4(x-2/3) = -18
4x - 8/3 = -18
4x = -54/3 + 8/3
4x = -46/3
x = -46/3 * 1/4
x = -46/12
x = -23/2
2x = -23/2 * 2
2x = -46/2
2x = -23
Answer:
The 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean when the population standard deviation is not known is:
![CI=\bar x\pm t_{\alpha/2, (n-1)}\ \frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=CI%3D%5Cbar%20x%5Cpm%20t_%7B%5Calpha%2F2%2C%20%28n-1%29%7D%5C%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
The information provided is:
![n=25\\\bar x=23.9\ \text{feet}\\s=0.50\ \text{feet}\\t_{\alpha/2, (n-1)}=t_{0.05, 24}=1.71\\](https://tex.z-dn.net/?f=n%3D25%5C%5C%5Cbar%20x%3D23.9%5C%20%5Ctext%7Bfeet%7D%5C%5Cs%3D0.50%5C%20%5Ctext%7Bfeet%7D%5C%5Ct_%7B%5Calpha%2F2%2C%20%28n-1%29%7D%3Dt_%7B0.05%2C%2024%7D%3D1.71%5C%5C)
Compute the 90% confidence interval for population mean length of eastern rods as follows:
![CI=\bar x\pm t_{\alpha/2, (n-1)}\ \frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=CI%3D%5Cbar%20x%5Cpm%20t_%7B%5Calpha%2F2%2C%20%28n-1%29%7D%5C%20%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
![=23.9\pm 1.71\times\frac{0.50}{\sqrt{25}}\\\\=23.9\pm 0.171\\\\=(23.729, 24.071)\\\\\approx (23.73, 24.07)](https://tex.z-dn.net/?f=%3D23.9%5Cpm%201.71%5Ctimes%5Cfrac%7B0.50%7D%7B%5Csqrt%7B25%7D%7D%5C%5C%5C%5C%3D23.9%5Cpm%200.171%5C%5C%5C%5C%3D%2823.729%2C%2024.071%29%5C%5C%5C%5C%5Capprox%20%2823.73%2C%2024.07%29)
Thus, the 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).
Answer:
6x^2 +12x -1
Step-by-step explanation:
The perimeter is the sum of the two leg lengths and the base length:
P = 2(3x^2 +4x +2) +(4x -5)
= 6x^2 +8x +4 +4x -5
P = 6x^2 +12x -1
If she has 78 ounces of rice and has to split it into 12 bags, you would divide 78/12 which equals 6.5 ounces in each bag. The answer is already a decimal:)