Solve each system of equations by substitution. List the ordered pair.

Mathematics

1 answer:

Anit [1.1K]3 years ago

8 0

Y=6x-11
-2x-3y=-7
-2x-3(6x-11)=-7
-2x-18x+66=-7
-20x=-73
x=3.65
y=6(3.65)-11=10.9

y=-3x+5
5x-4y=-3
5x-4(-3x+5)=-3
5x+12x=17
x=1
y=-3(1)+5=2

2x-3y=-1
y=x-1
2x-3(x-1)=-1
-x=-4
x=4
y=4-1=3

-3x-3y=3
y=-5x-17
-3x-3(-5x-17)=3
12x=-48
x=-4
y=-5(-4)-17=3

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0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals

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Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

Mean 490 mg and variance of 400.

This means that $\mu = 490, \sigma = \sqrt{400} = 20$