Center : Mean Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5 After the introduction of the new course, center = average(121,134,106,93,149,130,119,128,45) = 113.9 The center has moved to the left (if plotted in a graph) because of the low intake for the new course. Spread before introduction of the new course : Arrange the numbers in ascending order: (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132 Spread = Interquartile range = Q3-Q1 = 19.5 After addition of the new course,
(45,93, 106,119,) 121, (128, 130,134, 149)
Q1=median(45,93,106,119)=99.5
Q3=median (128, 130,134, 149)= 132
Spread = Interquartile range = 132-99.5 =32.5
We see that the spread has increased after the addition of the new course.
The ratio of the side measures are 6:7:9.
Let's assume length of three sides of the triangle is 6x, 7x and 9x.
Given,perimeter of a triangle is 110 inches.. Perimeter is the sum of all three sides of the triangle. So, we can set up an equation as follows:
6x+7x+9x= 110
22x =110
Dividing each sides by 22.
x=5.
Now we can plug in x=5 in all the expressions of sides.
So, 6x=6(5)=30,
7x=7(5)=35
9x=9(5)=45.
So, the sides of the triangle are 30 inches, 35 inches and 45 inches.
Answer: 3|x| = 3x when x 
0 and 3|x| = -3x when x < 0
Step-by-step explanation: Absolute value basically refers to the distance of a point from the origin (zero), regardless of the direction. The absolute value of a number is represented by two vertical lines enclosing the number. For example, |6| = 6, or in this case, 3|x| = 3x. Here, the value is replaced by the term "x". "x" is used as a term for an unknown value/variable. so basically, we're solving for x kinda. Multiplying "x" (the unknown variable) by 3 gives us = 3x. We know from the sign that x <u>can't be below zero</u>, only <u>above or equal to</u>. So, 3lxl = 3x when x is above or equal to the origin (zero). We know from the second problem that x <u>can't be above zero </u>because of the sign <, only <u>below zero</u>. Because we can only go below zero, that positive 3 turns negative. Multiplying x by -3 gives us = -3x. So, 3|x| = -3x when x is blow the origin (zero).
Note: <u>the absolute value of a number is always positive</u>, but in this scenario this rule doesn't apply because "x" is not a number, only a unknown value.
Sorry in advance if my explanation still doesn't make sense. Math isn't my thing really.
12. ∆ABD is similar to ∆PQD, so
QD/z = BD/x
Likewise ∆CDB is similar to ∆PQB, so
QB/z = BD/y
Since QD + QB = BD, you have
QD/z + QB/z = BD/x + BD/y
BD/z = BD/x + BD/y
Dividing by BD gives the desired result:
1/x + 1/y = 1/z
13. Triangles ABD, BCD, and ACB are all similar. This means
AB/AC = AD/AB
AB² = AC×AD = (4 cm)×(9 cm)
AB² = 36 cm²
AB = 6 cm
and
BD/CD = AD/BD
BD² = CD×AD = (5 cm)×(4 cm)
BD² = 20 cm²
BD = 2√5 cm
X=61 is your answer, hope this helps
