All categories

3 years ago

Which expression is a perfect cube?

Mathematics

2 answers:

Alex17521 [72]3 years ago

5 0

Answer:

Only $y^{24}$ is a perfect cube.

Step-by-step explanation:

$x^{8}$ is not a perfect cube because 8 is not a multiple of 3.

Now, $y^{24}$ is a perfect cube since 24 is a multiple of 3.

So, $y^{24}$ can be expressed as

$y^{24} =y^{8+8+8}= y^{8} \times y^{8} \times y^{8}= (y^{8}) ^{3}$

Again, $m^{28}$ is not a perfect cube as 28 is not a multiple of 3.

And also $s^{64}$ is not a perfect cube as 64 is not a multiple of 3.

Therefore, only $y^{24}$ is a perfect cube. (Answer)

Ainat [17]3 years ago

5 0

Answer:

Option B.

Step-by-step explanation:

We need to find the expression that is a perfect cube.

First expression is $x^8$ . The degree of x is 8 which is not divisible by 3. So, $x^8$ is not a perfect cube.

Second expression is $y^{24}$ . The degree of y is 24 which is divisible by 3.

$y^{24}=y^{8\times 3}=(y^8)^3$ $[\because (x^m)^n=x^{mn}]$

So, $y^{24}$ is a perfect cube.

Third expression is $m^{28}$ . The degree of m is 28 which is not divisible by 3. So, $m^{28}$ is not a perfect cube.

Fourth expression is $s^{64}$ . The degree of s is 64 which is not divisible by 3. So, $s^{64}$ is not a perfect cube.

Therefore, the correct option is B.

You might be interested in

Determine the following:

dolphi86 [110]

Answer:

a) P(X = 0) = 0.5997

b) P(X = 9) = 0.0016

c) P(X = 8) = 0.0047

d) P(X = 5) = 0.4018

Step-by-step explanation:

These following problem are examples of the binomial probability distribution.

Binomial probability

Th 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) for n = 4 and π = 0.12, what is P(X = 0)?

$P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997$

(b) for n = 10 and π = 0.40, what is P(X = 9)?

$P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016$

(c) for n = 10 and π = 0.50, what is P(X = 8)?

$P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0047$

(d) for n = 6 and π = 0.83, what is P(X = 5)?

$P(X = 5) = C_{6,5}.(0.83)^{5}.(0.17)^{1} = 0.4018$

3 0

2 years ago

Plsss helppp, tysmm!!

Vinvika [58]

Answer:

It should be PT and NO

Hope this helps!

4 0

2 years ago

According to the Knot, 22% of couples meet online. Assume the sampling distribution of p follows a normal distribution and answe

Ann [662]

Using the <em>normal distribution and the central limit theorem</em>, we have that:

a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$ , as long as $np \geq 10$ and $n(1 - p) \geq 10$ .