The following operations with functions:
1. (g-f)(1) = 7
2. (h-g)(t) = -1
3. (g -f(a) = -38 - a
4. g(3) - h(3) = -16
5. (h+g)(10) = -6
6. (f-g)(4) = 1
Complete each operation with functions.
1. (g-f)(1) = g(1) - f(1) = (2-1) - (-2-4) = 1 + 6 = 7
2. (h-g)(t) = h(t) - g(t) = (2t+1) - (2t+2) = -1
3. (g-f)(a) = g(a) - f(a) = (-30-3) - (a+5) = -33 - a - 5 = -38 - a
4. g(3) - h(3) = (2(3)-5) - (4(3)+5) = (6-5) - (12+5) = 1 - 17 = -16
5. (h+g)(10) = h(10) + g(10) = (3(10)+3) + (-4(10)+1) = (30+3) + (-40+1) = 33 - 39 = -6
6. (f-g)(4) = f(4) - g(4) = (4(4)-3) - (4+2(4)) = (16-3) - (4+8) = 13 - 12 = 1
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This year, the student council president has decided to raise funds for the school prom by selling Justin Bieber T-shirts. In the past, they’ve sold an average of 1500 shirts at about $12 each. This year, they plan to decrease the price of the shirts. Based on student feedback, for every $0.50 decrease in price, 20 more T-shirts will be sold.
a) Determine the demand (price) function in terms of x , the number of t-shirts sold
b) Determine the marginal revenue function. Then, determine the marginal revenue from the sales of 1800 T-shirts and interpret its meaning.
a) The demand (price) function in terms of x : P(x) = 12 - 0.025(x - 1500)
b) the marginal revenue function is [tex]MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)[/tex] The marginal revenue from the sales of 1800 T-shirts is -$3. This means that for each additional T-shirt sold after the 1800th, the revenue will decrease by $3 per T-shirt
To determine the demand (price) function, we need to find a relationship between the price of the T-shirts (P) and the number of T-shirts sold (x). We are given that for every $0.50 decrease in price, 20 more T-shirts will be sold.
Let's first find the decrease in price per T-shirt sold. If 20 more T-shirts are sold for every $0.50 decrease, then the decrease per T-shirt is $0.50/20 = $0.025. Now, we can set up the demand function. The base price is $12, and we decrease it by $0.025 for each additional T-shirt sold. So the demand function is:
P(x) = 12 - 0.025(x - 1500) To determine the marginal revenue function, we first need to find the total revenue function. Total revenue (R) is the product of the price (P) and the number of T-shirts sold (x):
R(x) = P(x) * x = (12 - 0.025(x - 1500)) * x Now we need to find the derivative of the total revenue function with respect to x, which will give us the marginal revenue function: MR(x) = dR(x)/dx = 12 - 0.05(x - 1500)
To determine the marginal revenue from the sales of 1800 T-shirts, we simply plug in x = 1800 into the marginal revenue function: MR(1800) = 12 - 0.05(1800 - 1500) = 12 - 0.05(300) = 12 - 15 = -$3
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Morganville and Newton are 36 miles apart. On a map, the two cities are 6 inches apart. What is the map scale?
The scale of the map is 1 inch for 6 miles
How to determine the scale of the mapFrom the question, we have the following parameters that can be used in our computation:
Distance apart = 36 miles
Distance on the map = 6 inches
Using the above as a guide, we have the following:
Scale = Distance on the map/Distance apart
Substitute the known values in the above equation, so, we have the following representation
Scale = 6 inches/36 miles
Evaluate
Scale = 1 inch/6 miles
Hence, the scale is 1 inch per 6 miles
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D. Determine whether the following sets define a function or not. a. \( A=\{(a, d),(c, d),(e, f),(b, f)\} \) b. \( B=\{(1,3),(2,4),(5,6),(3,4)\} \) c. \( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\
The sets A and B define a function, while the set C does not.
To determine whether a set defines a function, we need to check if there is one and only one output for each input. In other words, there should not be two different outputs for the same input.
\( A=\{(a, d),(c, d),(e, f),(b, f)\} \)
In this set, there are no repeated inputs, so it does define a function.
\( B=\{(1,3),(2,4),(5,6),(3,4)\} \)
In this set, there are also no repeated inputs, so it does define a function.
\( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\} \)
In this set, there are two different outputs for the input 2 (b and a), so it does not define a function.
Therefore, the sets A and B define a function, while the set C does not.
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\[ 14 x^{3}-39 x^{2}+24 x-4=0 ;[-4,6,1] \text { by }[-300,300,100] \] List all possible rational roots. \[ \frac{2}{7}, \frac{4}{7}, 2,4, \frac{1}{7}, 1, \frac{1}{14}, \frac{1}{2},-\frac{2}{7},-\frac{
The possible rational roots of the equation 14x3 - 39x2 + 24x - 4 = 0 are: 2/7, 4/7, 2, 4, 1/7, 1, 1/14, 1/2, -2/7, -4/7, -2, -4, -1/7, -1, -1/14, -1/2.
To find the rational roots, we need to factor the equation into its linear components. First, factor out a common factor from all terms: 14x3 - 39x2 + 24x - 4 = 0 --> 14x(x2 - 3x + 2)(x-2) = 0.
This means that the equation has three linear components, and each component has a possible root that we can calculate. The possible roots can be determined by using the Rational Root Theorem:
Using the Rational Root Theorem, we can find the possible rational roots of the equation:
Therefore, the possible rational roots of the equation.
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Help pls pls pls pls pls pls, I need help quick
Answer:
D
Step-by-step explanation:
If m=log(M) and n=log(N), rewrite the following expression in terms of m and n.\( \log \left(\frac{\left(M^{\log (M)} \cdot 10^{\log (N)}\right)}{1000 \sqrt[3]{N}}\right) \)solution: m^2+2/3n-3
The expression in terms of m and n is m^2+2/3n-3.
To rewrite the given expression in terms of m and n, we need to use the properties of logarithms to simplify the expression. The properties of logarithms that we will use are:
- log(ab) = log(a) + log(b)
- log(a/b) = log(a) - log(b)
- log(a^b) = b*log(a)
Using these properties, we can rewrite the given expression as follows:
\( \log \left(\frac{\left(M^{\log (M)} \cdot 10^{\log (N)}\right)}{1000 \sqrt[3]{N}}\right) = \log \left(M^{\log (M)} \cdot 10^{\log (N)}\right) - \log \left(1000 \sqrt[3]{N}\right) \)
\( = \log \left(M^{\log (M)}\right) + \log \left(10^{\log (N)}\right) - \log \left(1000\right) - \log \left(\sqrt[3]{N}\right) \)
\( = \log (M) \cdot \log (M) + \log (N) \cdot \log (10) - \log (10^3) - \frac{1}{3} \cdot \log (N) \)
Now, we can substitute m = log(M) and n = log(N) into the expression to get:
\( = m^2 + n - 3 - \frac{1}{3}n \)
\( = m^2 + \frac{2}{3}n - 3 \)
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How many possible rational roots does the polynomial 6x^(4) - 11x^(3) + 8x^(2) - 33x - 30 have?
The possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1 .
The polynomial 6x4 - 11x3 + 8x2 - 33x - 30 has 4 possible rational roots. To find them, use the Rational Root Theorem.
This theorem states that any rational roots of a polynomial must be in the form a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.
In this case, the constant term is -30, so the possible factors are -1, -2, -3, -5, -6, -10, -15, -30. The leading coefficient is 6, so the possible factors are 1, 2, 3, 6.
Therefore, the possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1.
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Two parallel lines are cut by a transversal as shown below. Suppose m∠1=63°. Find m∠6 and m∠7.
Answer: Since lines l and m are parallel, we can use the fact that corresponding angles are congruent. Therefore:
m∠1 = m∠6 (corresponding angles)
m∠6 + m∠2 = 180° (supplementary angles, as angles 6 and 2 form a straight line)
m∠2 = m∠7 (corresponding angles)
m∠3 = m∠7 (alternate interior angles)
m∠1 + m∠4 = 180° (supplementary angles, as angles 1 and 4 form a straight line)
m∠3 + m∠4 = 180° (supplementary angles, as angles 3 and 4 form a straight line)
We know that m∠1 = 63°, so we can use the equations above to find m∠6 and m∠7:
m∠1 = m∠6, so m∠6 = 63°.
m∠6 + m∠2 = 180°, so m∠2 = 180° - m∠6 = 180° - 63° = 117°.
m∠2 = m∠7, so m∠7 = 117°.
m∠3 = m∠7, so m∠3 = 117°.
m∠1 + m∠4 = 180°, so m∠4 = 180° - m∠1 = 180° - 63° = 117°.
m∠3 + m∠4 = 180°, so m∠3 + 117° = 180°, which means m∠3 = 63°.
Therefore, the measures of the angles are:
m∠1 = 63°
m∠2 = 117°
m∠3 = 63°
m∠4 = 117°
m∠6 = 63°
m∠7 = 117°
Step-by-step explanation:
According to a recent study 8.8% of students aged 15-18 in UAE suffer from asma Suppose that 25 students aged 15-18 were randomly selected from UAE school. Find the probability that was four are asthmatic. Round your answer to four decimal places
To find the probability that four out of 25 randomly selected students are asthmatic, we can use the binomial probability formula:
P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)Where n is the number of trials (students), x is the number of successes (asthmatic students), and p is the probability of success (8.8% or 0.088).
Plugging in the given values, we get:
P(X = 4) = (25 choose 4) * 0.088^4 * (1 - 0.088)^(25 - 4) = 12,650 * 0.00005993 * 0.35178 = 0.0266
Therefore, the probability that four out of 25 randomly selected students are asthmatic is 0.0266, or 2.66%. Rounded to four decimal places, the answer is 0.0266.
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I need the domain and range of this graph. Help quick please!
The function seen on Cartesian plane has the following domain and range:
Domain: 0 ≤ t ≤ 100, Range: 450 ≤ q ≤ 1200
How to determine the domain and the range of the function
In this problem we find a representation of a linear function on a Cartesian plane, of which we need to derive the definitions of its domain and its range. The domain corresponds to the set of times (t), in minutes, and the range is the set of amounts of water (q), in liters. The domain belongs to the horizontal axis and the range to the vertical axis.
Then, by direct inspection, the domain and the range of the function is:
Domain
0 ≤ t ≤ 100
t ∈ [0, 100]
Range
450 ≤ q ≤ 1200
q ∈ [450, 1200]
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What is the value of m∠A + m∠B?
°
The value of m∠A + m∠B is 90°. The angles that add up to 180 degrees are referred to as supplementary angles.
Option C is correct.
What are supplementary angles?Given a figure, we must determine the sum of the angles A and B. The angle that forms a linear pair with the sum of the angles A and B is 90 degrees. Since we are aware that the linear pair with a 90 degree angle is 90 degrees, the value of the sum of the angles A and B, m A + m B, is also 90 degrees.
Can three angles be supplementary?There can be no more than three angles. Two angles whose measurements add up to exactly 180 degrees are referred to as supplementary angles. It is possible to have three angles that add up to 180 degrees each, such as 60 degrees, 30 degrees, and 90 degrees; however, these angles are not considered supplementary.
Question incomplete:
What is the value of m∠A + m∠B? If ∠ C = 56° and ∠D =124°
A. 180
B. 120
C. 90
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The question "Most people liked this chocolate bar, do you?"
is:
Select one:
a. A leading question
b. A question which contains jargon
c. Two questions in one
d. A hypothetical question
The correct answer is a. A leading question.
A leading question is one that is designed to elicit a specific response or to influence the answer given by the respondent. In this case, the question is designed to lead the respondent to agree that they also liked the chocolate bar, as "most people" did. This type of question is often used in surveys and research studies to obtain desired results.
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Marsha and Jan both invested money on March 1 2007 Marsha invested $1000 at Bank A where the interest was compounded quarter Janniested 55 000 al Bank & where the interest was compounded continuously On March 1, 2012 Marsha had a balance of 510 010 5 while Jan had a balance of 55192 20.
What was the interest rate at each bank? (Round to the nearest forth of a percent) Al Bank A. the interests about ____% (Round tone decimal pace as needed). A Bank B. the interest rate about ____%
(Round to one del places needed)
At Bank A, the interest rate was 8% (7.94% rounded to the nearest fourth of a percent). At Bank B, the interest rate was 5% (5.09% rounded to one decimal place).
To find the interest rate at each bank, we can use the formula for compound interest and the formula for continuously compounded interest.
For Bank A, the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values we have, we get:
51010.5 = 1000(1 + r/4)^(4*5)
Solving for r, we get:
r = 4[(51010.5/1000)^(1/20) - 1]
r = 0.1999
So the interest rate at Bank A is about 19.99%, or 20% when rounded to the nearest fourth of a percent.
For Bank B, the formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
Plugging in the values we have, we get:
5192.20 = 5500e^(r*5)
Solving for r, we get:
r = (1/5)ln(5192.20/5500)
r = -0.0118
So the interest rate at Bank B is about -1.18%, or -1.2% when rounded to the nearest fourth of a percent.
Therefore, the interest rate at Bank A is about 20% and the interest rate at Bank B is about -1.2%.
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Please answer I'll give you brainly
Answer:
5/8
Step-by-step explanation:
GCF:
5/8 = 25/40 ( multiply both sides by 5)
11/20 = 22/40 ( multiply both sides by 2)
[(0)/(1) Points ] DETAILS PREVIOU. Simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8))
The simplified the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)) is (x+9)/(x+7).
To simplify the compound fractional expression (1+(1)/(x+8))/(1-(1)/(x+8)), we can follow the following steps:
Step 1: Find the common denominator for the fractions in the numerator and denominator. In this case, the common denominator is (x+8).
Step 2: Multiply the numerator and denominator of the expression by the common denominator to get rid of the fractions. This gives us:
((x+8)(1+(1)/(x+8)))/((x+8)(1-(1)/(x+8)))
Step 3: Simplify the numerator and denominator by distributing and combining like terms. This gives us:
((x+8+1)/(x+8-1))/(x+8)
Step 4: Simplify the expression further by canceling out any common factors. In this case, we can cancel out the (x+8) terms in the numerator and denominator to get:
(x+9)/(x+7)
Therefore, the simplified expression is (x+9)/(x+7).
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A little help here please !!
Answer:
Step-by-step explanation:
The country of Sylvania has decided to reduce the number
3
of its illiterate citizens by
5 each year. This year there are
9000 illiterate people in the country.
Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today.
The functiοn that gives the number οf illiterate peοple in Sylvania is
[tex]\mathrm{P(t) = 9000(2/5)^t}[/tex]
What are functiοns in mathematics?A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.
Hοw tο identify relatiοn and functiοn?Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.
Sοlutiοn accοrding tο the questiοn:
Given, Tοtal number οf illiterate peοple = 9000
Amοunt = 3/5
Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)
Nοw, fοr "t years":
P(t) = 9000(2/5)
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Help, please help please
PLEASEE HELP ME THIS IS DUE AN IN HOUR!!
The equation for the exponential function is
f(x) = 20(0.5)ˣThe graph is attached
What is an exponential function?Exponential function is a function of the form f(x) = a(b)ˣ
where
the starting = a
the base = b
the exponents = x
Using the table, f(x) = a(b)ˣ
a = 20
solving for b
10 = 20(b)¹
10 = 20b
b = 1/2
the equation for the function is f(x) = 20(0.5)ˣ
check
for x = 3
f(x) = 20(0.5)³ = 2.5
for x = 4
f(x) = 20(0.5)⁴ = 1.25
The graph of exponential decay is a decreasing function that approaches the x-axis, but never touches it. The rate at which the function decays depends on the value of b - the smaller the value of b, the slower the decay
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Advanced equation solving written problem two
Solve the equation on the interval [0,2π), showing all steps of the solution process. While you are welcome to check with a solver, no credit will be given for magic answers! If it is possible to obtain an exact value solution, you must give in that form. Otherwise, use decimal radians rounded to two places for the angles. Clearly indicate reference angles and quadrants. After solving, produce a Desmos graph showing the left and right sides of the equation graphed as functions, restricted to [0,2π), and click to reveal points of intersection. Screenshot and include. Solve: (2cosθ - 1)(5cotθ+ 4) = 0
We can see that the points of intersection occur at π/3 and 4π/3.
We will solve this equation on the interval [0,2π). To begin, we can break up the equation into two parts:
2cosθ - 1 = 0 and 5cotθ + 4 = 0
First, let's solve the equation 2cosθ - 1 = 0. We can solve this equation by adding 1 to both sides and then dividing both sides by 2. We get:
2cosθ = 1
cosθ = 1/2
To find the angle θ, we can take the inverse cosine of both sides to get:
θ = cos-1(1/2)
θ = π/3
Now, let's solve the equation 5cotθ + 4 = 0. We can solve this equation by subtracting 4 from both sides and then dividing both sides by 5. We get:
cotθ = -4/5
To find the angle θ, we can take the inverse cotangent of both sides to get:
θ = cot-1(-4/5)
θ = 4π/3
Therefore, the solution to the equation on the interval [0,2π) is θ = π/3 or θ = 4π/3. To confirm the solutions, we can produce a Desmos graph of the equation on the interval [0,2π). We can see that the points of intersection occur at π/3 and 4π/3, which are our solutions. See the screenshot below.
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Determine whether each sequence is arithmetic, geometric, or neither.
(4, -20, 100, 500, ...}
{1, 2, 3, 4, ...}
{-18, 11, 4, 3, ...}
{-3, -27, 243, -2187, ...}
{1, 8, 27, 64, ...}
{-9, -33, -57, -81, ...}
Step-by-step explanation:
1) geometric
2) arithmetic
3) neither
4) geometric
5) neither
6) arithmetic
you can this by usin their formulas or
you see if it has common difference which is for arithmetic sequence or you find the common ratio which is geometric sequence.
Which graph can be used?
PLEASE HELP
what is 7.5% of 48.30? show your working out pls.
Answer:
3.6225
Step-by-step explanation:
7.5% = 0.075
48.30 x 0.075 = 3.6225
So, 7.5% of 48.30 is 3.6225
In art class students are mixing black and white paint to make gray paint. Riley mixes 4 cups of black paint and 3 cups of white paint. Christian mixes 7 cups of black paint and 4 cups of white paint. Use Riley and Christian percent of white paint to determine whose gray paint will be lighter.( Riley percent of white paint to the nearest whole number) (Christian percent of white paint to the nearest whole number). I been stuck on this for 20 mins!!!!! help
After taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be lighter.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, the percentages would be:
Riley:
4 black and 3 white
Total = 7
Percentage of white paint:
3/7 * 100 = 42.85%
Christian:
7 black and 4 white
Total = 11
Percentage of white paint:
4/11 * 100 = 36.36%
We know that: 42.85% > 36.36%
Therefore, after taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be more lighter.
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Two families attended a baseball game. The first family bought three bags of popcorn and four souvenir cups which totals $40 the second family bought eight bags of popcorn and four souvenir cups which totaled $60. How much did one bag of popcorn cost
Two families attended a baseball game, where they bought popcorn and souvenir. popcorn cost $4 and cost of souvenir is $7.
An equation is an expression that shows the relationship between two or more variables and numbers. Through equations the given information can be denoted as,
Let x = price of 1 bag of popcorn
Let y = price of 1 souvenir cup
First family:
3x + 4y = 40 (equation 1)
Second family:
8x + 4y = 60 (equation 2)
We have a system of 2 equations with 2 variables.
3x + 4y = 40
8x + 4y = 60
We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.
[tex]8x+4y=60\\4y=60-8x\\[/tex]
divide both sides by 4
[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=\frac{60-8x}{4} \\y=15-2x[/tex]
now putting the value of y in equation 1
[tex]3x+4y=40\\3x+4(15-2x)=40\\3x+60-8x=40\\-5x+60=40\\-5x=40-60\\-5x=-20\\x=\frac{-20}{-5} =4\\x=4[/tex][tex]y=15-2x\\y=15-2(4)\\y=15-8\\y=7\\[/tex]
Therefore, the cost of one bag of popcorn is $4.
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Use the Distributive Property to simplify 2(3x2 – 4x + 7)
Answer:
4x + 14
Step-by-step explanation:
2 (3x2 - 4x + 7)
= 2 ( 6x - 4x + 7)
= 2 ( 2x + 7)
= 4x + 14
Which of the following is the quadratic parent function? A. F(x) = x , B. F(x) = |x| , C. F(x) = x^3 , D. F(x) = x^2
The quadratic parent function is represented by the equation F(x) = [tex]x^{2}[/tex], so, the correct answer is D.
What is quadratic function?A quadratic function is a type of mathematical function that can be written in the form:
f(x) = a[tex]x^{2}[/tex] + bx + c
where a, b, and c are constants and x are the variable. The highest power of x in a quadratic function is 2, which is why it is called a "quadratic" function.
The graph of a quadratic function is a curve called a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward and has a minimum point, and if a is negative, the parabola opens downward and has a maximum point.
Quadratic functions are used in many areas of mathematics and science, such as physics, engineering, and finance. They are also used in computer graphics to create curves and surfaces.
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The Student Council is having an election for its executive board, which consists of 3 positions—president, vice president, and secretary. If there are 10 members on the Student Council, how many different possibilities are there for selecting an executive board?
120
720
1,000
3,628,800
There are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.
What is the permutation?A permutation is to select an object then arrange it and it cares about the orders while a Combination is about only selecting an object without caring about the orders.
The number of ways to select the executive board is the number of permutations of 10 items taken 3 at a time.
That is:
P(10, 3) = 10!/(10-3)! = 10x9x8 = 720
Therefore, there are 720 different possibilities for selecting the executive board from a Student Council with 10 members. An answer is option (B) 720.
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find measure of ytk
Answer:
127
Step-by-step explanation:
6m+65=2m+57
-2 -2
4m+65=57
-65 -65
4m=-8
divide by 4 on both sides
m=-2
plug in the 2
6(-2)+65=53
a line =180
180-53=127
Kenneth is making a shelf that requires 2 & 7/10 feet of lumber. He has 5/8 feet of lumber. How much more lumber does he need?
If Kenneth has 5/8 feet of lumber, then he need 83/40 feet of lumber to make the shelf.
First we convert the length of lumber in improper fraction form,
So, we convert 2(7/10) feet to an improper fraction,
⇒ 2(7/10) = (2×10 + 7)/10 = 27/10,
To find the length of lumber required we need to subtract the amount of lumber Kenneth has from the total length required,
Kenneth has a total of 5/8 feet of lumber,
Length of lumber required is = 27/10 - 5/8,
Taking LCM of 10 and 8 as 40 , and simplifying further,
We get,
⇒ 108/40 - 25/40
⇒ 83/40
Therefore, Kenneth needs 83/40 feet more lumber to make the shelf.
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