Answer:
The circle's diameter is
Step-by-step explanation:
we know that
The circumference of a circle is equal to
where
D is the diameter of the circle
In this problem we have
substitute the values and solve for D
How do you find the sine and tangent of an angle if you are given the cosine?
1 answer:
Answer:
- sin = √(1 -cos²)
- tan = (√(1 -cos²))/cos
Step-by-step explanation:
_____
If you draw a triangle with a hypotenuse of 1 and an "adjacent" leg of "cos", then using the Pythagorean theorem, you can see that the "opposite" leg will be √(1-cos²) and the tangent will be (√(1-cos²))/cos. Whether or not you're allowed to draw such a triangle on paper, you can certainly do it in your mind.
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Answer:
c) Is not a property (hence (d) is not either)
Step-by-step explanation:
Remember that the chi square distribution with k degrees of freedom has this formula
Where N₁ , N₂m .... are independent random variables with standard normal distribution. Since it is a sum of squares, then the chi square distribution cant take negative values, thus (c) is not true as property. Therefore, (d) cant be true either.
Since the chi square is a sum of squares of a symmetrical random variable, it is skewed to the right (values with big absolute value, either positive or negative, will represent a big weight for the graph that is not compensated with values near 0). This shows that (a) is true
The more degrees of freedom the chi square has, the less skewed to the right it is, up to the point of being almost symmetrical for high values of k. In fact, the Central Limit Theorem states that a chi sqare with n degrees of freedom, with n big, will have a distribution approximate to a Normal distribution, therefore, it is not very skewed for high values of n. As a conclusion, the shape of the distribution changes when the degrees of freedom increase, because the distribution is more symmetrical the higher the degrees of freedom are. Thus, (b) is true.