Answer:
the expected total amount of time in minutes is 88.4
Step-by-step explanation:
The computation of the expected total amount of time in minutes is given below:
= Standard deviation × needed to answer calls each day
= 1.7 × 52
= 88.4
hence, the expected total amount of time in minutes is 88.4
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
Answer:
The correct option is option (3) 4 ÷ 25.
Step-by-step explanation:
The expression in terms of <em>m</em> and <em>n</em> is:
![F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}](https://tex.z-dn.net/?f=F%28m%2Cn%29%3D%5B%5Cfrac%7B2m%5E%7B-1%7Dn%5E%7B5%7D%7D%7B3m%5E%7B0%7Dn%5E%7B4%7D%7D%5D%5E%7B2%7D)
Exponent rule of division:
Compute the value of the expression for <em>m</em> = -5 and <em>n</em> = 3 as follows:
![F(-5,3)=[\frac{2\csdot (-5)^{-1}\cdot (3)^{5}}{3\cdot (-5)^{0}\cdot (3)^{4}}]^{2}](https://tex.z-dn.net/?f=F%28-5%2C3%29%3D%5B%5Cfrac%7B2%5Ccsdot%20%28-5%29%5E%7B-1%7D%5Ccdot%20%283%29%5E%7B5%7D%7D%7B3%5Ccdot%20%28-5%29%5E%7B0%7D%5Ccdot%20%283%29%5E%7B4%7D%7D%5D%5E%7B2%7D)
![=\{\frac{2}{3}\times [(-5)^{-1-0}\times (3)^{5-4}}]\}^{2}\\\\=\{\frac{2}{3}\times \frac{-1}{5}\times 3\}^{2}\\\\=\{-\frac{2}{5}\}^{2}\\\\=\frac{4}{25}](https://tex.z-dn.net/?f=%3D%5C%7B%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5B%28-5%29%5E%7B-1-0%7D%5Ctimes%20%283%29%5E%7B5-4%7D%7D%5D%5C%7D%5E%7B2%7D%5C%5C%5C%5C%3D%5C%7B%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B-1%7D%7B5%7D%5Ctimes%203%5C%7D%5E%7B2%7D%5C%5C%5C%5C%3D%5C%7B-%5Cfrac%7B2%7D%7B5%7D%5C%7D%5E%7B2%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B25%7D)
Thus, the correct option is option (3) 4 ÷ 25.
Answer:
a = 5.81 m
Step-by-step explanation:
We can use the Pythagorean theorem
a^2 + b^2 = c^2
where b= 1.5 and c= 6
a^2 +1.5^2 = 6^2
a^2 +2.25 = 36
Subtract 2.25 from each side
a^2 +2.25-2.25 = 36-2.25
a^2 = 33.75
Take the square root of each side
sqrt(a^2) = sqrt(33.75)
a = 5.809475019
We only take the positive root because length must be positive
Vertex is (-2,-3) and it's a minimum.
