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<span>4. Simplify the expression.
sine of x to the second power minus one divided by cosine of negative x</span>
</span>sin2x+cos2x=1</span> <span>1−sin2x=cos2x<span>
</span>cos2(x)/(sin(x)−csc(x))</span> <span>csc(x)=1/sin(x)</span> <span>cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))</span> <span>sin2(x)− 1=-cos2(x)</span> <span>cos2(x)/(( -cos2(x))/sin(x))
=-sin(x)</span>
<span>the answer is the letter a) -sin x
</span><span>5. Find all solutions in the interval [0, 2π). (6 points)
sin2x + sin x = 0
</span> using a graphical tool
the solutions x1=0 x2=pi <span>x3=3pi/2
the answer is the letter </span><span>D) x = 0, π, three pi divided by two</span>
90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the giver confidence interval [ 0.3026, 0.3348 ].
Here, we have given:
Number of adults (n) = 2272
Number of adults who believe in UFO (x) = 724
Sample proportion (p) = x/n
p = 724 / 2272
p = 0.3187
now, let q = 1 - p
q = 1 - 0.3187
q = 0.6813
Confidence level → 90%
The 90% confidence interval for population proportion is
where 1.645 is Zac value at 90% confidence level.
= 0.3187 - 0.0161 = 0.3026
= 0.3187 + 0.0161 = 0.3348
90% confidence interval for the population proportion is
[ 0.3026, 0.3348 ]
Hence, With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the giver confidence interval [ 0.3026, 0.3348 ]
Learn more about " Population Proportion " from here: brainly.com/question/15087042
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