Bob, a farmer in Florida, has an orange grove. In the grove are 120 trees. Each tree ordinarilyproduces 650 oranges. Bob would like to increase his orange production and knows that becauseof lost space and sunlight, each additional tree he plants will cause a reduction of 5 oranges fromevery tree.How many trees can Bob have in his grove in order to maximize his orange production? What isthe maximum number of oranges that Bob will produce with these trees?
Answers
Bob has 120 trees in the grove. Each tree produces about 650 oranges.
Bob wants to maximize this orange production by adding new trees to the grove. Space limitations and sunlight make it to reduce each tree's production by 5 oranges per tree added.
The total number of oranges actually produced is the product of the number of trees by the number of oranges per tree, that is, 120 * 650 = 78,000 oranges.
Now suppose Bob adds x trees to the grove. The new number of trees is 120 + x and each tree now produces 650 - 5x oranges.
The number of oranges produced under this new condition is:
\(N=(120+x)\cdot\mleft(650-5x\mright)\)Operating:
\(N=120\cdot650-600x+650x-5x^2\)Simplifying:
\(N=78,000+50x-5x^2\)To maximize the number of oranges, we use derivatives:
\(N^{\prime}=50-10x\)Equating the first derivative to 0:
\(50-10x=0\)Solving for x:
x = 50 / 10 = 5
This means that Bob should add only 5 more orange trees to maximize production.
The new number of trees would be 120+5= 125 trees
Each tree would produce 650 - 5*5 = 625 oranges
The total production would be 125*625 = 78,125 oranges
Related Questions
please help me i really need help please
Answers
I NNEEEDDDDDD HELPPPPP PLEASEEEE
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
An employee at a party store is assembling balloon bouquets. For a graduation party, he assembled 7 small balloon bouquets and 8 large balloon bouquets, which used a total of 193 balloons. Then, for a Father's Day celebration, he used 92 balloons to assemble 8 small balloon bouquets and 2 large balloon bouquets. How many balloons are in each bouquet?
The small balloon bouquet uses___ balloons and the large one uses___ balloons.
Answers
Answer:
The small balloon bouquet uses 7 balloons and the large one uses
18 balloons.
Step-by-step explanation:
Let's say that small balloon bouquets are S and large balloon bouquets are L. For the graduation party the employee assembled 6 small bouquets and 6 large bouquets, the total number of balloon used is 150. To put the sentence into an equation will be:
6S + 6L= 150
S+L= 25 ----> 1st equation
For Father's Day, the employee uses 6 small bouquet and 1 large bouquet, the total number of balloons used is 60. The equation will be:
6S + 1L= 60
1L= 60- 6S ----> 2nd equation
We can solve the number of small balloon bouquet by substitute the 2nd equation into 1st. The calculation will be:
S+L = 25
S+ (60-6S)= 25
-5S= 25-60
-5S= -35
S= -35/-5
S=7
Then we can find L by substitute S value to 1st or 2nd equation.
S+L=25
7+L=25
L=18
Hope this helps ;)
Answer:
193 = 7s + 8l ( Grad Party Equation)
92 = 8s + 2l (Father's Day Equation)
The small balloon bouquet uses 7 balloons and the large one uses 18 balloons
Step-by-step explanation:
First we need to separate something, I chose l...
92 = 8s + 2l2l = 92 - 8sl = 46 - 4s...and we can replace this for l in the other equation!
193 = 7s + 8( 46 - 4s )193 = 7s + 368 - 32s-175 = -25s7 = sNow that we have found the number of balloons needed for a small bouquet we can place that in an equation to find out how many balloons it takes to make a large bouquet.
l = 46 - 4(7)l = 46 - 28l = 18Now just to make sure we got that right. Just check them!
Grad Party Equation
193 = 7s + 8l193 = 7(7) + 8(18)193 = 49 + 144193 = 193We got one right and the other one...
Fathers Day Equation
92 = 8s + 2l92 = 8(7) + 2(18)92 = 56 + 3692 = 92We got both right yay!
) Emily baked a cake in 42.5 minutes. She finished making dinner 9 1/10 minutes sooner than the cake. How long did it take her to make dinner? Hint: Change the 9 1/10 to a decimal
Answers
It took Emily 33.4 minutes to make dinner.
Define a mixed number?A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.
To solve the problem, we have to convert the mixed number \(9 \frac{1}{10}\) to a decimal number:
⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)
⇒ \(\frac{91}{10}\) = 9.1
This means that Emily finished making dinner 9.1 minutes sooner than the cake.
To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:
⇒ 42.5 - 9.1 = 33.4 minutes
Therefore, it took Emily 33.4 minutes to make dinner.
To know more about mixed number, visit:
https://brainly.com/question/414559
#SPJ1
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
x = 6y = 5z = 11.5Step-by-step explanation:
Reflections of a line or a figure across an axis does not change its lengths.
Therefore, the corresponding parts are equal.
5x = 302y = 102z - 1 = 22Solving for x
5x = 30Divide each side by 55x/5 = 30/5x = 6Solving for y
2y = 10Divide each side by 22y/2 = 10/2y = 5Solving for z
2z - 1 = 22Add 1 to each side2z - 1 + 1 = 22 + 12z = 23Divide each side by 22z/2 = 23/2z = 11.5Select the correct word from the drop-down menu to complete the sentences.
are branching diagrams that depict the evolutionary relationship among species.
Answers
Answer: Cladograms
Step-by-step explanation:
The evolutionary relationship among species is described as Cladograms.
How are Cladograms constructed?
Cladograms are constructed by selecting and sorting organisms into classes based on the derived traits or characteristics that they share.
How to read a Cladogram
In a cladogram, there are lines and nodes where the lines cross. While the lines depict evolutionary time and or a series of organisms, the nodes represent common ancestors between species.
Learn more about Cladograms in the link below:
https://brainly.com/question/787826
In the United States between 1910 and 1994, the amount of currency in circulation M ( in billions of dollars) can be approximated by the function M = 2.08 * (1.06) ^ t where t represents the number of years since 1910. Determine the amount of currency in circulation in the year 1980. (round to the nearest hundredth).
A.3.32
B.122.88
C.220.06
D.2.65
Answers
Answer:
B. 122.88
Step-by-step explanation:
Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:
t = 1980 - 1910 = 70
Now, we can plug in 70 for t to find the amount of currency in 1980:
\(M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88\)
Thus, the amount of currency in 1980 according to the model was $122.88 billion
Please anyone that can help me
Answers
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
Nicholas says that two pairs of congruent angles can be used to show that the two
triangles are similar. Is he correct?
Answers
Answer:
yes he is correct
Step-by-step explanation:
we know that he is correct because if two of the angles are congruent then the third is also congruent.
further explanation
lets say the angles are 90 and 50.
a triangle measures 180 degrees, so to know the third we add those angles and subtract it by 180. 90+50=140, 180-140=40
40 is the third angle for both angles so we can say Nicholas is correct :)
Nicholas says that two pairs of congruent angles can be used to show that the two triangles are similar. So, 40 is the third angle for both angles.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Nicholas says that two pairs of congruent angles can be used to show that the two triangles are similar.
let's say the angles are 90 and 50.
A triangle measures 180 degrees,
so to find the third we add those angles and subtract it by 180.
90 + 50 + x = 180,
x = 180 - 140
x = 40
Therefore, 40 is the third angle for both angles.
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ2
Select each angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z
Answers
The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are
180 degrees
540 degrees
900 degrees
How to find the angle of rotationThe transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.
The rule is (x, y) will become (-x, -y)
Where 540 degrees = 360 + 180
where 900 degrees = 360 + 360 + 180
Learn more about angle of rotation at
https://brainly.com/question/28672446
#SPJ1
can you please help me with this question and whoever gives me the right answer will be called brainliest
Answers
Answer:
! 2 red cards !
Step-by-step explanation:
Sia draws blue cards for each of her 3 turns: 4 • 3= 12
Sia draws red cards and ends up back at 0: 6 • 2 = 12
12 - 12 = 0
Sia drew 2 red cards since 6 • 2 = 12.
Hemp bell bell help math
Answers
Answer:
This is indeed a function!
Step-by-step explanation:
fractions less than 1/2
show how you got the answer
Answers
The fractions from the given options that is less than 1/2 hence option A.
How can the fraction be determined?The concept that will be used is division of the numerator by the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line.
The given fraction is 1/2, if we convert to decimal, by dividing the numerator by the denominator we have 0.5
Then we can conert the given options one after the other.
Option A ; 3/8 = 0.375
Option B = 5/8 = 0.625
Now from the result we can see that 0.375 < 0.5 < 0.625 , hence option A is correct.
Learn more about fraction at:
https://brainly.com/question/78672
#SPJ1
A target with a diameter of 70 cm has 4 scoring zones formed by concentriccircles. The diameter of the center circle is 10 cm. The width of each ring is 10cm. A dart hits the target at a random point. Find the probability that it will hit apoint in the yellow region.
Answers
The probability is equal to divide the area of the yellow region by the area of the complete circle
so
step 1
Find the area of teh complete circle
r=70/2=35 cm
substitute
\(\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ cm2} \end{gathered}\)step 2
Find the area of the yellow region
\(\begin{gathered} A=\pi(35^2-25^2) \\ A=600\pi\text{ cm2} \end{gathered}\)step 3
find the probability
P=600pi/1,225pi
P=0.4898
or
P=48.98%
Find the lateral surface area of the cylinder. Round your answer to the nearest hundredth.
A)
315.04 in 2
B)
370.62 in2
C)
395.84 in 2
D)
408.92 in 2
Answers
Answer:
C) 395.84 in^2
Step-by-step explanation:
I took the test
What is the distance between the points (-2,1) and (5,-4)
Answers
Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Distance between the points (-2,1) and (5,-4)In this case, you know:
(x1, y1): (-2,1)(x2, y2): (5,-4)Replacing in the definition of distance:
distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)
distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)
distance= \(\sqrt{7^{2} +(-5)^{2} }\)
distance= \(\sqrt{49+25 }\)
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Learn more about distance between two points:
https://brainly.com/question/23848540
https://brainly.com/question/7243416
https://brainly.com/question/15973889
#SPJ1
Find the measures of the exterior angle.
Answers
Answer:126
Step-by-step explanation:
There were 48 cookies on the counter. That is 6 times the number of cookies in the oven. How many cookies are in the oven?
Answers
Answer:
The Answer is: 8
Step-by-step explanation:
If there are 48 cookies on the counter and 48 is 6 times the cookies in the oven, you divide 48 by 6 to get the answer, which is 8. 48 divided by 6 is 8.
Answer: 8 cookies in the oven
Step-by-step explanation:
48 counter cookies/6 = 8 oven cookies
Check it: oven cookies (8) times 6 = 48 counter cookies.
The students put recycling bins in the teachers lounge at school at the end of the week there was a total of 48.9 pounds of cans and bottles they split them evenly into three bags how many pounds did each bag weigh
Answers
Answer:
16.3 pounds
Step-by-step explanation:
the wheel of a bike has a diameter of 27 inches. find the circumference of the wheel.
Answers
The circumference of the wheel of the bike given the diameter is 84.78 inches
What is the circumference of the wheel?As evident from the task content; it is required that the circumference of the bike's wheel be determined.
Given that the Diameter of the wheel = 27 inches
Recall; Radius = diameter / 2
= 27/2
= 13.5 inches
π = 3.14
Since the formula for the Circumference of the wheel which is circular = 2πr
= 2 × 3.14 × 13.5
= 84.78 inches
In conclusion, the circumference of the wheel according to the given description is 84.78 inches.
Read more on circumference of circle:
https://brainly.com/question/12823137
#SPJ1
6√-20
Simplify the equation in simplest radical form
≅
Answers
Answer:
12i sqrt5
Step-by-step explanation:
that is your answer so brainliest please
The recipe for chocolate cake called for 3/4 of a cup of chocolate frosting if the bakery used one 5 1/4 of chocolate frosting how many chocolate cakes does the bakery make?
Answers
Answer:
It would make 7 batches of chocolate cake
Classify the triangle shown below. Check all that apply.
Answers
equilateral and acute
Answer:
A, E, F
equilateral, acute, and isosceles
Step-by-step explanation:
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
A. Two
B. One
C. Zero
D. Infinitely many
Answers
The two lines have only one intersection
\(\therefore\) There are only one solution to the system of equation.
Select three ratios that are equivalent to 11:1.
Choose 3 answers:
1:11
22:2
55:5
9:99
Answers
Answer:
22:2, 55:5, 1:11
Step-by-step explanation:
Answer:
22:2 55:5 and no others
Step-by-step explanation:
The factor equivalent to 10/12
Answers
Answer:
Step-by-step explanation:
So, here are some examples: 56 is equivalent to 1012 because 5 x 12 = 6 x 10 = 60. 1518 is equivalent to 1012 because 15 x 12 = 18 x 10 = 180. 2024 is equivalent to 1012 because 20 x 12 = 24 x 10 = 240.
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval
Answers
Did you manage to solve it?
Find the equation of the lines in point-slope form with the
following properties.
slope = -5 and passes through (4, -1).
Answers
Answer:
y +1 = -5(x -4)
Step-by-step explanation:
You want the point-slope equation of the line with slope -5 through point (4, -1).
Point-slope equationThe point-slope equation of a line has the form ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
ApplicationSubstituting m=-5 and (h, k) = (4, -1), the equation is ...
y -(-1) = -5(x -4) . . . . . . values substituted
y +1 = -5(x -4) . . . . . . . simplified a bit
what is 24divided by 2
Answers
Answer:12
Step-by-step explanation:
24/2 = 12 bc 12*2=24
PLEASE HELP ME ITS URGENTT
Answers
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).