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frosja888 [35]
3 years ago
15

A magician is performing for an audience of 32 men and 20 women. He selects a volunteer from the audience, has the volunteer sta

nd behind a curtain, and then selects another volunteer. What is the probability that both volunteers are men? (shown as a percent)
Mathematics
1 answer:
statuscvo [17]3 years ago
6 0
32+20=52 so there are 52 people in all. 
32/52  people are men.
we now have to subtract 1 from this fraction like so 32-1/52-1 since the magician took away 1 man from the audience (therefore reducing the amount of men as well as the audience as a whole) resulting in 31/51
we multiply 32/52 with 31/51 to get 248/663. simply turn this fraction into a percent by multiplying the quotient by 100 and rounding it to the nearest tenth to get 37.4%
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2. 6.25 feet

3. 1 feet

4. 6 feet

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1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

       $=0-0+6$

       $=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

   It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴  x coordinate = $\frac{-(-7)}{2 \times 1} $

                         $\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

         = -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get   $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts  are the points where the parabola crosses the x-axis, which is the height $h(x)=0$. The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$.

Thus Kendra dives out of the water surface at 6 feet from the board.

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2 years ago
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