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3 years ago

Find the constant of variation k for the direct variation. 4x = –6y

Mathematics

2 answers:

FromTheMoon [43]3 years ago

8 0

Answer:

either -6/4 or -4/6 I thing it's -4/6 or 2/3 im not to sure

Step-by-step explanation:

Gennadij [26K]3 years ago

4 0

Answer:

The constant k is equal to $-(2/3)$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In this problem we have

$4x=-6y$

Isolate the variable y

$y=-(4/6)x$

Simplify

$y=-(2/3)x$

In a direct variation the constant k is equal to the slope of the line

$m=k=-(2/3)$

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Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, w

MrRa [10]

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that $p = 0.42$

Three Americans are randomly selected

This means that $n = 3$

What is the probability that none of them voted in the last election

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951$

19.51% probability that none of them voted in the last election

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3 years ago

The desert temperature, H, oscillates daily between 30ºF at 4am and 70ºF at 4pm. Write a possible formula for H in terms of t, m

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