choosing ten students from a box that contains the names of the entire group
choosing five students each from seventh and eighth grade
choosing five female students and five male students
Answer:
Choosing ten students from a box that contains the names of the entire group
Step-by-step explanation:
If each and every unit has equal chance of being selected in a sample then it is called Random Sampling. Here choice of sample should be unbiased and independent.
Option (a) is incorrect because here selection of student is not independent as only those students are choosing who also participate in music class.
Option (b) is correct option as selection of students are independent and unbiased. Also here each student has equal chance of being selected in sample.
Option (c) can't be chosen as selection of student is done from particular cluster.
Option (d) is also incorrect as here we put condition of male and female students.
B) yes, by SAS criterion
C) yes, by SSA criterion
D) no, not possible to tell.
Answer:
ΔABE ~ ΔCDE by AA criterion .
Option (A) is correct .
Step-by-step explanation:
As given
∠BAE = 45° and ∠CED = 70°
Now in the ΔABE .
By apply angle sum property of a triangles .
∠ABE + ∠BEA + ∠BAE = 180 °
(As ∠BAE = 45° , ∠ABE = 65°)
65 + ∠BEA + 45 = 180 °
∠BEA = 180° - (65+45)°
∠BEA = 180° - 110°
∠BEA = 70°
As in ΔCED .
∠CDE + ∠DEC + ∠ECD = 180°
(As ∠CED = 70° , ∠CDE = 65°)
65 + 70+ ∠ECD = 180°
∠ECD = 180° - (65+70)°
∠ECD = 180° - 135°
∠ECD = 45°
Now in the ΔABE and ΔCDE .
(1) ∠BAE =∠ECD = 45°
(2) ∠BEA=∠CED = 70°
(3) ∠ABE = ∠CDE = 65°
Thus ΔABE ~ ΔCDE by AA criterion .
Option (A) is correct .
Answer:
12<x≤12.2
Step-by-step explanation:
To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.
The length of frame is x cm.
Length of frame must be longer than 12 cm.
Inequality, x>12
Length of frame not longer than 12.2 cm
In equality, x≤12.2
Now we make compound inequality of question
"Length of frame, x must be longer than 12 cm and not longer than 12.2 cm"
Inequality: 12<x≤12.2
Length of glass fit in the frame, 12<x≤12.2
Hence, The inequality 12<x≤12.2