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1 year ago

Find the cube root of 8x7x9x49x3

Mathematics

1 answer:

vodka [1.7K]1 year ago

5 0

Answer:

=42

Step-by-step explanation:

The expression 8×7×9×49×3 can be written in its simplest factor form as follows.

8=2³

49=7²

9=3²

Thus the expression becomes:2³×7×3²×7²×3

Combine the indices to the same base.

2³×3³×7³

Finding the cube root involves dividing the index by three.

Thus ∛(2³×3³×7³)= 2×3×7

=42

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Speed going up = 5 ft/(2min * 60 s/1 min) = 1/24 ft/s
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2 years ago

A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y de

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Answer:

a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

a= μ-3.16*σ , b= μ+3.16*σ

b) P(Y≥ μ+3*σ ) ≥ 0.90

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Step-by-step explanation:

from Chebyshev's inequality for Y

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

where

Y = the number of fish that need be caught to obtain at least one of each type

μ = expected value of Y

σ = standard deviation of Y

P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean

k= parameter

thus for

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16

then

P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

using one-sided Chebyshev inequality (Cantelli's inequality)

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2 years ago

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Answer:

a. The population does not become extinct in finite time.

Step-by-step explanation:

The model for the population of the fishery is

$dP/dt = P(a-bP)-h, P(0) = P_0$

If we rearrange and replace the constants we have:

$\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}$

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To be a finite time, t>0

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Because P0 is a positive constant, we can say that the population does not become extint in finite time.

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2 years ago

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Let's say

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2 years ago

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1 year ago

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