Answer:
h(x) = x - 2
Step-by-step explanation:
h(x) = x - 2
Answer:
We fail to reject the null hypothesis because -1.7678 does not fall inside the rejection region {z | z < -1.96 or z >1.96}
Step-by-step explanation:
We have that the machine will fill bottles according to a normally distributed process, let's say is a random variable that represents this process. We know that has a mean of 47 fluid ounces and a standard deviation of 0.4 fluid ounces. We have a sample of n = 50 bottles and the observed value .
We want to test
vs (two-tailed alternative)
We have n = 50 large enough, and the point estimator of the mean , which is normally distributed with the same mean than , i.e., , and with standard deviation given by . Therefore, our test statistic is
and
.
As we want a significance level of 0.05, we should find the values and , i.e., the 2.5th quantile and the 97.5th quantile for the standard normal distribution. These values are -1.96 and 1.96 respectively. The rejection region is given by {z | z < -1.96 or z >1.96}. We fail to reject the null hypothesis because -1.7678 does not fall inside the rejection region.
The two labeled angles are alternate interior angles, and as such, they are the same.
From this result you can build the equation
and solve it for x: subtract 13x from both sides to get
and add 2 to both sides to get
Check: if we plug the value we found we have
So the angles are actually the same, as requested.
You're going to have to set up a proportion. So it'd be 5:18=x:12 or if in fraction form, 5/18=x/12. Then you cross multiply. Where you get 5*12=18x. Then isolate the variable, (60/18) and you get 3.33 cm.