If you’re solving for x, it’s x= 17/2 - y
If you’re solving for y, it’s y= 17/2 - x
Answer:
B 41.4
Step-by-step explanation:
complete Pythagoras for general triangles :
c² = a² + b² - 2ab×cos(C)
with "c" being the side opposite of the angle C.
=>
8² = 10² + 12² - 2×10×12×cos(C)
64 = 244 - 240×cos(C)
240×cos(C) = 244 - 64 = 180
cos(C) = 180/240 = 18/24 = 3/4 = 0.75
C = 41.40962211... ≈ 41.4
Answer:
a) Sample correlation coefficient, r = 0.7411
bi) test statistic, t = 4.102
bii) P-value = 0.000736
Step-by-step explanation:
a) The formula for the sample correlation coefficient is given by the formula:
![r = \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} }} }](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7BS_%7Bxy%7D%20%7D%7B%5Csqrt%7BS_%7Bxx%7D%20S_%7Byy%7D%20%7D%7D%20%7D)
![S_{xx} = 2,648,130.357\\S_{yy} = 36.7376,\\S_{xy} = 7408.225](https://tex.z-dn.net/?f=S_%7Bxx%7D%20%3D%202%2C648%2C130.357%5C%5CS_%7Byy%7D%20%3D%2036.7376%2C%5C%5CS_%7Bxy%7D%20%3D%207408.225)
![r = \frac{7408.225}{\sqrt{2648130.357*36.7376} }](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B7408.225%7D%7B%5Csqrt%7B2648130.357%2A36.7376%7D%20%7D)
r = 0.7511
b)
i) formula for the test statistic is given by the formula:
![t = \frac{r\sqrt{n-1} }{\sqrt{1 - r^{2} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Br%5Csqrt%7Bn-1%7D%20%7D%7B%5Csqrt%7B1%20-%20r%5E%7B2%7D%20%7D%20%7D)
sample size, n = 4
![t = \frac{0.7511\sqrt{14-1} }{\sqrt{1 - 0.7511^{2} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B0.7511%5Csqrt%7B14-1%7D%20%7D%7B%5Csqrt%7B1%20-%200.7511%5E%7B2%7D%20%7D%20%7D)
t = 4.102
ii) Degree of freedom, df = n -2
df = 14 -2
df = 12
The P-value is calculate from the degree of freedom and the test statistic using excel
P-value =(=TDIST(t,df,tail))
P-value = (=TDIST(4.1,12,1)
P-value = 0.000736
Answer:
For 5/11 shade in the third bubble (0.45 repeating)