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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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. Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs
dimulka [17.4K]

Answer:

18 L

Step-by-step explanation:

Given :  she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution.

To Find: How much of the 67% solution must she use?

Let x = amount of 67% solution needed

Then 42-x=amount of 46% solution needed

Now we know that the pure herbicide in the 67% solution

So, pure herbicide = (0.67x)

The amount of pure herbicide in the 46% solution (0.46(42-x))

Now 42 liters of a 55% solution = (0.46(42-x))

So,

Amount of 67% solution + Amount of 46% solution  = 42 liters of a 55% solution

⇒0.67x+0.46(42-x)=0.55*42  

⇒0.67x+19.32-0.46x=23.1

⇒0.21x=3.78

⇒x=\frac{3.78}{0.21}

⇒x = 18 liters

Hence she use 18 liters of the 67% solution

5 0
3 years ago
Read 2 more answers
Need help with equations with variables on both sides, giving 100 points, tysm if you help :) 6 (2x-4) = 8(x +2) A. 3 B. 10 C. 2
scoundrel [369]

Answer:

B. 10

C. All real numbers.

Step-by-step explanation:

6 (2x-4) = 8(x + 2)

Distribute the numbers outside of the factors:

12x - 24 = 8x + 16

Subtract both sides by '8x'

12x - 8x - 24 = 8x - 8x + 16

4x - 24 = 16

Add '24' to both sides:

4x = 40

Divide both sides by 4:

x = 10. Therefore, <u>B. 10</u> is the correct answer.

3(4p - 2) = -6(1 - 2p)

Distribute the numbers similarly to the example before:

12p - 6 = -6 + 12p

Subtract '12p' from both sides:

12p - 12p -6 = -6 + 12p - 12p

0 -6 = -6

Add '6' to both sides:

0 - 6 + 6 = -6 + 6

0 = 0

Therefore, the solution consists of <u>all real numbers.</u>

3 0
3 years ago
The radius of a circle is 4 m. Find its area in terms of <br> π<br> π.
wlad13 [49]

Answer:

16π

Step-by-step explanation:

Given:

\text{Radius of circle}: 4 \ \text{m}

<u>Formula:</u>

\text{Area of circle} = \pi r^{2}

Replace the radius in the formula:

\implies \text{Area of circle} = \pi (4)^{2}

Evaluate the area:

\implies \text{Area of circle} = \pi (4)(4)

\implies \text{Area of circle} = 16\pi

Since the question says to determine the area in terms of π, the final answer is 16π.

8 0
2 years ago
I need help with this question
goldenfox [79]
Take a picture of your work and send it so I can help you
3 0
2 years ago
The fare for an Uber is $5 per trip plus $0.50 per mile. The fare for the trip from the airport to the school center was $11.50.
Vinvika [58]

Answer:

13 miles

Step-by-step explanation:

The fare for the Uber

Cost= 5+ .5 m  

where m is the number of miles

We spent 11.50

11.50 = 5 + .5 m

Subtract 5 from each side

11.5 -5 = 5+.5m -5

6.50 = .5 m

Divide by .5 on each side

6.5/.5 = .5m/.5

13 = m

We went 13 miles

6 0
3 years ago
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