Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this proble
2 answers:
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Answer:
The correct option is Mean and standard deviation.
Step-by-step explanation:
The data set provided, arranged in ascending order is:
S = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 4}
Now, it is provided that Macy was absent when the data was collected and the class guessed she had 4 siblings. When she returned, they found out she actually has 9 siblings.
So, the new data set is:
X = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 9}
The mean of a data set is the average value representing the entire data.
The median is the middle value of the data set.
The inter-quartile range is the difference between the first and the third quartile.
The standard deviation is the value that represents how dispersed the data values are.
From all the above statistic, the mean and standard deviation are the only ones that uses all the observations in the data set to compute their value.
So, on changing one of the 4s by a 9, the set of measures that will be affected are the mean and standard deviation.
Thus, the correct option is Mean and standard deviation.
Answer:
Intersection at (-1, 0, 1).
Angle 0.6 radians
Step-by-step explanation:
The helix r(t) = (cos(πt), sin(πt), t) intersects the paraboloid
z = x2 + y2 when the coordinates (x,y,z)=(cos(πt), sin(πt), t) of the helix satisfy the equation of the paraboloid. That is, when
But
so, the helix intersects the paraboloid when t=1. This is the point
(cos(π), sin(π), 1) = (-1, 0, 1)
The angle of intersection between the helix and the paraboloid is the angle between the tangent vector to the curve and the tangent plane to the paraboloid.
The <em>tangent vector</em> to the helix in t=1 is
r'(t) when t=1
r'(t) = (-πsin(πt), πcos(πt), 1), hence
r'(1) = (0, -π, 1)
A normal vector to the tangent plane of the surface
at the point (-1, 0, 1) is given by
where
since
so, a normal vector to the tangent plane is
(-2,0,-1)
Hence, <em>a vector in the same direction as the projection of the helix's tangent vector (0, -π, 1) onto the tangent plane </em>is given by
The angle between the tangent vector to the curve and the tangent plane to the paraboloid equals the angle between the tangent vector to the curve and the vector we just found.
But we now
where
= angle between the tangent vector and its projection onto the tangent plane. So
and
Answer:
Martha is incorrect.
Amount paid by Renee =
Amount paid by Susan = $297.5
Amount paid by Martha =
Step-by-step explanation:
Given: Renee will pay 40% of the cost. Susan will pay 0.35 of the cost.Martha will pay the remainder of the cost. Martha thinks she will pay 13 of the cost.
To find: Is Martha correct?
To find: amount paid by each of Renee, Susan, and Martha
Solution:
Percentage of an amount paid by Renee = 40%
Percentage of an amount paid by Susan = 35%
So,
Percentage of an amount paid by Martha =
But Martha thinks she will pay 13 of the cost. So, she is incorrect.
Amount paid by Renee =
Amount paid by Susan =
Amount paid by Martha =