Answer:
2√6 ft
Step-by-step explanation:
Tan Ф = opposite/ adjacent
tan 60 = t / 2√2 ft
tan 60 = √3
t = (tan 60 )(2√2 ft)
t = (√3)(2√2 ft) = 2√6 ft
Answer:
The 95 % confidence intervals (653.3 , 657.0) for the population mean test score
Step-by-step explanation:
Given school districts n = 420
The average score (Population mean) μ = 655.2
and standard deviation σ = 19.1
The 95% of confidence intervals μ± 1.96 σ/√n
The 95% of confidence intervals (μ- 1.96 σ/√n , μ+ 1.96 σ/√n)
The 95% of confidence intervals
( (
) ,
(655.2-1.826 , 655.2+1.826)
(653.3 , 657.0)
<u>Conclusion</u>:-
The 95 % confidence intervals (653.3 , 657.0) for the population mean test score
Answer:
V=πr^2(h/3)
Step-by-step explanation:
V=π6^2(8/3)
Answer:
<h2>
![\bold{\left(\dfrac{3}{13}\ ,\ \dfrac{4\sqrt{13}}{13}\right)\qquad\vee\qquad \left(\dfrac{3}{13}\ ,\ -\dfrac{4\sqrt{13}}{13}\right)}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cleft%28%5Cdfrac%7B3%7D%7B13%7D%5C%20%2C%5C%20%5Cdfrac%7B4%5Csqrt%7B13%7D%7D%7B13%7D%5Cright%29%5Cqquad%5Cvee%5Cqquad%20%5Cleft%28%5Cdfrac%7B3%7D%7B13%7D%5C%20%2C%5C%20-%5Cdfrac%7B4%5Csqrt%7B13%7D%7D%7B13%7D%5Cright%29%7D)
</h2>
Step-by-step explanation:
x - y² = -1 ⇒ - y² = - x - 1 ⇒ y² = x + 1 {x≥-1}
4x² + 9y² = 72
4x² + 9(x + 1)² = 72
4x² + 9(x² + 2x + 1) = 72
4x² + 9x² + 18x + 9 - 72 = 0
13x² + 18x - 63 = 0 ⇒ a = 13, b = 18, c = -63
![x=\dfrac{-18\pm\sqrt{18^2-4\cdot13\cdot(-63)}}{2\cdot13}=\dfrac{-18\pm\sqrt{324+252}}{26}=\dfrac{-18\pm\sqrt{576}}{26}\\\\x=\dfrac{-18+24}{26}=\dfrac3{13}\qquad\vee\qquad x=\dfrac{-18-24}{26}=-\dfrac{21}{13}\\\\ y^2= x + 1\quad\iff\quad x\ge-1\\\\y^2=\dfrac3{13}+1\\\\ y^2=\dfrac{16}{13}\\\\y=\dfrac{4}{\sqrt{13}}=\dfrac{4\sqrt{13}}{13}\qquad\vee\qquad y=-\dfrac{4\sqrt{13}}{13}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-18%5Cpm%5Csqrt%7B18%5E2-4%5Ccdot13%5Ccdot%28-63%29%7D%7D%7B2%5Ccdot13%7D%3D%5Cdfrac%7B-18%5Cpm%5Csqrt%7B324%2B252%7D%7D%7B26%7D%3D%5Cdfrac%7B-18%5Cpm%5Csqrt%7B576%7D%7D%7B26%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-18%2B24%7D%7B26%7D%3D%5Cdfrac3%7B13%7D%5Cqquad%5Cvee%5Cqquad%20x%3D%5Cdfrac%7B-18-24%7D%7B26%7D%3D-%5Cdfrac%7B21%7D%7B13%7D%5C%5C%5C%5C%20y%5E2%3D%20x%20%2B%201%5Cquad%5Ciff%5Cquad%20x%5Cge-1%5C%5C%5C%5Cy%5E2%3D%5Cdfrac3%7B13%7D%2B1%5C%5C%5C%5C%20y%5E2%3D%5Cdfrac%7B16%7D%7B13%7D%5C%5C%5C%5Cy%3D%5Cdfrac%7B4%7D%7B%5Csqrt%7B13%7D%7D%3D%5Cdfrac%7B4%5Csqrt%7B13%7D%7D%7B13%7D%5Cqquad%5Cvee%5Cqquad%20y%3D-%5Cdfrac%7B4%5Csqrt%7B13%7D%7D%7B13%7D)
The answer is 73.
365/19-14