The tuition would be $6143.94 next year
<h3>How to detemrine the tuition amount?</h3>
The given parameters are:
- Current amount = $5,742
- Rate of increment, r = 7%
The tuition next year is then calculated as:
Tuition = Current * (1 + Rate)
This gives
Tuition = $5,742 * (1 + 7%)
Evaluate
Tuition = $6143.94
Hence, the tuition would be $6143.94 next year
Read more about rates at:
brainly.com/question/25545513
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Answer:
B
Step-by-step explanation:
The sum of the angles of the triangle add up to 180 degrees.
x and y are equal to each other in this type of the triangle.
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
<em />
We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
Answer:
The probability of getting all heads is 
.
Step-by-step explanation:
For each time the coin is tossed, there are only two possible outcomes. Either it is heads, or it is not. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem, we have that:
A coin is tossed 8 times. This means that 
In each coin toss, heads or tails are equally as likely. So 
What is the probability of getting all heads?
This is 
![[tex]P(X = 8) = C_{8,8}*(\frac{1}{2})^{8}*(1 - \frac{1}{2})^{0}](https://tex.z-dn.net/?f=%5Btex%5DP%28X%20%3D%208%29%20%3D%20C_%7B8%2C8%7D%2A%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B8%7D%2A%281%20-%20%5Cfrac%7B1%7D%7B2%7D%29%5E%7B0%7D)
=
The probability of getting all heads is .
