Write the equation for the following relation. Include all of your work in your final answer. Submit your solution.

Mathematics

1 answer:

ella [17]4 years ago

5 0

Answer:

$y=x^3$

Step-by-step explanation:

The given relation is Q = {(x, y): (2, 8), (3, 27), (4, 64), (5, 125), . . .}

We can quickly recognize a pattern to write the equation of the given relation.

We can observe the following pattern among the x and y coordintaes.

$8=2^3$

$27=3^3$

$64=4^3$

$125=5^3$

We can see that the base of the powers on the right are the x-values of the relation and the values on the left are the y-values.

Hence, for any ordered pair (x,y), the equation is

$y=x^3$

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mylen [45]

Answer:

B.2 1/41

Step-by-step explanation:

In a perfect square trinomial of the form ax+bx+c where a, b and c are constants, the value of (b/2)²=ac

In the provided equation the value of a=1, b=-3 c=?

Therefore, (-3/2)²=c since a-the coefficient of x²=1 and 1×c=c

c=2.25= 2 1/4

Thus the trinomial x² - 3x + 2 1/4 is a perfect square.

5 0

3 years ago

Suppose 88% of all batteries from a supplier have acceptable voltages. A certain type of flashlight requires two D batteries, an

ira [324]

Answer:

0.3036 = 30.36% probability that at least 9 of the flashlights function properly.

Step-by-step explanation:

For each flashlight, there are only two possible outcomes. Either it works, or it does not. Flashlights are independent. This means that 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.

Flashlight works correctly if both its batteries have acceptable voltages:

Each battery has an 88% = 0.88 probability of working correctly(having acceptable voltage), so the probability of the flashlight working correctly is given by:

$p = (0.88)^2 = 0.7744$