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3 years ago

Simplify -3y(y + 2)^2 - 5 + 6y

Mathematics

2 answers:

ser-zykov [4K]3 years ago

7 0

Answer:

That'll help a lot of people in the future ^.^

Step-by-step explanation:

tigry1 [53]3 years ago

5 0

Answer:

-3y^3 - 12y^2 - 6y - 5.

Step-by-step explanation:

-3y(y + 2)^2 - 5 + 6y

= -3y(y^2 + 4y + 4) - 5 + 6y

= -3y^3 - 12y^2 - 12y - 5 + 6y

= -3y^3 - 12y^2 - 6y - 5.

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2 years ago

Read 2 more answers

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

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

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

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

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

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

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

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

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

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

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

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

The graph of F(x) shown below resembles the graph of G(x) = x4, but it has

DerKrebs [107]

Using translation concepts, the equation of F(x) is:

A. $F(x) = \frac{1}{3}x^4 - 2$

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is:

$G(x) = x^4$

For function F(x), we have that:

It was shifted down 2 units, hence F(x) = G(x) - 2.

It was vertically compressed by a factor of 3, hence $F(x) = \frac{1}{3}G(x) - 2$

Then the equation is:

A. $F(x) = \frac{1}{3}x^4 - 2$

More can be learned about translation concepts at brainly.com/question/28098112

#SPJ1

3 0

1 year ago