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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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The vertices of a triangle are P(-1, 3), Q(2, -1), and R(5, 3).
Morgarella [4.7K]
Ok so to find which sides are congruent we need to know their lengths.

To find the length we need the distance formula between two point ->

√(X2-X1)∧2 +(Y2-Y1)∧2

Ok lets find the first side PQ

P(-1,3) Q(2,-1)
   X1 Y1  X2 Y2

√(2-(-1)∧2 + (-1-3)∧2 = 5

Now PR

P (-1,3) R (5,3)
    X1 Y1  X2 Y2

√(5-(-1))∧2 + (3-3)∧2) = 6

Now the last side QR

Q (2, -1) R (5,3)
   X1  Y1    X2 Y2

√(5-2)∧2 + (3-(-1))∧2 = 5

From the above work we see that PQ and QR are congruent becuase they are equal PQ=QR

Also the opposite angles of these sides are congruent. Hope this helps :).

8 0
3 years ago
Read 2 more answers
Can you help me with this word problem?​
dangina [55]

Answer:

The ratio of flour to sugar is 2:1

Step-by-step explanation:

Let f = weight of a bag of flour

Let s = weight of a bag of sugar

3f+2s = 32

4f = 32

We have 2 equations and 2 unknowns, we can solve

4f=32

Divide by 4

4f/4 = 32/4

f = 8

Each bag of flour weights 8 pounds

Substitute this back into the first equation

3(8) +2s = 32

24+2s = 32

Subtract 24 from each side

24-24 +2s =32-24

2s = 8

Divide by 2

2s/2 = 8/2

s = 4 pounds

Flours weighs 8 pounds and sugar weights 4 pounds

We want the ratio of flour to sugar

Flour: sugar

8:4

We can divide each side by 4

8/4: 4/4

2:1

4 0
3 years ago
Solve: 2x + 18 - 1 = 33
Alecsey [184]

Answer: x=8

<u>Simplify both sides of the equation</u>

<u />2x+18+-1=33<u />

<u />(2x)+(18+-1)=33(Combine Like Terms)

2x+17=33

<u>Subtract 17 from both sides</u>

<u></u>2x+17-17=33-17\\2x=16<u></u>

<u></u>

<u>Divide both sides by 2</u>

<u></u>2x/2=16/2\\x=8<u></u>

7 0
2 years ago
Read 2 more answers
Please please i need help i will mark u brill
zvonat [6]

Answer:

106 - 8h = 34

Whenever a math question says "when <em>h </em>= 9," they mean you substitute this number where <em>h </em>is in the equation.

106 - 8(9) = 34

106 - 72 = 34

34 = 34

This means the fact that h = 9 <u>is a solution for h.</u>

<em>I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!</em>

6 0
2 years ago
If △ABC ~ △DEF, find the length EF.
hodyreva [135]

Answer:

EF=BC (by CPCT) if both Triangle are ~

8 0
3 years ago
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