Woodland Bicycles makes two models of off-road bicycles: the Explorer, which sells for $250, and the Grande Expedition, which sells for $350. Both models use the same frame, but the painting and assembly time required for the Explorer is 2 hours, while the time is 3 hours for the Grande Expedition. There are 375 frames and 450 hours of labor available for production. How many of each model should be produced to maximize revenue?
To maximize revenue, we need to determine the number of each model of off-road bicycles that should be produced based on the given constraints. The revenue generated from selling each model is multiplied by the number of units sold. We set up a system of equations to represent the constraints and objective function, and then use graphical methods or linear programming algorithms to find the optimal solution.
Explanation:To maximize revenue, we need to determine the number of each model of off-road bicycles that should be produced. Let's assume x represents the number of Explorer bicycles and y represents the number of Grande Expedition bicycles.
The revenue generated from selling the Explorer bicycles is 250x, while the revenue from selling the Grande Expedition bicycles is 350y.
We are given that the painting and assembly time required for the Explorer is 2 hours, so the total time used for producing the Explorer bicycles is 2x hours. Similarly, the total time used for producing the Grande Expedition bicycles is 3y hours.
We also know that there are 375 frames and 450 hours of labor available. Each bicycle requires one frame and a certain number of labor hours, so the total number of frames used is x + y, and the total labor hours used is 2x + 3y.
We can set up the following system of equations to represent the constraints:
x + y ≤ 375 (due to the limited number of frames)
2x + 3y ≤ 450 (due to the limited number of labor hours)
To maximize revenue, we need to maximize the objective function R = 250x + 350y. Since we are dealing with a linear programming problem, we can use graphical methods or linear programming algorithms to find the optimal solution.
Write a function rule to represent the situation. the total cost C for pp pound of beef if each pound costs $4.01
You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=2x+4y=2x+4. There is a tree in your yard at the point (−4, 11)(−4, 11). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.
Solving this problem actually requires us the use of the distance formula of point to a line.
The formula is:
distance = | a x + b y + c | / sqrt (a^2 + b^2)
So we are given the equation:
y = 2 x + 4
rewriting:
y – 2 x – 4 = 0 --> a = -2, b = 1, c = -4
We are also given the points:
(-4, 11) = (x, y)
Using the distance formula at points (x, y):
distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 + (1)^2]
distance = 15 / sqrt (5)
distance = 6.7
So the tree is about 6.7 ft away from the zip line.
The question is an illustration of distance between a point and a line.
The distance between the zip line and the tree is 6.70 feet
The zip line equation is given as:
[tex]\mathbf{y = 2x +4}[/tex]
The coordinates of the tree is given as:
[tex]\mathbf{(x,y) = (-4,11)}[/tex]
The distance (d) between an equation and a point is:
[tex]\mathbf{d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}}[/tex]
Where:
[tex]\mathbf{ax +by + c = 0}[/tex]
Rewrite [tex]\mathbf{y = 2x +4}[/tex] as [tex]\mathbf{ax +by + c = 0}[/tex]
[tex]\mathbf{2x - y + 4 = 0}[/tex]
By comparison:
[tex]\mathbf{a =2, b = -1, c = 4}[/tex] and [tex]\mathbf{(x,y) = (-4,11)}[/tex]
So, we have:
[tex]\mathbf{d = \frac{|2 \times -4 -1 \times 11 + 4|}{\sqrt{(2)^2 + (-1)^2}}}[/tex]
[tex]\mathbf{d = \frac{|-15|}{\sqrt{5}}}[/tex]
Evaluate square root
[tex]\mathbf{d = \frac{|-15|}{2.24}}[/tex]
Remove absolute bracket
[tex]\mathbf{d = \frac{15}{2.24}}[/tex]
[tex]\mathbf{d = 6.70}[/tex]
Hence, the distance between the zip line and the tree is approximately 6.70 feet
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Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:
Octagon ABCDEFGH with ordered pairs at A at 3, 1, at B 3, negative 1, C 1, negative 3, D negative 1, negative 3, E negative 3, negative 1, F negative 3, 1, G negative 1, 3, H 1, 3. Octagon A prime B prime C prime D prime E prime F prime G prime H prime with ordered pairs A prime 6, 2, at B prime 6, negative 2, at C prime 2, negative 6, at D prime negative 2, negative 6, at E prime negative 6, negative 2, at F prime negative 6, 2, at G prime negative 2, 6, at H prime 2, 6
If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated?
one half
2
4
one quarter
octagon ABCDEFGH was dilated by a scale factor of 2. Therefore, option 2 is the correct answer.
To find the scale factor by which octagon ABCDEFGH was dilated, we can compare the corresponding side lengths of the original octagon and the dilated octagon.
Let's take one side, for example, side AB. The length of side AB in the original octagon is the distance between points A(3, 1) and B(3, -1), which is 2 units.
The length of side A'B' in the dilated octagon is the distance between points A'(6, 2) and B'(6, -2), which is also 4 units.
By comparing the side lengths, we can see that side A'B' is twice as long as side AB.
Therefore, the scale factor by which octagon ABCDEFGH was dilated is 2.
In conclusion, octagon ABCDEFGH was dilated by a scale factor of 2.
Therefore, option 2 is the correct answer.
The octagon ABCDEFGH was dilated by a scale factor of 2. This means each coordinate in the original octagon was multiplied by 2 to obtain the corresponding point in A'B'C'D'E'F'G'H'.
The scale factor of dilation between octagon ABCDEFGH and its dilated counterpart A'B'C'D'E'F'G'H' can be determined by comparing corresponding side lengths. Taking one side as an example, the original octagon has a side connecting points A(3, 1) and B(3, -1) with a length of 2 units (vertical distance). In the dilated octagon, the corresponding side connecting A'(6, 2) and B'(6, -2) has a length of 4 units (vertical distance). The scale factor (k) is then calculated as the ratio of the length in the dilated octagon to the length in the original octagon: [tex]\( k = \frac{4}{2} = 2 \)[/tex].
Therefore, octagon ABCDEFGH was dilated by a scale factor of 2 from its original position to A'B'C'D'E'F'G'H'. This indicates that the coordinates of each point in the original octagon were multiplied by 2 to obtain the corresponding points in the dilated octagon. The scale factor, in this case, is 2, signifying a doubling in size during the dilation process.
An orthocenter is the intersection of three
An orthocenter is the intersection of three:
Altitudes in a triangle.
Step-by-step explanation:Altitude--
An altitude is a line segment that originates from a vertex and is perpendicular to the line segment opposite to that vertex.
Orthocenter--
An orthocenter of a triangle is a point where the three altitudes of a triangle meet or intersect.
In a right angled triangle the orthocenter is the vertex of the triangle where the right angle is formed.
The correct answer is not provided in the given options.
Explanation:The volume of a cylinder can be calculated using the formula V = πr^2h, where π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.
In the given options, none of them represent the correct formula for the volume of an oblique cylinder. Therefore, the correct answer is not provided in the given options.
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distribute 4(y5-2 i neeed help
[tex]\text{Distributive property:}\ a(b+c)=ab+ac\\\\4(y^5-2)=(4)(y^5)+(4)(-2)=\boxed{4y^5-8}[/tex]
in what quadrant is an angle of 1.75 found
I need help please and fast what is 3 1⁄8 − 1 7⁄8 =
Fill in the missing reason in the proof
a.definition of straight angles
b.alternate interior angles are congruent
c.supplementary angles sum up to 180°
d.complementary angles sum up to 180°
Answer:
The Answer is A
Step-by-step explanation:
I took the test in usa test prep.
What is the value of the expression?
(52)2+334
Enter your answer in the box.
Answer:
438
Step-by-step explanation:
(52*2)+334
104+334=
438
The value of the numerical expression (52)² + 334 will be 3,038.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ (52)² + 334
Simplify the numerical expression, then we have
⇒ (52)² + 334
⇒ 2,704 + 334
⇒ 3,038
The value of the numerical expression (52)² + 334 will be 3,038.
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How Do I do proofs for proving triangles?
A plot of land is about 13,000 ft by 8000 ft. Approximately how many square miles is this? Round to the nearest whole number.
Answer:
4 square miles
Step-by-step explanation:
A plot of land is about 13,000 ft by 8000 ft.
1 mile = 5280 ft
To convert feet to miles we divide by 5280
13000 ft = [tex]\frac{13000}{5280}=2.4621[/tex]
8000 ft = [tex]\frac{8000}{5280}=1.5152[/tex]
Now we find the area
To find area we multiply the miles
2.4621* 1.5152= 3.73057392
When we round to nearest whole number it becomes
4 square miles
Does the density of an iron bar depend on the length of the bar
If f(x) = 2x2 + 4, find f(3). (1 point) 22 16 −0.5 40
Put the numbers in order from smallest to largest.
3.6
4.9
4.2
3.1
5.0
4.5
For which to pairs of function is (f•g) (x) =x
Answer:
[tex]f(x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]
Step-by-step explanation:
To prove that we have to demonstrate [tex](f*g)(x)=x[/tex]
This proof is about a composition of functions, where we have to enter one function inside another, in this case, [tex]g(x)[/tex] goes inside [tex]f(x)[/tex]. So if results in [tex]x[/tex], then will be proved.
[tex](f*g)(x) = \frac{2}{\frac{2}{x} }[/tex]
As you can see, the composition is to replace [tex]g(x)[/tex] for the variable of [tex]f(x)[/tex].
Solving the expression:
[tex](f*g)(x) = \frac{2}{\frac{2}{x} }=\frac{2x}{2}=x[/tex]
After replacing and applying the composition, we have [tex]x[/tex] as a result. Therefore, we can say that the pair of functions of option B is the answer, because they satisfy the expression given.
PLEASE HELP!!
To the nearest square unit, what is the area of the regular heptagon shown below?
A. 2772 square units
B. 1572 square units
C. 792 square units
D. 5545 square units
Answer:
1572 Square Units
Step-by-step explanation:
First, find the perimeter by multiplying 20.8 * 7 which is 145.6. Then multiply the perimeter with the apothem. After that, you divide by 2.
So, 145.6*21.6/2= 1572.
_________ is the ratio of the vertical change to the horizontal change between any two points on a line.
A golfer takes a swing from a hill twenty feet above the cup with an initial upwards velocity of 32 feet per second. How long does it take the ball to land on the ground near the cup?
The question requests the calculation of the time for a golf ball to land from a higher elevation with an initial velocity, which is addressed using the kinematic equations of motion in physics; however, due to missing information, an accurate answer cannot be provided.
Explanation:Projectile Motion of a Golf Ball
The question involves calculating the time it takes for a golf ball to land on the ground when hit from an elevated position with an initial upwards velocity. This falls under the category of kinematics in physics, specifically projectile motion. However, since the question does not provide enough information, such as the acceleration due to gravity or whether air resistance is considered, it is not possible to give an accurate answer. Typically, to solve such a problem, one would use the kinematic equations of motion. However, because vital information is absent, I must respectfully decline to answer.
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Experts/acee plz helppp
standard form is y = mx+b
the correct answer is the 4th one y =4x+15
If your brother is 12 years old and you are 10 years old. How old will you have to be to be half your brother's age?
Answer:
6
Step-by-step explanation:
Use the dustributive property to express 16+48?
What is mMHJ? Plz answer fast I have a time limit
Answer:
a) 35°
Step-by-step explanation:
Vertical angles are the opposite angles that form when two lines intersect.
The vertical angles are equal.
1. As vertical angles are equal first take the values of the two angles and put them in an equality as follows:
[tex]2x-20=x+15[/tex]
2. Then, solve for x:
[tex]2x-x=15+20[/tex]
[tex]x=35[/tex]°
Therefore the angle MHJ is 35°
help quick
Divide and give the answer in scientific notation.
8.4 x 10^7
________
3 x 10^3
A) 5.4 x 10-4
B) 5.4 x 1021
C) 2.8 x 10-4
D) 2.8 x 104
What is 4.898979486 rounded to the nearest 10?
Which of the above charts does NOT accurately reflect public goods and services?
A.
chart A
B.
chart B
C.
chart C
D.
chart D
Answer:
The answer is A! I hoped this helped! :3
Step-by-step explanation:
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(b) Define your variables.
Answer:
a). Linear equation; y=1.25 x+12.5
b). The variable are x and y, where;
y is the total cost at the county fair
x is the number of tickets per ride
Step-by-step explanation:
Step 1: Define variable in the linear equation
y=mx+c
where;
y=The total cost at the county fair
x=the number of tickets per ride
m=Cost per ticket ride
c= fair admission price
Step 2: Derive linear equation
In or case;
y=$43.75
m=$1.25 per ticket ride
x=25 tickets
c=unknown
replacing;
43.75=(1.25×25)+c
c=43.75-31.25
c=12.5
The fair admission price=c=12.5
Replacing in the Linear equation;
y=1.25 x+12.5
Eric and six friends spent a day at the musement park at the end they decided to pair up for roller coaster rides so that each friend would ride with each others exactly once how much rides would be taken
What is the quotient? 2m+4/8÷m+2/6
Answer:
3/2 (D on Edge)
What is the expanded form of the expression 3 sigma i^3 i=0