Answer:
The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1
A=45
Step-by-step explanation:
Answer:
$11,250 divided by 15 is 750, which means that the answer is the rate is $750 dollars spent in each sport.
For this case we have the following expression:
![2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B16x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B81x%7D%29-4%28%5Csqrt%5B4%5D%7B32y%7D%29)
Rewriting the numbers within the roots we have:
![2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%2A3%2A3%2A3x%7D%29-4%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%2A2y%7D%29)
Then, by properties of powers we have:
![2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%5E4x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%5E4x%7D%29-4%28%5Csqrt%5B4%5D%7B2%5E42y%7D%29)
Then, by radical properties we have:
![2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})](https://tex.z-dn.net/?f=2%282%5Csqrt%5B4%5D%7Bx%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%283%5Csqrt%5B4%5D%7Bx%7D%29-4%282%5Csqrt%5B4%5D%7B2y%7D%29)
Rewriting the expression we have:
![4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}](https://tex.z-dn.net/?f=4%5Csqrt%5B4%5D%7Bx%7D-2%5Csqrt%5B4%5D%7B2y%7D%2B9%5Csqrt%5B4%5D%7Bx%7D-8%5Csqrt%5B4%5D%7B2y%7D)
Finally, adding similar terms we have:
![(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}](https://tex.z-dn.net/?f=%284%2B9%29%5Csqrt%5B4%5D%7Bx%7D-%282%2B8%29%5Csqrt%5B4%5D%7B2y%7D)
![13\sqrt[4]{x}-10\sqrt[4]{2y}](https://tex.z-dn.net/?f=13%5Csqrt%5B4%5D%7Bx%7D-10%5Csqrt%5B4%5D%7B2y%7D)
Answer:
The simplified form of the expression is:
Answer:
10. Let m<Y = y.
Then,
m<Y + m<X +m<Z = 180 [ Sum of angles of triangle is 180 degrees]
or, y + (6x-23) + (4x + 9) = 180
or, y + 10x -14 = 180
or, y = 194 - 10x
or, m<Y = 194 - 10x
12. Solution,
a. m<1 = 60 degrees [Each angles of equilateral triangle is equal to 60 degrees]
b. In triangle WYZ,
m<Z + m<ZWY + m<ZYW =180 [Sum of angles of triangle is 180]
or, 138 + m<ZWY +m<ZWY =180 [Base angles of isosceles triangle are equal, i.e. m<ZYW = m <ZWY]
or, 2 (m<ZWY) = 180 -138 = 42
or, m<ZWY = 21 = m<ZYW
or, m<3 = 21 = m<5
c. Solution,
m<XWY = m<2 + m<3 [Addition axiom]
or, 60 = m<2 + 21 [Each angle of equilateral triangle is 60]
or, m<2 = 39
d. Solution,
m<4 + m<5 =60 [<XYW = 60 ]
or, m<4 + 21 = 60
or, m<4 = 39
