Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
Finally, we know that the sum of probablities has to be 1, or 100%.
We can solve this by sustitution:
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
Answer:
v = 2744 m³
Step-by-step explanation:
Volume of cube
= length³
= l³
= 14³
= 2744 m³
make as the brainliest
The correct answer is option B.
From the graph we can see the following discontinuities:
a) A hole at x = -2
b) A jump at x = 0
c) A hole at x = 8
The hole refers to the point discontinuity and the jump refers to as jump discontinuity. The function is defined and is continuous at x = 3
Thus, the given graph has jump discontinuity at x = 0 and point discontinuity at x = -2 and x = 8
Answer:
![z_1=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{7\pi}{16}+i\sin\dfrac{7\pi}{16}\right).](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B7%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B7%5Cpi%7D%7B16%7D%5Cright%29.)
![z_2=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{15\pi}{16}+i\sin\dfrac{15\pi}{16}\right).](https://tex.z-dn.net/?f=z_2%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B15%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B15%5Cpi%7D%7B16%7D%5Cright%29.)
![z_3=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{23\pi}{16}+i\sin\dfrac{23\pi}{16}\right).](https://tex.z-dn.net/?f=z_3%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B23%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B23%5Cpi%7D%7B16%7D%5Cright%29.)
![z_4=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{31\pi}{16}+i\sin\dfrac{31\pi}{16}\right).](https://tex.z-dn.net/?f=z_4%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B31%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B31%5Cpi%7D%7B16%7D%5Cright%29.)
Step-by-step explanation:
The complex number 
has the real part 
and the imaginary part 
Hence,
From the last two equalities, 
and the trigonometric form is
The square roots can be calculated using the formula:
![\sqrt[4]{z}=\left\{\sqrt[4]{|z|}\left(\cos\dfrac{\varphi+2\pi k}{4}+i\sin\dfrac{\varphi+2\pi k}{4}\right),\text{ where }k=0,1,2,3\right\}.](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bz%7D%3D%5Cleft%5C%7B%5Csqrt%5B4%5D%7B%7Cz%7C%7D%5Cleft%28%5Ccos%5Cdfrac%7B%5Cvarphi%2B2%5Cpi%20k%7D%7B4%7D%2Bi%5Csin%5Cdfrac%7B%5Cvarphi%2B2%5Cpi%20k%7D%7B4%7D%5Cright%29%2C%5Ctext%7B%20where%20%7Dk%3D0%2C1%2C2%2C3%5Cright%5C%7D.)
At k=0:
![z_1=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{\frac{7\pi}{4}}{4}+i\sin\dfrac{\frac{7\pi}{4}}{4}\right)=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{7\pi}{16}+i\sin\dfrac{7\pi}{16}\right).](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%7D%7B4%7D%2Bi%5Csin%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%7D%7B4%7D%5Cright%29%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B7%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B7%5Cpi%7D%7B16%7D%5Cright%29.)
At k=1:
![z_2=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{\frac{7\pi}{4}+2\pi}{4}+i\sin\dfrac{\frac{7\pi}{4}+2\pi}{4}\right)=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{15\pi}{16}+i\sin\dfrac{15\pi}{16}\right).](https://tex.z-dn.net/?f=z_2%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B2%5Cpi%7D%7B4%7D%2Bi%5Csin%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B2%5Cpi%7D%7B4%7D%5Cright%29%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B15%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B15%5Cpi%7D%7B16%7D%5Cright%29.)
At k=2:
![z_3=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{\frac{7\pi}{4}+4\pi}{4}+i\sin\dfrac{\frac{7\pi}{4}+4\pi}{4}\right)=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{23\pi}{16}+i\sin\dfrac{23\pi}{16}\right).](https://tex.z-dn.net/?f=z_3%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B4%5Cpi%7D%7B4%7D%2Bi%5Csin%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B4%5Cpi%7D%7B4%7D%5Cright%29%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B23%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B23%5Cpi%7D%7B16%7D%5Cright%29.)
At k=3:
![z_4=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{\frac{7\pi}{4}+6\pi}{4}+i\sin\dfrac{\frac{7\pi}{4}+6\pi}{4}\right)=\sqrt[4]{3\sqrt{2}}\left(\cos\dfrac{31\pi}{16}+i\sin\dfrac{31\pi}{16}\right).](https://tex.z-dn.net/?f=z_4%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B6%5Cpi%7D%7B4%7D%2Bi%5Csin%5Cdfrac%7B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B6%5Cpi%7D%7B4%7D%5Cright%29%3D%5Csqrt%5B4%5D%7B3%5Csqrt%7B2%7D%7D%5Cleft%28%5Ccos%5Cdfrac%7B31%5Cpi%7D%7B16%7D%2Bi%5Csin%5Cdfrac%7B31%5Cpi%7D%7B16%7D%5Cright%29.)
Answer:
84
Step-by-step explanation:
180-51-45=84
I think this would be the answer since triangles add up to be 84 and we are just finding the last missing angle.
hope this helps :)
