How do you do this question?

Mathematics

1 answer:

oksian1 [2.3K]2 years ago

3 0

Answer:

(-2, 0)

Step-by-step explanation:

ƒ(x) <0 in the intervals where the function is below the x-axis.

The only interval where ƒ(x) < 0 is (-2.0, 0.0).

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The waking time of a student under common conditions is normally distributed with mean of 30 hours and a standard deviation of 5

Elina [12.6K]

Answer:

If the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 hours

Standard Deviation, σ = 5 hours

We are given that the distribution of waking time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.95

$P( X < x) = P( z < \displaystyle\frac{x - 30}{5})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 30}{5} = 1.645\\\\x = 38.225$

Thus, if the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

4 0

3 years ago

F(x) =?. Vertex is (2,-4) the other given point is (1,-2)

dalvyx [7]

Given the vertex, (2, -4) as the minimum point, and that it is an upward-facing parabola that passes point (1, -2):

We could substitute these values into the vertex form of the quadratic function,

f(x) = a(x - h)^2 + k

where:

(h,k) is the vertex

The axis of symmetry is the vertical line x = 2

The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.

The value of “h” determines how far left or right the parent function is translated.

The value of “k” determines how far up or down the parent function is translated.

Now that we’ve established these definitions, we can substitute the given values into the vertex form:

f(x) = a(x - 2)^2 - 4

In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:

f(x) = a(x - 2)^2 - 4

-2 = a(1 - 2)^2 - 4

-2 = a(-1)^2 - 4
-2 = a - 4

Add 4 to both sides to solve for “a”

-2 + 4 = a - 4 + 4
2 = a

Now that we have the value of a = 2, we can establish our quadratic function in vertex form:

f(x) = 2(x - 2)^2 - 4

I’m also including a screenshot of the graph of the function we came up with.

Please mark my answers as the Brainliest if you find my explanations helpful :)