Answer:
6
Step-by-step explanation:
![nth \: term \: of \: geometric \: \\ sequence \: is \: given \: as : \\ a_n = a {r}^{n - 1} \\ (a = ?, \: \: r = 2)\\ \\ a_4 =48......(given) \\ \\ \therefore \: a {(2)}^{4 - 1} = 48 \\ \\ \therefore \: a {(2)}^{3} = 48\\ \\ \therefore \: 8a = 48 \\ \\ \therefore \: a = \frac{48}{8} \\ \\ \therefore \:a = 6](https://tex.z-dn.net/?f=nth%20%5C%3A%20term%20%5C%3A%20of%20%5C%3A%20geometric%20%5C%3A%20%20%5C%5C%20sequence%20%5C%3A%20is%20%5C%3A%20given%20%5C%3A%20as%20%3A%20%20%5C%5C%20a_n%20%3D%20a%20%7Br%7D%5E%7Bn%20-%201%7D%20%20%5C%5C%20%28a%20%3D%20%3F%2C%20%5C%3A%20%20%5C%3A%20r%20%3D%202%29%5C%5C%20%20%5C%5C%20a_4%20%3D48......%28given%29%20%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20a%20%7B%282%29%7D%5E%7B4%20-%201%7D%20%20%3D%2048%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20a%20%7B%282%29%7D%5E%7B3%7D%20%20%3D%2048%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%208a%20%20%20%3D%2048%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20a%20%20%20%3D%20%20%5Cfrac%7B48%7D%7B8%7D%20%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3Aa%20%3D%206)
You can use the Pythagoras theorem for this since a right triangle is formed.
![c^2 = a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2)
C = 12
A = 4
B = x
Input values:
![12^2 = 4^2 + x^2](https://tex.z-dn.net/?f=12%5E2%20%3D%204%5E2%20%2B%20x%5E2)
![144 = 16 + x^2](https://tex.z-dn.net/?f=144%20%3D%2016%20%2B%20x%5E2)
![128 = x^2](https://tex.z-dn.net/?f=128%20%3D%20x%5E2)
![x = \sqrt{128}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B128%7D)
![x = 11.3137...](https://tex.z-dn.net/?f=x%20%3D%2011.3137...)
So, about 11ft.
C. Is the answer I believe. At least in Canada. That’s why we have the senate here. To listen to the majority while still protecting minority rights
Answer:
p = 0.07
p-hat = 0.035
p0 = 0.07
p-value = 0.003
Step-by-step explanation:
p = population parameter, in this case, the rate of infestations across all trees in the forest
p-hat = test statistic, in this case, the rate of infestations found in the sample of trees, i.e. those in Doug's backyard
p0 = the null hypothesis, in this case, the rate of infestations within the forest is correctly evaluated at 0.07 or 7%
p-value = the likelihood any difference between p and p-hat is down to chance
In this case 0.003 as the p-value means there is only 0.3% probability of our statistic value of 0.035 being down to variability and chance meaning it is 99.7% likely that there is some reason behind this difference;
We would accept the alternative hypothesis which says the current parameter value, 0.07, is in fact incorrect (either too high or too low, in this case, likely too high).