A table titled Text messages sent has entries 7, 100, 1, 3, 17, 10, 15, 12, 7, 38. What is the mean of this sample, which consis
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<u>Answer:</u>
The probability of rolling a number less than 4 and spinning a consonant is .
<u>Step-by-step explanation:</u>
The probability of rolling a number less than 4 and spinning a consonant
= P(rolling a number less than 4) x P(spinning a consonant)
Step 1:Finding P(rolling a number less than 4)
The total number of outcomes = 6
The number of possible outcomes for getting a number less than 4 = 3
So the probability =
Step 2: Finding P(spinning a consonant)
Total number of outcomes = 26
The number of consonant = 21
Thus P(spinning a consonant) =
Step 3: The probability of rolling a number less than 4 and spinning a consonant
From (1) and (2)
=>
=>
=>
Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA⊥PA
OB⊥PB
In △OPA and △OPB
∠OPA=∠OPB (Using (1))
OA=OB (Radii of the same circle)
OP=OP (Common side)
Therefor △OPA≅△OPB (RHS congruency criterion)
PA=PB
(Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
The length of tangents drawn from any external point are equal.
So statement is correct
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA⊥PA
OB⊥PB
In △OPA and △OPB
∠OPA=∠OPB (Using (1))
OA=OB (Radii of the same circle)
OP=OP (Common side)
Therefor △OPA≅△OPB (RHS congruency criterion)
PA=PB
(Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
The length of tangents drawn from any external point are equal.
So statement is correct