Four books, one each on physics, chemistry, mathematics, and biology are about to be stacked on a shelf. If the books are stacke
2 answers:
Answer: The required probability is 25%.
Step-by-step explanation: Given that four books, one each on physics, chemistry, mathematics, and biology are about to be stacked on a shelf.
We are to find the probability that the mathematics book is on top if the books are stacked randomly.
Let, 'M' be the event that the topmost book is of mathematics.
Then, n(M)=1.
Let 'S' represents the sample space for the experiment.
Then, n(S) = 4.
Therefore, the probability that the mathematics book is on top is given by
Thus, the required probability is 25%.
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Given:
M is the midpoint of AB.
M(2,0) and A(-3, 3).
To find:
The coordinates of point B.
Solution:
Midpoint formula:
Let the coordinates of point B are (a,b). Then, using the midpoint formula, we get
On comparing both sides, we get
And,
Therefore, the coordinates of point B are (7,-3).
The value of x is 120°
Explanation:
It is given that ABC is a straight line.
Also, ∠CBE = 20° and ∠CAF = 40°
We need to determine the value of ∠DBE
Let ∠DBE = x
Since, ∠CAF and ∠ABD are alternate interior angles.
By the alternate interior angles theorem, "if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal".
Thus, ∠CAF and ∠ABD are equal.
Hence, ∠CAF = ∠ABD = 40°
Since, we know that, the angles in a straight line add up to 180°, we have,
∠ABD + ∠DBE + ∠CBE = 180°
Substituting the values, we get,
40° + x + 20° = 180°
Adding, we have,
60° + x = 180°
Subtracting both sides by 60, we have,
x = 120°
Thus, the value of x is 120°
