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castortr0y [4]
3 years ago
6

Simplify ^3_/125x^21y^33

Mathematics
1 answer:
Grace [21]3 years ago
7 0

\sqrt[3]{125x^{21}y^{33}}=\sqrt[3]{125}\cdot\sqrt[3]{x^{21}}\cdot\sqrt[3]{y^{33}}=\sqrt[3]{5^3}\cdot\sqrt[3]{(x^7)^3}\cdot\sqrt[3]{(y^{11})^3}\\\\=\boxed{5x^7y^{11}}\\\\Used:\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt[n]{a^n}=a\\\\(a^n)^m=a^{nm}

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Solve the system of equations.<br> -10x+3y=5 <br> x=y-4
blsea [12.9K]

Answer:

x=y-4                                          -10x+3y=5

y=x+4                                     y=10/3x+5/3

        x+4  =10/3x+5/3              

x=1

y=1+4                                      y=10/3(1)+5/3

y=5                                                    y=5

so

x=1

y=5

(1,5)

5 0
3 years ago
What is the value of<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B2%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes
erma4kov [3.2K]

Answer:

2*2*2*2*9=144

√144

=12

8 0
2 years ago
Read 2 more answers
Evaluate the radical.
zaharov [31]
5*5*5=125
5²*5=125
5√5 is your answer
4 0
3 years ago
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Show all steps<br> question is in the photo.
Lady bird [3.3K]

\\ \sf\longmapsto \sqrt{108x^2y^3}-\sqrt{12x^2y^3}+x\sqrt{75y^3}

\\ \sf\longmapsto \sqrt{2\times 2\times 3\times 3\times 3\times x\times x\times y\times y\times y}-\sqrt{2\times 2\times 3\times x\times x\times y\times y\times y}+\sqrt{5\times 5\times 3\times y\times y\times y}

\\ \sf\longmapsto 6\sqrt{3}xy\sqrt{y}-2\sqrt{3}xy\sqrt{y}+5\sqrt{3}xy\sqrt{y}

\\ \sf\longmapsto \sqrt{3}xy\sqrt{y}(6-2+5)

\\ \sf\longmapsto 9\sqrt{3}xy\sqrt{y}

5 0
2 years ago
Read 2 more answers
In the Salk vaccine field trial, 400,000 children were part of a randomized controlled double-blind experiment. Just about half
EastWind [94]

Answer:

Step-by-step explanation:

From the given information:

The number of children that were randomly allocated to each vaccination group; n₁ = 200,000

No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

\hat p_1 = \dfrac{57}{200000}

=  0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

\hat p_2 = \dfrac{142}{200000}

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.  

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic  can be computed as:

Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}

Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}

Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}

Z = - 6.03

P-value =  2P(Z < -6.03)

From the Z - tables

P-value =  2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

7 0
2 years ago
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