To find the revenue function, we need to multiply the price (p) by the quantity sold (x). The price function given is p = 5,300 - dollars, so we can substitute this into our revenue function as follows:
Revenue = p * x
Revenue = (5,300 - dollars) * x
We also know that production is limited to 100 units, so we need to take that into account when determining the revenue function. If x is greater than 100, then the revenue will be limited to 100 units sold. If x is less than or equal to 100, then the revenue will be based on the actual quantity sold.
To incorporate this constraint into our revenue function, we can use a piecewise function:
Revenue = { (5,300 - dollars) * 100 if x > 100
(5,300 - dollars) * x if x <= 100 }
Simplifying the piecewise function, we get:
Revenue = { 530,000 - (dollars * 100) if x > 100
(5,300 - dollars) * x if x <= 100 }
Therefore, the revenue function for this monopoly is:
Revenue = { 530,000 - 100 * dollars if x > 100
(5,300 - dollars) * x if x <= 100 }
Hi! To find the revenue function, we first need to determine the total revenue, which is the product of the price per unit (p) and the number of units sold (x). Given the demand function p = 5,300 - x dollars and the average cost function C = 3,010 + 2x dollars, we can find the revenue function as follows:
Revenue function, R(x) = p * x
R(x) = (5,300 - x) * x
By simplifying the equation, we get:
R(x) = 5,300x - x^2
So, the revenue function for this monopoly is R(x) = 5,300x - x^2.
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callum says 300cm2 is the same as 3m2 because there are 100cm in 1m so you divide by 100 callums method is wrong explain why
Answer:
Callum’s method is incorrect because he is confusing the conversion of linear units with the conversion of square units. There are indeed 100 cm in 1 m, but when converting square units, you need to square the conversion factor. So 1 m² is equal to (100 cm)² or 10,000 cm². Therefore, 300 cm² is equal to 0.03 m², not 3 m².
Step-by-step explanation:
Answer:
The answer is wrong because the 3m is still squared if you divided it by 100 then it should only be 3m not 3m^2.
Step-by-step explanation:
I am not 100% sure this is correct so please dont get mad at me.
i need to figure it out
The solution to the equation 4x + 17 = 23 is x = 3/2.
How to solve the equationIt should be noted that to solve this equation, we need to isolate the variable x on one side of the equation.
First, we can subtract 17 from both sides of the equation:
4x + 17 - 17 = 23 - 17
Simplifying the left side of the equation:
4x = 6
Next, we can divide both sides of the equation by 4:
4x/4 = 6/4
Simplifying:
x = 3/2
Therefore, the solution to the equation 4x + 17 = 23 is x = 3/2.
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Write the explicit formula for the following sequence, then generate the first five terms. A1 = 256, r = 0. 25
The explicit formula for the given sequence is An = 256 * (0.25)ⁿ⁻¹, where n is the term number. Using this formula, we can generate the first five terms of the sequence as follows:
A1 = 256 * (0.25)¹⁻¹ = 256 * 1 = 256
A2 = 256 * (0.25)²⁻¹ = 256 * 0.25 = 64
A3 = 256 * (0.25)³⁻¹ = 256 * 0.0625 = 16
A4 = 256 * (0.25)⁴⁻¹ = 256 * 0.015625 = 4
A5 = 256 * (0.25)⁵⁻¹ = 256 * 0.00390625 = 1
In simpler terms, the explicit formula for the given sequence is found by multiplying the first term by the common ratio raised to the power of n-1, where n is the term number. This results in a decreasing sequence as the common ratio is less than 1. The first five terms of the sequence are 256, 64, 16, 4, and 1, respectively.
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The rate of change dP/dt of the number of students who heard a rumor is modeled by a logistic differential equation. The maximum capacity of the school is 732 students. At 12 PM, the number of students who heard the rumor is 227 and is increasing at a rate of 24 students per hour. Write a differential equation to describe the situation. dP/dt =?
The differential equation to describe the situation is:
dP/dt = 0.000508 * P * (1 - P/732)
We can write a logistic differential equation to describe the rate of change of students who heard the rumor. The equation is:
dP/dt = k * P * (1 - P/M)
where dP/dt is the rate of change in the number of students who heard the rumor, k is a constant, P is the number of students who have heard the rumor at a given time, and M is the maximum capacity of the school (732 students).
At 12 PM, P = 227 and dP/dt = 24 students per hour. We can plug these values into the equation:
24 = k * 227 * (1 - 227/732)
Now, solve for k:
k ≈ 0.000508
So, the differential equation to describe the situation is:
dP/dt = 0.000508 * P * (1 - P/732)
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The distance from Atlanta, Georgia, to Boise, Idaho is 2,214 miles. The distance from Atlanta, Georgia, to Houston, Texas is 789 miles. How much farther is it from Atlanta to Boise than from Atlanta to Houston?
Answer:
1,425 miles
Step-by-step explanation:
To find out how much farther it is from Atlanta to Boise than from Atlanta to Houston, we need to subtract the distance from Atlanta to Houston from the distance from Atlanta to Boise:
[tex]\sf:\implies 2,214\: miles - 789\: miles = \boxed{\bold{\:\:1,425\: miles\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, it is 1,425 miles farther from Atlanta to Boise than from Atlanta to Houston.
1) Last year a computer cost $1,600 to purchase. A year later the same computer cost $1,850 to purchase. By what percent did the cost of the computer increase? (please show your work)
2)A flock of 50 geese landed at a pond. Later that day there were 75 in the pond. By what percent did the number of geese increase?
a
80%
b
50%
c
2%
d
10%
Answer:
1) 15.625% increase. 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.
2) 50%
Step-by-step explanation:
1) 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.
2) 75-50=25. 25/50=0.5. 0.5x100=50
The sequence 10, 9. 5, 9. 0, 8. 5,. Has a common difference on
The sequence 200, 100, 50, 25,
has a common ratio of
The sequence 10, 9. 5, 9. 0, 8. 5,. has a common difference on -0.5
The sequence 200, 100, 50, 25, has a common ratio of 1/2
Let's start by discussing the sequence 10, 9.5, 9.0, 8.5. We can observe that each term is decreasing by 0.5. This means that the sequence has a common difference of -0.5.
In mathematical terms, the common difference is the constant value that is added or subtracted from each term in the sequence to obtain the next term. In this case, we can write the sequence as:
10, 10 - 0.5, 10 - 1.0, 10 - 1.5
where the common difference is -0.5.
Now, let's consider the sequence 200, 100, 50, 25. We can observe that each term is obtained by dividing the previous term by 2. This means that the sequence has a common ratio of 1/2.
In mathematical terms, the common ratio is the constant value that is multiplied by each term in the sequence to obtain the next term. In this case, we can write the sequence as:
200, 200/2, (200/2)/2, ((200/2)/2)/2
where the common ratio is 1/2.
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I need help with this question.
Answer: The answer is (C
Step-by-step explanation:
Math geometry question please help
Answer:
LP is a raym∠LMO = 90°m∠LPO = 90°m∠MLP = 26°arc MP = 154°arc MNP = 206°Step-by-step explanation:
You want various angle and arc measures in the given figure.
RelationshipsThe relevant angle relationships are ...
a radius to a point of tangency makes a right angle with the tangentan arc has the same measure as its central anglethe sum of the arcs of a circle is 360°the sum of angles in a quadrilateral is 360°an angle is formed from two rays whose endpoints are the vertex of the angleThese answer the given questions as follows:
LP is a ray.
The angle at M is 90°.
The angle at P is 90°.
The angle at L is 360° -90° -90° -154° = 26°
Arc MP has the same measure as angle MOP, 154°
Arc MNP completes the circle, so is 360° -154° = 206°
Bob and two friends each were able to juggle with bean bags for 3/4 of a minute. How long did they juggle together? No decimals pls!
Answer:
Step-by-step explanation:
They each juggled for 3/4 of a minute
There were 3 people in total
3 people times 3/4 of a minute equals 2 1/4 minutes
1)Change point A in the scatterplot to point (1,12). Calculate the correlation coefficient and note how much it differs from .96. (2)Change point A back to (1,2) and change point B to (4,15). Calculate the correlation coefficient and note how much it differs from .96. Did the correlation coefficient change more when the point you raised 10 units was in the middle of the scatterplot or at the edge of the scatterplot? Why do you think this is so? (3)Move only one point and make the correlation coefficient become negative. Write about what you did and why it made the correlation go negative.(4) Suppose you had a scatterplot with only two points. Assuming your two points don't define either a horizontal line (both y-values the same) or a vertical line (both x-values the same), what is the correlation coefficient? Why do you think this is true? What happens as you try different points (again, without defining a horizontal or vertical line)?(5)Enter the points (1,2) and (3,2) — this defines a horizontal line. Try to calculate the correlation coefficient. What did your graphing calculator tell you? What happened?(6) Enter the points (1,2) and (1,3) — this defines a vertical line. Try to calculate the correlation coefficient. What did your graphing calculator tell you? What happened? The following scatterplot was constructed by reversing the x- and y-values in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? (7)Graph depicts 16 scatter plots on a coordinate plane without coordinate points. 7 scatter plots in quadrant 3, 1 scatter plot in quadrant 4, and 8 scatter plots in quadrant 1. The following scatterplot was constructed by taking the negative of each x-value in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? What would the correlation coefficient be if we took the negative of all the x-values and all the y-values? Graph depicts 15 scatter plots on a coordinate plane without coordinate points. 7 scatter plots in quadra
The new regression coefficient is about 0.663, viz. lesser than the previous regression coefficient by 0.297. Thus, a single outlier creates a significant drop in the correlation
How to solveChanging A to (1,12) gives below scatterplot and regression parameters
(check image)
2. In this case, r is about 0.766, a drop of 0.194 which is substantial, but lower than the previous drop. The regression coefficient changed much more when the outlier was in the middle of the scatterplot. This happens because the data series itself is increasing.
So the effect of 10 points in a middle point is much more of an outlier compared to when this 10-point increase happens for the highest value of x. Hence, the r value drops more in the former case.
3. r can become negative if drop the point B to a highly negative y-value. Consider taking it to (4, -50). Then we get the following regression parameters
We obtain r = -0.275. Since the expected y-value was highest for point B, so changing it drastically to a large negative value leads to a negative correlation between the two variables.
4. With only two points that are parallel to neither of the axes, the correlation coefficient is always exactly either 1 or -1. The correlation is 1 if the slope of the line joining the two points is positive, and -1 if the slope is negative.
That is, there is always either a perfect positive correlation or a perfect negative correlation. This is so because there is always a unique line joining two points, which leads to a perfect correlation between them. Even by differing the pairs, this relation shall always hold true.
5. If the points are parallel to the X axis, we should obtain r=0, because it indicates no relation between the variables. So points (1, 2) and (3, 2) lead to r=0. This can be verified using any calculator.
A vertical line also leads to r=0. Since the y value does not change, so no correlation can be established. Actually, it is just like flipping the x and y variables, and we know flipping does not change the correlation coefficient. So we should obtain r=0 even for a vertical line.
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2 Gracie created the table of x and y
values shown here.
X
y
1
0
Fy=2x-2
Gy= 2x + 2
MathWarm-Ups.com
3
-4
5
-8
7
-12
Which equation represents the relationship
between the x values and the y values in
the table?
7.11A
H y = -2x + 2
J_y=-2x - 2
7.7A
r
F
The equation of the line passing through the given points is y = -2x+2.
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (1, 0) and (3, -4),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (1, 0) and (3, -4),
Therefore, the required equation is =
y-0 = -4-0/3-1 (x-1)
y = -2x + 2
Hence, the equation of the line passing through the given points is y = -2x+2.
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ALGEBRA
Farha Gadhia has applied for a $100,000 mortgage loan
at an annual interest rate of 6%. The loan is for a period of 30 years
and will be paid in equal monthly payments that include interest.
Use the monthly payment formula to find the payment.
A square a rectangle have the same perimeter of a square has a side length of 8x units. The rectangle has a length of (5x + 12) and a width of 10 units. what will be the perimeter of both a rectangle and the square
Answer:
Step-by-step explanation:
The perimeter of a square is calculated by multiplying the length of one side by 4. Since the side length of the square is 8x units, the perimeter of the square is 4 * 8x = 32x units.
The perimeter of a rectangle is calculated by adding the lengths of all four sides or by using the formula 2 * (length + width). Since the length of the rectangle is (5x + 12) units and the width is 10 units, the perimeter of the rectangle is 2 * ((5x + 12) + 10) = 10x + 44 units.
Since both shapes have the same perimeter, we can set their perimeters equal to each other and solve for x:
32x = 10x + 44 22x = 44 x = 2
Substituting this value of x back into the expression for the perimeter of either shape, we find that the perimeter of both the square and the rectangle is 64 units.
How many non-identical triangles can be made using
these side lengths: 4 cm, 8 cm, and 14 cm?
With side lengths of 4, 8, and 14 cm, only one non-identical triangle can be formed.
This is due towards the triangle inequality theorem, which stipulates that the total of any two triangle sides must be bigger than the third side. In this instance, 4 cm plus 8 cm equals 12 cm, that is smaller than 14 cm.
A triangle cannot be formed with these side lengths since they do not meet the triangle inequality theorem. To elaborate, a triangle is created by joining three line segments to create a closed form with three angles.
These line segments' lengths are referred to as the triangle's sides. The total of both sides must be higher than the length of the third one to qualify for a triangle to be present. The triangle inequality hypothesis is what this states.
It is impossible to build a triangle with the side lengths of 4 cm, 8 cm, and 14 cm since the sum of the two shorter sides (4 cm + 8 cm = 12 cm) is less than the length of the longest side (14 cm). Hence, One non-identical triangle can be made.
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The prism shown has a surface area of 1,500 mm squared. What is the height, h, of the prism?
The height of the triangular base prism is 10 mm.
How to find the surface area of a prism?The prism above is a triangular base prism. The surface area of the prism can be calculated as follows:
surface area of the triangular prism = (a + b + c)l + bh
where
a, b, and c are the side of the triangular basel = height of the prismb = base of the triangleh = height of the triangleTherefore,
surface area of the triangular prism = (20 + 30 + 40) + 20 × 30
1500 = 90l + 600
1500 - 600 = 90l
90l = 900
divide both sides by 90
l = 900 / 90
l = 10 mm
Therefore,
height of the prism = 10 mm
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Penny decided to travel to Palawan. The airplane flew at an average rate of 300 miles per hour and covered 1500 miles. How long will the flight will take? *
A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
The time it will take the flight is C) 5 hours.
To solve this problem, we can use the formula: distance = rate x time. In this case, we know that the distance is 1500 miles and the rate (or speed) is 300 miles per hour. We can rearrange the formula to solve for time: time = distance / rate. Plugging in the values we have, we get:
time = 1500 miles / 300 miles per hour
time = 5 hours
Therefore, the correct answer is C. It will take Penny 5 hours to fly from her starting point to Palawan at an average speed of 300 miles per hour. This calculation assumes that the plane maintains a constant speed throughout the entire flight, which may not be the case due to factors such as wind and turbulence.
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Find f such that f(x) = 5/
. (16) = 49.
Let's find a function f(x) such that f(x) = 5x and f(16) = 49.
To find the function, we first plug in the given input (x = 16) and output (f(16) = 49):
49 = 5 * 16
Next, we solve for the unknown constant in the function:
49 = 80
5 = 49/80
Now, we have found the function f(x): f(x) = (49/80)x
The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Functions can also be defined as a relation "f" in which every element of set "A" is mapped to just one element of set "B." Additionally, there cannot be two pairs in a function that share the same first element.
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Determine whether each set of measures can be the measures of the sides of a
right triangle. then state whether they form a pythagorean triple.
13. 12, 16, 20
14. 16, 30, 32
15. 14, 48, 50
16.
2 4 6
5' 5' 5
17.2v6,5,7
18. 2v2, 2v7,6
13. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
14. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
15. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
16.They're unfit to be a right triangle's side measures. The forecourt of the longest side( 62 = 36) can not be calculated by adding the places of the two lower sides( 22 42 = 20).
17. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
18. They're unfit to be a right triangle's side measures.
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find the general solution of the following linear system. y′ = [2 2 −4 2 −1 −2 4 2 −6] y with λ = −1,−2,−2
To find the general solution of the linear system y' = [2 2 -4; 2 -1 -2; 4 2 -6] y, we need to first find the eigenvectors and eigenvalues of the coefficient matrix A = [2 2 -4; 2 -1 -2; 4 2 -6].
Using the characteristic equation, we can find the eigenvalues:
det(A - λI) = 0
=> det([2-λ 2 -4; 2 -1-λ -2; 4 2 -6-λ]) = 0
=> (2-λ)[(-1-λ)(-6-λ) - 4] - 2[(-2)(-6-λ) - 8] + 4[2(-1-λ) - 4] = 0
=> λ^3 - + 8λ - 4 = 0
=> (λ-1)(λ-2[tex])^2[/tex] = 0
Thus, λ = 1, 2 (with multiplicity 2). For each eigenvalue, we need to find a corresponding eigenvector.
For λ = 1, we need to find the null space of the matrix (A - λI):
A - λI = [1 2 -4; 2 -2 -2; 4 2 -7]
=> R2 <- R2 - 2R1, R3 <- R3 - 4R1
[1 2 -4; 0 -6 6; 0 -6 9]
=> R3 <- R3 - R2
[1 2 -4; 0 -6 6; 0 0 3]
So, we have a basic eigenvector of the form [4,-2,1]^T. To obtain a linearly independent eigenvector, we use the method of generalized eigenvectors. We need to find a vector v such that (A - λI) v = u, where u is the basic eigenvector.
(A - λI) v = u
=> [1 2 -4; 2 -2 -2; 4 2 -7] v = [4; -2; 1]
=> R2 <- R2 - 2R1, R3 <- R3 - 4R1
[1 2 -4; 0 -6 6; 0 -6 9] v = [4; -2; 1]
=> R3 <- R3 - R2
[1 2 -4; 0 -6 6; 0 0 3] v = [4; -2; 1]
=> -6v2 + 6v3 = -2
=> 3v3 = 1
=> 2v2 - 4v3 = -2
=> v2 = 0
So, we have v = [0; 1/3; 2/3[tex]]^T[/tex] as the second eigenvector corresponding to λ = 1.
For λ = 2, we need to find the null space of the matrix (A - λI):
A - λI = [0 2 -4; 2 -3 -2; 4 2 -8]
=> R1 <-> R2
[2 -3 -2; 0 2 -4; 4 2 -8]
=> R3 <- R3 - 2R1
[2 -3 -2; 0 2 -4; 0 8 -12]
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The area of the triangle below is \frac{2}{25}
25
2
square feet. What is the length of the base? Express your answer as a fraction in simplest form.
1/5 f
The length of the base of the given triangle can be simplified as 2√2/5 feet, which is equivalent to √8/5 feet.
What is the length of the base of a triangle if its area is (2/25) * 252 square feet and the height is twice the length of the base?We are given that the area of the triangle is (2/25) * 252 square feet.
Let the length of the base be x. Then, the height of the triangle can be expressed as (2/5)x, since the base divides the triangle into two equal parts.
The area of the triangle is given by the formula A = (1/2)bh, where b is the length of the base and h is the height of the triangle.
Substituting the given values, we get:
(1/2)x(2/5)x = (2/25)*252
Simplifying this equation, we get:
(1/5)x²= 20.16
Multiplying both sides by 5, we get:
x² = 100.8
Taking the square root of both sides, we get:
x =√(100.8)
Simplifying this expression, we get:
x = √(25*4.032)x = 5*√(4.032)x = (5/5)*√(4.032)x = 1*√(4.032)Therefore, the length of the base is √(4.032) feet, which can be expressed as a fraction in simplest form as 2√(2)/5 feet.
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What's 2x = 20 if 4y = 80
Answer:
x=10 and y=20, 2x=20=y
Step-by-step explanation:
2x=20 | Divide by 2 on both sides
x=10
4y=80 | Divide by 4 on both sides
y=20
Answer: 40
80 ÷ 2 = 20, so x = 40.
To check your answer;
40 x 2 = 80
(2) 44% of the students in Prof. Young's class are Liberal Arts major, 64% major in Business Administration, and 39% major in both. Compute the probability that a student selected at random in Prof. Young's class major in Liberal Arts or Business Administration.
The probability that a student selected at random from the class majors in Liberal Arts or Business Administration is 0.69 or 69%.
Let us say that the event that a student is a Liberal Arts major is 'LA' and the event that a student is a Business Administration major is 'BA'.
Now according to the question, we know that 44% of students are Liberal Arts majors, 64% of students are Business Administration majors,
and 39% of students are majoring in both.
With this information, we can say that:
P(LA) = 44% = 0.44
P(BA) = 64% = 0.64
• P(LAN BA) = 39% = 0.39
Now in order to find the probability that a student
is selected at random majors in either Liberal Arts
or Business Administration, we need to compute the value of P(LA U BA), which is the probability of either of the event happening.
The formula for the probability of the union of two events can be used to find the union that is: PILA U BA) = P(LA)+P(BA)-PILAN BA)
Now by substituting the values in the above equation, we get:
P(LA U BA) = 0.44 + 0.64 -0.39
P(LA U BA) = 0.69
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Suppose that the demand for a product is given by 2p²q = 10000 + 9000p² (a) Find the elasticity when p = $50 and q = 4502. (b) What type of elasticity is this? (elastic, unitary or inelastic?)
(c) How would the revenue be affected by an increase in price?
(a) The elasticity at p = $50 and q = 4502 is 2.778.
(b) The elasticity is elastic.
(c) An increase in price would result in a decrease in revenue.
How to determined the elasticity of demand?(a) To find the elasticity when p = $50 and q = 4502, we first need to find the partial derivatives of q with respect to p and then use the elasticity formula:
Demand: 2p²q = 10000 + 9000p²
Partial derivative of q with respect to p: 4pq = 18000p
When p = $50 and q = 4502:
4(50)(4502) = 900800
Elasticity:
e = (p/q) * (dq/dp) = (50/4502) * (900800/18000) = 2.778
(b) To determine what type of elasticity this is, we look at the value of the elasticity calculated in part (a). Since the elasticity is greater than 1, we know that this is an elastic demand.
(c) To determine how the revenue would be affected by an increase in price, we need to look at the relationship between elasticity and revenue. If demand is elastic,
Then an increase in price will result in a decrease in total revenue, and if demand is inelastic, then an increase in price will result in an increase in total revenue.
Since we know that the demand is elastic (from part (b)), we can conclude that an increase in price will lead to a decrease in revenue.
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A buyer purchases a 2022 Jeep Grand Wagoneer Series III for $109,000 and a 2023 Cadillac Escalade V for $149,000. How much money will he spend a year for car payments?
The amount of money that he will spend a year for car payment would be = $258,000
How to calculate the total amount of money that will be spent of car payments?To calculate the amount of money that will be used for car payment the following is carried out.
The cost for purchasing 2022 Jeep Grand Wagoneer Series III = $109,000
The cost for purchasing a 2023 Cadillac Escalade V = $149,000
The total amount spent of car payments = 109000+149000
= $258,000
Therefore, the buyer will spend up to $258,000 a year for car payment when the price for both cars he bought is being summed up.
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fast pls
in When calculating 4-√x+15 what option you get x?-1 lim X>1 1 the process -1 A) lim (x + 1) (4 + V1 +15) -1 B) lim 21 (1+1) (4 - V1-15) C) lim 16 - 2 - 1)(4+r+15) D) lím 16-1 (12 - 1) (4 - Vr+15)
None of the options are correct, and the value of x is simply 1.
Start with the given expression: 4 - √x + 15
Substitute x with the limit value of 1: 4 - √1 + 15 = 18
Therefore, the limit of the given expression as x approaches 1 from the right is 18.
To verify this result using the provided options, we can simplify each option and check which one equals 18 as x approaches 1 from the right.
Option A simplifies to (2/√2) + 2, which equals √2 + 2, not equal to 18.
Option B simplifies to 2(4 - √15), which equals 2(4 - 3.87), approximately equal to 2.27, not equal to 18.
Option C simplifies to 3(4 + √15), which equals 3(4 + 3.87), approximately equal to 23.61, not equal to 18.
Option D simplifies to 3(3)(3), which equals 27, not equal to 18.
Therefore, none of the options are correct, and the value of x is simply 1.
none of the options are correct, and the value of x is simply 1.
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Help with question in photo?
let's recall that two tangent lines to the same circle meeting outside it, will have the same length, so all those pair of tangent lines are equal in length.
Check the picture below.
The angle of depression from the top of a 150m high cliff to a boat at sea is 7°. How much closer to the cliff must the boat move for the angle of depression to become 19°?
The boat must move 785.82 m closer to the cliff for the angle of depression to become 19°.
We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.
Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)
distance=1221.49
Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)
distance=435.6665
Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression
Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))
difference=1221.49-435.6665
difference=785.8235
After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.
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from the following quadratic function , g(x)= -4(x+2)^2-3 identify the difference between its parent function f(x)=x^2
Thus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².
Explain about the parent function:The simplest function which nonetheless complies with a particular type of function's definition is a parent function. For instance, y = x would be the parent function when considering the linear functions that make a family of functions. The most basic linear function is this one.
In addition, by applying various transformations to the graph of the parent function, all of the functions in a family of functions can also be derived from it. Vertical shifts, extending or compressing both horizontally and vertically, reflecting and over x or y axes, and horizontal shifts are some of these transformations.Given parent function: f(x)=x²
new quadratic function , g(x)= -4(x+2)²-3
there is the translation of 2 units to right such that 2 is added to x.Now, there is dilation with the scale factor of -4.At last the function is shifted 3 units downThus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².
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Complete question:
from the following quadratic function , g(x)= -4(x+2)²-3 .identify the difference between its parent function f(x)=x² and g(x).
Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
The calculated value of the expression A/the area of XYZ is [tex]\frac{49\sqrt3}{216}[/tex]
Finding the value of A/the area of XYZFrom the question, we have the following parameters that can be used in our computation:
Center of the equilateral triangle XYZ = GDilation centered at G with scale factor = 3/4By the ratio of corresponding sides (see attachment for figure), we have
(x + 2y)/(2x + y) = 3/4
By comparison, we have
x + 2y = 3
2x + y = 4
This gives
(x, y) = (5/3, 2/3)
The triangles are equilateral triangles
So, we have
Area of XYZ = 1/2 * side length² * sin(60)
This gives
Area of XYZ = 1/2 * (2x + y)² * sin(60)
Substitute the known values in the above equation
Area of XYZ = 1/2 * (4)² * sin(60)
Evaluate
Area of XYZ = 4√3
The region A is a trapezoid
So, the area is
A = 1/2 * Sum of parallel sides * height
So, we have
A = 1/2 * (x + y) * (x² - y²)
Recall that (x, y) = (5/3, 2/3)
So, we have
A = 1/2 * (5/3 + 2/3) * ((5/3)² - (2/3)²)
Evaluate
A = 49/18
Finding A/the area of XYZ, we have
A/the area of XYZ = 49/18 ÷ 4√3
This gives
A/the area of XYZ = 49/72 ÷ √3
Rationalize
A/the area of XYZ = [tex]\frac{49\sqrt3}{216}[/tex]
Hence, the value of the expression is [tex]\frac{49\sqrt3}{216}[/tex]
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Complete question
Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
XY = 2x + y
X'Z' = x + 2y
Region A is a trapezoid with parallel sides y & x and height x² - y²