2/3 - 4/9 = 2/9 (Check the photo for proof)
![\bf 2=x^2+5x\implies 0=x^2+5x-2\\\\\\\qquad \qquad \qquad \textit{discriminant of a quadratic}\\\\\\0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2}~~~~~~~~\stackrel{discriminant}{b^2-4ac}=\begin{cases}0&\textit{one solution}\\positive&\textit{two solutions}\\negative&\textit{no solution}\end{cases}\\\\\\(5)^2-4(1)(-2)\implies 25+8\implies 33](https://tex.z-dn.net/?f=%20%5Cbf%202%3Dx%5E2%2B5x%5Cimplies%200%3Dx%5E2%2B5x-2%5C%5C%5C%5C%5C%5C%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bdiscriminant%20of%20a%20quadratic%7D%5C%5C%5C%5C%5C%5C0%3D%5Cstackrel%7B%5Cstackrel%7Ba%7D%7B%5Cdownarrow%20%7D%7D%7B1%7Dx%5E2%5Cstackrel%7B%5Cstackrel%7Bb%7D%7B%5Cdownarrow%20%7D%7D%7B%2B5%7Dx%5Cstackrel%7B%5Cstackrel%7Bc%7D%7B%5Cdownarrow%20%7D%7D%7B-2%7D~~~~~~~~%5Cstackrel%7Bdiscriminant%7D%7Bb%5E2-4ac%7D%3D%5Cbegin%7Bcases%7D0%26%5Ctextit%7Bone%20solution%7D%5C%5Cpositive%26%5Ctextit%7Btwo%20solutions%7D%5C%5Cnegative%26%5Ctextit%7Bno%20solution%7D%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%285%29%5E2-4%281%29%28-2%29%5Cimplies%2025%2B8%5Cimplies%2033%20)
so we have a 33, namely two real solutions for that quadratic.
usually that number goes into a √, if you have covered the quadratic formula, you'd see it there, namely that'd be equivalent to √(33), now 33 is a prime number, and √(33) is yields an irrational value, specifically because a prime number is indivisible other than by itself or 1.
so 33 can only afford us two real irrational roots.
Answer: B) y=1/4x+7/2
Step 1: Slope
Knowing that the equation will be perpendicular to the one given will only give us the slope. Perpendicular means that the slope will be opposite to what it is now.
The opposite of -4 (the current slope) is 1/4. Even knowing only this will tell us that the answer is b, but I will continue to explain for when no options are given.
Step 2: Y-intercept
Now that we know the slope, the perpendicular aspect of this equation will no longer be of any help.
To find the y-intercept, we need to substitute y and x with the point given.
Our current equation is— y= 1/4x+b
Let’s substitute the point into this. The point (-2,3) tells us that the y-value is 3 and the x-value is -2.
y= 1/4x+ b
3=1/4(-2)+b
3 = -1/2 +b
+1/2 +1/2
__________
3 1/2 =b
Step 3: Improper fraction
Being that it is preferred to leave fractions improper, let’s turn 3 1/2 into an improper fraction. This will turn into 7/2 (comment below if you need an explanation of how to do this)
Final answer: now that we know that the slope is 1/4 and the y-intercept is 7/2, we know that our equation will be y=1/4x+7/2
Hope this helps comment below for more questions:)
Answer:
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
N(489,6)
This means that ![\mu = 489, \sigma = 6](https://tex.z-dn.net/?f=%5Cmu%20%3D%20489%2C%20%5Csigma%20%3D%206)
What is the probability that the box will contain less than the advertised weight of 466 g?
This is the p-value of Z when X = 466. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{466 - 489}{6}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B466%20-%20489%7D%7B6%7D)
![Z = -3.83](https://tex.z-dn.net/?f=Z%20%3D%20-3.83)
has a p-value of 0.000064
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.