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Nesterboy [21]
3 years ago
11

Which expression is the simplest form of (27x^-9)^1/3?

Mathematics
1 answer:
lana [24]3 years ago
8 0
\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\sqrt[n]{a}=a^\frac{1}{n}\\\\(a^n)^m=a^{nm}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(27x^{-9})^\frac{1}{3}=27^\frac{1}{3}(x^{-9})^\frac{1}{3}=\sqrt[3]{27}\cdot x^{-9\cdot\frac{1}{3}}=3x^{-3}=\dfrac{3}{x^3}
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Find the interquartile range for each set of data.<br> Set 1: 21, 5, 14, 10, 8, 17, 2
tensa zangetsu [6.8K]

Answer:

12.

Step-by-step explanation:

First arrange in ascending order:

2 5 8 10 14 17 21

The median is 10.

the lower quartile is the middle number of 2 5 and 8 which is 5.

Similarly the upper quartile is 17.

IQR = 17 - 5 = 12.

6 0
3 years ago
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What is 15/20 simplest form
Fiesta28 [93]

Answer:

the simplest form of 15/20 is 3/4

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In a particular triathlon the athletes cover 1/24 of the total distance by
pav-90 [236]

Answer:

15/8

Step-by-step explanation:

Let "d" be the total distance, that is, the distance for swimming (s), running (r) and going by bike (b).

d = s + r + b   [1]

1/24 of the total distance is covered by  swimming.

s = 1/24 d   [2]

1/3 of the distance is covered by running.

r = 1/3 d  [3]

If we replace [2] and [3] in [1], we get

d = 1/24 d + 1/3 d + b

b = d - 1/24 d - 1/3 d

b = 24/24 d - 1/24 d - 8/24 d

b = 15/24 d = 5/8 d

The ratio of  the distance covered by bike to the distance covered by running is:

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5 0
3 years ago
Which is larger 0.7 or 3/4
Ksenya-84 [330]
3/4 is 0.75.
3/4 is larger than 0.7
3 0
3 years ago
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One leg of a right triangle is 7 inches longer than the smaller leg and the hypotenuse is 8 inches longer than the smaller leg.
Makovka662 [10]
Smaller leg = x
longer leg = y
hypotenuse = z

y=x+7
z=x+8

due to
{z}^{2}  =  {x}^{2}  +  {y}^{2}  \\ (x + 8) ^{2}  =  {x}^{2}  + (x + 7) ^{2}  \\  {x}^{2}  + 16x + 64 =  {x}^{2}  +  {x}^{2}  + 14x + 49 \\  {x}^{2}  + 16x + 64 = 2 {x}^{2}  + 14x + 49 \\  {x}^{2}  - 2 {x}^{2}  + 16x - 14x + 64 - 49 = 0 \\  -  {x}^{2}  + 2x + 15 = 0 \\  {x}^{2}  - 2x - 15 = 0 \:  \: (multiplied \: by \:  - 1) \\ (x - 5)(x + 3) = 0 \\ then \:  \: x = 5 \:  \: or \:  \: x =  - 3
but x cannot be -3
so smaller leg is 5 inches

then longer leg = 5+7 = 12 inches
and hypotenuse = 5+8 = 13 inches
3 0
3 years ago
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