Answer:
A
Step-by-step explanation:
It's hard to see but when x is 6, y is 4.5. Just plug that into each equation and see which one is correct.
X actually equals the cube root of 6
![{x}^{3} - 6 = 0 \\ {x}^{3} = 6 \\ x = \sqrt[3]{6}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B3%7D%20%20%20-%206%20%3D%200%20%5C%5C%20%20%7Bx%7D%5E%7B3%7D%20%20%3D%206%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B6%7D%20)
The hurdle and runner form a right triangle (see attached picture) such that
sin(30°) = <em>h</em> / (5 ft)
and
cos(30°) = <em>x</em> / (5 ft)
where <em>h</em> is the height of the hurdle and <em>x</em> is the horizontal distance from where the runner jumps to the hurdle. So
<em>h</em> = (5 ft) sin(30°) = 5/2 ft = 2.5 ft
<em>x</em> = (5 ft) cos(30°) = (5√3)/2 ft ≈ 4.33 ft
Answer:
95% confidence interval for the proportion of students supporting the fee increase is [0.767, 0.815]. Option C
Step-by-step explanation:
The confidence interval for a proportion is given as [p +/- margin of error (E)]
p is sample proportion = 870/1,100 = 0.791
n is sample size = 1,100
confidence level (C) = 95% = 0.95
significance level = 1 - C = 1 - 0.95 = 0.05 = 5%
critical value (z) at 5% significance level is 1.96.
E = z × sqrt[p(1-p) ÷ n] = 1.96 × sqrt[0.791(1-0.791) ÷ 1,100] = 1.96 × 0.0123 = 0.024
Lower limit of proportion = p - E = 0.791 - 0.024 = 0.767
Upper limit of proportion = p + E = 0.791 + 0.024 = 0.815
95% confidence interval for the proportion of students supporting the fee increase is between a lower limit of 0.767 and an upper limit of 0.815.
