Answer:
122.667
Step-by-step explanation:
23/3=7.667
7.667*16=122.667
Question:
The measures of the angles of △ABC are given by the expressions in the table. Angle Measure
A (6x−1)°
B 20°
C (x + 14)°
What are the measures of angles A and C? Enter your answers in the boxes.
m∠A= º
m∠C= º
Answer:
The measures of the angles A and C are
and ![$\angle \mathrm{C}=35^{\circ}$](https://tex.z-dn.net/?f=%24%5Cangle%20%5Cmathrm%7BC%7D%3D35%5E%7B%5Ccirc%7D%24)
Explanation:
The measures of angles of ΔABC are
,
and ![\angle C=(x+14)^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20C%3D%28x%2B14%29%5E%7B%5Ccirc%7D)
By angle sum property, we have,
![\angle A+ \angle B+ \angle C = 180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%2B%20%5Cangle%20B%2B%20%5Cangle%20C%20%3D%20180%5E%7B%5Ccirc%7D)
![6x-1+20+x+14=180](https://tex.z-dn.net/?f=6x-1%2B20%2Bx%2B14%3D180)
![7x+33=180](https://tex.z-dn.net/?f=7x%2B33%3D180)
![7x=147](https://tex.z-dn.net/?f=7x%3D147)
![x=21](https://tex.z-dn.net/?f=x%3D21)
Thus, substituting
in
, we get,
![\angle A =(6x-1)^{\circ}=(6(21)-1)^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%286x-1%29%5E%7B%5Ccirc%7D%3D%286%2821%29-1%29%5E%7B%5Ccirc%7D)
![\angle A = 126-1](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%20126-1)
![\angle A=125^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%3D125%5E%7B%5Ccirc%7D)
Also, substituting
in
, we get,
![\angle C=(x+14)^{\circ}=(21+14)^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20C%3D%28x%2B14%29%5E%7B%5Ccirc%7D%3D%2821%2B14%29%5E%7B%5Ccirc%7D)
![$\angle \mathrm{C}=35^{\circ}$](https://tex.z-dn.net/?f=%24%5Cangle%20%5Cmathrm%7BC%7D%3D35%5E%7B%5Ccirc%7D%24)
Hence, the value of A and C are
and ![$\angle \mathrm{C}=35^{\circ}$](https://tex.z-dn.net/?f=%24%5Cangle%20%5Cmathrm%7BC%7D%3D35%5E%7B%5Ccirc%7D%24)
Answer: 0.893
Step-by-step explanation:
Given : Sample size of residential water bills: n=100
Number of residences had reduced their water consumption over that of the previous year = 80
Then sample proportion: ![\hat{p}=\dfrac{80}{100}=0.8](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B80%7D%7B100%7D%3D0.8)
Critical value for 98% confidence= ![z_{\alpha/2}=2.326](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D2.326)
The upper bound for confidence interval for population proportion :
![\hat{p}+ z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%2B%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
![=0.8+ (2.326)\sqrt{\dfrac{0.8(1-0.8)}{100}}\\\\=0.8+0.09304=0.89304\approx0.893](https://tex.z-dn.net/?f=%3D0.8%2B%20%282.326%29%5Csqrt%7B%5Cdfrac%7B0.8%281-0.8%29%7D%7B100%7D%7D%5C%5C%5C%5C%3D0.8%2B0.09304%3D0.89304%5Capprox0.893)
Hence, the 98% upper confidence bound for the proportion of residences that reduced their water consumption.=0.893
Answer:
Step-by-step explanation:
% = (sucesses / attempts) * 100
% = (47/65) * 100
% = 0.723 * 100
% = 72.3 %