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3 years ago

Which monomials are perfect cubes? Check all that apply.

2 answers:

6 0

A perfect cube is a number that resulted from multiplying a number three times by itself. A perfect cube is also a number that has an exact cube root.

8x^12 ⇒ 2x^4 * 2x^4 * 2x^4
27x^9 ⇒ 3x³ * 3x³ * 3x³

Only two monomials are perfect cubes.

sergiy2304 [10]3 years ago

6 0

When a number is multiplied by itself three times, then the resultant number is called a perfect cube. It is also a number with an exact cube root.

Out of the given options, $8x^{12}$ and $27x^{9}$ are perfect cubes.

$8x^{12}$ = $2x^{4}\times 2x^{4}\times 2x^{4}$ (2's are multiplied and powers are added)

$27x^{9}$ = $3x^{3}\times 3x^{3}\times 3x^{3}$ (3's are multiplied and powers are added)

You might be interested in

If you vertically compress the absolute value parent function ?? What is the equation of the new function

Bumek [7]

Answer: Choice A -- f(x) = (1/3)*|x|

============================================

The input of a function is x and the output is y = f(x)

To vertically compress a function, we will multiply the y value by some fraction smaller than 1. This is so that the y coordinates are a fraction of what they once were.

In this case, we multiply y by 1/3 so that something that has a y coordinate of y = 81 becomes y = 27 (divide by 3)

So we have y = f(x) become (1/3)*y = (1/3)*f(x) = (1/3)*|x|

4 0

3 years ago

The southward translation of the rose garden is along which axis? What integer represents a change of four yards south?

Sphinxa [80]

Going south means you're going in the negative direction along the y axis

Going 4 yards south would be represented as -4 on the y axis number line (this is the vertical number line)

3 0

3 years ago

Mandy was making 6 pillows to give as gifts to her family. She needed 5/8 of a yard of material for each pillow. How many yards

tatiyna

9514 1404 393

Answer:

3 3/4

Step-by-step explanation:

Mandy needs 6 times 5/8 yards, or ...

6(5/8) = 30/8 = 3 6/8/ = 3 3/4 . . . yards

5 0

3 years ago

Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

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.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

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

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

In Youngtown the population reach 4420 people in 1993 in 1998 there were 5600 residents what was toe population in the year 2000

dybincka [34]

So, let's find the rates:
5 years = 1180 people
5n = 1180
n = 236
236*2 = 472
5600 + 472 = 6072
6072 people

8 0

3 years ago