Answer:
none of them are equal, but B is parallel
Step-by-step explanation:
plug them all into desmos to see
Answer:
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
![\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
The information provided is:
![p=0.22\\n=276](https://tex.z-dn.net/?f=p%3D0.22%5C%5Cn%3D276)
As the sample size is large, i.e. <em>n</em> = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of
as follows:
![P(\hat p-p](https://tex.z-dn.net/?f=P%28%5Chat%20p-p%3C0.06%29%3DP%28%5Cfrac%7B%5Chat%20p-p%7D%7B%5Csigma_%7B%5Chat%20p%7D%7D%3C%5Cfrac%7B0.06%7D%7B%5Csqrt%7B%5Cfrac%7B0.22%281-0.22%29%7D%7B276%7D%7D%7D%29%5C%5C%5C%5C%3DP%28Z%3C2.41%29%5C%5C%5C%5C%3D0.99202%5C%5C%5C%5C%5Capprox%200.992)
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
Check the picture below, that's the suspension bridge with supporting cables and traffic on it.
![\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ 0.1}}x^2&{{ -7}}x&{{ +150}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7B%20vertex%20of%20a%20vertical%20parabola%2C%20using%20coefficients%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Blccclll%7D%0Ay%20%3D%20%26%7B%7B%200.1%7D%7Dx%5E2%26%7B%7B%20-7%7D%7Dx%26%7B%7B%20%2B150%7D%7D%5C%5C%0A%26%5Cuparrow%20%26%5Cuparrow%20%26%5Cuparrow%20%5C%5C%0A%26a%26b%26c%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cleft%28-%5Ccfrac%7B%7B%7B%20b%7D%7D%7D%7B2%7B%7B%20a%7D%7D%7D%5Cquad%20%2C%5Cquad%20%20%7B%7B%20c%7D%7D-%5Ccfrac%7B%7B%7B%20b%7D%7D%5E2%7D%7B4%7B%7B%20a%7D%7D%7D%5Cright%29)
Answer:
![x=\frac{90}{13} .](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B90%7D%7B13%7D%20.)
Step-by-step explanation:
![\frac{x}{2} +\frac{x}{3} =\frac{2x}{5} +3;](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%20%2B%5Cfrac%7Bx%7D%7B3%7D%20%3D%5Cfrac%7B2x%7D%7B5%7D%20%2B3%3B)
![30*(\frac{x}{2} +\frac{x}{3} )=30*(\frac{2x}{5} +3);](https://tex.z-dn.net/?f=30%2A%28%5Cfrac%7Bx%7D%7B2%7D%20%2B%5Cfrac%7Bx%7D%7B3%7D%20%29%3D30%2A%28%5Cfrac%7B2x%7D%7B5%7D%20%2B3%29%3B)
15x+10x=12x+90; ⇔ 13x=90;
![x=\frac{90}{13}.](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B90%7D%7B13%7D.)
Answer:
m∠ACB = 49.88°
Step-by-step explanation:
From the figure attached,
Measure of wire AC attached to the top 'C' of the building BC = 340 m
Horizontal distance between the base 'B' of the building and point A = 260 m
Angle of depression = ∠ACB
By applying sine rule in the given triangle,
sin(∠ACB) = ![\frac{\text{Opposite side}}{\text{Hypotenuse}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BOpposite%20side%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D)
= ![\frac{AB}{BC}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BBC%7D)
= ![\frac{260}{340}](https://tex.z-dn.net/?f=%5Cfrac%7B260%7D%7B340%7D)
m∠ACB = ![\text{sin}^{-1}(764706)](https://tex.z-dn.net/?f=%5Ctext%7Bsin%7D%5E%7B-1%7D%28764706%29)
= 49.88°