Are the events below independent or dependent? You roll a die and get a 5. You roll the die a second time and get another 5.

Respond to each of the following questions. Be sure to include and thoroughly describe each transformation.

sergeinik [125]

Answer:

31. 1) Vertical shift up 4 units.

2) Horizontal shift right 1 unit.

3) Vertically stretched by a factor of 3.

32. $g(x)=-(x+3)^2+7$

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

- If $f(x)+k$ , the function is shifted up "k" units.

- If $f(x)-k$ , the function is shifted down "k" units.

- If $f(x+k)$ , the function is shifted left "k" units.

- If $f(x-k)$ , the function is shifted right "k" units.

- If $-f(x)$ , the function is reflected over the x-axis.

- If $bf(x)$ and $b>1$ , the function is stretched vertically by a factor of "b".

31. Given the function $f(x)=x^{2}$ and the function $g(x) = 3(x - 1)^2 + 4$ , we can notice that the transformations from the graph of f(x) to the graph of g(x) are:

1) $f(x)+k$

2) $f(x-k)$

3) $bf(x)$ , being $b>1$

Therefore, we can conclude that the transformations necessary to transform the graph of f(x) to the graph g(x) are:

1) Vertical shift up 4 units.

2) Horizontal shift right 1 unit.

3) Vertical stretch by a factor of 3.

32. Knowing the parent function:

$f(x)=x^{2}$

And given the transformations:

1) Reflection over the x-axis.

2) Horizontal shift left 3 units.

3) Vertical shift up 7 units.

We can define that the function g(x) is:

$g(x)=-(x+3)^2+7$

7 0

3 years ago

How many diagonals can be constructed from one vertex of an n-gon? State your answer in terms of n and, of course, justify your

natulia [17]

Answer:

$The \ total \ number \ of \ distinct \ diagonals \ in \ a \ polygon \ with \ n \ sides= \dfrac{n \times (n - 3)}{2}$

Step-by-step explanation:

A diagonal is defined in geometry as a line connecting to two non adjacent vertices.

Therefore, the minimum number of sides a polygon must have in order to have a diagonal n - 3 sides as the 3 comes from the originating vertex and the other two adjacent vertices

Given that the polygon has n sides, the number of diagonals that can be drawn from each of those n sides gives the total number of diagonals as follows;

Total possible diagonals = n × (n - 3)

However, half of the diagonals drawn within the polygon are the same diagonals drawn in reverse. Therefore, the total number of distinct diagonals that can be drawn in a polygon is given as follows;

$The \ total \ number \ of \ distinct \ diagonals \ in \ a \ polygon \ with \ n \ sides= \dfrac{n \times (n - 3)}{2}$

6 0

3 years ago

Ryan buys a bag of cookies that contains 8 chocolate chip cookies, 4 peanut butter cookies, 4 sugar

Pavlova-9 [17]

Answer:

4/69 to be exact. Slightly greater than 1/18

Step-by-step explanation:

The chance of selecting the PB cookie on the first try is 4 out of 24 or 1 out of 6. There are now 23 coolies left; 8 are chocolate, so 8/23 chance. (Slightly greater than 1/3) The chance of both events happening is the product if the individual events' chances. So multiply 1/6 times 8/23 to get 8/138. That reduces to 4/ 69. If he had put that first cookie back, the multiplication would have been 1/6×1/3. A lot easier.

4 0

2 years ago

Claire has a small personal business making scented candles. Her startup costs are $200. Her cost to make each candle is $1.50.

Svetllana [295]

Step-by-step explanation:

If we assume A = the amount of candles she produces and sells then we can assume this equation.

(4.00×A) - ((A×1.50)+200)

The first part is calculating how much Claire makes at first with her candles being sold while taking account of the amoubt of candles and the cost for making one.

The second part is for the Amount of candles and the cost of starting and the cost of each candle and that amount is the amount Claire will lose and subtracted by the first amount.

5 0

3 years ago

How do i solve this question.

algol [13]

Try a protractor to solve it

8 0

2 years ago