Answer:
80/81
Step-by-step explanation:
If a head is twice as likely to occur as a tail, then the probability of getting heads is 2/3 and the probability of getting tails is 1/3.
The probability of getting at least 1 head involves 4 scenarios:
1) 1 Head and 3 Tails
2) 2 Heads and 2 Tails
3) 3 Heads and 1 Tail
4) 4 Heads
Instead of calculate all these scenarios, you could calculate the opposite scenario: 4 Tails. The sum of all possible scenarios is 1, so:
P(at least one head) + P(no heads) = 1
Then, P(at least one head) = 1 - P(no heads)
The probability of 4 tails is:
P(no heads) = P(TTTT) = (1/3)(1/3)(1/3)(1/3)=1/81
Then, P(at least one head) = 1 - 1/81=80/81
Answer:
y=-2x + 8 which is the required equation
Which is option C
Step-by-step explanation:
Given:
Slope = m = -2
Given points are ( -2,12)
Which is
x = -2 and y =12
TO find:
Equation of line passing through these points = ?
Solution:
The point slope form of a line is
y = mx + c
Here we don't know the value of c
To find it
Putting y = 12 , x= -2 and y = -2 in the given equation
y = mx + c
Putting values it becomes
12 = (-2)*(-2) + c
12 = 4 + c
Subtracting 4 from both sides
12-4 = 4 -4 + c
8 = c
Now we have
m = -2 and c= 8
So equation of a line is given by
y = mx + c
Putting value of m and c
y = -2*x + 8
y=-2x + 8 which is the required equation
Answer:
Option 3) 
Step-by-step explanation:
In the given question we have to calculate the quotient after division.
To solve this question we will factorize (t²+7t+12) first and then we will will divide by this.
⇒ t²+7t+12 = ( t²+4t+3t+12)
⇒ t(t+4)+3(t+4)
⇒ (t+3)(t+4)
Now its a simpler form of divisor to get the answer.
We come back to the question
Or 
So the right answer is
The correct answer is a. 3x + 6
In order to find a compound function, you must use the first letter in the function (in this case f) and plug the second letter (g) in where you see x's.
f(x) = x + 2
f(g(x)) = (g(x)) + 2
f(g(x)) = (3x + 4) + 2
f(g(x)) = 3x + 6
Plug the x-values from the table into the given equation and solve for y.
y = 5 - x²
<u>First column</u>
replace x with -2
y = 5 - (-2)²
= 5 - (4)
= 1
(x, y) = (-2, 1)
<u>Second column</u>
replace x with -1
y = 5 - (-1)²
= 5 - (1)
= 4
(x, y) = (-1, 4)
<u>Third column</u>
replace x with 0
y = 5 - (0)²
= 5 - (0)
= 5
(x, y) = (0, 5)
<u>Fourth column</u>
replace x with 1
y = 5 - (1)²
= 5 - (1)
= 4
(x, y) = (1, 4)
<u>Fifth column</u>
replace x with 2
y = 5 - (2)²
= 5 - (4)
= 1
(x, y) = (2, 1)
