Answer:
Option (2)
Step-by-step explanation:
Given:
AC is an angle bisector of ∠DAB and ∠DAB
m∠BCA ≅ m∠DCA
m∠BAC ≅ m∠DAC
To Prove:
ΔABC ≅ ΔADC
Solution:
Statements Reasons
1). m∠BCA ≅ m∠DCA 1). Given
2). m∠BAC ≅ m∠DAC 2). Given
3). AC ≅ AC 3). Reflexive property
4). ΔABC ≅ ΔADC 4). ASA property of congruence
Therefore, Option (2) will be the correct option.
Answer:
Given Rate of interest is r=8%=0.08
Principal Amount is A=5,000
Time is t years
Interest is compounded yearly twice ⟹n=2
Amount =P(1+
n
r
)
nt
=5000×(1+
2
0.08
)
2t
=5,408
(1.0816)
t
=
5000
5408
⟹t=1
First find the numbers that are divisible by 3.
3, 6, 9, 12, 15, 18, 21, 24
There are 8 numbers divisible by 3 so there are 16 that are not divisible by 3.
P(not div by 3) = 16/24 = 2/3
Answer:
Step-by-step explanation:
A box plot is the diagrammatic representation of the five number summary. It includes 5 items:
The minimum.
Q1 = the first quartile or the 25% mark.
The median.
Q3 = the third quartile or the 75% mark.
The maximum.
Rearranging the data in ascending order, it becomes
169, 163, 153, 166, 149, 148, 146, 145, 152, 163
145, 146, 148, 149, 152, 153, 163, 163, 166, 169
Minimum = 145
Maximum = 169
Median = (152 + 153)/2 = 152.5
The median divides the data into two equal halves. The middle of the lower halve is Q1 while the middle of the upper halve is Q3
Q1 = 148
Q3 = 163
The diagram of the box plot is shown in the attached photo