Answer:
Last Option
Step-by-step explanation:
We have a triangle and we know its three sides.
We want to find one of your anguos. Then we use the cosine theorem.
![c ^ 2 = a ^ 2 + b ^ 2 -2abcosx](https://tex.z-dn.net/?f=c%20%5E%202%20%3D%20a%20%5E%202%20%2B%20b%20%5E%202%20-2abcosx)
Where
![c = 14\\a = 11\\b = 19](https://tex.z-dn.net/?f=c%20%3D%2014%5C%5Ca%20%3D%2011%5C%5Cb%20%3D%2019)
Now we solve for x from the equation
![c ^ 2 = a ^ 2 + b ^ 2 -2abcosx\\\\\\14^2 = 11^2 + 19^2 -2(11)(19)cosx\\\\14^2 -11^2 -19^2 = 2(11)(19)cosx\\\\-286=2(11)(19)cosx\\\\cosx = \frac{-286}{2(11)(19)}\\\\x = arcos(\frac{-286}{2(11)(19)})\\\\x = 46.8\°](https://tex.z-dn.net/?f=c%20%5E%202%20%3D%20a%20%5E%202%20%2B%20b%20%5E%202%20-2abcosx%5C%5C%5C%5C%5C%5C14%5E2%20%3D%2011%5E2%20%2B%2019%5E2%20-2%2811%29%2819%29cosx%5C%5C%5C%5C14%5E2%20-11%5E2%20-19%5E2%20%3D%202%2811%29%2819%29cosx%5C%5C%5C%5C-286%3D2%2811%29%2819%29cosx%5C%5C%5C%5Ccosx%20%3D%20%5Cfrac%7B-286%7D%7B2%2811%29%2819%29%7D%5C%5C%5C%5Cx%20%3D%20arcos%28%5Cfrac%7B-286%7D%7B2%2811%29%2819%29%7D%29%5C%5C%5C%5Cx%20%3D%2046.8%5C%C2%B0)
Answer:
b = 17.55
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + b^2 = 18^2
16 + b^2 = 324
<u>-16 -16</u>
b^2 = 308
square root them
<u>b = 17.55</u>
let me know if it is correct!
Answer:
Yes. Fertilization increases grape yields by more than 5 pounds.
Step-by-step explanation:
Let f-fertilized and o-old(unfertilized)
#First, we use our data to calculate the standard error:
![SE(\bar y_f-\bar y_o)=\sqrt{\frac{s_f^2}{n_f}+\frac{s_o^2}{n_o}}\\\\=\sqrt{\frac{3.7^2}{44}+\frac{3.4^2}{47}}\\\\=0.7464](https://tex.z-dn.net/?f=SE%28%5Cbar%20y_f-%5Cbar%20y_o%29%3D%5Csqrt%7B%5Cfrac%7Bs_f%5E2%7D%7Bn_f%7D%2B%5Cfrac%7Bs_o%5E2%7D%7Bn_o%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%5Cfrac%7B3.7%5E2%7D%7B44%7D%2B%5Cfrac%7B3.4%5E2%7D%7B47%7D%7D%5C%5C%5C%5C%3D0.7464)
#State both null and alternative hypothesis:
![H_o:\mu_f-\mu_o=0\\\\H_A=\mu_f-\mu_o>0](https://tex.z-dn.net/?f=H_o%3A%5Cmu_f-%5Cmu_o%3D0%5C%5C%5C%5CH_A%3D%5Cmu_f-%5Cmu_o%3E0)
#We determine our degrees of freedom as 87.02(using R), we now compute the t-value as:
![t=\frac{\bar y_f-\bar y_o}{\sqrt{\frac{s_f^2}{n_f}+\frac{s_o^2}{n_o}}}\\\\\\t=\frac{53.4-52.1}{\sqrt{\frac{s_f^2}{n_f}+\frac{s_o^2}{n_o}}}\\\\\\t=\frac{1.3}{0.7464}\\\\t=1.7417\\\\P=P(t_{87.0>1.7417}=1-0.9575=0.0.0425](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Cbar%20y_f-%5Cbar%20y_o%7D%7B%5Csqrt%7B%5Cfrac%7Bs_f%5E2%7D%7Bn_f%7D%2B%5Cfrac%7Bs_o%5E2%7D%7Bn_o%7D%7D%7D%5C%5C%5C%5C%5C%5Ct%3D%5Cfrac%7B53.4-52.1%7D%7B%5Csqrt%7B%5Cfrac%7Bs_f%5E2%7D%7Bn_f%7D%2B%5Cfrac%7Bs_o%5E2%7D%7Bn_o%7D%7D%7D%5C%5C%5C%5C%5C%5Ct%3D%5Cfrac%7B1.3%7D%7B0.7464%7D%5C%5C%5C%5Ct%3D1.7417%5C%5C%5C%5CP%3DP%28t_%7B87.0%3E1.7417%7D%3D1-0.9575%3D0.0.0425)
Since, the p-value is low, we Reject the null hypothesis. The is enough evidence suggesting that grape yields increase by more than 5 pounds than mean yields of unfertilized grapes.
Answer: 2. It is likely that a confounding variable could be a contributing explanation for the difference between these two groups.
3. This is an observational study, not an experiment.
Step-by-step explanation:
Based on the information given, the statement that's true include:
• It is likely that a confounding variable could be a contributing explanation for the difference between these two groups.
• This is an observational study, not an experiment.
It is an observational study as the researcher observed just observed the scenarios without him trying to change the people that are being exposed to it or controlling it.
Therefore, the correct options are II and III only.
The picture is really blurry