In the second quadrant, both cos and tan are negative while only sin is positive.
To find tan, we will use the following property below:
![\large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7B%20%7Btan%7D%5E%7B2%7D%20%20%5Ctheta%20%20%3D%20%20%7Bsec%7D%5E%7B2%7D%20%20%20%5Ctheta%20-%201%7D)
Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2
![\large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%7Btan%7D%5E%7B2%7D%20%20%5Ctheta%20%3D%20%20%7B%28%20-%20%20%5Cfrac%7B3%7D%7B2%7D%29%20%7D%5E%7B2%7D%20%20-%201%7D%20%5C%5C%20%20%20%5Clarge%7B%20%7Btan%7D%5E%7B2%7D%20%20%5Ctheta%20%3D%20%20%20%5Cfrac%7B9%7D%7B4%7D%20%20-%201%7D%20%5C%5C%20%20%20%5Clarge%7B%20%7Btan%7D%5E%7B2%7D%20%20%5Ctheta%20%3D%20%5Cfrac%7B9%7D%7B4%7D%20%20%20-%20%20%5Cfrac%7B4%7D%7B4%7D%20%5Clongrightarrow%20%20%5Cfrac%7B5%7D%7B4%7D%20%20%7D%20%5C%5C%20%20%5Clarge%7Btan%20%5Ctheta%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B5%7D%20%7D%7B%20%5Csqrt%7B4%7D%20%7D%20%7D%20%5C%5C%20%20%5Clarge%20%5Cboxed%7Btan%20%5Ctheta%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%7D)
Since tan is negative in the second quadrant. Hence,
![\large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ccancel%7B%20tan%20%5Ctheta%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%7D%20%5Clongrightarrow%20%5Cboxed%7Btan%20%5Ctheta%20%3D%20%20-%20%20%5Cfrac%7B%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%7D%7D)
Answer
Answer:
3/9
Step-by-step explanation:
15/45
divide both sides by a factor of each number; I'll be using 5.
3/9
It didn't have to be 5, I could have used 3, but in that case It wouldn't have been it's simplest form and I would have to divide again by another factor.
Answer: 17.14 pages per day
Step-by-step explanation:
Answer:
Option a) Type I error would occur if we reject null hypothesis and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.
Step-by-step explanation:
We are given the following information in the question:
![H_{0}: \mu \leq \$3,200\\H_A: \mu > \$3,200](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu%20%5Cleq%20%5C%243%2C200%5C%5CH_A%3A%20%5Cmu%20%3E%20%5C%243%2C200)
where μ is the average amount of money in a savings account for a person aged 30 to 40.
Type I error:
- Type I error is also known as a “false positive” and is the error of rejecting a null hypothesis when it is actually true.
- In other words, this is the error of accepting an alternative hypothesis when the results can be attributed by null hypothesis.
- A type I error occurs during the hypothesis testing process when a null hypothesis is rejected, even though it is correct and should not be rejected.
Thus, in the above hypothesis type error will occur when we reject the null hypothesis even when it is true.
Option a) Type I error would occur if we reject null hypothesis and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.
Answer:
amaro
Step-by-step explanation:
amaro has double the amount of cards as mateo and mateo has more than agustin, therefore amaro has the most cards.