This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.
Why is it called indifference curve?It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.
An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.
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The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p= -0.008x+330
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units
How to solve system of equation?Supply:
p=0.003x
x = p/0.003
x = 1/0.003p
Demand:
p= -0.008x+330
-0.008x = p - 330
x = (p - 330)/-0.008
Equilibrium price
Equate supply and demand price
0.003x = -0.008x+330
0.003x + 0.008x = 330
0.011x = 330
x = 330/0.11
x = 3,000
Substitute into
p=0.003x
p = 0.003(3000)
p = $9
Consequently, the equilibrium quantity and price is 3000 units and $9
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Scenario #1: Raul.
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account, which earns 1.5% interest per year.
1. what is the total balance in the account after 40 years?
2. how much of a total did Raul contribute himself?
3. how much money did Raul make through compound interest in this savings account?
4. identify one way Raul could have increased the total amount of money he made over 40 years. Explain your reasoning..
After 40 years, the account has a total balance of $49.450.80.
What is an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
here, we have,
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
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A sample, sized 5, was taken with the following measurements: 5, 10, 2, 7, and 6.
What is the point estimate of the population mean?
The point estimate of the population mean is 6
What is the point estimate of the population mean?From the question, we have the following parameters that can be used in our computation:
Measurements: 5, 10, 2, 7, and 6.
Sample size = 5
The point estimate of the population mean is the sample size of the mean
Using the above as a guide, we have the following:
Sample mean = Sum/Count
substitute the known values in the above equation, so, we have the following representation
Sample mean = (5 + 10 + 2 + 7 + 6)/5
Evaluate
Sample mean = 6
Hence, the estimate is 6
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Find the exact value of x
Answer:
When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.
You want to subtract 9 and 24 to get the x value:
24 - 9 = 15
x = 15
Step-by-step explanation:
Hope it helps! =D
Hi there, here's your answer:
Given a right angled triangle
With the hypotenuse as 24 units and one of the legs as 9 units
To find:
The 3rd side denoted as 'x'
Solution:
We use Pythagoras Theorem:
[tex]a^2 + b^2 = c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
We know the value of c and b
And a = x
Thus,
[tex]x^2 = c^2 - b^2[/tex]
[tex]x^2 = 576 - 81\\[/tex]
[tex]== > x^2 = 495\\[/tex]
Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units
Hope it helps! Please mark as Brainliest!
Find the total value of $6800 compounded quarterly at 6% for 3 years.
The total value of $6800 compounded quarterly at 6% for 3 years is $8,123
How to determine the total valueFrom the question, we have
A = final amount
P = principal amount (initial investment) = $6800
r = annual interest rate = 0.06 ie. 6%
n = number of times interest is compounded per year = 4
t = time (in years) = 3
The total value is calculated as:
A = P(1 + r/n)^(nt)
substitute the known values in the above equation, so, we have the following representation
A = 6800(1 + 0.06/4)^(4*3)
Evaluate
A = 8130.2
Hence,, the value is $8130.2
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6 3/14 divided by 250 + 5 2/7 divided by 250
Answer:
The solution is 23/500 or 0,046
Step-by-step explanation:
6 3/14÷250+5 2/7÷250
= 6 3/14×1/250+5 2/7×1/250
= (87/14×1/250)+(37/7×1/250)
= (87/3500)+(37/1750)
= 87+37(2)/3500
= 87+74/3500
= 161/3500
= 161÷7/3500÷7
= 23/500
= 0,046
6.88 + 3w= 17.98 find w
Answer:
3w= 17.98-6.88
3w=11.1
w =3.7
Step-by-step explanation:
After subtracting divide both side by 3
Answer:
w = 3.70
Step-by-step explanation:
Given that,
6.88 + 3w= 17.98 ..........(1)
Now subtracting both sides by 6.88 in equation (1), We have
6.88 + 3w - 6.88 = 17.98 - 6.88
or, 3w + 0 = 11.1
or, 3w = 11.1
Again dividing both sides by 3 in the above equation, We have
[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]
Hence the required answer is w = 3.70
Write 15*15*15*15 using an exponent
Answer:
15^4
Step-by-step explanation:
An exponent refers to the number of times a number is multiplied by itself,
so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.
[tex]15^{4} .[/tex]
Step-by-step explanation:1. General concept about exponents.When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].
2. Use the rule to rewrite the expression.As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:
[tex]15^{4} .[/tex]
A rectangle is formed from a square by increasing the latter length by 50 percent while reducing the width by 50 percent. The ratio of the area of the rectangle to that of the square is?
Answer:
3 : 4
Step-by-step explanation:
You want to know the ratio of areas of a rectangle and square such that the rectangle is 50% longer and 50% narrower than the square.
TransformationA square that is 2 units on a side will be transformed to a rectangle that is 1.5×2 = 3 units long, and 0.5×2 = 1 unit wide.
The rectangle area is 3×1 = 3. The square area is 2×2 = 4.
The ratio of areas is ...
rectangle area : square area = 3 : 4
write 76 in the base-nine system
The base-nine system of 76 base 10 is 84
What is 76 base 10 in the base-nine system?We will divide 76 by 9 and write down the remainder
9 | 76 R
9 | 8 | 4
9 |8 | 8
The remainder is then written from the bottom value giving us 84
Consequently, base 10 numbers can be converted to base 9 by dividing by 9 and writing the remainder in the reverse order of bottom to top.
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The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who obtained miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any outliers?
a) The value of z-score is -0.299.
c) The IQR value is measure of spread of data, IQR = 4.25.
d) There is outliers since observations are not less than 30.375 and greater than 47.375.
What is z- score?The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.
Given:
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
(a) The value of z-score is calculated as follows,
μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88
σ = 3.61
So, z = X - μ / σ
= 37.8 - 38.88/3.61
= − 0.299
(b) Quartile:
Q₁ = ( n+1/4)th value
= (24+1/4)th
= 6.25th
= 36.2 + 0.25 x ( 37.3 − 36.2 )
= 36.47
and, M = ( n+1/2)th value
= (24+1/2)th
= (24+1/4)th
= 12.5 t h
= 38.4 + 38.5/2
= 38.45
Q₃ = 3( n+1/4)th
= 3(24+1/4)th
= 18.75 t h
= 40.6 + 0.75 x ( 41.4 − 40.6 )
= 41.2
(c) Interquartile range
= Q ₃ − Q ₁
= 41.2 − 36.47
= 4.25
(d) Lower fences = Q₁− 1.5 ( I Q R )
= 36.75 − 1.5 ( 4.25 )
= 30.375
Upper fences = Q ₃+1.5
= 41 + 1.5( 4.25 )
= 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
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How do we rewrite 10^ -1 without using negative exponents?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
210 people are asked how many siblings they have?
# of Siblings Frequency Relative Frequency Cumulative Frequency
43
43
41
0
1
2
3
4
43
Submit Question
0.2048
0.2048
0.2048
0.1905
43
86
127
210
a. Complete the table (Use 4 decimal places when applicable)
b. What percent of the people have exactly one sibling?
Hint: Frequency Tables
The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.
What is Relative Frequency and Cumulative Frequency?Relative frequency is found by dividing the frequency with the total number of values.
Cumulative frequency is calculated by adding the previous frequencies together.
(a) From the table,
Total number of people = 210
So, Total frequency = 210
Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40
Relative frequency = Frequency / Total frequency
Relative frequency of number of siblings as 2 = 0.1952
Cumulative frequency of number of siblings as 3 = 127 + 43 = 170
(b) Percent of people having exactly 1 sibling = (43 / 210) × 100
= 20.48%
Hence the percent of people having exactly 1 sibling is 20.48%.
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Write the sentence as an equation.
242 fewer than the quantity 193 times n equals 131
I think this is it
252-(193×n) =131
what is the substitution for -3x+5y=21
Answer:
5
_ y - 7
3
the five is floating for some reason its supposed to be under the line
Given parallelogram abcd, in order to prove that opposite sides are congruent, what additional segments or points will you need?.
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:
The length of one pair of opposite sides is equal.
The two pairs of opposite sides are parallel.
To show these two conditions, you may need additional segments or points such as:
Perpendicular lines or segments to the sides to help show the sides are parallel.
Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.
By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.
Find the image of the given point
under the given translation.
P(12, 8)
T(x, y) = (x-8, y - 12)
P(12,8)
Move 8 units to the left (X) and 12 units down(Y).
P'(12-8, 8-12)
P'(4, -4)
If you don't how to do translation try plotting (12,8).
Please help will mark Brainly
Answer:
P=10x^2+38y
Step-by-step explanation:
its the answer
which is a true statement about two numerical sets of data that have negative association
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
Find the dimensions of a rectangular Persian rug whose perimeter is 22 ft and whose area is 10 ft squared
rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
How to calculated dimensions of a rectangular Persian rug?Let's say that the Persian rug is rectangular, with length "l" and width "w".
The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:
Perimeter = 2l + 2w
Given that the distance around it is 22 feet, we can write:
2l + 2w = 22
When we simplify this equation, we obtain:
l + w = 11
A rectangle's area is determined by the product of its length and breadth, which may be written as follows:
l x w = area
Given that the space is 10 square feet, we can write:
l x w = 10
Two equations with two variables are now available:
L+W = 11, and L x W = 10.
To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:
w = 11 - l
Using this expression as w's replacement in the second equation, we obtain:
l x (11 - l) = 10
The result of expanding and rearrangement is a quadratic equation:
l² - 11l + 10 = 0
Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:
(l - 10)(l - 1) = 0
so either l = 10 or l = 1 is true.
w = 1 if l = 10, otherwise. w equals 10 if l = 1.
As w is always smaller than l, we have
The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
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Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not
➡ There are 22 hundredths. That is enough to make a tenth.
What is the arithmetic operations?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the total volume of the slime, we need to add 1.5 and 0.72:
1.5 + 0.72 = 2.22
There are 22 hundredths, which is enough to make a tenth.
Hence, the answer is:
➡ There are 22 hundredths. That is enough to make a tenth.
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help help help help help help help help help help help help help help help
What is the number of sides of a regular polygon in which each interior angle has a measure of 165°?
Answer:
the answer is 24 sides
explanation
5.3A Find Two Numbers Whose Product and Sum is as Indicated
Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.
How to find a set of two real numbers
In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:
x₁ + x₂ = b
x₁ · x₂ = c
Whose solution can be found by numerical methods.
Now we proceed to determine the values for each cases:
(x₁, x₂) = (6, 1)(x₁, x₂) = (4, 9)(x₁, x₂) = (3, - 2)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (- 8, 2)(x₁, x₂) = (2, - 2)(x₁, x₂) = (4, - 2)(x₁, x₂) = (- 4, 3)(x₁, x₂) = (- 5, - 4)(x₁, x₂) = (5, - 3)(x₁, x₂) = (6, 2)(x₁, x₂) = (- 2, - 3)(x₁, x₂) = (- 2, - 7)(x₁, x₂) = (2, 8)(x₁, x₂) = (11, - 2)(x₁, x₂) = (5, - 4)(x₁, x₂) = (- 8, 1)(x₁, x₂) = (8, - 3)(x₁, x₂) = (7, 8)(x₁, x₂) = (8, 8)(x₁, x₂) = (6, 4)(x₁, x₂) = (6, 9)(x₁, x₂) = (3 - 2√2, 3 + 2√2)(x₁, x₂) = (9, - 4)(x₁, x₂) = (8, - 7)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (8, - 2)(x₁, x₂) = (- 9, - 9)(x₁, x₂) = (- 15, 3)(x₁, x₂) = (7, - 6)(x₁, x₂) = (- 7, - 7)(x₁, x₂) = (- 8, - 8)(x₁, x₂) = (12, - 3)(x₁, x₂) = (- 3, - 8)(x₁, x₂) = (4, - 3)(x₁, x₂) = (- 12 - √119, - 12 + √119)(x₁, x₂) = (7, - 4)(x₁, x₂) = (- 6, - 9)(x₁, x₂) = (5, 7)(x₁, x₂) = (- 8, 4)(x₁, x₂) = (- 7, 6)(x₁, x₂) = (5 / 2 + √73 / 2, 5 / 2 - √73 / 2)(x₁, x₂) = (5, 6)(x₁, x₂) = (- 10, 4)(x₁, x₂) = (- 9, 4)(x₁, x₂) = (- 9, 7)(x₁, x₂) = (6, 8)(x₁, x₂) = (- 7, 3)To learn more on real numbers: https://brainly.com/question/24908711
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The sum of the digits in a two-digit number is 14. If you reverse
and double the original number, and then add the result to the
original number, the sum is 222. Find the original number. Please help me.
Answer:
The original number is 86.
Step-by-step explanation:
The only two-digit numbers whose digits sum to 14 are:
5968778695If we reverse and double the original number:
59 reversed is 95 → 95 × 2 = 19068 reversed is 86 → 86 × 2 = 17277 reversed is 77 → 77 × 2 = 15486 reversed is 68 → 68 × 2 = 13695 reversed is 59 → 59 × 2 = 118If we add the result of reversing and doubling the original number to the original number:
59 + 190 = 24968 + 172 = 24077 + 154 = 23186 + 136 = 22295 + 118 = 213As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.
10 inches in 6 hours
80 inches in 2 days
The relation is a direct variation
How to determine if the relation is a direct variationFrom the question, we have the following parameters that can be used in our computation:
10 inches in 6 hours
80 inches in 2 days
Convert 2 days to hours
So, we have the following representation
10 inches in 6 hours
80 inches in 72 hours
For the relation to be a direct variation, the following must be equal
6/10 = 72/80
Evaluate
0.6 = 0.6
Hence, the relation is a direct variation
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Complete question
Determine if the following relation represents a direct variation
10 inches in 6 hours
80 inches in 2 days
verify the
identity algebraically.
Step-by-step explanation:
[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]
[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]
[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]
PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
The equation for the function is [tex]y=-0.15x+240[/tex].
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."
It is given that the amount of fuel filled up in Jon's semi truck is 240 gallons.
It is also given that for 1 mile the truck uses 0.15 gallons of fuel.
So, for "x" miles, the truck uses 0.15*x gallons of fuel.
So, the remaining fuel in the tank will be 240-0.15x.
Let the remaining fuel be "y".
This can be written as:
[tex]y=240-0.15x\\y=-0.15x+240[/tex].
Therefore the remaining fuel in the tank after Jon drives x miles will be a linear equation [tex]y=-0.15x+240[/tex]
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Charles and some friends ate at the Winterfield Café. Their bill was $50.00$ They paid $60.00. What percentage gratuity did they pay?
The percentage of gratuity paid is 20%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount for the bill = $50
Amount paid = $60
The amount of gratuity.
= 60 - 50
= $10
Now,
The percentage of gratuity.
= 10/50 x 100
= 20%
Thus,
The percentage of gratuity is 20%.
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Suki wants to pour 25 milliliters
of water, 35 milliliters of oil,
and 45 milliliters of syrup into
the same beaker for a science
experiment. The beaker holds up to 100 milliliters. Will the beaker hold all three liquids? Explain why or why not.
How many solutions does the system have? { � = 5 � + 1 � = − 2 � − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=5x+1 y=−2x−8
The given system of linear equations has a unique solution.
What are linear equations?A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given that, a system of linear equations, y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,
The rule for a system of linear equations, a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-
When the system has a unique solution :-a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.
When the system has a no solution :-a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.
When the system has infinite solution :-a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.
Checking for the given equations,
y = 5x+1 and y = -2x-8
Converting into standard form of the linear equations,
5x-y +1 = 0 and 2x+y+8 = 0
5/2 ≠ -1
The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]
Hence, the given system of linear equations has a unique solution.
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Answer:
One solution
Step-by-step explanation:
