All categories

3 years ago

A cube's side measures 6xy inches whet is the volume

Mathematics

1 answer:

liubo4ka [24]3 years ago

8 0

For a cube, $V = s^3.$

The volume is the cube of the side length.

$V = s^3$

$V = (6x^6y^8)^3$

To raise a product to an exponent, raise each factor to the exponent.

$V = (6^3) \times (x^6)^3 \times (y^8)^3$

To raise a power to a power, multiply powers.

$V = 216x^{18}y^{24}$

You might be interested in

Toronto FC have lost 25% of their games if they have played 16 games how many would they have lost

bija089 [108]

Answer:

Step-by-step explanation:

4 0

3 years ago

What is the interquartile range of this data?

jok3333 [9.3K]

Hello!

To find the interquartile range you subtract the lower quartile by the higher quartile

33 - 25 = 8

The answer is C)8

Hope this helps!

6 0

3 years ago

if you have a class with 32 students and 16 of them are boys how many girls are there in the class

MA_775_DIABLO [31]

Answer: if there are 32 students in the class and 16 are boys so the other half well be 16 girls. 16 + 16 = 32. Sooo the answer is 16 girls

Step-by-step explanation:

6 0

3 years ago

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr

ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

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.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so $\pi = 0.30$

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so $n = 10$

We want to find P(X = 1). So:

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

$P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211$

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is $P(X > 1)$

We have that:

$P(X \leq 1) + P(X > 1) = 1$

$P(X > 1) = 1 - P(X \leq 1)$

We also have that:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493$

Finally

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507$

There is a 85.07% probability that more than 1 has the marker.

3 0

3 years ago

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Stells [14]

Answer:

Step-by-step explanation:

let the two perfect cubes be a³ and b³. Factring the difference of these two perfect cubes we have;

a³ - b³

First we need to factorize (a-b)³

(a-b)³ = (a-b) (a-b)²

(a-b)³ = (a-b)(a²-2ab+b²)

(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³

(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²

(a-b)³ = a³-b³ - 3a²b+3ab²

(a-b)³ = (a³-b³) -3ab(a-b)

Then we will make a³-b³ the subject of the formula from the resultinh equation;

a³-b³ = (a-b)³+ 3ab(a-b)

a³-b³ = a-b{(a-b)²+3ab}

a³-b³ = a-b{a²+b²-2ab+3ab}

a³-b³ = (a-b)(a²+b²+ab)

a³-b³ = (a-b)(a²+ab+b²)

The long division problem that can be used is (a-b)(a²+ab+b²)

3 0

3 years ago