Answer:
280 student tickets
520 adult tickets
Explanation:
I'm guessing this is the question you meant to ask:
Eight hundred tickets were sold for a movie production and the receipts for the performance wear $8600. The tickets for adults and students sold for $12.50 and $7.50, respectively. How many of each ticket were sold?
Answer: a) (0.755, 0.925)
Step-by-step explanation:
Let p be the population proportion of 8th graders are involved with some type of after school activity.
As per given , we have
n= 100
sample proportion: ![\hat{p}=0.84](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D0.84)
Significance level : ![\alpha= 1-0.98=0.02](https://tex.z-dn.net/?f=%5Calpha%3D%201-0.98%3D0.02)
Critical z-value :
(using z-value table)
Then, the 98% confidence interval that estimates the proportion of them that are involved in an after school activity will be :-
![\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
i.e. ![0.84\pm (2.33)\sqrt{\dfrac{0.84(1-0.84)}{100}}](https://tex.z-dn.net/?f=0.84%5Cpm%20%282.33%29%5Csqrt%7B%5Cdfrac%7B0.84%281-0.84%29%7D%7B100%7D%7D)
i.e. ![\approx0.84\pm 0.085](https://tex.z-dn.net/?f=%5Capprox0.84%5Cpm%200.085)
i.e. ![(0.84- 0.085,\ 0.84+ 0.085)=(0.755,\ 0.925)](https://tex.z-dn.net/?f=%280.84-%200.085%2C%5C%200.84%2B%200.085%29%3D%280.755%2C%5C%200.925%29)
Hence, the 98% confidence interval that estimates the proportion of them that are involved in an after school activity : a) (0.755, 0.925)
Hey there :)
- tan²x + sec²x = 1 or 1 + tan²x = sec²x
sin²x + cos²x = 1
Divide the whole by cos²x
![\frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%5E2x%7D%7Bcos%5E2x%7D%20%2B%20%5Cfrac%7Bcos%5E2x%7D%7Bcos%5E2x%7D%20%3D%20%5Cfrac%7B1%7D%7Bcos%5E2x%7D%20)
![\frac{sinx}{cosx} = tanx](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsinx%7D%7Bcosx%7D%20%3D%20tanx)
so
![\frac{sin^2x}{cos^2x} = tan^2x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%5E2x%7D%7Bcos%5E2x%7D%20%3D%20tan%5E2x)
and
![\frac{1}{cosx} = secx](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bcosx%7D%20%3D%20secx%20)
so
![\frac{1}{cos^2x} = sec^2x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bcos%5E2x%7D%20%3D%20sec%5E2x)
Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}
1 = - tan²x = sec²x or sec²x - tanx = 1
The equation which represents the amount of money, y, that Lilia will save in x weeks is;
<h3>Slope-intercept form of linear equations</h3>
The slope-intercept form of linear equations usually takes the form;
According to the information given;
Therefore, the y-intercept of the equation is; $10.
- And since she saves $5 each week;
The slope of the equation is; $5.
By substitution, the required equation is;
Read more on slope-intercept form of equations;
brainly.com/question/1884491