#1.
Question: <span><span><span><span>2x^2 </span>− 3x</span> − 35</span> = 0</span>
<span><span><span>Step 1: Factor left side of equation): (<span>2x + 7</span>) </span><span>(x − 5) </span></span>= 0</span>
Step 2: Set factors equal to 0.): <span><span><span>2x + 7 </span>=<span><span> 0 or x </span>− 5</span></span> = 0</span>
ANSWER: <span><span>x =<span><span><span> −7/2</span> or </span>x </span></span>= 5</span>
_____________________________________________________
#2.
Question: 56z^2 + 2 = 22z
<span>Step 1: Subtract 22z from both sides.):
</span><span><span><span><span>56<span>z^2 </span></span>+ 2</span> −<span>22z</span></span> = <span><span>22z </span>−<span> 22z
</span></span></span><span><span><span><span>56<span>z^2 </span></span>−<span> 22z </span></span>+ 2 </span>= 0</span>
<span>Step 2: Factor left side of equation.):
</span>
<span><span><span>2<span>(<span><span>7z </span>− 1</span>)</span></span><span>(<span><span>4z </span>− 1</span>)</span></span> = 0
</span><span>Step 3: Set factors equal to 0.):
</span>
<span><span><span><span>7z </span>− 1 </span>=<span><span><span> 0 or </span><span>4z</span></span> − 1</span></span> = 0
ANSWER: </span><span><span>z =<span><span><span> 1/7</span> or </span>z </span></span>=<span> 1/4</span></span>
Given the following function:
Use the form a·cot(bx - c) to find the variables used to find the amplitude, period, phase shift and vertical shift.
We get,
a = 1
b = 1
c = -π/6
d = 0
Since the graph of the Cotangent function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
For the Period:
Therefore, the Period is π.
For the Phase Shift:
Therefore, Phase Shift is -π/6 → π/6 (To the left).
For the Vertical Shift:
Vertical Shift = 0
Plotting the function will be:
(a) <em>X</em> has a probabiliity density of
If the lower quartile is 5 and the upper quartile is 9, then
Computing the integrals gives the following system of equations:
5 - <em>a</em> = 0.25 (<em>b</em> - <em>a</em>) ==> 0.75<em>a</em> + 0.25<em>b</em> = 5 ==> 3<em>a</em> + <em>b</em> = 20
<em>b</em> - 9 = 0.25 (<em>b</em> - <em>a</em>) ==> 0.25<em>a</em> + 0.75<em>b</em> = 9 ==> <em>a</em> + 3<em>b</em> = 36
Eliminate <em>a</em> :
(3<em>a</em> + <em>b</em>) - 3 (<em>a</em> + 3<em>b</em>) = 20 - 3×36
-8<em>b</em> = -88
==> <em>b</em> = 11 ==> <em>a</em> = 3
and so P(<em>X</em> = <em>x</em>) = 1/(11 - 3) = 1/8 for all 3 < <em>x</em> < 11.
(b)
(c) The distribution function is then
Answer: 35
Step-by-step explanation:
3x + 15 = 2x + 50
3x = 2x + 35
x = 35