Final answer:
To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations and solve for the relationship between apples and bananas. The indifference curve will also pass through the point where Charlie consumes 4 apples and 2 bananas.
Explanation:
An indifference curve represents a set of choices that have the same level of utility. In this case, Charlie's utility function is u(xa, xb)=xaxb. To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations. If we plug in these points into the utility function, we get 32a*8b=4a*xb. Solving for b, we find that b=1/2a. This means that for every amount of apples, Charlie wants to consume half as many bananas to maintain the same level of utility. Therefore, the indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and 2 bananas.
what number must you add to complete the square x^2+24x=17
20d + 13 - 12d = -14
20d +13 -12d = -14
combine like terms
20d-12d = 8d
8d+13 = -14
subtract 13 from each side:
8d =-27
divide both sides by 8
d = -27/8
Solve the given initial-value problem. give the largest interval i over which the solution is defined. x dy dx + y = 6x + 1, y(1) = 8
What is the absolute difference between 1/2 and 1/3?
1/2 - 1/3 = 3/6-2/6 = 1/6
absolute value is 1/6
A rational number can be written as the ratio of one blank to another and be represented by a repeating or blank decimal. What are the two vocabulary for this sentence?
The answer is a rational number is one integer divided by another, and can be represented in either decimal of fraction form. The explanation behind this is visualize you are using long division to divide one number by one more. You divide, and then you acquire a remainder. Then you carry down a zero (multiply by ten) and divide again. Well, there are only so many balances you could perhaps have. For example, for 5, your choices are 0, 1, 2, 3, and 4. Sooner or later, you will replicate a remainder, at which fact you will just keep dividing the same method you did last time you saw that remainder -- and that's the reason why it repeats.
Jody, a statistics major, grows tomatoes in her spare time. she keeps a record of the weight of each tomato she grows. what percentage of all her tomatoes will be within one standard deviation of the mean weight? choose the correct answer below.
a. 50
b. 99.7
c. 95
d. 68
e. 10
what is an expression for twice a number,increased by 5
Write an even number between 7 and 16. Draw a picture and then write a sentence to explain why it's an odd number
Answer:
9, 11, 13 and 15
Step-by-step explanation:
Given numbers,
7 and 16,
In the number line the numbers are arranged in ascending order from left to right,
Thus, the numbers greater than 7 are,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17....
Also, the number less than 16,
.......6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
So, the numbers between 7 and 16,
8, 9, 10, 11, 12, 13, 14, 15
Now, a number with 1, 3, 5 or 7 in the ones place is an odd number.
Hence, the odd number between 7 and 16 are,
9, 11, 13 and 15
In a recent survey, two-thirds of the 234 students in a freshman class said they watch television shows on their computer. Determine the correct arithmetic set up for determining how many students watch television on their computer
If Argyl earns $93.00 for 7.75 hours of work, how many must he work to earn $571.50?
At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Explain how you can use the Commutative Property of Addition to find the total cost if three of each item are purchased!
The addition of all costs using commutative property will be $4.8.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Cost of one highlighter = $1.25
Cost of one ballpoint pen = $0.80
Cost of one spiral notebook = $2.75
The cumulative property states that the resultant of summation or multiplication does change by changing order.
Addition = 1.25 + 0.80 + 2.75
Total cost = $4.8.
Hence"The addition of all costs using commutative property will be $4.8".
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Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee.
In how many different ways can the curator of a museum arrange five of eight paintings horizontally on the wall?
The requried number of ways that 5 paintings to be chosen is 56 ways.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
Total number of paintings = 8
Total number of paintings to be arranged = 5
Number of ways = 8C5
= 8!/[8-5]!5! [nCr = n!/[n-r]!r!]
= 56 ways
Thus, the requried number of ways that 5 paintings to be chosen is 56 ways.
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0.4 ( 8 - 0.2w ) = -4
A number and it's absolute value are equal. If you subtract 2 from the number, the new number and it's absolute value are not equal. What do you know about the number? What is a possible number that satisfies these conditions?
If i buy a box of candy for $30 and make $52 selling the candy what is my profit
Suppose a card is drawn from a deck of 52 playing cards. what is the probability of drawing a 4 or an ace?
Which equation correctly applies the distributive property?
A. 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)
B.−1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57
C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2)
D. −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045
Multiply or find the special product. (Simplify your answer completely.)
[(x − 8y) + z][(x − 8y) − z]
You started on a bike trip, riding at a rate of 9 miles per hour. Your friend left one hour later and rode at the rate of 12 miles per hour. How long did it take your friend to catch up with you?
They need 3 hours to catch.
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
riding at a rate of 9 miles per hour
the friend left at rate of 12 miles per hour
Difference between
=12-9
=3 mph
So, the time they need to take
=9/3
= 3 hours
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what is 1.086 rounded to the nearest whole number
If candies have a cost X cents less per dozen, it would have cost 3 cents less for x+3 candies then if they had cost x cents more per dozen. What is x?
The answer is obtained by setting up a mathematical equation corresponding to the details given in the word problem. It is found that if the candies were 36 cents cheaper or dearer per dozen, it would affect the price by 3 cents for 39 candies.
Explanation:The problem can be solved by translating the words into a mathematical equation. Let's denote the original price of a candy as Y cents. Therefore, a dozen candies would cost 12Y cents.
First, we acknowledge that if candies are X cents less per dozen, each candy will be X/12 cents cheaper. And if you buy x+3 such candies, you will pay (x+3)*X/12 cents less.
Simultaneously, the problem also mentions that x+3 candies would have cost 3 cents less if they had been X cents *more* per dozen. This implies that buying x+3 candies would cost an extra (x+3)*X/12 cents, yet it is still 3 cents less.
Therefore, these two costs should be equal: (x+3)*X/12 = (x+3)*X/12 +3. By solving this equation: X = 36. Therefore, if candies were 36 cents cheaper or dearer per dozen, it would affect the cost by 3 cents for x+3 or 39 candies.
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A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 469 tickets overall. It has sold 112 more $20 tickets than $10 tickets. The total sales are $8300 How many tickets of each kind have been sold?
Final answer:
The basketball team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets. This was determined by setting up a system of linear equations based on the information given and solving for the variables representing the number of tickets of each kind.
Explanation:
The problem at hand is a classic example of a system of linear equations in the world of numerical problems. We need to find the number of $10, $20, and $30 tickets sold by the basketball team based on the given conditions. Let's denote the number of $10 tickets as x, the number of $20 tickets as y, and the number of $30 tickets as z.
The total number of tickets sold is 469: x + y + z = 469.The team has sold 112 more $20 tickets than $10 tickets: y = x + 112.The total sales amount to $8300: 10x + 20y + 30z = 8300.Substituting y from the second equation into the first and third equations, we get two new equations:
x + (x + 112) + z = 469, which simplifies to 2x + z = 357.10x + 20(x + 112) + 30z = 8300, which simplifies to 10x + 20x + 2240 + 30z = 8300, and further to 30x + 30z = 6060 by combining like terms and subtracting 2240 from both sides.Dividing the last equation by 30, we obtain x + z = 202. Now, we have a system of two equations with two variables:
2x + z = 357x + z = 202Subtracting the second equation from the first, we find x = 155. We can then substitute x into the second equation to find z = 202 - 155 = 47.
Finally, we substitute x into the second original equation to find y = 155 + 112 = 267.
Therefore, the team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets.
Paulita reads an average of 20 pages each day. She has 6 days to read 100 pages. Will she finish her reading in 6 days? Explain
Exact product of 379 and 8
54 3/11 as a decimal
Hans needs to memorize words on a vocabulary list for Latin class. He has memorized 20 of the words which is 1/4 of the list. How many words are in the list?
The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C.
The coordinates of the midpoint M, point A, and point C in the rhombus can be found using formulas. The coordinates of M are (4, 6), the coordinates of A are (0, 0), and the coordinates of C are (4, 2).
Explanation:To find the coordinates of the midpoint of BD, we can use the midpoint formula:
M = ( (x1+x2)/2, (y1+y2)/2 )
Substituting the coordinates of B and D into the formula, we get:
M = ( (2+6)/2, (10+2)/2 )
Simplifying, we get:
M = (4, 6)
Since A lies on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A are:
A = (0, 0)
To find the coordinates of C, we can use the fact that a rhombus has opposite sides equal in length and parallel. Since B and D have the same y-coordinate, the y-coordinate of C will also be the same. The x-coordinate of C will be the average of the x-coordinates of B and D. Therefore, the coordinates of C are:
C = ( (2+6)/2, 2 )
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what's the property of 34+0+18+26
Simplify . 4y4 4y8 8y4 8y8
Answer:
B
Step-by-step explanation:
Just did it.
Answer:
b
Step-by-step explanation: