33 ft. there’s like some leftover inches but idk if you need that. hopefully that works
To solve Az + 17 = -4z - b for z, we begin by combining like terms. We get:
Az + 4z = -b - 17, or z(A+4) = -(b+17).
Dividing both sides by (A+4), we get:
-(b+17)
z = --------------
A+4
Answer:
(i) The student who weighed the rock 20 times.
Step-by-step explanation:
The margin of error of a confidence interval is:
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which z is related to the confidence level,
is the standard deviation of the population and n is the size of the sample.
From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.
In this question:
A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.
So the correct answer is:
(i) The student who weighed the rock 20 times.
434/7 = 62/1
Hope this helped in any way :)
Try this solution:
1. Given: α:4x-y+2z=-4 and β:x+y-4z=3.
if vector n₁⊥α and n₂⊥β, then required cosine is:
![cos \gamma =|\frac{n_1*n_2}{|n_1|*|n_2|}|;](https://tex.z-dn.net/?f=%20cos%20%5Cgamma%20%3D%7C%5Cfrac%7Bn_1%2An_2%7D%7B%7Cn_1%7C%2A%7Cn_2%7C%7D%7C%3B%20)
where n₁*n₂=4*1+(-1)*1+2*(-4) and |n₁|*|n₂|=√(4²+1²+2²)*√(1²+1²+4²).
2. Using the formula of cosine:
![cos \gamma=|\frac{4-1-8}{\sqrt{21}*\sqrt{18}}|=\frac{5}{3\sqrt{42}}=0.2572](https://tex.z-dn.net/?f=%20cos%20%5Cgamma%3D%7C%5Cfrac%7B4-1-8%7D%7B%5Csqrt%7B21%7D%2A%5Csqrt%7B18%7D%7D%7C%3D%5Cfrac%7B5%7D%7B3%5Csqrt%7B42%7D%7D%3D0.2572%20)
answer: ≈0.2572