A small organization is responsible for distributing two craft products made in a small community, these products are jam and bread. The marginal utility function for the jam is f(x) = 55–4x, and the marginal utility for the package of bread is given by g(x) = 37–x.
Find:
a) The total utility function of the jam.
b) The total utility function of bread.
c) If the consumer wants to buy 2 jars of jam and 3 packages of bread, which of the items will produce more utility.
3 packages of bread would produce more utility than 2 jars of jam
The total utility function of the jamThe marginal utility function of jam is given as:
f(x) = 55 - 4x
Integrate the above function to determine the total utility function
f'(x) = 55x - 2x^2
Hence, the total utility function of the jam is f'(x) = 55x - 2x^2
The total utility function of breadThe marginal utility function of bread is given as:
g(x) = 37 - x
Integrate the above function to determine the total utility function
g'(x) = 37x - 0.5x^2
Hence, the total utility function of the bread is g'(x) = 37x - 0.5x^2
The items that produce more utilityWe have:
Jam = 2 jars
Bread = 3 packages
Substitute 2 for x in f'(x) = 55x - 2x^2
f'(2) = 55 * 2 - 2 * 2^2
f'(2) = 102
Substitute 3 for x in g'(x) = 37x - 0.5x^2
g'(3) = 37 * 3 - 0.5 * 3^2
g'(3) = 106.5
106.2 is greater than 102
Hence, 3 packages of bread would produce more utility
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Kojo is twice as old as Esi who in turn is 5 years older than kwaku .if their total age is 47 . How old is each of them?
The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
What is an Equation ?An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.
Let the age of Kwaku is x
Let the age of Esi is y
From the given data
The age of Kojo is 2y
y = x +5
Sum of their age = 47
2y = 2x +10
therefore the equation formed is
x + y +2y = 47
x + x+5 + 2x +10 = 47
4x +15 = 47
4x = 32
x = 8
y = 13
2y = 26
Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
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Can someone help me pleaseeee.
The figure is given in the below diagram.
The steps of constructing a square inside a circle are as follows:
Start from the middle O of the provided circle.
Finding the center of a circle's approach can be used to create the center of the circle's center point is not known.
1. Draw a circle and label point A. This will turn into one of the square's vertices.
2. Create point C by drawing a diameter line from point A through the center and back out to the outside of the circle.
3. Set the width of the compass to a little bit more than the distance to O.
4. Sketch an arc above and under O.
5. Repeat by moving the compass to C.
6. To create the new points B and D, draw a line across the intersection of the arc pairs that is long enough to touch the circle at both the top and bottom.
This diameter is perpendicular to the first AC.
7. Draw a line connecting each pair of points A, B, C, and D.
Done. The circle is circled by the square ABCD.
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Determine if the given statement is sometimes, always, or never true:
Alternate interior angles ______ congruent.
A.always
B.sometimes
C.never
What is the measurable quantity given by its formula with the appropriate units
Answer:
Where is the formula
Step-by-step explanation:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
The boat's travel from when it was first noticed until it stopped is 554.89 ft.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
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P(x)⋅Q(x)=R(x); if P(x)=x+1 and R(x)=2x3+2x2+3x+3, what is Q(x)?
A. 2x2+2
B. 2x2+3
C. 2x2−3
D. 2x2−2
Answer: B
Step-by-step explanation:
[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]
the heights of the students in a spanish class were measured. from the given data set, determine how many students are 65 inches or taller. a. 2 b. 3 c. 5 d. 4
There are 5 students who are 65 inches or taller. Option C is correct.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
The term "height" is frequently used to describe someone's or something's height.
The height of the student in the Spanish class in the data set;
65, 63, 67, 59, 73, 60, 68, 61, 64, 60, 69
Student's heights are 65 inches or taller from the data set are;
65,67,73,68,69
There are 5 students who are 65 inches or taller.
Hence, option C is correct.
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the lines shown are parrallel. if the green line has a slope of 5, what is the slope of the red line
Answer:
if a line is parallel they have the same slope
so the slope is 5
Hope This Helps!!!
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A. 7
B. 5
C. 9
D. 4
E. 3
Considering the given histogram, the mean of the data-set is closest to:
B. 5.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
Hence, considering the histogram, the mean is given by:
M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.
Which is closest to 5, hence option B is correct.
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The side of an equilateral triangle is given as 8 cm, correct to the nearest centimetre. What is the least possible length of its perimeter?
[tex]\textsf {21 cm}[/tex]
[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]
[tex]\textsf {Then, the least possible perimeter would be :}[/tex]
[tex]\mathsf {7 \times 3}[/tex]
[tex]\textsf {21 cm}[/tex]
Sarah transfer 450 from her saving account to her checking account she uses the check register to record her transaction but will her new balance.
After transferring $450 from the savings account to the checking account, the updated balance in :
the savings account is =previous balance-$450the checking account= previous balance +$450Calculation of the new balance?All of that is based on the notion that Sarah's savings and checking accounts are distinct from one another.
Assume that, Sarah's savings account balance was 'x' and checking account balance was 'y'.
She transferred $450 from the savings to the checking account.
∴Updated savings account balance= x-450 units
∴Updated checking account balance= y+ 450 units.
Therefore, it can be concluded that the current value of Sarah's savings account would be the amount >$450, and the updated value of her checking account would be the balance <$450 if she transferred $450 from her savings account to her checking account.
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Proving Vertical Angles Are Congruent
Answer:
Vertical angles are always congruent
Step-by-step explanation:
Answer:
Statement
Measure of angle 2 and 3 are a linear pair and
Reason
Definition of linear pair
Step-by-step explanation:
Hook me up with a 5 star and a Thanks :)
Jun 21, 6:41:12 PM
What is the slope of a line perpendicular to the line whose equation is x - 3y = 27.
Answer: [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
perpendicular = opposite recipricol
-3 = [tex]\frac{1}{3}[/tex]
switch the sign and flip it (3/1 => 1/3)
What ordered pair is a solution of the equation?
y=-2x-5
[tex] \sf \underline{Answer:}
[/tex]
Pick any value for x, like x = 0, plug it into the equation, and get the value for y. For x = 0,
2(0) + y = 5
y = 5
The ordered pair is (0,5). Find other ordered pairs using the same reasoning.
[tex]2(0) + y = 5[/tex]
[tex]y = 5[/tex]
The ordered pair is (0,5).12% profit on a computer is Rs.540.
(i) Find the cost price of the computer.
(ii) Find the sale price of the computer.
Answer:
the cost price is Rs. 4500 and the sale price is Rs. 5040.
Step-by-step explanation:
Let the cost price of the compute be Rs. x.
The profit earned is, Rs. 540.
The profit percentage is, 12%.
The formula to compute profit is:
Profit = SP - CP
\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500
Compute the selling price as follows:
SP = CP + profit
= 4500 + 540
= 5040
Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.
Question 10 of 13
by visual inspection, determine the best-fitting regression model for the
scatterplot.
o a. no pattern
o b. quadratic
o c. exponential
o d. linear
please help!
The best-fitting regression model for the scatter plot is exponential curve , Option C is the right answer.
The missing graph is attached with the answer.
What is an exponential graph ?An exponential graph is given by y = aˣ , the graph for an exponential growth is also attached with the answer,
From the graph given in the question it can be concluded that it is not linear , not quadratic and it is not true that it doesn't have a pattern , It is an exponential growth graph, Therefore Option C is the right answer.
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What is the simplified form of this expression? (3 − 13x − 7x2) − (5x2 12x − 10)
Answer:
-12x²-25x+13
Step-by-step explanation:
First open parenthesis.
(3 − 13x − 7x²) − (5x² + 12x − 10)
3 − 13x − 7x² − 5x² - 12x + 10
Now combine like terms.
3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²
Now put into standard form, exponents greatest to least.
-12x²-25x+13
Hope this helps!
If not, I am sorry.
Answer:-12x²-25x+13
Step-by-step explanation:
Solve the proportion for x. When applicable, simplify all radicals and show all of your
3/X = x/4
The simplified radical for the given equation is 2√3.
The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].
What are radicals?Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.
To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:
[tex]\frac{3}{x} =\frac{x}{4}[/tex]
⇒x×x=3×4
⇒x²=12
⇒x=±√12
From this, we can see that the solutions for the equation are the positive and negative roots of 12.
By simplifying the radical, we get √12 = √(2² x 3) = 2√3
Therefore, the simplified radical for the given equation is 2√3.
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Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?
Answer: 8
Step-by-step explanation:
We know that scale factor = (image)/(preimage).
Substituting in what we have,
[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]
Answer:
Step-by-step explanation:
We know that r's't' was formed by a scale factor of 5.
This means rst was multiplied by 5 to create r's't'.
Dividing the sides of r's't' by 5 will give us the sides of the
pre-image. If r's' = 40 - dividing 40 by 5 = 8.
So rs is 8.
number machine n -5 x 4
Solve the system of equations.
y = -2x + 5
y = x^2 + 3x +9
a. (-1,7), (-4,13)
b. (-1,-3), (-4,3)
c. (-1,13), (-4, 7)
d. (1,3), (4,13)
Answer:
A
Step-by-step explanation:
y = - 2x + 5 → (1)
y = x² + 3x + 9 → (2)
substitute y = x² + 3x + 9 into (1)
x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
substitute these values into (1) for corresponding values of y
x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )
x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )
f
Which graph represents the function r(x) = |x-21-1
I assume you meant r(x) = |x-2| -1.
Pool A starts with 300 gallons of water. It has a leak and is losing water at a rate of 6 gallons of water per minute. At the same time, Pool B starts with 400 gallons of water and also has a leak. It is losing water at a rate of 10 gallons per minute. The variable t represents the time in minutes. After how many minutes will the two pools have the same amount of water? How much water will be in the pools at that time?
Answer:
25 minutes
150 gallons
Step-by-step explanation:
Definition of variables
Let t = time in minutes
Let V = volume in gallons
Create two equations with the given information:
Pool A
Starting volume = 330 gallonsLeak rate = 6 gallons/min⇒ V = 300 - 6t
Pool B
Starting volume = 400 gallonsLeak rate = 10 gallons/min⇒ V = 400 - 10t
To find after how many minutes the two pools will have the same amount of water, substitute the equation for pool A into the equation for pool B and solve for t:
⇒ 300 - 6t = 400 - 10t
⇒ 300 - 6t + 10t = 400 - 10t + 10t
⇒ 300 + 4t = 400
⇒ 300 + 4t - 300 = 400 - 300
⇒ 4t = 100
⇒ 4t ÷ 4 = 100 ÷ 4
⇒ t = 25
Therefore, the two pools will have the same amount of water after 25 minutes.
To find how much water will be in the pools at that time, substitute the found value of t into one of the equations and solve for V:
⇒ V = 400 - 10t
⇒ V = 400 - 10(25)
⇒ V = 400 - 250
⇒ V = 150
Therefore, the amount of water in the pools at the time when they have the same amount of water is 150 gallons.
If time be x and volume be y
The equations are
y=300-6ty=400-10tEquate and solve
300-6t=400-10t4t=100t=25minNow
y=400-10(25)y=400-250y=150gallonsA recipe calls for 4 1/2 cups of flour. if you only make half of the recipe, then how many cups of flour do you need? express your answer as a mixed number. please help
Answer:
2 1/4
Step-by-step explanation:
Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4
Select the correct answer from each drop-down menu.
Determine the best measure of center and the skew of the data distribution.
(23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38)
The central tendency of the given data will be 22.79.
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
There are 3 ways in which we can express the centre of the data given: (1) mean or average, (2) mode, (3) median
For the mean, we sum up all the given and divide them by the number of data
mean = 433 / 19 = 22.79
For the mode, we just determine which among the given data appears more frequently and in this given that is 23.
For the median, we arrange the numbers from highest to lowest and determine which number will appear in the centre. Since there are 19 data, we need to find which among them will appear to be the 10th. That is also 23.
So, the value that would best describe the central tendency is 23. Since the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.
Therefore central tendency of the given data will be 22.79.
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On a number line, 1.84 would be located ______. Choose all answers that make a true statement.
1.84
《--|----|----|----|----|----|----|----|----|----|--》
A. between 1.74 and 1.94
B. to the left of 1.85
C. to the right of 1.83
D. between 1 and 2
Answer:
All answers are correct.
Step-by-step explanation:
A. 1.84 is between 1.74 and 1.84.
B. 1.84 < 1.85. Lower values go to the left.
C. 1.84 > 1.83. Higher values go to the right.
D. 1.84 is between 1.0 and 2.0.
What steps are used to solve this equation?
x
2
= 7
Answer:
x=3.5
Step-by-step explanation:
x × 2 = 7
÷2 ÷2
x=3.5
WILL GIVE ANOTHER 100 POINTS IN A SEPREATE QUESTION IF YOU ANSWER
Write a short essay researching different fields and how they use geometry or trigonometry. Discuss the field that you have chosen does (50 points) and how that field uses geometry or trigonometry (50 points). Use complete sentences and at least 3 paragraphs.
The fields in which Trigonometry is well applied and their explanations are as explained below.
What is the Importance of Trigonometry?The three fields that trigonometry is useful are as described below;
1) In construction;
Trigonometry is useful in Construction field because it can be used in measurement of walls parallel and perpendicular; Installing ceramic tiles; Roof inclination; the height of the building, the width length e.t.c. It is also useful in finding roof slopes, ground surfaces, sun shading and light angles.
2) In marine biology;
Marine biologists utilize trigonometry to establish measurements. For instance, when trying to find out the manner in which light levels at different depths affect the ability of algae to photosynthesize. Trigonometry is used in finding the distance between celestial bodies. Marine biologists also use it to create mathematical models to measure and understand sea animals and their behavior.
3) In criminology:
In criminology, trigonometry is useful in calculating a projectile’s trajectory in order to estimate the possible cause of a collision in a car accident or the manner in which an object fall down or in which angle a bullet was shot etc.
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The graph shows the function f(x)= |x-h| + K. What is the value of h ?
The value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a function:
f(x) = |x - h| + k is shown in the graph.
The above function is a transformation of a parent function:
F(x) = |x|
After applying transformation we get:
f(x) = |x + 1.5| - 3.5
On comparing:
h = -1.5
k = -3.5
Thus, the value of h is -1.5 if the graph shows the function f(x)= |x-h| + K or f(x) = |x + 1.5| - 3.5.
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