To find the hypotenuse of a right triangle, you must use a^2 + b^2 = c^2
* keep in mind the hypotenuse MUST be larger than the legs.
The Pythagorean Theorem comes from making 2 squares from the lengths of each leg (that is why it is a^2 and b^2). The hypotenuse must be equal to the area of the two squares created.
Answer:q=9
Step-by-step explanation:
Answer:
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the z-score that has a p-value of
.
427 had paid for coaching courses and the remaining 2733 had not.
This means that ![n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351](https://tex.z-dn.net/?f=n%20%3D%20427%20%2B%202733%20%3D%203160%2C%20%5Cpi%20%3D%20%5Cfrac%7B427%7D%7B3160%7D%20%3D%200.1351)
95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.1351%20-%201.96%5Csqrt%7B%5Cfrac%7B0.1351%2A0.8649%7D%7B3160%7D%7D%20%3D%200.1232)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.1351%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.1351%2A0.8649%7D%7B3160%7D%7D%20%3D%200.147)
The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).
Marie has a small copy of Rene margrittes famous painting. The Schoolmasters. Her copy has dimensions of 2 inches by 1.5 inches. The scale of her copy is 1 inch:40 cm What is the dimensions of the original painting?
Every 1 inch on her copy is the same as 40 cm on the original.
You just have to multiply by 40 and convert to centimetres.
2 x 40 = 80
1.5 x 40 = 60
So the original painting is:
80cm by 60cm
Answer: 2 1/4
Step-by-step explanation: