Answer:
The lengths of the sides are 6, 8 and 10.
Step-by-step explanation:
The vertices of a right angles triangle are E (2,2), F (2,8), and G (10,8)
The distance between the two points is
![d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
So, the lengths of the sides are
![EF=\sqrt{(8-2)^2+(2-2)^2} = 6 \\\\FG=\sqrt{(8-8)^2+(10-2)^2} = 8 \\\\GE=\sqrt{(8-2)^2+(10-2)^2} = 10 \\](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%288-2%29%5E2%2B%282-2%29%5E2%7D%20%3D%206%20%5C%5C%5C%5CFG%3D%5Csqrt%7B%288-8%29%5E2%2B%2810-2%29%5E2%7D%20%3D%208%20%5C%5C%5C%5CGE%3D%5Csqrt%7B%288-2%29%5E2%2B%2810-2%29%5E2%7D%20%3D%2010%20%5C%5C)
the are of parallelogram is A=bh
Answer:
12. $65.90, 13. 36.04cm
Step-by-step explanation:
12. the circumference of the circle is 2pi*r. lets say x is the circumference so x = 2*pi*3.8 = 23.876m. multiply x by 2.76 to get 65.898, round to get 65.90
13. the area of a circle is pi*r^2. the area of the pizza is 12*85=1020cm^2. divide by pi to get 324.676 cm^2. then find the square root to get r=18.019 cm. the diameter = 2r so multiply by 2 to get 36.038cm. I'm not sure what the problem wants to round to so you can round it yourself.
note: for these two problems i used the full pi instead of 3.14. using 3.14 will give you a different answer so it just depends. If the problem wants you to use 3.14, simply resolve the problems and use 3.14 instead of pi wherever required.
Answer:
Step-by-step explanation:
Let X denote the amount of time spending exercise in a given week
Given that X normal (3.8, (0.8)²)
Thus we know that
![Z= \frac{x-3.8}{0.8} N(0,1)](https://tex.z-dn.net/?f=Z%3D%20%5Cfrac%7Bx-3.8%7D%7B0.8%7D%20N%280%2C1%29)
i)P [ amount of time less than two hour ]
= P[x < 2]
ii)
![P [x < 2]=P[\frac{x-3.8}{0.8} < \frac{2-3.8}{0.8} ]\\\\=P[z](https://tex.z-dn.net/?f=P%20%5Bx%20%3C%202%5D%3DP%5B%5Cfrac%7Bx-3.8%7D%7B0.8%7D%20%3C%20%5Cfrac%7B2-3.8%7D%7B0.8%7D%20%5D%5C%5C%5C%5C%3DP%5Bz%3C-2.25%5D)
= P[z > 2.25] ∴ symmetric
= P[0 ≤ z ≤ ∞] - P[0 ≤ z ≤ 2.25]
= 0.5 - 0.48778
= 0.0122
iii)
P[2 < x < 4]
Answer:
x=30
Step-by-step explanation:
![\frac{4}{5}=\frac{20}{x-5} \\\\4(x-5)=20*5\\\\4x-20=20(5)\\\\4x=20(5)+20(1)\\\\4x=20(5+1)\\\\4x=20(6)\\\\x=\frac{20(6)}{4} \\\\x=5*6\\\\x=30](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D%3D%5Cfrac%7B20%7D%7Bx-5%7D%20%5C%5C%5C%5C4%28x-5%29%3D20%2A5%5C%5C%5C%5C4x-20%3D20%285%29%5C%5C%5C%5C4x%3D20%285%29%2B20%281%29%5C%5C%5C%5C4x%3D20%285%2B1%29%5C%5C%5C%5C4x%3D20%286%29%5C%5C%5C%5Cx%3D%5Cfrac%7B20%286%29%7D%7B4%7D%20%5C%5C%5C%5Cx%3D5%2A6%5C%5C%5C%5Cx%3D30)