Question:
Prove that:
Answer:
Proved
Step-by-step explanation:
Given
Required
Prove
Subtract tan(10) from both sides
Factorize the right hand size
Rewrite as:
Divide both sides by
In trigonometry:
So:
can be expressed as:
gives
In trigonometry:
So:
Because RHS = LHS
Then:
has been proven
Answer:
<em>Option A; the tournament did begin with 128 teams</em>
Step-by-step explanation:
We can see that this equation is represented by compound interest, in other words an exponential function, either being exponential growth or exponential decay;
f ( x ) = a + ( b )^x, where a ⇒ start value, b ⇒ constant, x ⇒ ( almost always considered ) time, but in this case rounds
Option A; The equation is given to be t ( x ) = 128 * ( 1/2 )^x. Given by the above, 128 should represent the start value, hinting that the tournament <em>did indeed begin with 128 teams</em>
Option B; As the rounds increase the number of teams approach 128. Now mind you 128 is the start value, not the end value, which would mean that <em>this statement is false</em>
Option C; The tournament began with 1/2 teams. Theoretically that would not be possible, but besides that the tournament began with 128 teams, only differed by 1/2 times as much every round. <em>This statement is thus false</em>
Option D; This situation actually represents exponential decay. If each round the number of teams differed by 1/2 times as much, the number of teams remaining is less than before, and thus this models exponential decay, not growth<em> ( statement is false )</em>
<em>Answer : Option A; the tournament did begin with 128 teams</em>
Its the first one. I typed them all in my graphing calculator to check
Answer:
Vertically opposite angles are equal.
Therefore,
<h3><u>x=27</u> is the right answer.</h3>
Answer:
Dependent event
Step-by-step explanation:
Given
Solving (a): Are the events dependent?
Yes, they are.
When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.
So, the probability of selecting a 2nd candy is dependent on the first candy selected.
Solving (b): P(Red = 2)
This is calculated as:
The first selection has the following probability:
The second selection has the following probability:
So, we have:
Reduce fraction
Multiply