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Alinara [238K]
2 years ago
15

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

etect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7.
What is the mean (±0.1) of the average number of moths x¯ in 40 traps? And the standard deviation? (±0.001) Use the central limit theorem to find the probability (±0.01) that the average number of moths in 40 traps is greater than 0.4:
Mathematics
1 answer:
7nadin3 [17]2 years ago
7 0

Answer:

Part A:

From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.

Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

Part C:

The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 given by:

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What are the domain and range of this relation? {(3, -9), (11,21), (121,34), (34,1), (23,45)}
Simora [160]

Answer:

domain = ( 3, 11, 121, 34, 23)

range = ( 21, 34, 1, 23)

7 0
2 years ago
What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?​
Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

 Given the equation:

\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}

Follow these steps to solve it:

- Subtract the fractions on the left side of the equation:

\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}

- Using the Difference of squares formula (a^2-b^2=(a+b)(a-b)) we can simplify the denominator of the right side of the equation:

\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}

- Multiply both sides of the equation by (m+3)(3-m) and simplify:

\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}

- Multiply both sides by m-3:

(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)

- Apply Distributive property and simplify:

(-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0

- Divide both sides of the equation by -6:

\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0

- Factor the equation and solve for "m":

(m-3)^2=0\\\\m=3

In order to verify it, you must substitute m=3 into the equation and solve it:

\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}

<em>NO SOLUTION</em>

7 0
3 years ago
PLEASE HELP ME WITH THIS ASAP
Arte-miy333 [17]
Eddie: $10-3=$7
Marsha: $8+$3=$11
7 0
2 years ago
NEED HELP! no links as answer pls
Nikolay [14]
-2* F




You do +3 +2 -4 -1 which equals to 0. Then you do 0 plus -2 which equals -2*F.
7 0
2 years ago
Next, rearrange the expression in part B using the Commutative Property so the terms with the same place value are next to each
Hunter-Best [27]

Answer:

70 + 2 + 0.3 + (-30) + (-9) + (-0.1) = 70 + (-30) + 2 + (-9) + 0.3 + (-0.1)

Step-by-step explanation:

i dont have an explanation but that is the answer i can confirm because i did it and got it wrong but then it showed the right answer hope it helps you

5 0
2 years ago
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