60 seconds in a minute, but if you divide 60/3, you’ll get 20. So 20*4=80 gallons/min. If you multiply 80*60=4,800 gallons/hr
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Answer:
Step-by-step explanation:
Let r = .25 probability of getting question right. and w = .75 prob getting it wrong.
since there are 10 questions, this will tell us what we want to know.
a) 1-
doesn't get them all wrong.
1-![\left (0.75\right )^{10}\\](https://tex.z-dn.net/?f=%5Cleft%20%280.75%5Cright%20%29%5E%7B10%7D%5C%5C)
=1-.0563
=.9437
b) Probability of getting 6-10 answers right
![\left (r\right )^{10}+10\left ( r \right )^{9}w+45\left ( r \right )^{8}w^{2}+120\left ( r \right )^{7}w^{3}+120\left ( r \right )^{6}w^{4}](https://tex.z-dn.net/?f=%5Cleft%20%28r%5Cright%20%29%5E%7B10%7D%2B10%5Cleft%20%28%20r%20%5Cright%20%29%5E%7B9%7Dw%2B45%5Cleft%20%28%20r%20%5Cright%20%29%5E%7B8%7Dw%5E%7B2%7D%2B120%5Cleft%20%28%20r%20%5Cright%20%29%5E%7B7%7Dw%5E%7B3%7D%2B120%5Cleft%20%28%20r%20%5Cright%20%29%5E%7B6%7Dw%5E%7B4%7D)
=.0197
c)
This means 9 or 10 answer should be right
![\left (r\right )^{10}+10\left ( r \right )^{9}w](https://tex.z-dn.net/?f=%5Cleft%20%28r%5Cright%20%29%5E%7B10%7D%2B10%5Cleft%20%28%20r%20%5Cright%20%29%5E%7B9%7Dw)
=.00003
d)
= 2.5 expected correct answers.
e)
Standard deviation for a binomial distribution is ![\sqrt{n\ast p\left ( 1-p \right )}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%5Cast%20p%5Cleft%20%28%201-p%20%5Cright%20%29%7D)
=![\sqrt{10\ast0.25\ast0.75}](https://tex.z-dn.net/?f=%5Csqrt%7B10%5Cast0.25%5Cast0.75%7D)
=![\sqrt{1.875}](https://tex.z-dn.net/?f=%5Csqrt%7B1.875%7D)
=1.369
Answer:
y+?=mx+b
Step-by-step explanation:
Answer:
The answer is the option A
![\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Csqrt%7B%5B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%5D%2A%5B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%5D%7D%29)
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The area of the triangle is equal to
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
where
b is the base
h is the height
In this problem
![b=AB, h=AC](https://tex.z-dn.net/?f=b%3DAB%2C%20h%3DAC)
the formula to calculate the distance between two points is equal to
Find the distance AB
![A(0,0), B(x2,y2)](https://tex.z-dn.net/?f=A%280%2C0%29%2C%20B%28x2%2Cy2%29)
substitute
Find the distance AC
![A(0,0), C(x1,y1)](https://tex.z-dn.net/?f=A%280%2C0%29%2C%20C%28x1%2Cy1%29)
substitute
Find the area of the triangle
we have
![b=\sqrt{(y2)^{2}+(x2)^{2}}, h=\sqrt{(y1)^{2}+(x1)^{2}}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%7D%2C%20h%3D%5Csqrt%7B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%7D)
substitute
![A=\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28%5Csqrt%7B%5B%28y2%29%5E%7B2%7D%2B%28x2%29%5E%7B2%7D%5D%2A%5B%28y1%29%5E%7B2%7D%2B%28x1%29%5E%7B2%7D%5D%7D%29)