Suppose that g(x) = x2 - 5. Which statement best compares the graph of g(x) with the graph of f(x) = x??
A. The graph of g(x) is shifted 5 units right.
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B. The graph of g(x) is shifted 5 units up.
C. The graph of g(x) is shifted 5 units down.
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D. The graph of g(x) is shifted 5 units left.

Step-by-step explanation:

The vertex, or work, form of a parabola is

, where h and k are the coordinates of the vertex. If the parabola has the equation

, the vertex is sitting at (2, 5)---> (h, k). h = 2, k = 5. If we have nothing in a set of parenthesis with the x, there is no side to side movement. Our parabola does not have any parenthesis around the x, so no side to side movement. But it does have a -5. That means that the parabola has moved DOWN 5 units from its starting position of (0, 0). -k means the parabola moves down; +k means the parabola moves up.

So our parabola has shifted 5 units down, choice C.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: