With Discrete Probability Distributions how do I find P(x) with no information other than (x)?

1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.

2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.

3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.

4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).

5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.

8 0

3 years ago

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HELP!!! Simplify cos^2 0 -1/ 4sin^2 0?

Shkiper50 [21]

We need to simpify the given expression. The given expression to us is ,

Given Expression :-

$\sf\implies \dfrac{ cos^2\theta -1}{4 \ sin^2\theta }$

Using Identity :-

$\sf\implies \red{ sin^2\theta + cos^2\theta = 1}$

So that :-

$\sf\implies - sin^2\theta = cos^2\theta -1$

We have :-

$\sf\implies \dfrac{ cos^2\theta -1}{4 \ sin^2\theta } \\\\\sf\implies\dfrac{ - sin^2\theta}{4sin^2\theta}=\boxed{\sf -\dfrac{1}{4}}$

Hence the required answer is -1/4. 

5 0

3 years ago

In 1950, Town A had a population of 200 people and the population increased by 200 people each year. In 1950, Town B had a popul

schepotkina [342]

Answer:

Town B will eventually overtake Town A

in 1990 Town B will have a larger population

Step-by-step explanation:

To work out how big town A will be in 1990 you need to do 200 + (200x40) because you add 40 years worth of increased population onto the starting population

To work out how big town B will be in 1990 you need to use the equation 200 X 1.1^40 because to work out plus 10 percent you need to do 1.1 and do it to the power of 40 for how many years

in 1990 town a will have a population of 8200 and town B will have a population of 9051.85

4 0

3 years ago