Answer:
21. 68
22. 76
Step-by-step explanation:
21. let the angle be x
x+36 =104(sum of two interior angle is equal to an exterior angle)
x = 104-36 =68
22. let the angle = y
104+y=180 (sum of angle on a straight line)
y = 180-104
y = 76
Trapezoid, Parallelogram,Rhombus, Kite, Arrowhead. etc...
If you want to solve for x, then the answer is x = 6*sqrt(2) where "sqrt" is shorthand for "square root"
Explanation:
All logs below are base 4
log(5) - log(18) = log(20) - 2*log(x)
log(5) - log(18) = log(20) - log(x^2)
log(5/18) = log(20/x^2)
5/18 = 20/x^2 ... raise both sides as exponents (base = 4); logs cancel
5x^2 = 18*20 ... cross multiply
5x^2 = 360
x^2 = 360/5 ... divide both sides by 5
x^2 = 72
x = sqrt(72) ... see note below.
x = sqrt(36*2)
x = sqrt(36)*sqrt(2)
x = 6*sqrt(2)
note: we only consider the positive solution for x because x cannot be negative. We cannot input negative x values into log(x). The domain of log(x) is x > 0. So we don't consider "plus/minus" for the square root.
Answer:
1.75 lt (1750 ml)
Step-by-step explanation:
Bottle size conversion
2.5 Lt = 2500 ml
Calculate how much is used to fill glasses
125*6=750 ml
Now you subtract the lemonade used from the bottle size and calc how much is left
2500-750=1750 ml or 1.75 Lt
Part A:
Given that in a sample of 400 registered voters, 204 were democrats, i.e. n = 400, <span>
![\hat{p}= \frac{204}{400} =0.51](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%20%5Cfrac%7B204%7D%7B400%7D%20%3D0.51)
</span>The 95% confidence interval for the proportion of registered democrats voters in the population is given by:
![95\%\ C.I.=\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ =0.51\pm1.96\sqrt{\frac{0.51(1-0.51)}{400}}=0.51\pm1.96\sqrt{\frac{0.2499}{400}} \\ \\ =0.51\pm1.96(0.025)=0.51\pm0.049=(0.51-0.049,\ 0.51+0.049) \\ \\ =\bold{(0.461,\ 0.559)}](https://tex.z-dn.net/?f=95%5C%25%5C%20C.I.%3D%5Chat%7Bp%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%20%5C%5C%20%20%5C%5C%20%3D0.51%5Cpm1.96%5Csqrt%7B%5Cfrac%7B0.51%281-0.51%29%7D%7B400%7D%7D%3D0.51%5Cpm1.96%5Csqrt%7B%5Cfrac%7B0.2499%7D%7B400%7D%7D%20%5C%5C%20%20%5C%5C%20%3D0.51%5Cpm1.96%280.025%29%3D0.51%5Cpm0.049%3D%280.51-0.049%2C%5C%200.51%2B0.049%29%20%5C%5C%20%20%5C%5C%20%3D%5Cbold%7B%280.461%2C%5C%200.559%29%7D)
Part B:
Given that t<span>here
are 169 million registered voters in the US, the interval for
the number of registered democrats in the population is given by
[0.461(169,000,000), 0.559(169,000,000)] = (77,909,000, 94,471,000)
</span>