Answer:
<h2>A. -2x³ - 6x² + 9x</h2>
Step-by-step explanation:
![f(x)=3x^3-4x^2+6x\\\\g(x)=5x^3+2x^2-3x\\\\f(x)-g(x)=(3x^3-4x^2+6x)-(5x^3+2x^2-3x)\\\\=3x^3-4x^2+6x-5x^3-2x^2-(-3x)\qquad\text{combine like terms}\\\\=(3x^3-5x^3)+(-4x^2-2x^2)+(6x+3x)\\\\=-2x^3-6x^2+9x](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3-4x%5E2%2B6x%5C%5C%5C%5Cg%28x%29%3D5x%5E3%2B2x%5E2-3x%5C%5C%5C%5Cf%28x%29-g%28x%29%3D%283x%5E3-4x%5E2%2B6x%29-%285x%5E3%2B2x%5E2-3x%29%5C%5C%5C%5C%3D3x%5E3-4x%5E2%2B6x-5x%5E3-2x%5E2-%28-3x%29%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%3D%283x%5E3-5x%5E3%29%2B%28-4x%5E2-2x%5E2%29%2B%286x%2B3x%29%5C%5C%5C%5C%3D-2x%5E3-6x%5E2%2B9x)
B= 20°
and c = 160°
b is equal to the given angle, b = 20°
c is 180 - 20 = 160°
Answer:
30 degrees
Step-by-step explanation:
The angles must add up to 180 degrees and the triangles have the same angles.
Answer:
22.29% probability that both of them scored above a 1520
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 1497, \sigma = 322](https://tex.z-dn.net/?f=%5Cmu%20%3D%201497%2C%20%5Csigma%20%3D%20322)
The first step to solve the question is find the probability that a student has of scoring above 1520, which is 1 subtracted by the pvalue of Z when X = 1520.
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{1520 - 1497}{322}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B1520%20-%201497%7D%7B322%7D)
![Z = 0.07](https://tex.z-dn.net/?f=Z%20%3D%200.07)
has a pvalue of 0.5279
1 - 0.5279 = 0.4721
Each students has a 0.4721 probability of scoring above 1520.
What is the probability that both of them scored above a 1520?
Each students has a 0.4721 probability of scoring above 1520. So
![P = 0.4721*0.4721 = 0.2229](https://tex.z-dn.net/?f=P%20%3D%200.4721%2A0.4721%20%3D%200.2229)
22.29% probability that both of them scored above a 1520