Answer:A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. (A) If the profit on a trick ski is $40$ and the profit on a slalom ski is $30,$ how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? (B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $25$ and all other data remains the same. (C) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $45$ and all other data remain the same.
Step-by-step explanation:
The optimal production plan for maximizing profit is to manufacture 48 slalom skis and 0 trick skis each day, resulting in a maximum profit of $2880.
Given data:
To solve this problem, we can use linear programming techniques to find the optimal number of trick skis and slalom skis that should be manufactured each day to maximize the profit.
x = number of trick skis
y = number of slalom skis
We need to maximize the profit function: P = 40x + 60y
Subject to the following constraints:
1x + 1y ≤ 336 (Fabricating department constraint)
1x + 1y ≤ 48 (Finishing department constraint)
x, y ≥ 0 (Non-negativity constraint)
We can graphically represent these constraints on a coordinate plane and find the feasible region, which is the region where all constraints are satisfied. Then, we can evaluate the profit function at the corner points of the feasible region to find the maximum profit.
After solving this system of linear inequalities, we find that the feasible region is a triangle with vertices at (0, 48), (0, 48), and (48, 48).
Evaluating the profit function at these vertices:
P(0, 48) = 40(0) + 60(48)
= $2880
P(0, 0) = 40(0) + 60(0)
= $0
P(48, 0) = 40(48) + 60(0)
= $1920
The maximum profit is $2880, which occurs when they produce 48 slalom skis and 0 trick skis.
Hence, the optimal production plan for maximizing profit is to manufacture 48 slalom skis and 0 trick skis each day, resulting in a maximum profit of $2880.
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Triangle PQR has vertices P(-2,2), Q(8,2) and R(4,6).
(a) Find the equation of the perpendicular bisector of segment PQ.
I got so confused on this question if I could get help it would mean a lot
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
You can forget about point R. It does not have any part in this problem, except to add confusion.
The given line PQ has the same y-coordinate values for points P and Q. This means the segment is a horizontal segment. Its perpendicular bisector will be a vertical line through its midpoint.
The midpoint (M) of PQ is ...
M = (P +Q)/2
M = ((-2, 2) +(8, 2))/2 = (-2+8, 2+2)/2 = (6, 4)/2
M = (3, 2)
The vertical line through a point with x-coordinate 3 will have the equation ...
x = 3
Write a sentence for the equation.
2(t+4q)=2q+4t
Two point three tens times m equals zero point forty six hundredths
The given equation in the form of a statement can be written as Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and four times of t.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be written in the form of an statement as:
Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and four times of t.
Hence, the given equation in the form of a statement can be written as Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and four times of t.
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if Brian is driving 50 miles per hour how far did he drive
Answer:
2.5 km long after 59 miles
Answer:
50 miles
Step-by-step explanation:
Consider the matrix.
6 3
5 4
What is the value of |C|?
|C|=
Answer:
e0
Step-by-step explanation:
\frac { 3 ^ { p + 1 } - 3 ^ { p } } { 2 \times 3 ^ { p } } = 1
Answer:
Given equation:
[tex](3^{p+1} - 3^p) /(2 *3^p) = 1[/tex]Solving for p:
[tex]3^{p+1} - 3^p = 2 *3^p[/tex][tex]3*3^p - 3^p = 2 *3^p[/tex][tex]2 *3^p =2 *3^p[/tex]p - any real number
We can state the initial expression is correct for any value of p.
Answer:
True for all p
Step-by-step explanation:
Given equation:
[tex]\dfrac{3^{p+1}-3^{p}}{2 \times 3^{p}}=1[/tex]
Multiply both sides by [tex]2 \times 3^p[/tex]:
[tex]\implies 3^{p+1}-3^p=2 \times 3^p[/tex]
Add [tex]3^p[/tex] to both sides:
[tex]\implies 3^{p+1}-3^p+3^p=2 \times 3^p+3^p[/tex]
[tex]\implies 3^{p+1}=3 \times 3^p[/tex]
Rewrite 3 as 3¹:
[tex]\implies 3^{p+1}=3^1 \times 3^p[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 3^{p+1}=3^{1+p}[/tex]
[tex]\implies 3^{p+1}=3^{p+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies p+1=p+1[/tex]
Subtract 1 from both sides:
[tex]\implies p+1-1=p+1-1[/tex]
[tex]\implies p=p[/tex]
Therefore as both sides are equal, true for all p.
In 2007, the number of tickets sold was again 210.
Adult tickets were $2.60 each and student tickets were $1.40 each.
The total amount received from selling the 210 tickets was $480.
How many student tickets were sold?
Step-by-step explanation:
1.40x + 2.60x = 480
4x =480
x=480÷4
x=120
168 and 312
{[(3x+8)+6(2.5x-3)]}
Answer: The answer is 18x + 26
Step-by-step explanation:
What I did was simplify the Expression of (3x+8)+6(2.5x-3) then combine the terms and last evaluate the Expression.
on average, what value is expected for the t statistic when the null hypothesis is true?
Answer:
0
Step-by-step explanation:
JJ withdraws $20 from his bank account every week for lunch. Suppose he does not make any additional deposits or withdrawals. What integer represents the change in value of JJ's bank account after nine weeks?
Answer:
-118
Step-by-step explanation:
Since he is withdrawing, the value of 20 will be negative.
And if he is withdrawing $20 over nine weeks, then it is a multiplication problem.
So,
-20 x 9 = -118
hi can anyone help with this question thx
first part of the question is in the pic
second part is here and it is:
York to London is a distance of 175miles
How many miles an hour faster was the first part of the journey?
Answer:
88 miles per hour
Step-by-step explanation:
12 + 122 = 134 minutes for the entire journey
The total distance was 197 miles.
The avarage speed is the total distance divided by the total time:
Convert the time from minutes to hours dividing it by 60:
134/60 = 2.24 hours
197/2.24 = 87.95 ≈ 88 miles per hour
are my choices correct?
pls check math geniuses!!
X would be 10, and 2 because:
(10-10) = 0 and (2-2) = 0
The extraneous solution is correct because the equation does not hold true when x is 2 and only hold trues when it is 10.
Edit: the extraneous solution is 2 is because it doesn't hold true to the equation.
What Is the slope of the line on the graph?
Answer:The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.
Step-by-step explanation:
A concert earned $3,745 in ticket sales. One ticket to the concert cost $35.
How many tickets were purchased for the concert?
Answer:
107 concert tickets were bought
Step-by-step explanation:
whats the error? I SOLVED AND CHECKED. Is it correct? Im confused… pls help il will give brainliest
Answer:
32 in represents perimeter u added length times width once which would only give half of the rectangle
Step-by-step explanation:
2(3w+8+w) =32
6w+16+2w =32
8w+16 = 32
8w=16
w=2
Please show all steps to 2- (-1)
Answer:
3
Step-by-step explanation:
2-(-1)=2+1=3
whats the answer for 6x+4y=−12
look at the figures how can u prove the triangles are congruent is it
A)
B)
C)
Answer:
ABC by the SSS postulate
ASA rule shows 1 side is congruent and 2 angles congruent
SAS rule shows 2 sides are congruent and 1 angle congruent
SSS rule shows 3 sides are congruent as angles already proven ASA and SAS
What are the two solutions of the equation x² – 14x - 32 = 0?
HI how was your day today
-
What is the equation of the line that passes through the point (-4,-7) and has a
slope of?
Answer:
y = -4 x -9
Step-by-step explanation:
If it wrong i'm sorry
why is this not a polynomial?
3^x - x/3 + x^3
Answer:
It is not a polynomial because the polynomial is the term given to an expression which has coefficients as well as variables with powers having a non-negative entegral value or we can say natural number. The power of the variable × here is not an integer so 3/× is not a polynomial
Step-by-step explanation:
I hope I helped you
Answer:
below
Step-by-step explanation:
-x/3 + x³ is polynomial
3ˣ IS NOT a polynomial, it makes the function be an "exponential function", which does not fit the criteria of polynomial definition.
HELPP FAST im tired and it's due realy really really soon
Here's a question ~
can anyone give the explanation ?
Answer:
See belowStep-by-step explanation:
As per the question we have:
The y - intercept is b = -1The slope has same angle with x- and y - axis.This can be a function with the slope of m = 1 or m = - 1 as these lines must be perpendicular to each other and make 90°/2 = 45° or 45° + 90° = 135° angle with the x- or y- axis.
So the lines could be:
y = x - 1 ory = -x - 1Lines must be perpendicular to each other as they are cutting at y intercept -1
Slope intercept form of line
for slope -1
y=-x-1For slope 1
y=x-1
You start at (9, 5). You move left 3 units and up 1 unit. Where do you end?
Hello!
(9,5)
3 units left: (6, 5) (we subtract 3 from the x-coordinate)
1 unit up: (6, 6) (we add 1 to the y-coordinate)
Hope this helps you!
~Just a joyful teen
[tex]SilentNature[/tex]
Tickets to see a movie cost $5 for children and $8 for adults. The equation 5x + 8y = 80 represents the number of children (x) and adults (y) who can see the movie with $80.
If no adults see the movie, how many children can see the movie with $80?
Answer:
40
Step-by-step explanation:
Answer:
44444444444444444444
Mrs. Shultz went to New York to do her Christmas shopping. She took a cab to go into the city and they charged her a flat fee of $6 plus $2 for every mile. Mrs. Shultz ended up paying the cab driver $30. How many miles did Mrs. Shultz travel?
Answer:
12 miles
Step-by-step explanation:
30-6=24
24/2=12 miles
By which rule are these triangles congruent. A. AAS B. ASA C. SAS D. SSS
find the greater common factor
2x^2+7x-30
Answer:
ty
Step-by-step explanation:
Rabbit populations can double every 30
days. If there are 10 rabbits on a farm,
how many rabbits will be on the farm
after 120 days?
First, complete the equation:
Future Amount = [?](1+10
=
Román preguntó en servicio al cliente si le podían fabricar los Zetas con medidas especiales aló cual respondieron que si él requiere una loseta cuadrada con un aria de 225 m² cuanto miden los lados de la loseta que le fabricaron
Answer:
Los lados de la lista cuadrada que le fabricaron miden 15 m
Step-by-step explanation:
Hola! Sabemos que la loseta tiene área cuadrada y que el área del cuadrado está dada por:
Ac = a²
Donde a es la medida de los lados del cuadrado.
Para hallar la medida de la lista cuadrada despejamos a aplicando raíz cuadrada a ambos miembros:
a = √(Ac)
a = √(225 m²)
a = 15 m
Los lados de la lista cuadrada que le fabricaron miden 15 m
Respuesta: Los lados de la lista cuadrada que le fabricaron miden 15 m
Explicación paso a paso:
Hola! Sabemos que la loseta tiene área cuadrada y que el área del cuadrado está dada por:
Ac = a²
Donde a es la medida de los lados del cuadrado.
Para hallar la medida de la lista cuadrada despejamos a aplicando raíz cuadrada a ambos miembros:
a = √(Ac)
a = √(225 m²)
a = 15 m
Los lados de la lista cuadrada que le fabricaron miden 15 m
use order of operations
Answer:
97
Step-by-step explanation:
[tex] {4}^{2} + 3(37 - (2 \times 5)) \\ {4}^{2} + 3(37 - 10) \\ {4}^{2} + 3(27) \\ {4}^{2} + 81 \\ 16 + 81 \\ 97[/tex]
Hope this helps! Brainliest would be really appreciated!