%7B16%7D%7B9%7D%20%2B1%5C%5Csec%5E2%28%5Calpha%29%3D%5Cfrac%7B25%7D%7B9%7D%20%5C%5Csec%28%5Calpha%29%20%3D%2B%2F-%20%5Cfrac%7B5%7D%7B3%7D%5C%5Ccos%28%5Calpha%29%3D%2B%2F-%20%5Cfrac%7B3%7D%7B5%7D)
Where we have used that the secant of an angle is the reciprocal of the cos of the angle.
Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:
![cos(\alpha)=-\frac{3}{5}](https://tex.z-dn.net/?f=cos%28%5Calpha%29%3D-%5Cfrac%7B3%7D%7B5%7D)
b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:
![cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=cos%20%28%5Cbeta%29%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%5C%5Csin%5E2%28%5Cbeta%29%3D1-cos%5E2%28%5Cbeta%29%5C%5Csin%5E2%28%5Cbeta%29%3D1-%5Cfrac%7B1%7D%7B4%7D%20%5C%5C%5C%5Csin%5E2%28%5Cbeta%29%3D%5Cfrac%7B3%7D%7B4%7D%20%5C%5Csin%28%5Cbeta%29%3D%2B%2F-%20%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5C%5Csin%28%5Cbeta%29%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
where we took the positive value, since we know that the angle is in the first quadrant.
c) We can now find
by using the identity:
![sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\](https://tex.z-dn.net/?f=sin%28%5Calpha%20-%5Cbeta%29%3Dsin%28%5Calpha%29%5C%2Ccos%28%5Cbeta%29-cos%28%5Calpha%29%5C%2Csin%28%5Cbeta%29%5C%5C)
Notice that we need to find
, which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:
![sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}](https://tex.z-dn.net/?f=sin%28%5Calpha%29%3D%5Csqrt%7B1-cos%5E2%28%5Calpha%29%7D%20%5C%5Csin%28%5Calpha%29%3D%5Csqrt%7B1-%5Cfrac%7B9%7D%7B25%7D%20%29%7D%20%5C%5Csin%28%5Calpha%29%3D%5Csqrt%7B%5Cfrac%7B16%7D%7B25%7D%20%29%7D%20%5C%5Csin%28%5Calpha%29%3D%5Cfrac%7B4%7D%7B5%7D)
Then:
![sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}](https://tex.z-dn.net/?f=sin%28%5Calpha%20-%5Cbeta%29%3D%5Cfrac%7B4%7D%7B5%7D%5C%2C%5Cfrac%7B1%7D%7B2%7D%20-%28-%5Cfrac%7B3%7D%7B5%7D%29%20%5C%2C%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5C%5Csin%28%5Calpha%20-%5Cbeta%29%3D%5Cfrac%7B2%7D%7B5%7D%2B%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B10%7D%3D%5Cfrac%7B4%2B3%5Csqrt%7B3%7D%20%7D%7B10%7D)
d)
Since ![sin(\alpha)=\frac{4}{5}](https://tex.z-dn.net/?f=sin%28%5Calpha%29%3D%5Cfrac%7B4%7D%7B5%7D)
then ![\alpha=arcsin(\frac{4}{5} )\approx 53.1^o](https://tex.z-dn.net/?f=%5Calpha%3Darcsin%28%5Cfrac%7B4%7D%7B5%7D%20%29%5Capprox%2053.1%5Eo)
100 times rolled total
32 times number 2 was rolled
32/100 chance of rolling a 2 on the number cube
Heads was flipped 55 times, 100 total flips so 55/100
(32/100) x (55/100) = .176
176/1000 x 10 =
1760/10000 A