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xeze [42]
3 years ago
7

Which expression is equivalent to √2x^5/18? Assume x > 0.

Mathematics
2 answers:
zmey [24]3 years ago
7 0

Answer: \frac{x^2\sqrt{x}}{3}

Step-by-step explanation:

Here the given expression is, \sqrt{\frac{2x^5}{18} }

= \sqrt{\frac{x^5}{9} }

= \sqrt{\frac{x^5}{9} }

= \sqrt{\frac{x^4.x^1}{9} }  (because x^{m+n}= x^m.x^n )

=\frac{x^2\sqrt{x} }{3}

Thus,\sqrt{\frac{2x^5}{18} } =\frac{x^2\sqrt{x} }{3}


lord [1]3 years ago
5 0
\sqrt{\dfrac{2x^5}{18}}=\sqrt{\dfrac{2}{18}\cdot x^2\cdot x^2\cdot x}=\sqrt{\dfrac{1}{9}\cdot x^2\cdot x^2\cdot x}=\sqrt{\dfrac{1}{9}}\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{x}=\\\\\\=\dfrac{1}{3}\cdot x\cdot x\cdot\sqrt{x}=\boxed{\dfrac{x^2\sqrt{x}}{3}}

Answer A.
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Which two values of x satisfy the equation square root 3-2cos x = 2?
Andrei [34K]

Answer: x=2π/3 and x=4π/3

Step-by-step explanation:

The equation we have is \sqrt{3-2cosx} =2. All we have to do is get cosine alone to find the 2 values of x.

3-2cosx=4\\-2cosx=1\\cosx=-\frac{1}{2}

Now that we have our cosine left, we can use our unit circle to figure out when does cosx=-1/2. Cosine is the x value of the coordinate.

x=2π/3

x=4π/3

8 0
3 years ago
3 times a number is 54 less than the square of that number. Find the negative solution.
son4ous [18]

Answer:

-6

Step-by-step explanation:

3n = n² - 54

n² - 3n - 54 = 0

n² - 9n + 6n - 54 = 0

n(n - 9) + 6(n - 9) = 0

(n - 9)(n + 6) = 0

n = 9 , -6

5 0
3 years ago
Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth.
Zigmanuir [339]
The mean is the average.
So, to find the mean you want o add up all of the numbers and then divide by the number of numbers.

49 + 49 + 54 + 55 + 52 + 49 + 575 = 363
363 / 7 = 51.85
Rounded to 52

For the median you want o line all of your number up from least to greatest and then find the middle number.

49,49,49,52,54,55,55

Your median is 52

The mode is the number that is listed most often

49 is listed 3 times
54 is listed 1 time
52 is listed 1 time
55 is listed 2 times

So, your mode is 49




4 0
3 years ago
Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one anothe
scZoUnD [109]

Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

              Blue    Brown     Green    Total

Blue        78         23            13          114

Brown     19         23            12          54

Green     11           9             16          36

Total      108       55            41          204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

7 0
3 years ago
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I could be wrong but i think it is 1998
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4 years ago
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