Answer:
Step-by-step explanation:
5
Functions for -4,-6,-9,-27/2,-81/2
The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)
Identifying the function of the sequence
from the question, we have the following parameters that can be used in our computation:
-4,-6,-9,-27/2,-81/2
The above sequence is a geometric sequence
This is because it has a common ratio calculated as
r = -6/-4
So, we have
r = 3/2
The sequence is then represented as
f(n) = ar^n-1
So, we have
f(n) = -4(3/2)^(n - 1)
Hence, the function is f(n) = -4(3/2)^(n - 1)
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Answer this now please
The answer is 8.6+(-6.1). This is because addition and subtraction are inverse operations.
What is subtraction?Subtraction that involves taking one number away from another. It is the inverse of addition and is represented by the minus sign (-).
This means that when you add two numbers and then subtract the same amount, the result is the same as just adding the two numbers.
Similarly, when you subtract two numbers and then add the same amount, the result is the same as just subtracting the two numbers.
Therefore, 6.1+8.6 is equivalent to 8.6+(-6.1).
Using mathematical notation, we can represent this expression as 6.1+8.6 = 8.6+(-6.1).
To add and subtract the numbers, we can use the traditional column method.
First, we write out 6.1+8.6 as 6.1 - (-8.6). Then, we add the numbers in each column, starting with the ones column:
Ones column: 1+6=7
Tens column: 8-8=0
And our answer is 7,0. We can also write this as 8.6+(-6.1) to show that the two expressions are equivalent.
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Which answer choice gives the correct classification(s) of the number 1,256?
integer
natural, whole
integer, rational
natural, whole, integer, rational
Answer:
natural, whole, integer, rational
Step-by-step explanation:
Natural Number:
All the numbers in the set {1, 2, 3, …} are natural numbers, 1256 lies in this set.
Whole Number:
All the numbers in the set {0, 1, 2, 3, …} are whole numbers, 1256 lies in this set.
Integer:
All the numbers in the set {… ,-1, 0, 1, 2 …} are integers, 1256 lies in this set.
Rational Number:
1256 can be represented as [tex]\dfrac{1256}{1}[/tex] or [tex]\dfrac{2512}{2}[/tex] etc., which is in the rational form (division of two non zero integers). therefore 1256 is also a rational number.
Hopefully this answer helped you!!
The Louvre Pyramid serves as a entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the aides are 32 meters long. Classify the triangle on the front of the Louvre Pyramid by the length of its sides and the measure of its angles.
The triangles on the front of the Louvre Pyramid are all isosceles triangles.
What is Louvre Pyramid?The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.
The Louvre Pyramid: What Makes It Famous?The primary entry point to the Louvre is the I.M. Pei Pyramid, which is situated in the courtyard. The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.
A graph on the right AB = 35 meters {Given}
AE = 32 meters {Given}
Because AE = BE = 32 meters
So <EAB = <ABE By measure,
<EAB=663°
So <ABE=663°.
So <AEB = 180° - LEAB-LABE.
= 180°-66.3° - 66.3° =47.4°
So, ΔABE is an isosceles triangle.
And the four triangles are all isosceles triangles.
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The sides of a triangle are x cm, (x − 4) cm and (x - 8) cm, respectively. If the cosine of the largest angle is, calculate the angles of the triangle.
DRAW THE TWO GRAPHS OF Y=+X^3 AND Y=-X^3 OF THE SAME AXEL SYSTEM
The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.
What are the quadrants?
The quadrant refers to one of the four regions in a two-dimensional coordinate system, formed by two perpendicular lines that intersect at their common origin, or point of intersection.
a graph of y = x³ and y = -x³ on the same axes:
We can see the graph of equations y = x³ and y = -x³ in the attached image.
The blue curve represents y = x³ and the red curve represents y = -x³.
They are symmetric about the origin, and the blue curve is in the first and third quadrants while the red curve is in the second and fourth quadrants.
Hence, The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.
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Baldwin received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded 12 songs and 19 movies, which cost a total of $195. Using another, he purchased 14 songs and 12 movies, which cost a total of $136. How much does each download cost?
Answer:
165.5
Step-by-step explanation:
Because you have to add them together and then divide
What is the missing width of the object below, if the volume is 352 cubic meters? 8 and 11 m
Answer: 4
Step-by-step explanation: 8x11=88.
352=88x
x=352/88
x=4
Check:
11x8x4=352
The salaries did not rise with inflation. The butter is now 25% costlier. By what percentage should a housewife reduce the consumption, so that her expenditure stays the same
The percentage of reduction in consumption required to keep the same expenditure is 25%.
What is Inflation?Inflation is an economic phenomenon that occurs when the prices of goods and services increase over time.
To find out the percentage of reduction in consumption, we need to calculate the difference between the current and the original prices of the butter.
This can be done by subtracting the original price of the butter from the current price of the butter (25% costlier).
The difference can be expressed as a percentage by dividing the difference by the original price.
Therefore, the percentage of reduction in consumption required to keep the same expenditure is 25%.
This means that a housewife needs to reduce her consumption of butter by 25% in order to keep her expenditure the same.
Thus, the percentage of reduction in consumption required to keep the same expenditure is 25%.
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Write 6.384 correct to 1 decimal place
Profit is defined as total revenue minus total cost. The profit function of a company that manufactures and sells x units of a product is given by P(x)= R(x)-C(x), where
Prepresents the company's profits, R represents the company's revenue, and C represents the company's cost. If a company sells a calculator for $11, its revenue
function is R(x)=11x. The cost of each calculator manufactured is $8. In addition, it renewed its lease on the plant, so its weekly fixed costs are $1220.
(a) Determine the profit function. (b) Determine and interpret P(800)
Answer:
a.) P(x)= 3x - 1120
b.) make $1,180 profit in 1 week by selling 800 calculators
Step-by-step explanation:
a.) P(x)=R(x)-C(x)
R(x)=11x; C(x)=8x + 1220 assuming they are asking for profit in a week
P(x)= 3x - 1220
b.) P(800) = 3(800) -1220 = 1180
Convert 41 divided by 2 day.
to an
hour
41/2 days is equivalent tο 492 hοurs.
What is divisiοn?Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.
We knοw that there are 24 hοurs in day therefοre,
Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:
41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs
Therefοre, 41/2 days is equal tο 492 hοurs.
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Can someone explain how to find cordinates from slop in graph to find angle
Answer:
Find the components of the line (x,y)
And then use Tan ^-1(y/x)= Theta or angle
I hope you understand, and I go explain further.
Step-by-step explanation: In "simple terms". Slope is rise/run. Rise is the change in y value, which will equal the length of the opposite side of the right triangle. Run is the change in x value, which is the length of the adjacent side. The trigonometric function Tangent is opposite/adjacent. Use the inverse tangent of the slope to find the angle.
The only catch is that sometimes inverse tangent will give you a negative angle. It is generally not acceptable to provide the angle in a triangle as the negative angle. If you get a negative angle, use the absolute value of the angle.
When Sally was 10 years old, she was 140 cm tall. Two years later, her height had increased by 10%. Find Sally's height when she was 12 years old.
Answer: 154cm
Step-by-step explanation:
10% of 140 is 14
add that 10% to get 154
solve for x using pythagorean theorem.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{257}}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ (\sqrt{257})^2= (x)^2 + (15)^2\implies 257=x^2 + 225 \\\\\\ 32=x^2\implies \sqrt{32}=x\implies 4\sqrt{2}=x\implies 5.66\approx x[/tex]
The volume of a cuboid is 108cm3.
The length is 4cm and the width is 9cm.
Work out the height of the cuboid.
Answer:
You can use the formula for the volume of a cuboid, which is Volume = length x width x height
You are given the volume of the cuboid as 108cm^3, the length as 4cm, and the width as 9cm. Let's substitute these values into the formula and solve for the height:
108cm^3 = 4cm x 9cm x height
To solve for height, you can divide both sides by 36 (which is equal to 4cm x 9cm) to isolate height:
108cm^3 ÷ 36 = 4cm x 9cm x height ÷ 36
3cm = height
So the height of the cuboid is 3cm.
For the given cost function
C(x)=12100+800x + x² find:
a) The cost at the production level 1200
b) The average cost at the production level 1200
c) The marginal cost at the production level 1200
d) The production level that will minimize the average cost
e) The minimal average cost
a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
What is an expression?An expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represent some combination of numbers or other mathematical objects. Expressions can be simple, such as a single number or variable, or complex, such as a series of terms connected by operators. Expressions can be evaluated, simplified, and manipulated using algebraic techniques to solve problems and analyze mathematical relationships.
According to the given information:a) The cost at the production level 1200 is[tex]C(1200) = 12100 + 800(1200) + (1200)^2 = 2522100.[/tex]
b) The average cost at the production level 1200 is [C(1200)]/1200 = 2101.75.
c) The marginal cost at the production level 1200 is the derivative of C(x) with respect to x evaluated at x = 1200. Thus, MC(1200) = 800 + 2(1200) = 3200.
d) The production level that will minimize the average cost is given by the formula x = -b/(2a) where a and b are the coefficients of [tex]x^2[/tex] and x, respectively. Thus, x = -800/(2(1)) = -400. This value is not meaningful, as it is not in the domain of production levels.
e) The minimal average cost is the average cost at the vertex of the parabola given by C(x). The x-coordinate of the vertex is x = -b/(2a) = -800/(2(1)) = -400, and the y-coordinate is C[tex](-b/(2a)) = C(-400) = 12100 + 800(-400) + (-400)^2 = 168900[/tex]. Therefore, the minimal average cost is 168900/(-400) = -422.25. This is not a meaningful answer, as average cost cannot be negative.
Therefore,a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
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Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 9 cm 11 cm 6 cm
The volume of the triangular prism is 135 cm³.
To calculate the volume of a triangular prism, we multiply the area of the triangular base by the height of the prism.
Given the dimensions provided:
Base: Length = 5 cm, Width = 9 cm
Height: 6 cm
To find the area of the triangular base, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Substituting the values:
Area = (1/2) * 5 cm * 9 cm
Area = 22.5 cm²
Now, to calculate the volume of the prism, we multiply the area of the base by the height:
Volume = Area * Height
Volume = 22.5 cm² * 6 cm
Volume = 135 cm³
Consequently, the triangular prism has a 135 cm3 volume.
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2sinx-1 = 0 (Solve with the inverse domain)
Answer:x = π/6 + 2πn , 5π/6 + 2πn, for any integer n
31 points
2a) Why wouldn’t a 2x2 area model (2 rows, 2 columns) with 4 smaller areas work to multiply
(x + 3)(2x
4 − 3x
3 − 2x
2 − 4x − 1) ? In your explanation, include a description of how to determine the correct rows
and columns for the area model [be sure to refer to and include the correct number of ‘terms’ and correct dimensions]
2b) Show what the area model SHOULD look like with the
correct lengths and widths labeled. DO NOT MULTIPLY!
2c) Draw an area model to find the ‘total area’ of a rectangle if the length is (x + 8) and the width is (x − 5). Write
your final ‘total area’ as a polynomial in Standard Form.
Final Area:
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
c) The final total area is 2x² - 10x - 15.
What is an area model?An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
2x⁴ − 3x³ − 2x² − 4x − 1
+---------------------------------------
x | 2x⁵ -3x⁴ -2x³ -4x² -x
|
3 | 6x⁴ -9x³ -6x² -12x -3
+---------------------------------------
c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.
x + 8 x - 5
+--------------------
x | x² + 8x x² - 5x
|
-5 | -5x + -40 -5x + 25
+--------------------
The final total area can be found by adding up the areas of the smaller rectangles:
Total area = x² + 8x + x² - 5x - 5x - 40 + 25
= 2x² - 10x - 15
= 2x² - 10x - 15.
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!!!!!!!!!!!!!!!!!!
she has a gross income of $105500
If she pays $26982
in income tax and $2110
for the Medicare levy, what is her net income?
Therefore, her net income is $77408.
What is coefficient?A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.
For example, in the polynomial function[tex]f(x) = 3x^2 + 2x - 1[/tex], the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable. [tex]x^2[/tex], the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.
Coefficients are also commonly used in statistics, where they are used to describe the relationship between variables in a statistical model. In regression analysis, for example, coefficients are used to represent the slope and intercept of a line that best fits the data.
by the question.
To calculate her net income, we need to subtract the total tax paid from her gross income:
[tex]Net Income = Gross Income - Income Tax - Medicare Levy[/tex]
Substituting the given values, we get:
[tex]Net Income = $105500 - $26982 - $2110[/tex]
[tex]Net Income = $77408[/tex]
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"2 Ans" is the answer. Is the answer correct? If not, why? What's the Correct answer?
The formula for Py(Y) = ∑P y,z (y, z) for z ∈ Z is consistent with the third Axiom of the probability measure.
The Relationship between the Formula for Discrete Random Variables and the Third Axiom of Probability MeasureThe third Axiom of the probability measure states that the sum of probabilities of all possible outcomes of an event is equal to 1. In the context of two discrete random variables Y and Z, this axiom means that the sum of probabilities of all possible pairs (y, z) is equal to 1.
The formula PY(Y) = ∑P y,z (y, z) for z ∈ Z is related to this axiom because it represents the probability of the random variable Y taking on a specific value y, regardless of the value of Z. The summation is taken over all possible values of z in Z, and P y,z (y, z) represents the joint probability of Y and Z taking on the specific values (y, z).
Since the sum of probabilities of all possible pairs (y, z) is equal to 1, the sum of probabilities of all possible values of Y, represented by PY(Y), must also be equal to 1.
Therefore, the formula for PY(Y) is consistent with the third Axiom of the probability measure.
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The cost of renting a chain saw is $3.90 per hour plus $6.50 for a can of gas. Find the cost of using the chain saw for 7.5 hours. Explanation and Answer
Answer:
$35.75
Step-by-step explanation:
$6.50 + $3.90(7.5) = $6.50 + $29.25 = $35.75
C(x)= 20+4000x+0.09x^2
A. Find the marginal cost function
Use it to estimate how fast the cost is increasing when x=4
The marginal cost function is $ 4000.72.
What is the marginal cost function?
The overall costs involved in producing an additional good are what is referred to as the marginal cost. Hence, it can be evaluated by changes in the costs associated with each extra unit. Marginal Cost is calculated as Total Expenditure Change / Unit Production Change.
Here, we have
Given: C(x) = 20+4000x+0.09x²
We have to find the marginal cost function.
We differentiate the given function and we get
C(x) = 20+4000x+0.09x²
C'(x) = 4000 + 2×0.09x
To determine how fast the cost is increasing when x=4.
C'(4) = 4000 + 2×0.09(4)
C'(4) = 4000.72
Hence, the marginal cost function is $ 4000.72.
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(1/64)^(2/3)
SOLVE LAW OF INDICES
Answer:
To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).
So, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.
Now, we have:
(1/64)^(2/3) = 1/(64^(2/3))
To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:
64^(2/3) = (64^(1/3))^2 = 4^2 = 16
So, substituting this back into the original expression, we have:
(1/64)^(2/3) = 1/16
Therefore, (1/64)^(2/3) simplifies to 1/16.
Step-by-step explanation:
Answer:
Using the law of indices, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Now we need to simplify the denominator by finding the cube root of 64:
64^(1/3) = 4
Substituting this value in the original expression, we get:
(1/64)^(2/3) = (1^(2/3))/(4^2)
Simplifying further, we have:
(1/64)^(2/3) = 1/16
Step-by-step explanation:
In Exercises 43-46, solve the equ
43. 33x+6=27* +2
Answer:
43. All real numbers
44. x = 1/4
45. No solution
Step-by-step explanation:
The technique here is two write two expressions with the same base that are equal. Then set the exponents equal and solve for the variable.
43.
[tex] 3^{3x + 6} = 27^{x + 2} [/tex]
[tex] 3^{3x + 6} = (3^3)^{x + 2} [/tex]
[tex] 3^{3x + 6} = 3^{3(x + 2)} [/tex]
[tex] 3^{3x + 6} = 3^{3x + 6} [/tex]
[tex] 3x + 6 = 3x + 6 [/tex]
Answer: all real numbers
44.
[tex] 3^{4x + 3} = 81 [/tex]
[tex] 3^{4x + 3} = 3^4 [/tex]
[tex] 4x + 3 = 4 [/tex]
[tex] 4x = 1 [/tex]
[tex]x = \dfrac{1}{4}[/tex]
45.
[tex] 4^{x + 3} = 2^{2(x + 1)} [/tex]
[tex] (2^2)^{x + 3} = 2^{2(x + 1)} [/tex]
[tex] 2^{2(x + 3)} = 2^{2(x + 1)} [/tex]
[tex] 2(x + 3) = 2(x + 1) [/tex]
[tex] x + 3 = x + 1 [/tex]
[tex] 3 = 1 [/tex]
No solution.
(100 points)
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 3.5 centimeters and is 7 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(3.5)2(7)
V = (3.14)(7)2(3.5)
V = (3.14)(7)2(1.75)
V = (3.14)(1.75)2(7)
Answer:
for making cupcakes we need to determine its volume first
that would be πr²h for a cylinder
hence your answer is
V = (3.14)(1.75)^2(7)
V = (3.14)(1.75)^2(7)
3/2 (as a fraction) by the power of 4
Answer:
5.0625
Step-by-step explanation:because it is 1.5 as a decimel and that to the power of 4 is 5.0625
Answer:
1.97
Step-by-step explanation:
(3/2)^4
3^4 / 2^4
81/16
A of apples has a mass of 4 kg. The average mass of each apple is 1/8 . How many apples are in the bag?
Answer:
There are 32 apples in the bag.
Step-by-step explanation:
To find the number of apples in the bag, we can use the formula:
number of apples = total mass of apples / average mass of each apple
Given that the bag of apples has a mass of 4 kg, and the average mass of each apple is 1/8 kg, we can substitute these values into the formula to get:
number of apples = 4 kg / (1/8) kg/apple
Simplifying the right-hand side by dividing 4 kg by (1/8) kg/apple, we get:
number of apples = 4 kg * 8/apple = 32 apples
Therefore, there are 32 apples in the bag.
Answer:
Step-by-step explanation:
It is simple by averaging formula as follows
Total mass/average mass = Total apples
4/(1/8)= 32 Apples
Please help me i need it for today!
1) The area of the garden in Design A and Design B is 108 [tex]feet^{2}[/tex]and 84[tex]feet^{2}[/tex]
2)The area of the deck not including the garden in Design A and Design B is 342 [tex]feet^{2}[/tex]and 372 [tex]feet^{2}[/tex]
3)The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B is $1890 and $1764 respectively
4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B is $151.2 and $117.6
5)Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.
Therefore Mr. and Mrs. Harper save money $159.6.
How to calculate the money saved by Mr. and Mrs. Harper By choosing the affordable design?1) The area of the rectangular garden in design A
Area = length * width
From the fig, length = 9 feet
width = 12 feet
Area = 12 * 9 = 108 [tex]feet^{2}[/tex]
The area of the triangular garden in Design B
From the fig, Height = 12 feet
base = 14 feet
Therefore the area of the triangle = [tex]\frac{1}{2} * base *height\\\frac{1}{2} * 14 * 12[/tex]
= 84 [tex]feet^{2}[/tex]
2) The area of the rectangular deck is in design A
Area = length * width
= 18 * 25
= 450 [tex]feet^{2}[/tex]
The area of the rectangular deck is in design B
Area = length * width
= 21 * 20
= 420 [tex]feet^{2}[/tex]
The area of the rectangular deck without a rectangular garden in design A is =
= 450 - 108 = 342 [tex]feet^{2}[/tex]
The area of the rectangular deck without a triangular garden in design B is =
= 420 - 84[tex]feet^{2}[/tex] = 372 [tex]feet^{2}[/tex]
3) The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B
Therefore the total cost required to install the deck in design A
= 450 * 4.20
= $ 1890
Therefore the total cost required to install the deck in Design B
= 420 * 4.20
= $ 1764
4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B
Therefore the total cost required to install the garden in design A
= 108 * 1.40
= $ 151.2
Therefore the total cost required to install the garden in Design B
= 84 * 1.40
= $ 117.6
5) Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.
Mr. and Mrs. Harper save money if they choose design B over design A
= (1890 + 151.2) - (1764 +117.6)
= 2041.2 - 1881.6
= $159.6
Therefore Mr. and Mrs. Harper save money $159.6.
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