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elena55 [62]
3 years ago
15

Use the associative law of multiplication to write an equivalent expression. 9[m(6+n)]

Mathematics
1 answer:
jek_recluse [69]3 years ago
8 0
The associative law states that it doesn't matter how we group numbers when we add and/or multiply. So we could rearrange the brackets and parentheses to get the equivalent equation:
9m(6+n)

Both equations total:
54m+9mn 
(I applied the distributive property to solve it). 
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2,400 meters

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Solve using the quadratic formula.<br>-v^2 + 9v - 5 = 0​
timama [110]

Answer:

v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2

Step-by-step explanation:

Solve for v over the real numbers:

-v^2 + 9 v - 5 = 0

Multiply both sides by -1:

v^2 - 9 v + 5 = 0

Subtract 5 from both sides:

v^2 - 9 v = -5

Add 81/4 to both sides:

v^2 - 9 v + 81/4 = 61/4

Write the left hand side as a square:

(v - 9/2)^2 = 61/4

Take the square root of both sides:

v - 9/2 = sqrt(61)/2 or v - 9/2 = -sqrt(61)/2

Add 9/2 to both sides:

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Add 9/2 to both sides:

Answer: v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2

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3 years ago
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 10.3
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Answer:

Confidence interval for the true mean number of reproductions per hour for the bacteria is (10.1,10.5).

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 10.3

Population standard deviation, σ = 2.1

Sample size, n = 728

Alpha, α = 0.01

Confidence interval:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58

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6 0
3 years ago
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