Answer:
![\frac{a}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B5%7D)
Step-by-step explanation:
That would be a divide by 5: ![\frac{a}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B5%7D)
Answer:
The smallest angle is 32 degrees
Step-by-step explanation:
The given parameters show that the triangle is a right angled triangle;
Let the two other angles be represented by x and y;
Since the angle between side 5 cm and side 8 cm is 90, we can represent any of this sides as the opposite and as the adjacent;
Scenario 1 (Calculating x)
Let opposite = 5 cm
Let adjacent = 8 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;
![Tan\ x = \frac{Opposite}{Adjacent}](https://tex.z-dn.net/?f=Tan%5C%20x%20%3D%20%5Cfrac%7BOpposite%7D%7BAdjacent%7D)
![Tan\ x = \frac{5}{8}](https://tex.z-dn.net/?f=Tan%5C%20x%20%3D%20%5Cfrac%7B5%7D%7B8%7D)
![Tan\ x = 0.625](https://tex.z-dn.net/?f=Tan%5C%20x%20%3D%200.625)
Take arctan of both sides
![x = tan^{-1}0.625](https://tex.z-dn.net/?f=x%20%3D%20tan%5E%7B-1%7D0.625)
![x = 32.0053832081](https://tex.z-dn.net/?f=x%20%3D%2032.0053832081)
(Approximated)
Scenario 2 (Calculating y)
Let opposite = 8 cm
Let adjacent = 5 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;
![Tan\ y = \frac{Opposite}{Adjacent}](https://tex.z-dn.net/?f=Tan%5C%20y%20%3D%20%5Cfrac%7BOpposite%7D%7BAdjacent%7D)
![Tan\ y = \frac{8}{5}](https://tex.z-dn.net/?f=Tan%5C%20y%20%3D%20%5Cfrac%7B8%7D%7B5%7D)
![Tan\ y = 1.6](https://tex.z-dn.net/?f=Tan%5C%20y%20%3D%201.6)
Take arctan of both sides
![y = tan^{-1}1.6](https://tex.z-dn.net/?f=y%20%3D%20tan%5E%7B-1%7D1.6)
![y = 57.9946167919](https://tex.z-dn.net/?f=y%20%3D%2057.9946167919)
(Approximated)
<em>By comparing the angles, the smallest angle is 32 degrees</em>
Answer:
B. 0.132
Step-by-step explanation:
For each time the dice is thrown, there are only two possible outcomes. Either it lands on a five, or it does not. The probability of a throw landing on a five is independent of other throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
Timothy creates a game in which the player rolls 4 dice.
This means that ![n = 4](https://tex.z-dn.net/?f=n%20%3D%204)
The dice can land in 6 numbers, one of which is 5.
This means that ![p = \frac{1}{6}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
What is the probability in this game of having exactly two dice or more land on a five?
![P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29)
In which
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 2) = C_{4,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{2} = 0.116](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B4%2C2%7D.%28%5Cfrac%7B1%7D%7B6%7D%29%5E%7B2%7D.%28%5Cfrac%7B5%7D%7B6%7D%29%5E%7B2%7D%20%3D%200.116)
![P(X = 3) = C_{4,2}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B4%2C2%7D.%28%5Cfrac%7B1%7D%7B6%7D%29%5E%7B3%7D.%28%5Cfrac%7B5%7D%7B6%7D%29%5E%7B1%7D%20%3D%200.015)
![P(X = 4) = C_{4,4}.(\frac{1}{6})^{4}.(\frac{5}{6})^{0} = 0.001](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B4%2C4%7D.%28%5Cfrac%7B1%7D%7B6%7D%29%5E%7B4%7D.%28%5Cfrac%7B5%7D%7B6%7D%29%5E%7B0%7D%20%3D%200.001)
![P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.116 + 0.015 + 0.001 = 0.132](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29%20%3D%200.116%20%2B%200.015%20%2B%200.001%20%3D%200.132)
So the correct answer is:
B. 0.132
Answer:
x^2 - 3
Step-by-step explanation:
they both contain the variable of x^2 and -3 when factored out it would be
3 and x + 2
<h2>Answer:</h2>
Cinderella is one of the most popular character in the Disney world or in barbies. A lot of young girls Do wants to copy her and would love to dress like Cinderella.
It would be probably shocking for me to see Cinderella with a barber. It would be an awkward moment for me to see her with a barer.
After her father unexpectedly dies, young Ella (Lily James) finds herself at the mercy of her cruel stepmother (Cate Blanchett) and stepsisters, who reduce her to scullery maid.