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mylen [45]
3 years ago
10

When (81x^2/7) (2/9x^3/7) is simplified, it can be written in the form ax^b where a and b are real numbers. Find ab.

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

Answer:

In improper form your solution will be \frac{90}{7}. As a mixed fraction it will be 12\frac{6}{7}.

Step-by-step explanation:

The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,

\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\: - Apply exponential rule " \:a^b\cdot \:a^c=a^{b+c} "

= 81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}} - Combine fractions \frac{2}{7} and \frac{3}{7}

= 81\cdot \frac{2}{9}x^{\frac{5}{7}} - Multiply the fractions, and simplify further

= \frac{162x^{\frac{5}{7}}}{9} = 18x^{\frac{5}{7}} - This is out simplified expression

Now that we have this simplified expression, we can see that a = 18, and b = \frac{5}{7}. Therefore, multiplying the two we should receive the improper fraction as follows,

18 * \frac{5}{7} = \frac{90}{7} - Note that this is in improper form. If you want your solution in a mixed fraction, it will be 12\frac{6}{7}.

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The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of
Varvara68 [4.7K]

Answer:

A) 68.33%

B) (234, 298)

Step-by-step explanation:

We have that the mean is 266 days (m) and the standard deviation is 16 days (sd), so we are asked:

A. P (250 x < 282)

P ((x1 - m) / sd < x < (x2 - m) / sd)

P ((250 - 266) / 16 < x < (282 - 266) / 16)

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P (-1 < z) = 0.1587

P (z < 1) = 0.8413

replacing

0.8413 - 0.1587 = 0.6833

The percentage of pregnancies last between 250 and 282 days is 68.33%

B. We apply the experimental formula of 68-95-99.7

For middle 95% it is:

(m - 2 * sd, m + 2 * sd)

Thus,

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6 0
3 years ago
Find the length of EF
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Answer:

9

Step-by-step explanation:

1. First, we need to set up an equation to find the value of x and then the length of EF.

2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of: 3x - 28 + 3x - 30 + x = 33

3. (Solving for x)

Step 1: Simplify both sides of the equation.

  • 3x - 28 + 3x - 30 + x = 33
  • (3x+3x+x) + (-28-30)=33
  • 7x - 58 = 33

Step 2: Add 58 to both sides.

  • 7x - 58 + 58 = 33 + 58
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Step 3: Divide both sides by 7.

  • \frac{7x}{7} = \frac{91}{7}
  • x = 13

4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.

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Therefore, the length of EF is 9.

7 0
3 years ago
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