try c im sorry if im wrong i tried
Answer:
1. x^2+12x+32
Step-by-step explanation:
(x+8)(x+4)
x(x+4)+8(x+4)
x^2+4x+8x+32
x^2+12x+32
Answer:
The required confidence inteval = 94.9%.
Step-by-step explanation:
Confidence interval: Mean ± Margin of error
Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).
i.e. Mean + Margin of error = 42.969 (i)
Mean - Margin of error = 36.191 (ii)
Adding (i) and (ii), we get
![2Mean =79.16\\\\\Rightarrow\ Mean= 39.58](https://tex.z-dn.net/?f=2Mean%20%3D79.16%5C%5C%5C%5C%5CRightarrow%5C%20Mean%3D%2039.58)
Margin of error = 42.969-39.58 [from (i)]
= 3.389
Margin of error = ![t^* \dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=t%5E%2A%20%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
here n= 25 ![, \ \sigma=8.25](https://tex.z-dn.net/?f=%2C%20%5C%20%5Csigma%3D8.25)
i.e.
![3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \](https://tex.z-dn.net/?f=3.389%3Dt%5E%2A%5Cdfrac%7B8.25%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%5C%20t%5E%2A%20%3D%20%5Cdfrac%7B3.389%7D%7B1.65%7D%5C%5C%5C%5C%5CRightarrow%5C%20t%5E%2A%20%3D2.0539%20%5C)
Using excel function 1-TDIST.2T(2.054,24)
The required confidence inteval = 94.9%.
So, how much acid is there in 6 gallons? well is 20% acid or (20/100), so the amount of acid in it just (20/100) * 6 or 1.2, the rest is say water.
now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.
now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.
we know whatever "x" and "y" amounts are, they -> x + 6 = y
and we also know that x + 1.2 = 0.9y
Let x be the mystery number
25% = 0.25
So, 24/x = 0.25
Now, we have to rearrange the equation to get:
x = 24/0.25 = 96
Don't hesitate to ask any further questions!
Hope I helped! xx