Given:
The graph of a system of inequalities.
To find:
The ordered pair which is a solution to the graphed inequality.
Solution:
The boundary lines are:
\(x-2y=4\)
\(2x-y=4\)
From the given graph it is clear that only point (3,1) lies in the shaded region.
Points (2,-1) and (4,0) lie on the boundary line \(x-2y=4\) but the boundary line is dotted. It means the points on the line are not in the solution set.
point (0,-1) does not belong to the shaded region.
Therefore, the correct option is A.
if you can guess my middle name will mark Brainlyest.
hint one: named after a British toffee
hint two: it starts with a h
Answer:
Heath
I think
Step-by-step explanation:
Answer:
is it Heath?
Hope it helps!!!
At a middle school, 74 students have freckles. There are 258 students in the school. To the nearest tenth of a percent, what percent of the students have freckles?
Question 1(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
A.
x: 1 1 0 1 1
y: −2 −1 0 1 2
B.
x: 0 1 2 3 4
y: −3 2 0 −2 3
C.
x: −2 −1 0 1 2
y: 2 0 −1 0 2
D.
x −2 −1 0 1 2
y 3 1 −1 −3 −5
The tables that reprsesent a linear function is (d)
How to determine the tables that reprsesent a linear functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
A table of value that is a linear function is a table that has a constant rate
i.e. as x changes, y changes constantly
Using the above as a guide, we have the following:
In table (d) x changes constantly by 1 and y constantly changes by -2
Hence, the table is table (d)
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f(x) = x
f(x) = 3
5
6
f(x)=3-x
f(x) = 1
Domain
3
0
x=2
2
f(x) = 2
Function Equation
f(x) = 5-x
f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1, f(x) = 1 is a constant function, f(x) = 2 is a constant function
What is a constant function?A constant function is a mathematical function whose output value is the same for every input value
From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies that for every unit increase in x, the value of y increases by 1.
Also, f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.
In the same way, f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.
The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.
The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.
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Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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f(x)=4x^2+5x-3
g(x)=4x^3-3x^2+5
Find (f-g)(x)
Answer:
For me the answer was (f+g)(x)=4x^3+x^2+5x+2
Step-by-step explanation:
A function assigns the values. The value of the (f-g)(x) is 4x³ + x² +2 is 4x³ + x² + 5x + 2.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that f(x)=4x²+5x-3 and g(x)=4x³-3x²+5, therefore, the value of the (f-g)(x) can be written as,
(f-g)(x) = f(x) - g(x)
= 4x² + 5x - 3 + 4x³ - 3x² + 5
= 4x³ + 4x² - 3x² + 5x + 5 - 3
= 4x³ + x² +2
Hence, The value of the (f-g)(x) is 4x³ + x² +2 is 4x³ + x² + 5x + 2.
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There are 103 pounds of wood pieces in a bag. Each wood piece weighs 53 pounds. How many wood pieces are there in the bag?
Answer:
Approximately 2
Step-by-step explanation:
103 divided by 53 is 1.94
Round 1. 94 up to a whole number is approximately 2 wood pieces.
Hello ! I can not solve this problem of equations can you help me please.
Three mobile operators offer, for the same phone, the following rates :
Operator A: 120€ per phone and 20€ per month subscription.
Operator B: 40€ per phone and 25€ per month subscription.
Operator C: 10€ per phone and 30€ per month subscription.
1) Complete: the one who will keep his phone for a long time will choose the operator ..., the one who will keep his phone for a short time will choose the operator ... and the operator ... is an intermediate choice.
2) Calculate the number of months for which each operator is advantageous.
Thanks in advance for your help !
1. The one who will keep his phone for a long time will choose the operator A, the one who will keep his phone for a short time will choose the operator C, and the operator B is an intermediate choice.
What is fixed and variable cost?Fixed costs are outlays that don't change no matter how much is produced or sold. Rent, salary, and insurance are a few examples of fixed costs. Contrarily, variable costs are expenses that vary according to the volume of production or sales. The costs of labour, commissions, and raw materials are a few examples of variable costs. Because they must be paid regardless of the volume of production or sales, fixed expenses are frequently referred to as "sunk costs," in contrast to variable costs, which are closely related to income and are simpler to control.
1. The one who will keep his phone for a long time will choose the operator A, the one who will keep his phone for a short time will choose the operator C, and the operator B is an intermediate choice.
2. Let us suppose number of months = X.
Thus,
For Operators A and B:
120 + 20X = 40 + 25X
5X = 16
X = 3.2
For Operators B and C:
40 + 25X = 10 + 30X
X = 6
Hence, Operator C is the best option for someone who intends to keep the phone for less than 3.2 months. Operator B is the ideal option for someone who intends to keep the phone for 3.2 to 6 months. Operator A is the greatest option for someone who intends to keep the phone for more than six months.
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is (4,3) a solution of the graphed inequality?
yes or no?
Answer:
no
Step-by-step explanation:
it is outside of the wanted area
Answer:
no
Step-by-step explanation:
Cause i was on khan acedemy and got it right
The door frames used in an industrialised building system are of one standard size.
If the heights of adults are normally distributed, men with a mean of 1.73m and standard deviation of 0.064m and women with a mean of 1.67 and standard deviation of 0.050m; then if women outnumber men (e.g. in a department store) in the ratio 19:1, for what proportion of people would a frame height of 1.83m be too low?
options are
1. 1
2. 0.0007
3. 0.0591
4. 0
The closest option provided is 0.94 (rounded to two decimal places), which is the proportion of people for whom the frame height would be too low.
To determine the proportion of people for whom a frame height of 1.83m would be too low, we need to calculate the probability that an individual's height exceeds 1.83m based on the given information about the height distributions of men and women.
1. Calculate the z-score for the height of 1.83m for both men and women:
- For men: z_men = (1.83 - 1.73) / 0.064
- For women: z_women = (1.83 - 1.67) / 0.050
2. Look up the corresponding probabilities (p-values) associated with the calculated z-scores using a standard normal distribution table or a calculator.
3. Calculate the proportion of people for whom a frame height of 1.83m would be too low:
- For men: Since the ratio of women to men is given as 19:1, we multiply the probability associated with the z-score for men by the ratio of women to the total population (19 / 20).
- For women: We multiply the probability associated with the z-score for women by the ratio of women to the total population (1 / 20).
4. Add the proportions calculated in step 3 to obtain the overall proportion.
Let's calculate the values:
1. For men:
z_men = (1.83 - 1.73) / 0.064 = 1.5625
2. For women:
z_women = (1.83 - 1.67) / 0.050 = 3.2
3. Using a standard normal distribution table or a calculator, we find:
- For men: The probability associated with a z-score of 1.5625 is approximately 0.9392.
- For women: The probability associated with a z-score of 3.2 is approximately 0.9993.
4. Calculate the proportions:
- For men: (0.9392) * (19/20) = 0.8924
- For women: (0.9993) * (1/20) = 0.04997
5. Add the proportions calculated in step 4:
0.8924 + 0.04997 = 0.94237
Therefore, the proportion of people for whom a frame height of 1.83m would be too low is approximately 0.94237.
Please note that this is a probability and should be expressed as a decimal or percentage. The closest option provided is 0.94 (rounded to two decimal places), which is the proportion of people for whom the frame height would be too low.
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Help me find the scale of the given dilation?
Answer:
The scale factor is 0.25 also written as 1/4
Step-by-step explanation:
1. Find the distance of each leg on the trapezoids
2. Use pathagreum thorum to find the slanted legs
3. Divide the little trapezoid leg to the corresponding big trapezoid leg to find the scale factor because you divide the dialated trapezoids legs by the original trapezoids legs
2÷8 = 0.25
1÷4 = 0.25
2.2360679775 ÷ 8.94427191 = 0.25
2÷8 again = 0.25
So the scale factor is 0.25
Hope this helps! :)
Ishi bought a canvas and 8 tubes of paints for $24.95. If the canvas cost $6.95, how much did each tube of paint cost. please made a two step Equations. please can you solve two step equations.
Answer:
24.95-6.95= 18
18 divided by 8 = 2.25
So each tube of paint cost 2.25 dollars
Step-by-step explanation:
for the first equation we are subtracting the cost of the canvas from the total cost to find the cost of 8 tubes of paint and we get that 8 tubes of paint cost 18 dollars. Next we divide 18 by 8 to get the cost of a single tube of paint and we get 2.25.
Joe is at the ice cream shop in his house is 9 blocks north of the shop the park is 9 blocks south of the ice cream shop where he is at the ice cream shop is Joe closer to the park or his house how could the number 0 be used in the situation explain using the number line to the right to help you
Answer:
pls could you explain the question a bit more?...
Step-by-step explanation:
Consider the linear equation y = 2x - 4. Write an equation in slope-
intercept form for a line parallel to the given line through (-1,6).
Amina wants to convert some of her money to Australian dollars (AUD ) for a vacation. She found out that 1AED =0.4AUD. How many AUD will Amina get for AED 800? What is the conversion factor that should be used to convert AED 800 to AUD?
To find out how many Australian dollars (AUD) Amina will get for AED 800, we can use the given conversion rate of 1 AED = 0.4 AUD.
To calculate the amount of AUD, we multiply the AED amount by the conversion rate:
AUD = AED Conversion Rate
In this case, AED 800 * 0.4 AUD/AED = 320 AUD.
Therefore, Amina will get 320 Australian dollars (AUD) for AED 800.
The conversion factor that should be used to convert AED 800 to AUD is 0.4, as 1 AED is equal to 0.4 AUD.
The conversion factor of 0.4AUD per 1AED indicates that for every 1 AED, Amina will receive 0.4 AUD. This conversion factor is used to convert the amount in AED to its equivalent value in AUD.
By multiplying the AED amount by the conversion factor, we can determine the corresponding AUD amount. In this case, multiplying AED 800 by 0.4 gives us 320 AUD.
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Identify the net that corresponds to the figure below. A. B. C. D.
Answer:
The net that corresponds to it is ,B
A small box measures 6 in. by 5 in. by 4 in. high. Find the volume of the box.
Answer:
120
Step-by-step explanation:
the volume of the box( which is a rectangle ) is: V =(l)(w)(h), which means length x width x height, which is also 6x5x4, which equals to 120
Solve: 4 1/5 − 3/7 plese sent the answer
Answer:
\(4 \frac{1}{5} - \frac{3}{7} \\ =4 + \frac{1}{5} - \frac{3}{7} \\ = \frac{21}{5} - \frac{3}{7} \\ \frac{147 - 15}{35} \\ = \frac{132}{35}
=3 27/35 \\ thank \: you\)
132/35
Step-by-step explanation:
\(4 \frac{1}{5} - \frac{3}{7} \\ \frac{21}{5} - \frac{3}{7} \\ lcm = 35 \\ \frac{21 \times 7}{5 \times 7} - \frac{3 \times 5}{7 \times 5} \\ \frac{147}{35} - \frac{15}{35} \\ = \frac{132}{35} \\ \)
A music teacher grades on an E (Excellent) S (Satisfactory) and U (Unsatisfactory) garding scale. A final score of more than 92 earns an E. A final score of 60 or less earns a U.Any other final score earns an S.A. Write two inequality one to represent a grade of E and one to represent a grade of U.B. Zeb say that inequality x > 60 represents a grade of S. Is zeb correct? Explain.
A final score of more than 92 earns an E, that means
E>92
A final score of 60 or less earns a U:
\(U\leq60\)The inequality to represent Satisfactory grade, could be:
\(92\leq S<60\)1. Which figure comes next in the pattern below?
The figure that comes next in the pattern below is option D.
Option D is the correct answer.
We have,
From the pattern,
The next figure must be a white figure.
Now,
We see that,
The two small figure inside the figure is moving in a clockwise direction.
So,
The next figure in the pattern is option D.
Thus,
The figure that comes next in the pattern below is option D.
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emma advertises a reward for the return of her lost dog. frank, who does not know of the reward, finds and returns the dog. frank cannot recover the reward because he
Frank cannot recover the reward because he was unaware of the reward being offered by Emma.
In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.
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Describe function transformations KT8
What kind of transformation converts the graph of
f(x) = 3x - 9
into the graph
of g(x) =-3x - 9?
Answer:
The answer is reflection on the y-axis
Step-by-step explanation:
Reflection on the x-axis will change the y-intercept
Horizontal shrink will change the slope but not to the point of making the 3 negative
Horizontal stretch is the same concept
Thus Reflection on the y-axis on the y-axisis the answer
Hope this helps!
Use factoring to write an expression that is equivalent to 28w - 40.
Answer:
4(7w+10)
Step-by-step explanation:
Answer:
4(7w+10)
Step-by-step explanation:
Write an equation if the perpendicular bisect or if the the segment with endpoint -1,-5 and 2,-3writing non integers
The linear equation perpendicular to the segment that also bisects it is:
y = (-3/2)*x - 11/4
How to find the equation of the line?Here we know that we have a segment whose endpoints are (-1, -5) and (2, -3)
Then the midpoint of the segment (where our linear equation passes by) is:
( (-1 + 2)/2, (-5 - 3)/2) = (0.5, -4)
Now, we also want our line to be perpendicular to the segment, so the slope of the line must be the opposite of the inverse of the slope of the segment.
The slope of the segment is:
a = (-3 + 5)/(2 + 1) = 2/3
Then the slope of our linear equation will be -3/2, it gives:
y = (-3/2)*x + b
Now we use the fact that our line passes through the point (0.5, -4), so we get:
-4 = (-3/2)*0.5 + b
-4 = -3/4 + b
-4 + 3/4 = b
-16/4 + 3/4 = b
-11/4 = b
The linear equation is:
y = (-3/2)*x - 11/4
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Read the word problem below. Jill had $90. She bought a skirt that normally costs $42 but was on sale for half price. She also bought a T-shirt that was $8 off its regular price. Before sales tax, the total cost of the clothes was $31. What was the regular price of the T-shirt? What question is being asked in this word problem? What is the regular price of the skirt? How much money does Jill have left? How much does the T-shirt normally cost? What is the amount Jill pays in sales tax?
Answer:
What was the regular price of the T-shirt?
$18What question is being asked in this word problem?
what is the regular cost of the t-shirt purchased by Jill.What is the regular price of the skirt?
$42How much money does Jill have left?
without considering sales tax, Jill has $90 - $31 = $59 left.If I use the sales tax from where I live, the sales tax = $1.86, so the money that Jill will have left = $59 - $1.86 = $57.14How much does the T-shirt normally cost?
$18 (same as question 1)What is the amount Jill pays in sales tax?
since you do not include the sales tax % in the question, I will simply use the sales tax from where I live = $31 x 6% = $1.86Step-by-step explanation:
skirt $21
t-shirt = p - $8
before sales tax, total cost was $31
$21 + p - $8 = $31
p = $18
Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.
well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)
\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)
now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)
Ronnie's Furniture Store had a sale on Saturday.
Every item was reduced by 15%. Mike purchased
these items.
Original Prices
one couch for $199.99
two tables for $149.99 each
one lamp for $99.99
Which amount is closest to the total cost of Mike's
purchases after the 15% discount and including the
6% sales tax?
A $410
B $510
C $540
D $640
We can see that option C, $540, is the same as the total cost we calculated in Step 3. Therefore, the answer is option C, $540.
To solve this problem, we need to follow a few steps, Let's go through each step in more detail.
Step 1: Calculate the reduced prices of each item after the 15% discount
To calculate the reduced price of each item, we need to multiply its original price by 0.15 (which represents the 15% discount) and then subtract that amount from the original price. Here are the calculations:
- Couch: 199.99 - (0.15 x 199.99) = $169.99
- Tables (2): 149.99 x 2 - (0.15 x 149.99 x 2) = $254.98
- Lamp: 99.99 - (0.15 x 99.99) = $84.99
So the reduced prices of the items are:
- Couch: $169.99
- Tables (2): $254.98
- Lamp: $84.99
Step 2: Calculate the subtotal by adding up the reduced prices of each item
To get the subtotal, we simply add up the reduced prices of each item:
169.99 + 254.98 + 84.99 = $509.96
So the subtotal is $509.96.
Step 3: Add the 6% sales tax to the subtotal to get the total cost of Mike's purchases after the discount and including the sales tax.
To get the total cost of Mike's purchases after the discount and including the sales tax, we need to add the 6% sales tax to the subtotal. We can do this by multiplying the subtotal by 0.06 and then adding the result to the subtotal:
509.96 + (0.06 x 509.96) = $540.55
So the total cost of Mike's purchases after the discount and including the sales tax is $540.55.
Step 4: Compare the total cost to the given options and choose the one closest to the answer
We need to compare the total cost of Mike's purchases that we calculated in Step 3 ($540.55) to the given options and choose the one that is closest to the answer. The given options are:
A) $410 , B) $510, C) $540, D) $640
We can see that option C, $540, is the same as the total cost we calculated in Step 3. Therefore, the answer is option C, $540.
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Find the median of the data: 22, 16, 14, 26, 32 and 30
Step-by-step explanation:
14 ,16,22,26,30,32
Have a great day
Answer:
\(\boxed {\boxed {\sf 24}}\)
Step-by-step explanation:
We are asked to find the median of the following data set:
22, 16, 14, 26, 32, 30The median is the middle number of the data set. It separates the higher half of the set from the lower half. We put the data set in order from least to greatest and find the middle number.
14, 16, 22, 26, 30, 32We eliminate a number from each side of the data set until we find the middle number.
16, 22, 26, 3022, 26However, the data set had 6 numbers, which is an even number. There isn't one middle number, so we must find the average of the middle 2 numbers. Add the numbers and divide by 2.
22+ 26 = 48 48 / 22= 24The median of the data set is 24.
Determine the scale factor for Triangle ABC to Triangle A’B’C
Answer:
C
Step-by-step explanation:
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The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect 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 a standard deviation of 0.5.
a. What is the mean (±0.1)(±0.1) of the average number of moths ¯x�¯ in 30 traps?
b. What is the standard deviation? (±0.001)(±0.001)
c. Use the central limit theorem to find the probability (±0.01)(±0.01) that the average number of moths in 30 traps is greater than 0.4.
The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855
a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.
b) The population deviation divided by the square root of the sample size gives the standard deviation value.
standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073
c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by
1 - P (X < x)= P (X > x)
= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))
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 is given by:
1 -P (X - 0.7) = P (X > 0.7)
= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)
= 1 - 0.91455 = 0.0855
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