This is an example of conditional probability because we are trying to find the probability of an event occurring GIVEN the occurrence of some other event. There is a formula for this (see image attached).
If we follow this formula, the numerator would be the probability of (A AND B) which in this case is "48% of the class passed BOTH exams." The denominator in the formula would be that "60% of the class passed ONLY THE SECOND exam."
Therefore, P(A and B) = 0.48, which is 48% expressed as a decimal and P(B)= 0.60, which is 60% expressed as a decimal. Then, you can figure out the answer by dividing.

7 0

3 years ago

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Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

4 0

3 years ago