246, 299, 360, 404, 379, 199, 279, 749, 794, 849, 914
1 answer:
Answer:
Mean = 497.5
Median = 379.0
First Quartile = 289
Third Quartile = 771.5
Step-by-step explanation:
Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.
⇒
⇒ Mean = 497.5
Median is the middle observation of given data. It can be found by following steps:
Arranging data in ascending or descending order.
Taking the average of middle two value if the total number of observation is even, and this average is our median.
or, if we odd number of observation then the most middle value is our median.
Here, number of observation is 11.
So the middle value is (11+1)÷2 = 6th term
⇒ Median = 379
The mode is the observation which has a high number of repetitions (frequency).
Here frequency of all observation is same. So, it is multi- modal data.
First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.
First Quartile (Q₁) = 289
The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.
Third Quartile (Q₃) = 771.5
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Answer:
Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)
Step-by-step explanation:
<u><em>The complete question is</em></u>
Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
Equation 1: (x – 3)2 = y – 4
Equation 2: y = -x + b
In order for Tom’s thinking to be correct, which qualifications must be met?
A: b must equal 7 and a second solution to the system must be located at the point (2, 5).
B: b must equal 1 and a second solution to the system must be located at the point (4, 5).
C: b must equal 7 and a second solution to the system must be located at the point (1, 8).
D: b must equal 1 and a second solution to the system must be located at the point (3, 4).
step 1
Find the vertex of the quadratic equation
The general equation of a vertical parabola in vertex form is
where
(h,k) is the vertex
we have
so
The vertex is the point (3,4)
step 2
Find out the value of b in the linear equation
we know that
If the vertex is a solution of the system of equations, then the vertex must satisfy both equations
substitute the value of x and the value of y of the vertex in the linear equation
For x=3, y=4
so
step 3
Find out the second solution of the system of equations
we have
-----> equation A
----> equation B
solve the system of equations by graphing
Remember that the solutions are the intersection points both graphs
The second solution of the system of equations is (2,5)
see the attached figure
therefore
b must equal 7 and a second solution to the system must be located at the point (2, 5)
