Answer:33
Step-by-step explanation:
Philip's bill for lunch at a restaurant was $7. He left a 15% tip. What was the amount of the
tip?
Answer:$1.05
Step-by-step explanation:
Step-by-step explanation:
:
=$7×15/100
=$1.05
One week Tony bought 6 soft shell tacos and 2 hard shell tacos for $12. The next week he bought 3 soft shell tacos and 1 hard shell tacos for $6. Write a system to find the cost for each type of taco. Explain your answer.
A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem
Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
[tex]P_{x}[/tex] = 2 , [tex]P_{y}[/tex] = 4
Now,
Budget constraint -
[tex]P_{x}[/tex] x + [tex]P_{y}[/tex] y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get
[tex]\frac{100y + 1}{100x + 2} = \frac{1}{2}[/tex]
⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y = [tex]\frac{250}{2}[/tex] = 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
The maximized value of the utility function is $3125500
The utility function is given as:
[tex]U(x,y) = 100xy + x + 2y[/tex]
The prices per unit are also given as:
[tex]P_x = 2[/tex]
[tex]P_y = 4[/tex]
When a person receives $1000, then the budget function is:
[tex]2x + 4y = 1000[/tex]
Divide through by 2
[tex]x + 2y = 500[/tex]
Differentiate the utility function with respect to x and y
[tex]U'(x) = 100y + 1[/tex]
[tex]U'(y) = 100x + 2[/tex]
So, we have:
[tex]U'(x) = P_x[/tex] and [tex]U'(y) = P_y[/tex]
The above equations become
[tex]100y + 1 = 2[/tex] and [tex]100x + 2 = 4[/tex]
Divide both equations
[tex]\frac{100y + 1}{100x + 2} = \frac 24[/tex]
Reduce the fractions
[tex]\frac{100y + 1}{100x + 2} = \frac 12[/tex]
Cross multiply
[tex]100x + 2 = 200y + 2[/tex]
Subtract 2 from both sides
[tex]100x = 200y[/tex]
Divide both sides by 100
[tex]x = 2y[/tex]
Recall that:
[tex]x + 2y = 500[/tex]
So, we have:
[tex]2y + 2y = 500[/tex]
[tex]4y=500[/tex]
Divide through by 4
[tex]y=125[/tex]
Recall that:
[tex]x = 2y[/tex]
So, we have:
[tex]x = 2 \times 125[/tex]
[tex]x = 250[/tex]
Also, we have:
[tex]U(x,y) = 100xy + x + 2y[/tex]
Substitute the values of x and y, in the above function
[tex]U(250,125) = 100 \times 250 \times 125 + 250 + 2 \times 125[/tex]
[tex]U(250,125) = 3125500[/tex]
Hence, the maximized value of the utility function is 3125500
Read more about utility functions at:
https://brainly.com/question/24922430
write an equation perpendicular to y=1/5 x+9 that passes through the point (-2,-2)
Answer:
-2= 1/5x-2 +9
-2= -0.4 +9
Step-by-step explanation:
w – 9 = 22 what is w
Answer:
31............
Step-by-step explanation:
22+9=31
Answer:
it is -13
Step-by-step explanation:
9-9-x=22-9 x=-13. 9-(-13)=22 brainliest please
I NEED IMMIEDIETE HELP PLEASE
SEVENTH GRADE MATH:
A candle 16 inches tall burns for 2.5 hours. When the flame is blown out, it is only 3.5 inches tall. At what rate is the height of the candle decreasing?
Answer:
5 inches per hour
Step-by-step explanation:
Answer: 5 inches per hour
Step-by-step explanation:
Starting height of 16 minus the end height of 3.5.
16- 3.5= 12.5
Take this number and divide it by the time the candle burned (2.5 hours)
12.5 inches/ 2.5 hours = 5 inches per hour
Please help me to solve the 5th part!
Step-by-step explanation:
hope this will help you.
See screenshot Please! :) and help ASAP thank youu!! <33
Answer:
A.
Step-by-step explanation:
A. makes the most sense out of all of them. But if it had to be another one, I'd say D. Sorry! I'm not the best at these either. :)
The student council is selling cupcakes at the school play.
The cost to make the cupcakes is a fixed \$ 75$75 plus \$ 0.17$0.17 per cupcake made.
Each cupcake sells for \$ 2.00$2.00.
Answer: 37.5
Step-by-step explanation:
75 divided by 2
Linda received 3/5 of the votes in the election for student council president. What percent of the votes did Linda receive
Answer:
60.
Step-by-step explanation:
Answer:
[tex]60%[/tex][tex]%[/tex]%
Can u gimme brain plz!if there are 300 seventh graders, and 80% passed the benchmark, how many passed the benchmark
Answer:
240 seventh graders passed
Step-by-step explanation:
300 x 0.8 = 240
Select all the equations where x = 3 is a solution.
Choose 2 answers:
А )x +4= 7
B) = 3 9 5 - 2 = 2
D) 8x = 32
E )X – 10 = 7
Answer:
Step-by-step explanation:
X +4=
8x=32
What is an equation of the line that passes through the point (-6,-2)(−6,−2) and is parallel to the line 3x-2y=23x−2y=2
Answer:
y = 3/2x + 7
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is 3x - 2y = 2. First, let's put this into standard form.
3x - 2y = 2
Add 2y to both sides to make y positive.
3x = 2y + 2
Subtract 2 from both sides to isolate y.
3x - 2 = 2y
Isolate y further by dividing both sides by 2.
3/2x - 1 = y or y = 3/2x - 1
This is now your first line. Its slope is 3/2. A line parallel to this one will also have a slope of 3/2.
Plug this value (3/2) into your standard point-slope equation of y = mx + b.
y = 3/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-6, -2). Plug in the x and y values into the x and y of the standard equation.
-2 = 3/2(-6) + b
To find b, multiply the slope and the input of x (-6)
-2 = -9 + b
Now, add 9 to both sides to isolate b.
7 = b
Plug this into your standard equation.
y = 3/2x + 7
This equation is parallel to your given equation (y = 3/2x - 1) and contains point (-6, -2)
Hope this helps!
I struggle on this one to
Answer:
13. acute
14. right
15. 36
16. x = 14
Step-by-step explanation:
Find the slope of the line passing through (3, 7) and (6, 11). Note: Use the y-y/x-x formula!
Answer:
Slope of the line [tex]m = \frac{4}{3}[/tex]
Step-by-step explanation:
Explanation:-
Given points are ( 3,7) and (6,11)
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]m = \frac{11-7}{6-3}[/tex]
[tex]m = \frac{4}{3}[/tex]
Slope of the line [tex]m = \frac{4}{3}[/tex]
Json has 4 gallons of hand sanitizer that contains 25% alcohol. He want sto make a hand santizer that contains 50% alchahol. How many gallons of pure alcohol should he add?
Answer:
2
Step-by-step explanation:
1+x/4+x = 1/2
4+x = 2 + 2x
x = 2
3.
What is the area of triangle ABC?
2in.
2in.
B
The area of triangle ABC is
please help thank you
the perimeter of the square is 4cm
figure out the riddle
Answer:
Four
Step-by-step explanation:
All the animals are on the bed, but the bed itself has four legs.
Answer: 6
Step-by-step explanation: the legs from the bed, and your 2 legs
Ray did yard work for 112 hours after school every day for 5 days. How many total hours did Ray do yard work?
5th grade
HELP
4x – 2y = -8
y = 2x + 4
Answer:
Set any x and then compute y as 2x + 4. The pair solves the equations.
Step-by-step explanation:
4x - 2y = -8
4x = 2y - 8
2x = y - 4
y = 2x + 4
2x + 4 = y
2x = y - 4
Both equations are the same, so any pair of x and y for which 2x = y - 4 works.
Set any y and then compute x as (y - 4)/2
Alternatively
2x = y - 4
2x + 4 = y
Set any x and then compute y as 2x + 4.
Help, please!!!!!!!!
y= 3/2 x+ 3 and 3x-2y=-6
Step-by-step explanation:
□y = -3/2x-9
□y=3x+3
□3x+2y=-9 = y=-9/2 -3/2x
□y=3/2x+3 correct
□3x-2y=-6 = y=3+ 3/2x correct
□2/3x +3
Write equivalent fractions for 2 2/5 and 1 3/4 using a common denominator
Answer:
12/5 and 15/5
Step-by-step explanation:
I think this is the answer based on ur question but sry if I'm incorrect. boom roasted.
Problem of the Day 7.7
Joshua swims 18 laps every day at swim practice. If he swims every day for 32 days, how many laps has he completed?
Answer:
576
Step-by-step explanation:
18 x 32 = 576
What is the vertex of the absolute value function below?
Answer:
add file/link/pdf
Pippin owns 2 cats, 3 dogs, and a lizard as pets. What is the ratio of the number of cats to the total number of pets Pippin owns?
Choose 1 answer:
is it
A 1/6
B 1/3
C 2/5
D 1/2
or E 2/3
Answer: B) 1/3
2 cats/6 total animals
simplified is 1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
plz make me brainliest
Which equation matches the graph shown?
Answer:
A
Step-by-step explanation:
Since it is upside down, it is the one with the negative sign in front of the x. The numbers will continue to increase in the negatives.
Answer:
ur ans is A
Step-by-step explanation:
GOODLUCK
Find the surface area of the rectangular prism.
3 in.
2 in.
4 in.
1.)60 in 2
2.)84 in 2
3.)26 in
4.)52 in2
Answer:
52 Inches³
Step-by-step explanation:
The surface area formula for a rectangular prism is 2 x (height x width + width x length + height x length)
SA= 2(4x2+2x3+4x3)
Find the difference in slopes. Can anyone help me with this? I need it, its a grade for my mah class.
Answer:
Slope of the graphed line, using 2 points (-1, 3) and (0, 0):
m₁ = 3/-1 = -3Slope of the line containing the points (-6, 2) and (-9, 5):
m₂ = (5 - 2)/(-9 - (-6)) = 3/-3 = -1The difference in number between the slopes:
-3 - (-1) = -2The difference in slopes:
The slope of the graphed line is 3 times steeper.Answer:
i like to know this answer
List and appraise a piece of music base on timbre
Explain how to find the slope of a vertical line
Answer:
its undefined because its only going up and never over 1/0