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Mathematics

1 answer:

Snezhnost [94]3 years ago

7 0

$3^{-3}= \frac{1}{3^3}= \frac{1}{27} \\ \\ 3^{-2}= \frac{1}{3^2}= \frac{1}{9} \\ \\ 3^{-1}= \frac{1}{3^1}= \frac{1}{3} \\ \\3^{0}=1 \\\\ 3^1=3\\\\3^2=9\\\\3^3=27$

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If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.

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Answer:

x=11, y=8/3

Step-by-step explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

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and

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Thus,

$\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.$

Solve this system of two equations. From the first equation:

$4x-5x=-7-4\\ \\-x=-11\\ \\x=11$

Substitute it into the second equation:

$11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}$

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Answer:

Probability of stopping the machine when $X < 9$ is 0.0002

Probability of stopping the machine when $X < 10$ is 0.0013

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Step-by-step explanation:

There is a random binomial variable $X$ that represents the number of units come off the line within product specifications in a review of $n$ Bernoulli-type trials with probability of success $0.91$ . Therefore, the model is ${15 \choose x} (0.91) ^ {x} (0.09) ^ {(15-x)}$ . So: