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borishaifa [10]
2 years ago
7

Express 27x2y3z4 using rational exponents.

Mathematics
2 answers:
Kazeer [188]2 years ago
7 0

Answer:

xyz^{2}(y^{\frac{1}{2}})

Step-by-step explanation:

There is no way to express:

27x^{2} y^{3} z^{4} since this is a algebraic expression with exponents.

However, if the expression is:

\sqrt[2]{x^{2} y^{3} z^{4}}

We can express it like:

(x^{2} y^{3} z^{4})^{\frac{1}{2} }  which is the same as square root can be expressed like "1/2" exponent.

This can be simplified by:

xyz^{2}(y^{\frac{1}{2}})

This was done by multiplying the exponent of each variable by the 1/2 exponent.

Svetradugi [14.3K]2 years ago
5 0
The answer is 6,318 i hope im right
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The total square footage of mini storage units being rented in a city is graphed to forecast future demand. The scatter plot has
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Answer:

B 160,000 sq ft

Step-by-step explanation:

2018 is 13 years after 2005.

Put x=13 in the equation and evaluate:

... y = 0.538·13 +9.02 = 6.994 +9.02 = 16.014

This is the number of 10,000 sq ft, so the required area is ...

... 16 times 10,000 sq ft = 160,000 sq ft.

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2 years ago
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Tiffany is monitoring the decay of two radioactive compounds in test tubes at her lab. Compound A is continuously decaying at a
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Answer:

30e-0.12t

40e-0.18t

Step-by-step explanation:

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2 years ago
a motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in
tangare [24]

Answer:

  • rate of the boat in still water = 6.5 miles / hour

  • rate of the current = 2.5 miles / hour.

Explanation:

<u>1) Name the two variables:</u>

  • c: rate of the current
  • b: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

  • down the river: b + c
  • upstream: b - c

<u>2) Now set the equations for the distance as a function of the times and the rates:</u>

  • distance = rate × time

  • downstream: 18 miles = (b + c) × 2 hours
  • upstream: 18 miles = (b - c) × 4.5 hours

<u>3) Set the system of equations:</u>

  • 18 = 2(b + c) ⇒ 9 = b + c . .  . Equation (1)
  • 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

<u>4) Solve the system by </u><u>elimination</u><u>:</u>

  • Add equations (1) and (2): 9 + 4 = 2b
  • Divide both sides by 2: 13/2 = b
  • Simplify: b = 6.5

  • Replace b with 6.5 in equation (2) and solve:

       4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

<u>5) Results:</u>

  • b = rate of the boat in still water = 6.5 miles / hour

  • c = rate of the current = 2.5 miles / hour.

   

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2 years ago
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A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14 for π?
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A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w
sveta [45]

Answer:

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion for business  

\hat p_A =\frac{75}{400}=0.1875 represent the estimated proportion for Business

n_A=400 is the sample size required for Business

p_B represent the real population proportion for non Business

\hat p_B =\frac{137}{500}=0.274 represent the estimated proportion for non Business

n_B=500 is the sample size required for non Business

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

And replacing into the confidence interval formula we got:  

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

7 0
2 years ago
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