To answer the questions, we need to understand the utility functions and budget constraints for both Joey and Jim. Let's break it down step by step:
Joey's Utility Function and Budget Constraint:
Joey's utility function for whisky (w) and beer (b) is given by: U(w, b) = 5 + (w^0.3 * b^0.7)
w: The quantity of whisky (in bottles) consumed by Joey
b: The quantity of beer (in cans) consumed by Joey
Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.
To find how many cans of beer and bottles of whisky Joey consumes, we need to maximize his utility function while staying within his budget constraint.
Joey's Budget Constraint:
Joey's total expenditure on drink (E) is given by: E = 2b + 6w
And we know that E = £75.
So, the budget constraint is: 2b + 6w = 75
Now, we can solve this problem using optimization techniques. However, without specific numerical values for the utility function and budget constraint, it's not possible to determine the exact quantities of beer and whisky consumed by Joey. We can only find the optimal consumption bundle if the specific values are given.
Joey's Indifference Curve and Budget Constraint Diagram:
To illustrate Joey's optimal consumption bundle, we would need to plot his indifference curve (representing his preferences) and his budget constraint (showing all possible affordable combinations of beer and whisky). However, without the exact values, we cannot draw the diagram.
Jim's Utility Function and Consumption:
Jim's utility function for beer (b) and whisky (w) is given by: U(b, w) = min{5, (w^0.3 * b^0.7)}
Jim's utility function shows that he insists on drinking beer and whisky together, and his utility is the minimum of 5 and the product of whisky and beer raised to certain powers.
Again, without specific numerical values for the utility function, we cannot determine the exact quantities of beer and whisky consumed by Jim.
In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint. With those values, we could then calculate the optimal consumption bundles for both Joey and Jim.
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If the area of a rectangle is x2 – 13x + 40, what are the lengths of
the two sides?
Answer:
5 and 8
Step-by-step explanation:
quadratic formula.
-(b)+sqrt(b)^2-4(a)(c)
^ans
divide the whole thing by 2(a).
If the formula isn't clear, search quadratic formula up.
No Solutions 2x + 5 + 2x + 3x = One Solution 2x+5+ 2x + 3x = Infinitely Many Solutions 2x + 5 + 2x + 3x =
Answer:
2x+5+2x +3x=7x+5 2x +5+ 2x + 3x = 7x+5
Step-by-step explanation:
Liza wants to have more than $750 in her
savings account before she will leave for college.
Right now she has $300, and she is going to
baby sit to earn $ 12.00 an hour. How many hours
will Liza need to babysit before she leaves for
college? What’s the inequality
Answer:
x is equal to or greater than 38.
Step-by-step explanation:
use the equation 300+12x to find the amount of money in total dependent on x, the number of hours she worked.
Step-by-step explanation:
750-300= $450 left that needs to be save to meet her goal.
set an equation to equal 450 that includes the next part of the information given which is $12 and hour
450=12x
isolate x by dividing 12 to both sides
x= 37.5 hrs
the inequality could be :
750<_ 300+ 12x
A family's home is currently worth $1,553,426, which is 70% higher than the home was
worth when they bought it. What was the value of the home when they bought it?
Answer:
The value of home when bought was $913,780.
Step-by-step explanation:
Given that:
Current worth of the house = $1,553,426
This is 70% more than the original worth of the house.
Let,
100 be the original percent and x be the original worth
Percent increase = (100+70)% = 170%
170% of x = $1,553,426
[tex]\frac{170}{100}x=1553426[/tex]
1.7x = 1553426
Dividing both sides by 1.7
[tex]\frac{1.7x}{1.7}=\frac{1553426}{1.7}\\x= 913780[/tex]
Hence,
The value of home when bought was $913,780.
If I was given the explicit formula how to I find the recursive formula?
9514 1404 393
Answer:
solve for f(n) in terms of f(n-1)
Step-by-step explanation:
In general, you solve for f(n) in terms of f(n-k) for k = 1, 2, 3, ....
__
Usually, such questions arise in the context of arithmetic or geometric sequences.
Arithmetic sequence
The explicit formula for an arithmetic sequence has the general form ...
a(n) = a(1) +d(n -1) . . . . . . . first term a(1); common difference d
The recursive formula for the same arithmetic sequence will look like ...
a(1) = a(1) . . . . . . . the first term is the first term
a(n) = a(n-1) +d . . . the successive terms are found by adding the common difference to the term before
__
Note: The explicit formula may be given as the linear equation a(n) = dn +b. Then the first term is a(1) = d+b.
__
Geometric sequence
The explicit formula of a geometric sequence has the general form ...
a(n) = a(1)·r^(n -1) . . . . . . first term a(1); common ratio r
The recursive formula for the same geometric sequence will be ...
a(1) = a(1) . . . . . . the first term is the first term
a(n) = a(n-1)·r . . . the successive terms are found by multiplying the term before by the common ratio
__
Note: The explicit formula may be given as the exponential equation a(n) = k·r^n. Then the first term is a(1) = kr.
__
Other sequences
Suppose you're given the quadratic sequence ...
a(n) = pn^2 +qn +r
Since the sequence is known to be quadratic (polynomial degree 2), we expect that we will only need the two previous terms a(n-1) and a(n-2). Effectively, we want to solve ...
a(n) = c·a(n-1) +d·a(n-2) +e
for the values c, d, and e. Doing that, we find ...
(c, d, e) = (2, -1, 2p)
So, the recursive relation is ...
a(1) = p +q +r
a(2) = 4p +2q +r
a(n) = 2a(n-1) -a(n-2) +2p
__
Additional comment
The basic idea is to write the expression for a(n) in terms of terms a(n-1), a(n-2) and so on. That will be easier for polynomial sequences than for sequences of arbitrary form.
There are some known translations between explicit and recursive formulas for different kinds of sequences, as we have shown above. If you recognize the sequence you have as being of a form with a known translation, then you would make use of that known translation. (For example, Fibonacci-like sequences are originally defined as recursive, but have explicit formulas of a somewhat complicated nature. If you recognize the form, translation from the explicit formula may be easy. If you must derive the recursive relation from the explicit formula, you may be in for a lot of work.)
8m + 34 = 10 - 16m
How do I do?
Answer:
m=-1
Step-by-step explanation:
8m + 34 = 10 - 16m
fist add 16m to each side
8m+16m+34=10
then subtract 34 from each side
8m+16m=10-34
add like terms
24m=-24
divide both sides by 24
m=-1
(91+5) +(31-6)=?
Thanks
Answer:
121
Step-by-step explanation:
96+25=121
Answer:
121
Step-by-step explanation:
(91+5) + (31-6) = ?
The first step is to solve what's in the parenthesis.
91 + 5 = 96
31 - 6 = 25
(96) + (25) =
96 + 25 = 121
(91+5) + (31-6) = 121
Therefore, the correct answer is 121.
Hope this helps :)
Which polynomial correctly combines the like terms and puts the given polynomial in standard form?
one-thirdx + 8x4 – two-thirdsx2 – x
Answer:
c: 8x↑4-2/3x↑2-2/3x
Step-by-step explanation:
eight x to the fourth power minus two-thirds x to the second power minus two-thirds x
its c on the edge
Answer:
c
Step-by-step explanation:
0.2(3b - 15c)
plz help me
Answer:
if you meant to simplify here you go
Step-by-step explanation:
0.2(3b - 15c)=
0.2(3b)+0.2(−15c)=
0.6b−3c
Answer:
0.6b-3c
Explination:
0.2(3b - 15c)
we can use dispributive property because of the parentheses
by distributing 0.2 to 3b and -15c
we get 0.6b and -3c
you could be thinking why did the numbers shrink?
the numbers decrease because every time you multiply by a decimal the number decreases
High Hopes
Barry-
Question 4 of 10 The slope of the line below is - 2. Use the coordinates of the labeled point to find a point-slope equation of the line. (4,-6)
Answer:
y = -2x + 2
Step-by-step explanation:
Air Jordans cost the Nike Corporation $25 to manufacture in a factory.
A. The cost of the shoes is marked up 760% to obtain the retail price. What is the retail price?
B. You have a coupon for 20% off the retail price of a pair of Air Jordans. If there is a 6% sales tax, what is the final price to buy these shoes?
C. The retail price used to be $125 many years ago. What is the percent of increase from the former retail price to its current retail price (from your answer to part A)?
Answer:
n4ur84234r
Step-by-step explanation:
3874rfbh dc
3x - 8 = 4(x+5) plz plz plz solve it
Answer:
=−28
Step-by-step explanation:
The scale on a drawing is 2:in:5yd. If a length on the drawing is 6 inches, what is the actual length.
Answer:
15 yards
Step-by-step explanation:
proportion:
2/5:6/X
2x=30
x=15
A combo meal and a salad cost $12
and 2 combo meals and a salad cost
$20.
How much is a combo meal?
How much is a salad?
Answer:
The cost of a combo meal is $8 and a salad is $4.
Step-by-step explanation:
You have to form simultaneous equations with the given informations. Let combo meal be m and salad is s :
[tex]m + s = 12 - - - (1)[/tex]
[tex]2m + s = 20 - - - (2)[/tex]
Next, you have to solve these equations :
[tex](2) - (1)[/tex]
[tex]2m + s - m - s = 20 - 12[/tex]
[tex]m = 8[/tex]
[tex]sub \: \: m = 8 \: \: into \: \: (1)[/tex]
[tex](1)⇒[/tex]
[tex]8 + s = 12[/tex]
[tex]s = 4[/tex]
Answer: 8$,4$
Step-by-step explanation:
Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 60 grams, how much of the element would remain after 30 years, to the nearest whole number?
Answer:
2,325 grams !
Step-by-step explanation:
What is the maximum of the sinusoidal function?
Answer: 2
Step-by-step explanation:
Solve the following system of equations using substitution.
3m + 4n = - 12
n = - m - 2
A.m = -4, n = 2 O B.m = 4, n= -6
C. m = -8, n = 6 O D.m = 3, n = 1
Find the angle of w please
At Silver Gym, membership is $20 per month, and personal training sessions are $35 each. At Fit Factor, membership is $40 per month, and personal training sessions are $25 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
NEED IT DONE ASAP BY 6:00
Answer:
20+35x=40+25x, 35x- 25x=40-20, 10x=20, x=2 , 2 sessions
which shape has diagonals that bisect each other but not at 90 degrees?
Please help me. You will be marked brainliest.
Answer:
What do you need help with?
Step-by-step explanation:
y-y, = m (x - x) if
Slope = 3
Passes though the point (2,-4)
The CEO of a cell-phone company has recently noticed a 26% sales decrease in the month of July compared to June. Let n represent June’s sales. If y represents July’s sales, which equation can be used to determine the sales in July?
Answer:
y = n - 0.26n
y = 0.74n
Step-by-step explanation:
The equation that can be used to express the function above is given an Exponential Decrease function
Where:
y = a(1 - r)^t
Where
y = July sales
a = n = June sales
r = rate of decrease = 26% = 0.26
t = time in months = June to July = 1 month
t = 1
Hence, our equation =
y = n( 1 - 0.26)¹
y = n(1 - 0.26)
y = n - 0.26n
y = 0.74n
The equation that can be used to determine the sales in July is given as:
y = n - 0.26n
y = 0.74n
Bill is h cm tall. Sienna is 4 cm taller than Bill. What is the expression in terms of h for sienna height in centimeters.
can someone help me with this
Answer:
A.) 3/4
Step-by-step explanation:
You can find this by dividing the distance from point Z to point Y by the distance of point X to point Y. The distance from Z to Y is 6 and the distance from X to Y is 8, so that means that the slope is 6/8, which simplifies to 3/4.
Find the value of x and the value of y.
A. x = 130, y = 50
B. x = 135, y = 45
C. x = 140, y = 40
D. x = 145, y = 35
Answer:
B. x = 135, y = 45Step-by-step explanation:
x° + y° = 180° {suplementary angles}
x° = 3y° {corresponding angles by parallel lines}
So:
3y° + y° = 180°
4y° = 180°
y° = 45°
y = 45
x° = 3×45° = 135°
x = 135
need help quickly! please
Answer:
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Step-by-step explanation:
Write down the gradient of the line
(1 Point)
y=1/2x
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The equation of a line in point- slope form is
y = mx + c ( m is the slope ( gradient ), c is the y- intercept )
y = [tex]\frac{1}{2}[/tex] x ← is in point- slope firm
with gradient = [tex]\frac{1}{2}[/tex]
The price p of a pizza is $6.95 plus $0.95 per topping t on the pizza, write a function rule
Answer:
y= 6.95+0.95t
Step-by-step explanation:
Given data
The price p of a pizza is $6.95
plus $0.95 per topping
let the number of toppings be t
and let the total cost be y
Hence for any number of topping t the cost function is
[tex]y= 6.95+0.95t[/tex]
The function rule for the prize of a pizza is
[tex]P=0.95t +6.95[/tex]
Given :
The price p of a pizza is $6.95 plus $0.95 per topping t on the pizza
Initial price of the pizza is 6.95
The cost of each topping is 0.95 .
Let 't' be the number of toppings on the pizza
Price of a pizza = initial cost of pizza + cost per pizza ( number of toppings)
[tex]p=6.95 +0.95(t)\\P=0.95t +6.95[/tex]
The function rule for the prize of a pizza is
[tex]P=0.95t +6.95[/tex]
Learn more : brainly.com/question/5747203
Solve by factoring.
s2 + 8s + 15 = 0