Answer:
18-6x is the right answer
Step-by-step explanation:
-6x+18
18-6x
Superbats Inc, manufactures two different types of wood baseball bats, the Homer-Hitter and the Big
Timber, The Homer-Hitter takes 8 hours to trim and turn on the lathe and 2 hours to finish. Each
Homer-Hitter sold makes a profit of $17. The Big Timber takes 5 hours to trim and turn on the lathe
and 5 hours to finish, and its profit is $29. The total time available for trimming and lathing is 80
hours. The total available time for finishing is 50 hours.
The optimal number of each type of baseball bat to be produced is
given by linear programming.
(a) The variables are;
x is for the number of Homer-Hitter manufacturedy is for the number of Big Timber manufactured(b) The objective quantity is profit
The equation for the objective quantity is; P = 17·x + 29·y(c) The system of inequalities are;
8·x + 5·y ≤ 80, which gives; y ≤ 16 - 1.6·x2·x + 5·y ≤ 50, which gives; y ≤ 10 - 0.4·xx ≥ 0y ≥ 0(d) Please find attached the graph of the system of inequalities created with MS Excel;
The vertex points are; \(\underline{(0, \, 10), \, (5, \, 8), \, (10, \, 0), \, (0, 0)}\)(e) The number of each type to be produced to maximize profit are;
5 Homer-Hitter and 8 Big TimberThe maximum profit is $317Methods used for the linear programmingTime to trim and turn the Homer-Hitter = 8 hours
Time it takes to finish the Homer-Hitter = 2 hours
Profit each Homer-Hitter sold, makes = $17
Time to trim and turn the Big Timber = 5 hours
Time to finish the Big Timber = 5 hours
Profit each Big Timber sold, makes = $29
Total available time for trimming and lathing = 80 hours
Total time for finishing = 50 hours
(a) The variables to be used to describe the constraints in the situation are;
Variable x represents the Homer-Hittery represents the Big Timber(b) A general objective of a manufacturing company is profit, and the objective equation is therefore;
\(\underline{P = 17 \cdot x + 29 \cdot y}\)(c) The system of inequalities which describes the given constraints are presented as follows;
8·x + 5·y ≤ 802·x + 5·y ≤ 50x ≥ 0, y ≥ 0(d) The equations for the graph are therefore;
\(y \leq \dfrac{80}{5} - \dfrac{8}{5} \cdot x = 16 - \dfrac{8}{5} \cdot x = 16 - 1.6 \cdot x\)
\(y \leq \dfrac{50}{5} - \dfrac{2}{5} \cdot x = 10 - \dfrac{2}{5} \cdot x = 10 - 0.4 \cdot x\)
Which gives;
y ≤ 16 - 1.6·xy ≤ 10 - 0.4·xThe vertices of the feasible region are;
\(\underline{ (0, \, 10), \, (5, \, 8), \, (10, \, 0), \, (0, \, 0)}\)Please find attached the graph of the above system of inequalities created with MS Excel(e) The profits at the margins of the feasible region are;
Profit at (0, 10), P = 17 × 0 + 29 × 10 = 290
Profit at (5, 8), P = 17 × 5 + 29 × 8 = 317
Profit at (10, 0), P = 17 × 10 + 29 × 0 = 170
Profit at (0, 0), P = 17 × 0 + 29 × 0 = 0
Therefore, the for maximum profit, the number of each type to be produced are;
5 Homer-Hitter and 8 Big Timber baseball batsThe maximum profit is; $317The above responses are based on the order and questions obtained from a similar online uploaded question.
Learn more about linear programming here:
https://brainly.com/question/15356519
How long will a soccer ball kicked from ground with an initial velocity of 72ft/s be in the air
A soccer ball kicked from the ground with an initial velocity of 72 ft/s will be in the air for 4.5 seconds.
The time that a soccer ball will be in the air is determined by the equation:
t = (2 × v₀) / g
where:
t is the time in seconds
v₀ is the initial velocity in feet per second
g is the acceleration due to gravity, which is 32 feet per second squared
In this case, the initial velocity is 72 ft/s, so the time in the air is:
t = (2 × 72) / 32 = 4.5 seconds
Therefore, a soccer ball kicked from the ground with an initial velocity of 72 ft/s will be in the air for 4.5 seconds.
The time in the air will be longer if the initial velocity is higher, and shorter if the initial velocity is lower. The time in the air will also be shorter if the acceleration due to gravity is lower.
Learn more about equation here:
brainly.com/question/29657983
#SPJ11
Find the slope of the line.
1/3
-1/3
3
-3
Answer:
if a line is like so it has a positive slope: / . IF a line is like this it has a negative: \
Therefore that leaves out -1/3 and -3
Either A or C is correct
From the y intercept (where the line intercepts the y axis), in this case 2, to the next point on the line (3, 3) it goes up 1 and over 3 to get to that point from the intercept. Therefore the slope is 1/3. (Rise/run)
1/3
Step-by-step explanation:
find the value of x so that
f (x) = 7
GIVING BRAINLIEST TO WHOEVER ANSWERS THE FATEST BUT ALSO CORRECT.
The value of x so that f(x) = 7 is -3.
Given,
The function f(x) = 7
We have to find the value of x.
Function;-
In a function, one variable is expressed in terms of another. "Y is a function of x" (denoted y = y(x)) denotes that y changes depending on the value that x takes on. Although it is frequently suggested that "x causes y," this is not *necessarily* the case.
Here,
From the graph find the value of x when y = 7.
When y = 7, the value of x in the graph is -3.
Then,
The value of x so that f(x) = 7 is -3.
Learn more about value of x here;
https://brainly.com/question/19807056
#SPJ1
I NEED HELP ASAP PLS HURRY
Answer: C
Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.
Which statement about f(x) =x2 + 16x + 3 is true?
Answer:
The answer is D
Step-by-step explanation:
I am very sure that the correct answer.:)
if a data set features have x coordinates between -180 and 180, what is the coordinate system likely to be? in what units are the coordinates?
The coordinate system with x-coordinates between -180 and 180 is likely to be the geographic coordinate system, specifically longitude values. This system represents positions on the Earth's surface using two angles: longitude (x-coordinates) and latitude (y-coordinates).
Longitude values range from -180 degrees (180 degrees West) to 180 degrees (180 degrees East) along the Earth's equator. Latitude values, on the other hand, range from -90 degrees (90 degrees South) to 90 degrees (90 degrees North). The origin (0, 0) of this coordinate system is the intersection of the Prime Meridian (Greenwich Meridian) and the Equator.
The units for these coordinates are typically expressed in decimal degrees (DD). These values can be converted into other units such as degrees-minutes-seconds (DMS) or radians, depending on the application or preference. When working with geographic coordinate systems, it is essential to consider the Earth's curvature and potential distortions when calculating distances or areas.
In summary, if a data set has x-coordinates between -180 and 180, the coordinate system is most likely the geographic coordinate system, representing longitude values. The coordinates are typically expressed in decimal degrees, and their positions relate to the Earth's surface.
Learn more about x-coordinates here:
https://brainly.com/question/16634867
#SPJ11
Use the distributive property to find the value of x.
-1.2(3 – x) = -1.8
-3.6 + 1.2x = -1.8
1.2x = 1.8 I saw the answer on another question but there was no explanation pleas help me
Answer:
x = 1.5
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityDistributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
-1.2(3 - x) = -1.8
Step 2: Solve for x
(Parenthesis) Distribute -1.2 [Distributive Property]: -3.6 + 1.2x = -1.8[Addition Property of Equality] Add 3.6 on both sides: 1.2x = 1.8[Division Property of Equality] Divide 1.2 on both sides: x = 1.5A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 13 cubic feet. A total of 19 boxes of paper were
shipped with a combined volume of 156 cubic feet. Determine the number of small
boxes shipped and the number of large boxes shipped.
There were
Submit Answer
small boxes shipped and
large boxes shipped.
There were 13 small boxes shipped and 6 large boxes shipped.
Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.
According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.
Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.
We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:
6s + 13l = 156 ...(1)
Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:
s + l = 19 ...(2)
Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.
From equation 2, we can rewrite it as s = 19 - l.
Substituting this value of s into equation 1, we get:
6(19 - l) + 13l = 156
Simplifying the equation:
114 - 6l + 13l = 156
Combining like terms:
7l = 42
Dividing both sides by 7:
l = 6
Now, we can substitute this value of l back into equation 2 to find the value of s:
s + 6 = 19
s = 13
The number of small boxes shipped is 13, and the number of large boxes shipped is 6.
There were 13 small boxes shipped and 6 large boxes shipped.
For more questions on shipped
https://brainly.com/question/29352184
#SPJ8
Consider the following sequences, assuming that sequence 2 is geometric, what would be the following two terms?
Sequence 1 : 2,6
Sequence 2 : 24,12,
Sequence 3 : 1,5,
answers to choose from :
0,- 12
6,3
6,0
0, 12
Answer:
6,3
Step-by-step explanation:
if im not mistaken geometric sequences are multiply/dividing & right here you are decreasing by×2 so 6,3 would be your answer
There are 5 positions available in the new school. Of the applicant, 12 are men and 8 are women. In how many ways can 3 men and 2 women be chosen if they are equally considered?
There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
What is the multiplication principle of countingThe multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).
where n is the total number of men and r is the number of men chosen
so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.
Similarly, we evaluate the number of ways to choose 2 women from the 8 women
as = ⁸C₂ = 14
Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.
220 x 14 = 3080
Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
Know more about multiplication principle here:https://brainly.com/question/10275154
#SPJ1
Simplify. 3x5/6 A.15/6 B.23/6 C.2 2/1 D. 3 5/6
Therefore, expression 3x5/6 simplifies to 3 5/6.
What is expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables. Expressions can be evaluated, simplified, and manipulated using mathematical rules and operations to obtain new expressions or values.
Here,
To simplify 3x5/6, we can rewrite it as (3/1) × (5/6). Multiplying the numerators and denominators, we get:
(3/1) × (5/6) = 15/6
= 2 3/6
Since 3/6 can be simplified to 1/2, we have:
2 3/6 = 2 1/2
To know more about expression,
https://brainly.com/question/1859113
#SPJ1
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55
in 5-8, find each reciprocal. 5/9 8 7/3 1/12
the answer
155
324
5/9 (87/3(1/12)= 155/324
I am so sorry if you keep seeing me ask for help
Answer:
67°-------------------
Given three interior angle measures of a triangle:
38°, 75° and xUse the triangle sum theorem to find the missing angle:
38 + 75 + x = 180x + 113 = 180x = 180 - 113x = 67So the missing angle is 67°.
-3(3x+1) - (2+x) =0
resoude l'equation
The solution of the expression -3(3x+1) - (2+x) =0 is,
x = -1/2 or -0.5
The given mathematical expression is ,
-3(3x+1) - (2+x) =0
To solve it,
Expand the expression
⇒ -9x - 3 - 2 - x = 0
We can write it as,
⇒ -10x - 5 = 0
Add 5 both sides,
⇒ -10x - 5 + 5 = 5
⇒ -10x = 5
Divide both sides by -10 we get
⇒ x = -5/10
⇒ x = -1/2
Hence,
The required value of x = -1/2.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
What is the complete factprization -18a^2+8?
Answer:
(-6a+4)(3a+2)
Step-by-step explanation:
(-6a+4)(3a+2)
-18a^2+12a-12a+8 (checking answer)
-18a^2+8
Proofs in Propositional Logic. Show that each of the following
arguments is valid by constructing a proof
G⊃~J
F⊃H
(F • G) ⊃ [H ⊃ (I • J)]
~F∨~G
We will prove that each of the arguments is valid by constructing a proof. Before proceeding, let's recall some necessary laws of propositional logic. Laws of Propositional Logic Commutative Law of ∧ and ∨.
To prove the validity of the argument, we need to assume the premises and show that the conclusion follows as a necessary result of those premises . Assuming the premises:(5) G [from (1) and (4)](6) ~J [from (5) and (1)](7) F [from (2) and (4)](8) H [from (7) and (2)](9) F•G [from (5) and (7)]
Now, we will make use of the third premise to derive the conclusion:(10) H⊃(I•J) [from (3) and (9)](11) I•J [from (8) and (10)]Therefore, we have shown that the argument is valid.
To know more about Laws visit:
https://brainly.com/question/6590381
#SPJ11
what is the value of the expression shown 24-52
Answer:
-28
Step-by-step explanation:
It is negative so:
52-24=28
-28
What is the answer to 2/3x = -8?
Please answer it now in two minutes
Answer:
135.5
hope this helps :)
what is the perimeter of the warehouse?
Answer:
(100)
Step-by-step explanation:
Hope I helped
Evaluate the expression when a=5 and b=28.b+(30)/(a)
Answer:
34
Step-by-step explanation:
Just substitute in the valuesThis would give 28 + 30/5 = 28 + 6 = 34Consider the system of equations.
5x + 2y = 12
5x – 2y = 28
What is the solution to the system of equations? Show work using substitution or elimination to support your answer.
A (4, -4)
B (-4, 4)
C (5, -6.5)
D (4, 16)
Show how u got the answer.
Answer:
(4, -4) = (x, y) = A
Step-by-step explanation:
5x + 2y = 12
- (5x - 2y = 28)
4y = -16
y = -4
5x + 2(-4) = 12
5x - 8 = 12
5x = 20
x = 4
What is SSS congruence rules?
SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .
The Two Triangles can be called as Congruent Triangles if their sides have same length and the angles also have the same measure.
One of the 4 rules in proving the triangles congruent is SSS .
The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,
then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .
Therefore , The SSS Congruence rule means Side-Side-Side Congruence .
Learn more about Congruence here
https://brainly.com/question/29548914
#SPJ4
a frog swims 8 miles downstream in 2 hours. she returns upstream in 14 hours. how fast does the frog swim in still water?
The frog's speed in still water is 2.2857 miles per hour.
Let's call the frog's speed in still water "s", and the speed of the current "c".
When the frog is swimming downstream, its effective speed is the sum of its speed in still water and the speed of the current. So the distance it covers in 2 hours is:
distance = speed x time
8 = (s + c) x 2
Simplifying this equation, we get:
s + c = 4
When the frog is swimming upstream, its effective speed is the difference between its speed in still water and the speed of the current. So the distance it covers in 14 hours is:
distance = speed x time
8 = (s - c) x 14
Simplifying this equation, we get:
s - c = 0.5714
Now we have two equations with two unknowns:
s + c = 4
s - c = 0.5714
We can solve for s (the frog's speed in still water) by adding these two equations:
2s = 4.5714
s = 2.2857
To learn more about speed here:
https://brainly.com/question/4926312
#SPJ4
Solve for x. Show your steps
The value of x is -7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the equation as
\(8^{x + 3} = 2 ^{x - 5}\)
Solving the equation as;
\(8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}\)
Then we have;
3x + 9 = x - 5
2x = -14
x = -7
The value of x is -7.
Learn more about equations here;
brainly.com/question/25180086
#SPJ1
what are the domain restrictions of this expression x+5/27x^7y^5
there are no domain restrictions for the expression x+5/27x^7y^5.
This is because there are no variables in the denominator and the only exponent is on the variable x. To determine domain restrictions, we need to look for values of the variables that would make the expression undefined. This can occur when there are variables in the denominator or when there are even roots (such as square roots) of negative numbers. However, in this expression, there are no variables in the denominator and no even roots. Therefore, there are no restrictions on the values that x and y can take. In summary, the expression x+5/27x^7y^5 has no domain restrictions and can be evaluated for any values of x and y.
To know more about variables visit:
brainly.com/question/29696241
#SPJ11
The number of hours julie practices her violin each week, y, is 3 hrs more than the numbers of hours she studies, x. write an equation to show the relationship of the two activities.
The equation is y = x + 3 which shows the relationship of the two activities.
The equation to show the relationship between the number of hours Julie practices her violin each week (y) and the number of hours she studies (x) is:
y = x + 3
This means that the number of hours Julie practices her violin each week is equal to the number of hours she studies, plus three additional hours.
A linear equation is an equation that represents a straight line on a graph. It can be written in the form:
y = mx + b
To learn more about equation
https://brainly.com/question/29174899
#SPJ11
A chain saw requires 5 hours of assembly and a wood chipper 2 hours. A maximum of 20 hours of assembly time is
available. The profit is $190 on a chain saw and $210 on a chipper. How many of each should be assembled for
maximum profit?
An assembly time, chain saw requires 5 hours of assembly and a wood chipper 2 hours. From linear programming for maximum profit, number of chain saw assembled are 0 and number of wood chipper are 10.
This problem is related to the topic of linear programming. We use a graphical method to solve the equation. To determine the maximum profit we write the equation of profit. Let we consider x chain saw and y wood chipper. We have a chain saw requires 5 hours of assembly. But wood chipper require 2 hours of assembly. Maximum hours of assembly time available = 20 hours
So, 5x + 2y ≤ 20 --(1) and x ≥ 0, y≥ 0
Profit of chain saw = $190
Profit on wood chipper = $210
Maximize profit, Max Z = 190x + 210y
Now, using graphical method, draw a graph is present in above figure. To determine the profit at point A and B
At point A( 0, 10)
Z = 190 ×(0)+ 210× (10) = 2100 --(1)
At point B(5,0)
Z = 190×(5)+230×(0) = 950 --(2)
Clearly from equation (1), maximum profit is at point A, number of chain saw assembled are 0 and number of wood chipper arre 10.
For more information about linear programming, visit :
https://brainly.com/question/14309521
#SPJ4