A boxplot is a graph that displays the middle 50 percent of a data set, using the minimumvalue, first quartile, median, third quartile, and maximumvalue.
A boxplot is a type of graph that visually displays the middle 50 percent of a data set. It is constructed using the minimum value, first quartile, median, third quartile, and maximum value.
The firstquartile is the median of the lower half of the data, while the third quartile is the median of the upper half.
The whiskers extend from the box to the minimum and maximum values within a certain range. The range can vary, but it's often defined as 1.5 times the IQR. Data points beyond the whiskers are considered outliers and are typically marked individually.
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Answer:
less than and less than
Step-by-step explanation:
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The required image of the point (-1, 1) is (-3, -1).
Given that,
To determine the image point of (-1,1)(−1,1) after a translation left 2 units and down 2 units.
Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
The given point, (-1, 1)
This point has been translated left 2 units and down 2 units
Whenever it is right or left translation, there is a change in the coordinate of x and when there is up and down translation there is a change in the coordinate of the y-axis,
Now,
2 units left
x = -1 - 2 = -3
2 units down
y = 1 - 2 = -1
Thus, the required image of the point (-1, 1) is (-3, -1).
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Moving from the point (-1, 1) left 2 units and down 2 units, the point would end up being:
(-3, -1)
Answer:
a. Rational number 1.26
Simplest radical 3−√3
b. Simplest radical 28+10√3
Rational number 45.32
c. Rational number 89
Step-by-step explanation:
a. √3(√3-1)
To get the simplest radical
Apply the distributive property.
√3*√3-√3
Combine using the product rule for radicals.
√3*3+√3*−1
Move −1 to the left of √3.
√3*√3*3-1*√3
Multiply 3 by 3.
√9−1*√3
Rewrite 9 as 3^2
√3^2-1 *√3
Pull terms out from under the radical, assuming positive real numbers.
3−1*√3
Rewrite −1√3 as −√3.
3−√3
Rational number 1.26
b. (5+√3)²
Expand
(5+√3)²= 25 +5*√3+5*√3+3= 28 +10√3
Simplest radical 28+10√3
Rational number 45.32
c. (10+√11)(10-√11)
Expand
(10+√11)(10-√11)= 10*10+ 10*-√11+10*√11+√11*-√11
=100+ 10*-√11+10*√11- 11
=89- 10*√11+10*√11
=89