(3,3p) and (4,p²+1) has gradient -1 find p
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Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
Direction: Opens Up
Vertex: <span>(−<span>5/8</span>,−<span>41/16</span>)</span>
Focus: <span>(−<span>5/8</span>,−<span>5/2</span>)</span>
Axis of Symmetry: <span>x=−<span>5/8</span></span>
Directrix: <span>y=−<span>21/8</span></span><span><span> x. y
</span><span><span>−3. </span>20
</span><span><span>−2. </span>5
</span><span><span>−<span>5/8. </span></span><span>−<span>41/16
</span></span></span><span> 0. <span>−1
</span></span><span>1. <span>8
</span></span></span>
The numerical values of the mean and standard deviation are 4 and 1.55, respectively
<h3>The numerical value of the probability that x = 6. </h3>The given parameters are:
n = 10
π = 0.4
The probability is then calculated as:
So, we have:
Apply the combination formula
So, we have:
Evaluate
P(6) = 0.1115
Hence, the numerical value of the probability that x = 6 is 0.1115
<h3>The numerical values of the mean and standard deviation </h3>The mean value is:
This gives
The standard deviation value is:
This gives
Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively
Read more about mean and standard deviation at:
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