You're basically looking for the square root of 49. In fact, if a number [tex] x [/tex] gives [tex] y [/tex] when multiplied by itself two times, then you have [tex] x^2 = y [/tex], which also means that [tex] x [/tex] is the square root of [tex] y [/tex], i.e. [tex] x = \sqrt{y} [/tex]
In your case, the answer is 7, because you have
[tex] \sqrt{49}=7 \iff 7^2 = 49 [/tex]
which is indeed true
Answer:
Step-by-step explanation:
You want the square root of 49, which is 7
The ratio of side lengths of square a to square b is 2 : 3. The perimeter of square a is 16 inches. What is the area of square b?
if the ratio of sides is 2:3, the ratio of the perimeters will be the same
2 16
------- = ---------
3 P
Using cross product 2*P = 3*16
2P = 48
P = 24 inches
Molly hikes 1/6 miles everyday to hike a total of 11/6 she would have to hike for how many days
Molly would have to hike for 11 days for it to equal 11/6
What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56?
Answer:
[tex]a_{24}=146[/tex]
Step-by-step explanation:
The formula of a nth term of n arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
--------------------------------------
[tex]a_m=a_1+(m-1)d\\\\a_m-a_n=(a_1+(m-1)d)-(a_1+(n-1)d)\\\\=a_1+(m-1)d-a_1-(n-1)d=(m-1)d-(n-1)d=(m-1-n+1)d=(m-n)d[/tex]
Therefore
[tex]a_9-a_1=(9-1)d=8d[/tex]
[tex]8d=56-8\\8d=48\qquad|:8\\d=6[/tex]
Substitute:
[tex]a_1=8,\ d=6,\ n=24\\\\a_{24}=8+(24-1)(6)=8+(23)(6)=8+138=146[/tex]
I went to the store and bought 0.89 pounds of apples. Apples cost $1.39 a pound. How much did i pay for apples?
An airplane is flying at an altitude of 3000 feet . The pilot dives 630 feet and then rapidly crimes 1048 feet. The pilot then dives Again 888 feet before making another climb of 1067 feet. Again 888 feet before making another climb of 1067 feet. How far above the ground is airplane ?
Answer:
The plane is at an altitude of 3597 feet
Step-by-step explanation:
Airplane is flying at an altitude of 3000 feet.
Now it dives 630 feet, then the altitude is 2370 (3000-630).
Then it rapidly climbs 1048 feet, then the altitude will be 3418 (2370+1048).
Then it again drops 888 feet, meaning now its at at altitude 2530 (3418-88).
Then it again climbs 1067 feet, now the altitude will be 3597 (2530+1067)
Therefore, the plane is at an altitude of 3597 feet. (Assuming that Again 888 feet before making another climb of 1067 feet has been typed twice by mistake. I considered only 1 drop of 888 and climb of 1067)
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y + 2x = 8 2y - 4x = 2
The solution of the given equations is equal to (x,y) = (1,3)
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given equations:-
2y + 2x = 82y - 4x = 2The equation will be solved as:-
2y = 8 - 2x (divide by 2 on both sides)
y = 4 - x (insert this into the second equation
2 x ( 4 - x ) - 4x = 2
8 - 2x - 4x = 2
8 - 6x = 2
-6x = 2 - 8
-6x = -6
x = 1 (insert this into either of the first two equations)
2y + 2 x 1 = 8
2y + 2 = 8
2y = 8 - 2
2y = 6
y = 6/2
y = 3
Therefore the solution of the given equations is equal to (x,y) = (1,3)
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Simplify the polynomial expression. 3x(-2x+7)-5(x-1)(4x-3)
A.
14x^2-14x+15
B.
-26x^2+21x-15
C.
-26x^2+56x-15
D.
-2x^2+14x-2
The answer is c. have a good day
To simplify the given polynomial expression, distribute coefficients to terms within each parentheses, combine like terms, and simplify further to obtain the simplified form of the expression: 14x^2 - 14x - 15.
Explanation:To simplify the given polynomial expression, we'll start by distributing the coefficients to the terms within each parentheses:
Now, we'll combine like terms and simplify further:
Therefore, the simplified form of the given polynomial expression is 14x^2 - 14x - 15.
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A furniture company currently produces 7500 chairs per month if production decreases 5% find the amount of decreases and the new number of chairs produced each month
The new number of chairs produced per month is 7125
To find the amount of decrease:
Calculate 5% of 7500 chairs: 7500 x 0.05 = 375.
The decrease is 375 chairs.
To find the new number of chairs produced:
Subtract the decrease from the original amount: 7500 - 375 = 7125.
The new number of chairs produced per month is 7125
Please help!!! 15 points problem below
We are given height function of the bridge
h(x) =-0.5(x-4)^2 +2.
Where height is the height of the bridge in feet and x is the distance between two bases.
We have height =0 on the base of the bridge. In order to find the both bases, we need to plug h(x) as 0 and solve for x.
-0.5(x-4)^2 +2 = 0
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}[/tex]
[tex]-0.5\left(x-4\right)^2+2-2=0-2[/tex]
[tex]-0.5\left(x-4\right)^2=-2[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]
[tex]-0.5\left(x-4\right)^2\cdot \:10=-2\cdot \:10[/tex]
[tex]-5\left(x-4\right)^2=-20[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-5[/tex]
[tex]\frac{-5\left(x-4\right)^2}{-5}=\frac{-20}{-5}[/tex]
[tex]\left(x-4\right)^2=4[/tex]
Taking square root on both sides, we get
[tex]x-4=\sqrt{4}[/tex]
[tex]\:x-4=\sqrt{4} \ and \ x-4=-\sqrt{4}[/tex]
[tex]x-4=2 \\x-4=-2[/tex]
[tex]x=6,\:x=2[/tex]
We got horizontal distances 2 feet and 6 feet.
Therefore, correct option is D.
PLEASE HELP 50 POINTS!!
Answer: 225
Step-by-step explanation:
n₁ = 2(1) - 1
= 2 - 1
= 1
n₁₅ = 2(15) - 1
= 30 - 1
= 29
[tex]S_{15} =\frac{n_{1}+ n_{15}}{2}*15[/tex]
[tex]=\frac{1+29}{2}*15[/tex]
[tex]=\frac{30}{2}*15[/tex]
= 15 * 15
= 225
➷ The sum would be 225
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Andy told Lena that he spent $16.33 on 4.6 pounds of ground beef at the grocery store. How much will Lena spend if she needs 3 pounds of ground beef?A.$3.55B.$5.44C.$10.65D.$23.93
Total amount spent on 4.6 pounds of ground beef = $16.33
We have to determine the amount spend on 3 pounds of ground beef.
We will use unitary method to solve this problem.
So, amount spent on 1 pound of ground beef = [tex]$16.33 \div 4.6[/tex]
= $3.55
So, amount earned on 3 pounds of ground beef = [tex]3 \times $3.55[/tex]
= $10.65
Therefore, Lena will spend $10.65 on 3 pounds of ground beef.
So, Option C is the correct answer.
To determine Lena's expense for 3 pounds of ground beef, the cost per pound is calculated as $3.55, resulting in a total cost of $10.65.
To calculate how much Lena will spend for 3 pounds of ground beef, we first need to determine the price per pound that Andy paid. Andy spent $16.33 for 4.6 pounds of ground beef, so we divide the total cost by the number of pounds to find the price per pound:
Price per pound = $16.33 / 4.6 pounds = $3.55 per pound
Lena needs 3 pounds of ground beef, so we multiply the price per pound by the number of pounds Lena needs:
Cost for Lena = $3.55 per pound × 3 pounds = $10.65
Therefore, Lena will spend $10.65 for 3 pounds of ground beef, which corresponds to option C.
Ashley has sold 70% of the 20 candy bars she is suppose to sell how many candy bars does she have left
She has sold 70% of 20
= 0.70 * 20
= 14 candy bars.
So she has 20 - 14 = 6 candy bars left
The admission fee at a fair is $3.25 for children and $6.75 for adults. On a certain day, 870 people enter the fair and $3,772.50 is collected. Write a system of linear equations that you can use to determine how many children and adults attended. Be sure to define your variables. Solve the system. SHOW YOUR WORK PLEASE!
Given that admission fee for 1 child = $3.25
If there are x children then admission fee for x children = $3.25x
Given that admission fee for 1 adult = $6.25
If there are y adults then admission fee for y adults = $6.75y
Then total fee collected = 3.25x+6.75y
Given that On a certain day, 870 people enter the fair then equation will be
x+y=870
or y=870-x...(i)
And $3,772.50 is collected means we get equation:
3.25x+6.75y = 3772.50
or 325x+675y = 377250...(ii)
Hence required system of equation is {x+y=870, 3.25x+6.75y = 3772.50}
Now we solve both to find values of x and y
Plug (i) into (ii)
325x+675(870-x) = 377250
325x+587250-675x = 377250
587250-350x = 377250
-350x = 377250-587250
-350x = -210000
x=600
now plug value of x into (i)
y=870-x=870-600=270
Hence final answer is:
Number of children = 600
Number of adults = 270
For this case we have the following variables:
x: Represents the number of children at the fair
y: Represents the number of adults at the fair
If 870 people enter the fair we have:
[tex]x + y = 870[/tex]
If that day is collected 3772.50 dollars, we have:
[tex]3.25x + 6.75y = 3772.50[/tex]
So, we have two equations with two unknowns:
[tex]x + y = 870[/tex] -----> (1)
[tex]3.25x + 6.75y = 3772.50[/tex] -----> (2)
Clearance of (1):[tex]y = 870-x[/tex]
Substituting in 2:
[tex]3.25x + 6.75 (870-x) = 3772.50\\3.25x + 6.75 * 870-6.75x = 3772.50\\3.25x-6.75x = 3772.50- (6.75 * 870)\\3.25x-6.75x = 3772.50-5872.5\\-3.5x = -2100[/tex]
[tex]x = \frac{-2100}{-3.5}\\x = 600[/tex]
Thus, there were 600 children at the fair.
To know the number of adults, we cleared and from the equation (1):
[tex]y = 870-x\\y = 870-600\\y = 270[/tex]
Thus, there were 270 adults at the fair.
Answer:
600 children and 270 adults
What is 21m−49n factored using the gcfyou get lots of points if you help!
answer which is equal to 7(3m-7n)
What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 4]? x f(x) -6 27 -3 6 -1 2 0 3 1 6 4 27 A. -6 B. -3 C. 3 D. 6 E. 21
Answer:
The correct option will be: C. 3
Step-by-step explanation:
The given table is..........
[tex]x :[/tex] -6 -3 -1 0 1 4
[tex]f(x) :[/tex] 27 6 2 3 6 27
The formula for average rate of change is: [tex]\frac{f(b)-f(a)}{b-a}[/tex] , where [tex][a,b][/tex] is the given interval.
Here the interval is [-3, 4]. So, [tex]a=-3[/tex] and [tex]b=4[/tex]
Now, plugging the values of [tex]a[/tex] and [tex]b[/tex] into the above formula, we will get........
[tex]\frac{f(4)-f(-3)}{4-(-3)}[/tex]
From the given table, we will get [tex]f(4)=27[/tex] and [tex]f(-3)=6[/tex]
So, the average rate of change will be: [tex]\frac{27-6}{4-(-3)}= \frac{21}{7}=3[/tex]
Answer:
The person that answered it above me is correct
Step-by-step explanation:
A length of rope is 6 1/2 feet long. How many total feet long are 2 3/4 lengths of rope?
Multiply the two together.
(13/2)(11/4)
143/8
= 17 and 7/8
There are 17 and 7/8 feet in 2 and 3/4 lengths of rope.
Rocky has 7 bottles of water. He will buy more bottles of water from the store. The store has 8 cases in stock and each case contains 24 bottles of water. The store will not sell partial cases. The function that models the number of bottles of water Rocky will have after his purchase is f(c)=24c+7, where c is the number of cases of water he buys. What is the practical domain of the function?
A) {1, 2, 3, 4, 5, 6, 7, 8}
B) all real numbers from 1 to 8, inclusive
C) all real numbers
D) {31, 55, 79, 103, 127, 151, 175, 199}
The practical domain of the function f(c) = 24c + 7 is the set of positive integers from 1 to 8, inclusive.
Explanation:The practical domain of a function represents the set of input values for which the function is defined and has a meaningful output. In this case, the number of cases of water Rocky buys, represented by 'c', cannot be negative because you cannot buy a negative number of cases. Additionally, the store has a limited stock of 8 cases, so Rocky cannot buy more than 8 cases. Therefore, the practical domain of the function f(c) = 24c + 7 is the set of positive integers from 1 to 8, inclusive.
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The practical domain of the function is the set of integers from B) 1 to 8, inclusive.
Explanation:The practical domain of the function can be determined by considering the limitations of the problem. In this case, Rocky can only buy a whole number of cases, so the number of cases he buys must be a positive integer.
Additionally, since the store has 8 cases in stock, Rocky cannot buy more than 8 cases. Therefore, the practical domain of the function is the set of integers from 1 to 8, inclusive. Thus, the practical domain of the function f(c) = 24c + 7 is the set of positive integers from 1 to 8, inclusive.
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What does 3,146 round to nearest thousand
The length of rectangular field is twice its breadth.If the perimeter of the field is 228,find the dimensions of the field
We have the equations: l = 2b and 2l + 2b = 228;
Then, 4b + 2b = 228;
6b = 228;
b = 228/6;
b = 38 (breadth);
l = 2·38;
l = 76 (length);
Mark earned $40 mowing lawns last week. He spent 3/5 of his money on two CDs. How much did he spend on these two CDs?
Select all the possible solutions for 2x+7 is less than or equal to 3x-5
2x + 7 <= 3x - 5
Treat <= as an = sign unless you divide or multiply by a negative number.
2x + 12 <= 3x
x <= 12
The answer is all real numbers less than or equal to 12.
2x + 7 ≤ 3x - 5
Isolate the x. Subtract 3x and 7 from both sides
2x (-3x) + 7 (-7) ≤ 3x (-3x) - 5 (-7)
2x - 3x ≤ -5 - 7
Combine like terms
(2x - 3x) ≤ (-5 - 7)
-x ≤ -12
Isolate the x. Divide -1 from both sides. Remember that when dividing by a negative number, you must flip the sign.
(-x)/-1 ≤ (-12)/-1
x ≥ -12/-1
x ≥ 12
x ≥ 12 is your answer
~Rise Above the Ordinary
PLS HELP ASAP 15 PTS
Use rounding to determine whether the following answers are reasonable. a. 96 ÷ 48 = 20 b. 713 ÷ 99 = 72
a. is unreasonable because 96/48 = 2
b. is unreasonable because 713/99=7.2020.... which would be rounded to 7.2 not 72
hope this helps :)p
Final answer:
By rounding the numbers, we find that 96 ÷ 48 is roughly 2, not 20, and 713 ÷ 99 is roughly 7, not 72, indicating both provided answers are not reasonable.
Explanation:
When rounding to check if answers are reasonable, we look at the numbers given and round them to numbers that are easier to work with. Let's apply this to the provided problems:
For a. 96 ÷ 48 = 20, we can round 96 down to 90 (since it's closer to 90 than 100) and 48 up to 50 (since it's closer to 50 than 40). We then estimate the division: 90 ÷ 50 is approximately 2, not 20. Therefore, the answer of 20 is not reasonable.For b. 713 ÷ 99 = 72, we can round 713 to 700 (since it's closer to 700 than 800) and 99 to 100 (since it's closer to 100 than 90). The estimated division is then 700 ÷ 100, which equals 7, not 72. Thus, the answer of 72 is not reasonable either.Write the equation of the line parallel to the given line and passing through the given point.
y = 6 through (3,4)
y = 6 it a horizontal line. The line parallel to horizontal line is horizontal line with the equation y = a.
The line passing through the point (3, 4) → y = 4.
Therefore your answer is : y = 4.
Answer:
y = 4.
Step-by-step explanation:
I checked :)
What is the definition of a statistic?
A. a numerical measurement describing some characteristic of a population
B. a numerical measurement describing some characteristic of a sample
C. the complete collection of all individuals to be studied
D. a subcollection of members selected from a population
Here we have to find which of the following options is correct definition of statistic.
Statistic can be defined as numerical measurement describing some characteristic of a SAMPLE
So we can say that out of the four options, option B. a numerical measurement describing some characteristic of a sample represents the definition of statistic exactly.
Answer: B. a numerical measurement describing some characteristic of a sample
A statistic is a numerical measurement describing some characteristic of a population or a sample.
Explanation:The definition of a statistic is a numerical measurement describing some characteristic of a population or a sample. In option A, a statistic is described as a numerical measurement describing some characteristic of a population, while in option B, it is described as a numerical measurement describing some characteristic of a sample. Option C refers to the population itself, which is the complete collection of all individuals to be studied. Option D describes a sample, which is a subcollection of members selected from a population.
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In what diffrent ways can 440 be written as the product of two positve integers
440 = 1 x 2 x 2 x 2 x 5 x 11
(1): 1 x 440
(2): 2 x 220
(2 x 2): 4 x 110
(5): 5 x 88
(2x2x2): 8 x 55
(2 x 5): 10 x 44
(11): 11 x 40
(2x2x5): 20 x 22
No need to continue because the next number is 2 x 11 = 22 and we already have that on the right side, so we have found all of the multiplicative pairs of 440.
The following data show the number of candies in 15 different bags.
35, 48, 36, 48, 43, 37, 43, 39, 45, 46, 40, 35, 50, 38, 48
Represent the data set on a dot plot.
A.
B.
C.
D.
Answer:
Im pretty sure its c
Step-by-step explanation:
Answer with explanation:
The data points in the question are given by:
35, 48, 36, 48, 43, 37, 43, 39, 45, 46, 40, 35, 50, 38, 48
On making a table of these data values based on the frequency of these points i.e. the number of times they appear in the data.
Points Frequency
35 2
36 1
37 1
38 1
39 1
40 1
43 2
45 1
46 1
48 3
50 1
Hence, the dot plot will be a horizontal line such that the number are at a increment of 1 starting from 35 and shows up to 50.
This means that there are 1 dots over: 36,37,38,39,40,45,46 and 50.
2 dots over 35 and 43.
and 3 dots over 48.
The correct dot plot is attached to the answer.
A recipe calls for 2 and 2/3 cups of flour. Terell wants to make 3/4 of the recipe
2 cups are needed to make 3/4 of the recipe.
Multiply 2 2/3 by 3/4, you will get the answer of 2
What is the value of the 5 in 9,9009,121.15
The value of 5 is hundredths
f(x)=2/3x+3
What is the value of f(12)?
[tex]f(x)=\dfrac{2}{3}x+3\\\\f(12)\to\text{put x = 12 to the equation of a function}\\\\f(12)=\dfrac{2}{3}\cdot12+3=\dfrac{2}{1}\cdot4+3=8+3=11\\\\Answer:\ f(12)=11[/tex]
Answer:
11
Step-by-step explanation:
Vista company inc. Had a beginning inventory of 100 units of product RST at a cost of $8 per unit. During the year, purchases were. Determine the cost of goods available for sale
a) The cost of goods available for sale is $16,800.
b) The calculated values for the cost of goods sold under the FIFO and LIFO methods match the values obtained using the formulas, proving their accuracy.
(a) Beginning Inventory:
100 units at $8 per unit = $800
Purchases:
Feb. 20:
600 units at $9 per unit
= $5,400
May 5: 500 units at $10 per unit
= $5,000
Aug. 12: 400 units at $11 per unit
= $4,400
Dec. 8: 100 units at $12 per unit
= $1,200
Total Cost of Goods Available for Sale
= $800 + $5,400 + $5,000 + $4,400 + $1,200
= $16,800
Therefore, the cost of goods is $16,800.
(b) Given the sales of 1,500 units,
FIFO (First-In, First-Out):
The ending inventory consists of the most recent purchases.
Ending Inventory (FIFO):
Dec. 8: 100 units at $12 per unit
= $1,200
Cost of Goods Sold (FIFO):
Beginning Inventory: 100 units at $8 per unit = $800
Feb. 20: 600 units at $9 per unit
= $5,400
May 5: 500 units at $10 per unit
= $5,000
Aug. 12: 200 units at $11 per unit
= $2,200
Total Cost of Goods Sold (FIFO):
$800 + $5,400 + $5,000 + $2,200
= $13,400
LIFO (Last-In, First-Out):
Ending Inventory (LIFO):
Beginning Inventory: 100 units at $8 per unit = $800
Feb. 20: 400 units at $9 per unit = $3,600
Cost of Goods Sold (LIFO):
May 5: 500 units at $10 per unit
= $5,000
Aug. 12: 400 units at $11 per unit
= $4,400
Dec. 8: 100 units at $12 per unit
= $1,200
Total Cost of Goods Sold (LIFO):
= $5,000 + $4,400 + $1,200
= $10,600
Average-Cost:
Total Cost of Goods Available for Sale: $16,800
Total Units Available for Sale:
Beginning Inventory: 100 units
Feb. 20: 600 units
May 5: 500 units
Aug. 12: 400 units
Dec. 8: 100 units
Total Units Available for Sale:
= 100 + 600 + 500 + 400 + 100
= 1,700 units
Average Unit Cost:
= Total Cost of Goods Available for Sale / Total Units Available for Sale
= $16,800 / 1,700 units
= $9.882 per unit
Ending Inventory:
Remaining Units: 1,700 units - 1,500 units (sold)
= 200 units
Ending Inventory = Remaining Units x Average Unit Cost
= 200 units x $9.882
= $1,976.40
Cost of Goods Sold (Average-Cost):
Total Cost of Goods Available for Sale - Ending Inventory
$16,800 - $1,976.40 ≈ $14,823.60
Therefore, under the average-cost method:
Ending Inventory ≈ $1,976.40
Cost of Goods Sold ≈ $14,823.60
Compare the calculated values with the cost of goods sold formulas.
FIFO Cost of Goods Sold:
Beginning Inventory: 100 units at $8 per unit
= $800
Feb. 20: 600 units at $9 per unit
= $5,400
May 5: 500 units at $10 per unit
= $5,000
Aug. 12: 200 units at $11 per unit
= $2,200
Total Cost of Goods Sold (FIFO):
= $800 + $5,400 + $5,000 + $2,200
= $13,400
LIFO Cost of Goods Sold:
May 5: 500 units at $10 per unit
= $5,000
Aug. 12: 400 units at $11 per unit
= $4,400
Dec. 8: 100 units at $12 per unit
= $1,200
Total Cost of Goods Sold (LIFO):
= $5,000 + $4,400 + $1,200
= $10,600
The match the values obtained using the formulas, proving their accuracy.
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The question attached here seems to be incomplete, the complete question is:
Vista Company Inc. had a beginning inventory of 100 units of Product RST at a cost of $8 per unit. During the year, purchases were:
Feb. 20 600 units at $9
Aug. 12 400 units at $11
May 5 500 units at $10
Dec. 8 100 units at $12
Vista Company uses a periodic inventory system. Sales totaled 1,500 units.
Instructions
(a) Determine the cost of goods available for sale.
(b) Determine the ending inventory and the cost of goods sold under each of the assumed cost flow methods (FIFO, LIFO, and average-cost). Prove the accuracy of the cost of goods sold under the FIFO and LIFO methods. (Round average unit cost to three decimal places.)
To find the total variable cost for 6 jackets, calculate the average variable cost per jacket from the 7 jackets and multiply by 6. Other given economic scenarios involve calculating firm profits, break-even points, and shutdown points based on provided cost structures and market conditions.
The question relates to determining the total variable cost of 6 jackets, based on the given information that 7 jackets have a total variable cost of $300. Without specific details on how the costs change with each additional jacket, a direct calculation is not possible. However, if we assume that the variable cost per jacket is consistent, we can calculate the average variable cost per jacket by dividing the total variable cost for 7 jackets by 7, which is roughly $42.86. We would then multiply this average variable cost by 6 to find the total variable cost for 6 jackets.
For the firm with a total fixed cost of $1,000, a total cost of $4,200, and an output of 500 units, the total variable cost is $3,200. Similarly, for the firm with a total fixed cost of $1,200, a total cost of $4,000, and an output of 1,000 units, the total variable cost is $2,800. This information helps to determine the firm's break-even and shutdown price points.