Please be certain to use the symbol "^" to denote exponentiation. Your function y should be written as
y = x^3 + 3x2 - 2x + 4.
Principle: if the derivative of a function is negative on a certain x-interval, the function is decreasing on that interval. Thus, you must differentiate the given function: find dy/dx. Set this dy/dx = to 0 and solve the resulting equation for x. Set up intervals on the # line based upon your solutions.
For example, if x=-1 and x=2, then set up 3 intervals: (-infinity,-1), (-1,2), and (2, infinity). Looking at each interval separately, identify the interval or intervals on which the derivative dy/dx is negative.
This is a critically important skill in calculus and well worth the time and effort required to learn it.
Answer:
315
Step-by-step explanation:
Answer:
I would use a proportion for each ingredient:
Cup sugar
4:10=½:x (10×½)÷4= 1,25 cup sugar
Cup brown sugar:
4:10=¼:x (10×¼)÷4= 0.625 cup brown sugar
Peanut butter
4:10=⅔:x (10×⅔)÷4= 1,65 cup peanut butter
Cup oats
2×¼ = ½
4:10=½:x (10×½)÷4= 1,25 cup oats
Cup milk
4:10=¾:x (10×¾)÷4= 1,875 cup milk
Tsp salt
4:10=1:x (10×1)÷4= 2,5 tsp salt
2 tbsp cocoa
4:10=2:x (10×2)÷4= 5 tbsp cocoa
1 tsp vanilla
4:10=1:x (10×1)÷4= 2,5 tsp vanilla
2 eggs
4:10=2:x (10×2)÷4= 5 eggs
3 cups flour
4:10=3:x (10×3)÷4= 7,5 cups flour
12 oz nuts
4:10=12:x (10×12)÷4= 30 oz nuts
Answer:
The mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.
Step-by-step explanation:
Let the random variable <em>X</em> follow a Normal distribution with mean <em>μ </em>and standard deviation <em>σ.</em>
The <em>z</em>-scores are standardized form of the raw scores <em>X</em>. It is computed by subtracting the mean (<em>μ</em>) from the raw score <em>x</em> and dividing the result by the standard deviation (<em>σ</em>).
These <em>z</em>-scores also follow a normal distribution.
The mean is:
![E(z)=E[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma}\times [E(x)-\mu] =\frac{1}{\sigma}\times [\mu-\mu]=0](https://tex.z-dn.net/?f=E%28z%29%3DE%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5BE%28x%29-%5Cmu%5D%20%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5B%5Cmu-%5Cmu%5D%3D0)
The standard deviation is:
![Var(z)=Var[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma^{2}}\times [Var(x)-Var(\mu)] =\frac{\sigma^{2}-0}{\sigma^{2}}=1\\SD(z)=\sqrt{Var(z)}=1](https://tex.z-dn.net/?f=Var%28z%29%3DVar%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%5E%7B2%7D%7D%5Ctimes%20%5BVar%28x%29-Var%28%5Cmu%29%5D%20%3D%5Cfrac%7B%5Csigma%5E%7B2%7D-0%7D%7B%5Csigma%5E%7B2%7D%7D%3D1%5C%5CSD%28z%29%3D%5Csqrt%7BVar%28z%29%7D%3D1)
Thus, the mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.
Answer: 7hours≥t
Given the data, the following inequality can be made.
90.90≥37+7.70t
subtract 37 from both sides
53.90≥7.70t
divide both sides by 7.70
7hours≥t
The meeting room can be rented for no more than 7 hours.
