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3 years ago

Simplify. square root (108 x^5 y^6)

1 answer:

3 0

$\bf \sqrt{108x^5y^6}\qquad 
\begin{cases}
108=2\cdot 2\cdot 3\cdot 3\cdot 3\\
\qquad 2^2\cdot 3^2\cdot 3\\
\qquad (2\cdot 3)^2\cdot 3\\
\qquad 6^2\cdot 3\\
x^5=x^{4+1}\\
\qquad x^4\cdot x^1\\
\qquad x^{2\cdot 2}\cdot x\\
\qquad (x^2)^2\cdot x\\
y^6=y^{3\cdot 2}\\
\qquad (y^3)^2
\end{cases}\implies \sqrt{6^2\cdot 3\cdot (x^2)^2\cdot x\cdot (y^3)^2}
\\\\\\
6x^2y^3\sqrt{3x}$

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A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain us

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Answer:

Given:

Sham: n= 20, x=0.44, s=1.24,

Magnet:n= 20, x =0.49, s= 0.95

For Sham:

Sample size, n = 20

Sample mean = 0.44

Standard deviation = 1.24

For Magnet:

Sample size = 20

Sample mean = 0.49

Standard deviation = 0.95

The null and alternative hypotheses:

H0: s1²=s2²

H1: s1² ≠ s2²

a) To find the test statistics, use the formula:

$\frac{s1^2}{s2^2}$

$\frac{1.24^2}{0.95^2} = \frac{1.5376}{0.9025} = 1.7037$

Test statistics = 1.7037

b) P-value:

Sham: degrees of freedom $= n - 1 = 20 - 1 = 19$

Magnet: degrees of freedom $= n - 1 = 20 - 1 = 19$

The critical values:

[Za/2, df1, df2)], [(1 - Za/2), df1, df2]

$f[0.05/2, 19, 19], f[(1 - 0.05/2), 19, 19]$

$f[0.025, 19, 19], f[0.975, 19, 19]$

$(2.526, 0.3958)$

The rejection region:

Reject H0, if F < 0.3958 or if F > 2.526

c) Conclusion:

Since the critical values of test statistic is between (0.3958 < 1.7037 < 2.526), we fail to reject null hypothesis H0.

There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets

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3 years ago

In a fruit cocktail, for every 20 ml of orange juice you need 10 ml of apple juice and 15 ml of coconut milk. What proportion of

MariettaO [177]

Answer:

1/3

Step-by-step explanation:

20 ml + 10 ml + 15 ml = 45 ml total

15 ml coconut milk/45 ml total = 15/45 = 1/3 (as a fraction)

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3 years ago

Q2) The following travel times were measured for vehicles traversing a 2,000 ft. segment of an arterial: Vehicle Travel Time (s)

adelina 88 [10]

Answer:

TMS = 45.78 m/s

SMS = 45.66 m/s

Step-by-step explanation:

Vehicle Travel Time (s)

1 40.5

2 44.2

3 41.7

4 47.3

5 46.5

6 41.9

7 43.0

8 47.0

9 42.6

10 43.3

Time mean speed and space mean speed are parameters used to express the speed of a group of vehicles in traffic flow.

Time mean speed is given as the average speed of all the cars

The speed for each vehicle is calculated by dividing the (2000 ft) distance by the time taken by each vehicle to complete that segment of the journey.

Let vehicle = V

Travel time = time

Speed = s

V | Time | speed (ft/s)

1 | 40.5 | 49.383

2 | 44.2 | 45.249

3 | 41.7 | 47.962

4 | 47.3 | 42.283

5 | 46.5 | 43.011

6 | 41.9 | 47.733

7 | 43.0 | 46.512

8 | 47.0 | 42.553