The formula is in a quadratic formula shape: ![y = ax^2+bx+c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%2Bbx%2Bc)
The function is negative since the value 'a' the coefficient of x^2 is negative meaning that the quadratic function is facing downards. If you don't get this explanation, take a look at the diagram I uploaded.
That means the highest point of the graph is its vertex.
But we must find where the vertex is at or the 't' value.
't' value at which vertex is = ![-\frac{b}{2a} =-\frac{16}{2*(-16)} =\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7Bb%7D%7B2a%7D%20%3D-%5Cfrac%7B16%7D%7B2%2A%28-16%29%7D%20%3D%5Cfrac%7B1%7D%7B2%7D)
Now plug this 't' value into h(t) to find the maximum height, and we will get 36 feet.
Hope that helps!
Answer:
The sample size used to compute the 95% confidence interval is 1066.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population proportion is:
![CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D)
The 95% confidence interval for proportion of the bank's customers who also have accounts at one or more other banks is (0.45, 0.51).
To compute the sample size used we first need to compute the sample proportion value.
The value of sample proportion is:
![\hat p=\frac{Upper\ limit+Lower\ limit}{2}=\frac{0.45+0.51}{2}=0.48](https://tex.z-dn.net/?f=%5Chat%20p%3D%5Cfrac%7BUpper%5C%20limit%2BLower%5C%20limit%7D%7B2%7D%3D%5Cfrac%7B0.45%2B0.51%7D%7B2%7D%3D0.48)
Now compute the value of margin of error as follows:
![MOE=\frac{Upper\ limit-Lower\ limit}{2}=\frac{0.51-0.45}{2}=0.03](https://tex.z-dn.net/?f=MOE%3D%5Cfrac%7BUpper%5C%20limit-Lower%5C%20limit%7D%7B2%7D%3D%5Cfrac%7B0.51-0.45%7D%7B2%7D%3D0.03)
The critical value of <em>z</em> for 95% confidence level is:
![z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.05%2F2%7D%3Dz_%7B0.025%7D%3D1.96)
Compute the value of sample size as follows:
![MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.03=1.96\times \sqrt{\frac{0.48(1-0.48)}{n}}\\(\frac{0.03}{1.96})^{2}=\frac{0.48(1-0.48)}{n}\\n=1065.404\\n\approx1066](https://tex.z-dn.net/?f=MOE%3Dz_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D%5C%5C0.03%3D1.96%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.48%281-0.48%29%7D%7Bn%7D%7D%5C%5C%28%5Cfrac%7B0.03%7D%7B1.96%7D%29%5E%7B2%7D%3D%5Cfrac%7B0.48%281-0.48%29%7D%7Bn%7D%5C%5Cn%3D1065.404%5C%5Cn%5Capprox1066)
Thus, the sample size used to compute the 95% confidence interval is 1066.
Ok I’ll break this down so it’s easier to understand:
So you start of with $80
The first step is to find 20% off
An easy way to find 20% is to divide it by 5.
80/5= 16
And since it’s 20% OFF we subtract 16 from 80
80-16= 64
Next we need to do the coupon
It is $5 off so
64-5= 59
And finally the rebate which is $2
59-2= 57
Answer:
57