Answer:
720
Step-by-step explanation:
4x180=720 u have to multiply because 4 miled in 180 days is the same as 4x180
Triangle ABC ~ triangle DEF. Use the image to answer the question.
Determine the measurement of EF.
EF = 1.1
EF = 1.39
EF = 2.37
EF = 3.3
Answer:
EF = 2.37
Step-by-step explanation:
It's given that these are similar triangles.
In similar triangles, the side lengths are proportional.
We can write the following equation based on this information:
\( \frac{11}{3.3} = \frac{7.9}{ef} \)
Cross multiply fractions11EF = 27.03
Divide both sides by 11EF = 2.37
help me solve thank youuu for a brainlist (best answer)
Answer:
B
Step-by-step explanation:
increasing would be going into positive numbers and decreasing would be going into negative numbers
4
Type the correct answer in each box.
If 4 pounds of sugar cost $2, the cost of 1 pound of sugar is $
and the cost of 10 pounds of sugar is $
Reset
Next
Answer:50 cents. $5
Step-by-step explanation: each pound of sugar costs 50 cents. you can find that out by dividing the amount of sugar you have by the cost.
Given a set of 10 letters { I, D, S, A, E, T, C, G, M, W}, answer the following: len ( I, D, S, A, a) With the given letters above, we can construct a binary search tree (based on alphabetical
ordering) and the sequence < C, D, A, G, M, I, W, T, S, E is obtained by post-order traversing this tree. Construct and draw such a tree. NO steps of construction required.
The Binary Search Tree is as follows:
E
/ \
S T
/ \
I W
/ \
A M
/ \
C G
\
D
The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5
Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:
post-order sequence is: C, D, A, G, M, I, W, T, S, E.
To draw the binary search tree for the given post-order sequence, follow the steps below:
Start with the root node E and mark itFor the given post-order sequence C, D, A, G, M, I, W, T, S, E, identify the last element E as the root node. This node will be at the center of the drawing.Place the node containing the element S to the left of E, and mark it. Similarly, place the node containing the element T to the right of E, and mark it.Place the node containing the element I to the left of S, and mark it. Similarly, place the node containing the element W to the right of T, and mark it.Place the node containing the element A to the left of I, and mark it. Similarly, place the node containing the element M to the right of W, and mark it.Place the node containing the element C to the left of A, and mark it. Similarly, place the node containing the element G to the right of M, and mark it.Place the node containing the element D to the right of C, and mark it. Similarly, place the node containing the element E to the right of G, and mark it. This completes the construction of the binary search tree.To know more about Binary Search Tree, visit:
https://brainly.com/question/30391092
#SPJ11
Sketch and graph please
We have drawn the graph for the given inequality.
What is inequality?
Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variables.
For the given inequality y > -x - 5
we can draw the graph as shown below:
Hence, we have drawn the graph for the given inequality.
To learn more about the inequalities, visit:
https://brainly.com/question/25275758
#SPJ1
The box that the kite came in is a rectangular prism with dimensions of 21/2” x 9 1/2” x 2”
The volume of the box is given as follows:
V = 199.5 in³.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem, in inches, are given as follows:
10.5, 9.5 and 2.
Hence the volume of the box is given as follows:
V = 10.5 x 9.5 x 2
V = 199.5 in³.
Missing InformationThe problem asks for the volume of the box.
More can be learned about the volume of a rectangular prism at brainly.com/question/22070273
#SPJ1
Explain why a variable will usually have only one conceptual
definition but can have multiple operational definitions.
While a variable typically has one conceptual definition that represents its underlying construct, it can have multiple operational definitions to accommodate different research needs and approaches. Conceptual definitions provide the theoretical basis, while operational definitions specify how the variable will be measured or manipulated in a particular study.
A variable in the context of scientific research represents a concept or phenomenon that we are interested in studying. It is often defined conceptually, which means that it refers to an abstract idea or construct. The conceptual definition of a variable provides a broad understanding of what the variable represents and its theoretical significance.
On the other hand, operational definitions define how a researcher intends to measure or manipulate the variable in a specific study. They provide clear and concrete instructions on how the variable will be observed, quantified, or manipulated within the confines of a particular experiment or investigation.
The reason why a variable usually has only one conceptual definition is because it represents a specific construct or idea within a research context. The conceptual definition serves as the foundation for understanding the variable across different studies and theories. It ensures consistency and coherence when communicating about the variable's meaning and theoretical implications.
However, a variable can have multiple operational definitions because researchers may choose different ways to measure or manipulate it depending on their specific research goals, constraints, and methods. Different operational definitions may be employed to capture different aspects or dimensions of the conceptual variable.
These operational definitions can vary based on factors such as measurement tools, scales, procedures, or experimental conditions. Researchers may select different operational definitions to suit their specific research objectives, practical considerations, or theoretical frameworks. Additionally, advancements in technology and methodology over time may lead to the development of new and more refined operational definitions for variables.
By employing multiple operational definitions, researchers can explore different facets of a variable and examine its properties from various perspectives. This approach enhances the robustness and comprehensiveness of scientific investigations, allowing for a deeper understanding of the variable under study.
In summary, while a variable typically has one conceptual definition that represents its underlying construct, it can have multiple operational definitions to accommodate different research needs and approaches. Conceptual definitions provide the theoretical basis, while operational definitions specify how the variable will be measured or manipulated in a particular study.
Learn more about variable from
https://brainly.com/question/28248724
#SPJ11
Find the slope of the line through the points (12, -9) & (-11, -9)
Answer:
0
Step-by-step explanation:
Answer:
no. why?
Step-by-step explanation:
A portfolio is 70% invested in an index fund and 30% in a risk-free asset. The index fund has a standard deviation of returns of 15%. Calculate the standard deviation for the total portfolio returns.
The standard deviation for the total portfolio returns can be calculated using the weighted average of the standard deviations of the index fund and the risk-free asset. The standard deviation for the total portfolio returns is 10.5%.
The standard deviation of a portfolio measures the variability or risk associated with the portfolio's returns. In this case, the portfolio is 70% invested in an index fund (with a standard deviation of returns of 15%) and 30% invested in a risk-free asset.
To calculate the standard deviation of the total portfolio returns, we use the weighted average formula:
Standard deviation of portfolio returns = √[(Weight of index fund * Standard deviation of index fund)^2 + (Weight of risk-free asset * Standard deviation of risk-free asset)^2 + 2 * (Weight of index fund * Weight of risk-free asset * 1Covariance between index fund and risk-free asset)]
Since the risk-free asset has a standard deviation of zero (as it is risk-free), the second term in the formula becomes zero. Additionally, the covariance between the index fund and the risk-free asset is also zero because they are independent. Therefore, the formula simplifies to:
Standard deviation of portfolio returns = Weight of index fund * Standard deviation of index fund
Plugging in the values, we get:
Standard deviation of portfolio returns = 0.70 * 15% = 10.5%
Hence, the standard deviation for the total portfolio returns is 10.5%. This means that the total portfolio's returns are expected to have a variability or risk represented by this standard deviation.
Learn more about standard deviation here : brainly.com/question/13498201
#SPJ11
Andy goes shopping with his friend Silvio, an exchange student from Brazil. Silvio wants to know what everything costs in
Brazilian reals. He knows 1 American dollar is equivalent to 2 Brazilian reals. Let x represent American dollars and y represent Brazilian reals. This situation is graphed below. Which equation represents this situation?
A) y=-2x
B) y=4x
C) y-2x
D) y=1/2x
Answer:
Step-by-step explanation:
answer is b
Find sinR,cosR,tanR,sinS,cosS, and tanS. Express each ratio as a fraction and as a decimal to the nearest hundred th. 7. r=16,5=30,t=34 8. r=10,s=24,t=26
The values of sinR = 5/13, cosR = 12/13, tanR = 5/12, sinS = 12/13, cosS = 5/13, tanS = 12/5.
For the right triangle RST in which r=16, s=30, and t=34, find sinR, cosR, tanR, sinS, cosS, and tanS.
Express each ratio as a fraction and as a decimal to the nearest hundredth.
sinR = r/t = 16/34 = 8/17,
cosR = s/t = 30/34 = 15/17,
tanR = r/s = 16/30 = 8/15,
sinS = s/t = 30/34 = 15/17,
cosS = r/t = 16/34 = 8/17,
tanS = s/r = 30/16 = 15/8.
Therefore sinR = 8/17, cosR = 15/17, tanR = 8/15, sinS = 15/17, cosS = 8/17, tanS = 15/8.
The second right triangle is RST, with r = 10, s = 24, and t = 26.2.
sinR = r/t = 10/26 = 5/13,
cosR = s/t = 24/26 = 12/13,
tanR = r/s = 10/24 = 5/12,
sinS = s/t = 24/26 = 12/13,
cosS = r/t = 10/26 = 5/13,
tanS = s/r = 24/10 = 12/5.
Hence the values are;
sinR = 5/13, cosR = 12/13, tanR = 5/12, sinS = 12/13, cosS = 5/13, tanS = 12/5.
To know more about sin,cos and tan click here:
https://brainly.com/question/2292761
#SPJ11
HELP PLEASE LOOK AT IMAGEE BELOW
Answer:
y = 7x -9
Step-by-step explanation:
This is a linear equation.
The change in y over the change in x is 9. The y-intercept will be (0, -9).
If you follow the pattern as x is -1 and you go up 1 to zero, the the y goes up 7 from -16 to get -9
Answer:
y = 7x - 9
Step-by-step explanation:
y = 7x - 9
Let checks
-16 = 7(-1) - 9
-16 = -16
-23 = 7(-2) - 9
-23 = -23
So, y = 7x - 9 is the correct answer.
Given: ∆MNP, PM = 8 m∠P = 90°, m∠N = 58° Find: Perimeter of ∆MNP
(Not 22.4 or 22.43)
Please answer ASAP, brainly awarded.
Answer:
Step-by-step explanation:
Triangle MNP is a right triangle with the following values:
m∠P = 90°m∠N = 58°PM = 8Interior angles of a triangle sum to 180°. Therefore:
m∠M + m∠N + m∠P = 180°
m∠M + 58° + 90° = 180°
m∠M + 148° = 180°
m∠M = 32°
To find the measures of sides MN and NP, use the Law of Sines:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Substitute the values into the formula:
\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)
\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)
Therefore:
\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)
\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)
To find the perimeter of triangle MNP, sum the lengths of the sides.
\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)
At a carnival, there are 30 children and 18 adults.
What fraction shows the ratio of children to the total number of people at the carnival
PLZ HELP
Diego's high school soccer team started a fundraiser selling treats at their games. they spent $1000 to start and an additional $0.30 on each candy bar and can of soda. they decide to sell both the candy and the soda for the same price, to make things simple. choose a reasonable price for the team to sell the candy bars and sodas. in your discussion post, share the equations that you used to model this situation and answer the following questions (remember that profit is the revenue minus the costs): how much do they need to sell to break even (where revenue is equal to cost)? how much do they need to sell to make at least $5,000 in profit? do you think it is likely for them to make at least $5,000 in profit? in what situations would it be possible for them to make at least $5,000 in profit?
It is more likely for them to make at least $5,000 in profit if they sell a larger quantity of treats. This can be achieved by implementing effective marketing strategies, setting an appealing price, and targeting a wide audience.
Let's say the team decides to sell the candy bars and sodas for $1 each. In this case, they will make $1 in revenue for each candy bar and can of soda sold.
Now, let's calculate the costs. The team spent $1000 to start the fundraiser, which is a fixed cost that does not depend on the number of treats sold. In addition, they spend $0.30 on each candy bar and can of soda sold.
To break even, the revenue needs to equal the total cost. Let's denote the number of treats they need to sell to break even as "x". The revenue from selling x treats would be $1 multiplied by x. The total cost would be the sum of the fixed cost and the cost per treat multiplied by the number of treats sold.
Equation to break even: Revenue = Cost
1x = $1000 + $0.30x
To solve for x, we can subtract $0.30x from both sides and then divide both sides by 0.70:
0.70x = $1000
x = $1000 / 0.70
x ≈ 1428.57
So, they need to sell approximately 1429 treats to break even.
To make at least $5,000 in profit, we need to calculate the revenue required to cover the costs and generate the desired profit. Let's denote the number of treats they need to sell to make this profit as "y".
Equation to make at least $5,000 in profit: Revenue = Cost + Profit
1y = $1000 + $0.30y + $5000
Simplifying the equation:
0.70y = $6000
y = $6000 / 0.70
y ≈ 8571.43
So, they need to sell approximately 8572 treats to make at least $5,000 in profit.
Whether it is likely for them to make at least $5,000 in profit depends on various factors, such as the demand for treats, the number of people attending the games, and the team's marketing efforts. If they can attract a large number of customers and successfully sell the treats, it is possible for them to make at least $5,000 in profit.
In general, it is more likely for them to make at least $5,000 in profit if they sell a larger quantity of treats. This can be achieved by implementing effective marketing strategies, setting an appealing price, and targeting a wide audience.
Additionally, if they can minimize their costs (such as by negotiating better deals for purchasing treats), they would have a better chance of reaching their profit goal.
To know more about effective marketing refer here:
https://brainly.com/question/33716162#
#SPJ11
Is it possible to solve 3 equations with 4 variables?
A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.
What is linear system?A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.
Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.
The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.
Learn more about linear system
https://brainly.com/question/28977228
#SPJ4
how can confidence intervals help researchers attain their purpose of using a sample to understand a population?
The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .
In the question ,
we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,
we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .
the confidence interval are useful because ,
(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .
(ii) they make data analyses richer and help us to make more informed decisions about the research questions .
Therefore , the reason how confidence interval helps is mentioned above.
Learn more about Confidence Interval here
https://brainly.com/question/20309162
#SPJ4
ILL GIVE BRAINLY FOR RIGHT ANSWER HELP!!!!!
Answer:
3 apples.
Step-by-step explanation:
Answer:
6 apples? maybe
Step-by-step explanation:
a car is traveling at a 3 of 57 miles per hour. What is the car's speed in miles per minute? how many miles will the car travel in 20 minute? (do not round your answer)
The speed of car is found as : 1 of 1140 miles per minutes.
The total number of miles the car will travel in 20 minutes is: 1 / 50 miles.
Explain about the unit conversions?The same attribute is expressed using a unit conversion, but in a diverse unit of measurement.
For e.g., time can be highlighted in minutes rather than hours, and distance can be verbalized in kilometers, feet, or another comparable measurement unit instead of miles.
Speed of car = 3 of 57 miles per hour.
Speed of car = 3 mi / 57 hr
We know, 1 hour = 60 minutes;
So,
Speed of car = 3 mi / 57*60 min
Speed of car = 1 mi / 57*20 min
Speed of car = 1 mi / 1140 min
Thus, the speed of car is found as : 1 of 1140 miles per minutes.
In 20 minute:
Number of miles = 1 mi / 1140 min * 20 min
Number of miles = 20 / 1140 min
Number of miles = 1 / 50 miles
Thus, the total number of miles the car will travel in 20 minutes is: 1 / 50 miles.
Know more about the unit conversions
https://brainly.com/question/13016491
#SPJ1
How do you find the missing coordinate using the midpoint formula?
The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:
Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.
To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.
For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:
Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )
(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )
So, by solving above equation we can get the missing coordinate
(x₂, y₂) = (5,7)
In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.
Learn more about midpoint at
https://brainly.com/question/28224145
#SPJ4
(50 POINTS) Subtract. (−8.3x+4)−(3.2x−5)
Enter your answer, in simplified form, in the box. (Combine and simplify the equation.)
Answer:
Hello!!!Step-by-step explanation:
The first step for solving this expression is to remove the first set of parenthesis.
-8.3x+4 - (3.2x-5)
Remember that when there is a "_" sign in front of the parenthesis, we must change the sign of the expression to the following
-8.3x + 4 - 3.2x + 5
Collect the like terms with an x variable.
-11.5x + 4 + 5
Lastly, add the number to get your final answer
-11.5x + 9
Hope that helps you dear...
Have a nice day..
Buhbye!
ANSWER ALL QUESTIONS Please
Answer: 90 degrees X=7 X=5 3,3,8 all in order but i couldn't solve the one with the measure lines
PLEASE HELP BRAINLIEST PLUS POINTS!!!!!!!!!!!!!!!!!!!
Using the parallelogram, find the values of x and y.
Answer:
x = 24
y = 19
Step-by-step explanation:
2x - 8 = x + 16
x - 8 = 16
x = 24
2y = y + 19
y = 19
Answer:
x = 24, y = 19
Step-by-step explanation:
Hi there!
Since opposite sides of a parallelogram are congruent, we know that
\(2x-8 = x+16\)
Using orders of operations,
x = 24
This also applies to the other sides. We can set this up as
\(2y = y+19\)
Using orders of operations,
y = 19
I hope this helped!
what are the maximum dimensions of a div with the following properties?div.container { min-height: 150px; max-height: 600px; min-width: 300px; max-width: 900px;
For a random sample of 75 kindergartners, mothers' incomes are plotted on the x-axis and fathers' incomes are plotted on the y-axis. The resulting scatter plot produces a linear association described by the equation y=1. 23x+5. 3. Which conclusion can be made about this sample?
The intercept of 5.3 suggests that even if a mother had no income, the expected minimum fathers' income would be $5.30.
In mathematical terms, the equation y=1.23x+5.3 is in slope-intercept form, where y represents the fathers' incomes and x represents the mothers' incomes. The slope of the line, 1.23, represents the change in fathers' incomes for every one unit increase in mothers' incomes. The y-intercept of the line, 5.3, represents the minimum fathers' income when the mothers' income is zero.
With this equation, we can make several conclusions about this sample. Firstly, the positive slope suggests a positive correlation between the incomes of mothers and fathers. As the mothers' incomes increase, the fathers' incomes also tend to increase.
Secondly, the slope value of 1.23 suggests that fathers' incomes increase by $1.23 for every $1 increase in mothers' incomes.
To know more about equation here
https://brainly.com/question/10413253
#SPJ4
A triangular prism is 12 meters long and has a triangular face with a base of 8 meters and a height of 9 meters. What is the volume of the triangular prism?
The volume of the triangular prism is 216 cubic meters.
To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.
Calculate the area of the triangular base.
The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.
Plugging in the values, we get:
Area = (1/2) * 8 meters * 9 meters = 36 square meters.
Multiply the area of the base by the length of the prism.
The length of the prism is given as 12 meters.
Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.
Adjust for the shape of the prism.
Since the prism is a triangular prism, we need to divide the volume by 2.
Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.
Therefore, the volume of the triangular prism is 216 cubic meters.
For more such information on volume of triangular prism, visit:
https://brainly.com/question/31637705
#SPJ8
Write an inequality using variables x and y whose graph is described by the given information. The points (2,5) and (-3,-5) lie on the boundary line. The points (6,5) and (-2,-3) are solutions of the inequality.
The inequality using variables x and y which satisfy the points are; y>-3x+3.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given that the points (2,5) and (-3,-5) lie on the boundary line.
The system of inequality is given by:
y>-3x+3-
Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies the inequality.
a) (6, 5)
when x=6 and y= 5
then we have:
y>-3x+3
6 > -3×5 + 3
6>- 15+3
5 > -12
This means that the point will lie in the solution set.
Also, (-2, -3) when x= -2 and y= -3
then we have:
5 > -3×(-2) + 3
5> 6 + 3
5> 9
Hence, the inequality using variables x and y which satisfy the points are; y>-3x+3.
Learn more about inequality ;
brainly.com/question/14164153
#SPJ1
v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
Bethany sells roses and petunias. The expression 3r + 2.5p gives the cost (in dollars) of r roses and p petunias.
What is the cost of 7 roses and 8 petunias?
b) During the first market day, Fatuma bought 30 oranges and 12 mangoes and paid Ksh. 936 for all the fruits. In the second market day, the price of an orange increased by 20% while that of a mango reduced in the ratio 3:4. Fatuma bought 15 oranges and 20 mangoes and paid Ksh. 780 for all the fruits. Given that the cost of an orange and that of a mango during the first market day was Ksh. x and Ksh. y respectively: (i) Write down simultaneous equations to represent the information above. (2 marks) (ii) Use matrix in (a) above to find the cost of an orange and that of a mango in the first market day. (4 marks) (iii) Fatuma sold all the fruits bought on the second market day at a profit of 10% per orange and 15% per mango. Calculate the total amount of money realized for the sales. (2 marks)
Answer:Let the cost of an orange and that of a mango during the first market day be Ksh. x and Ksh. y respectively.
From the first market day:
30x + 12y = 936
From the second market day:
15(1.2x) + 20(3/4y) = 780
Simplifying the second equation:
18x + 15y = 780
(ii) Using matrix to find the cost of an orange and that of a mango in the first market day:
Rewriting the equations in matrix form:
|30 12| |x| |936|
|18 15| x |y| = |780|
Multiplying the matrices:
|30 12| |x| |936|
|18 15| x |y| = |780|
|30x + 12y| |936|
|18x + 15y| = |780|
Using matrix inversion:
| x | |15 -12| |936 12|
| y | = | -18 30| x |780 15|
|x| |270 12| |936 12|
| | = |-360 30| x |780 15|
|y|
Simplifying the matrix multiplication:
|x| |1194| |12|
| | = | 930| x |15|
|y|
Therefore, the cost of an orange in the first market day was Ksh. 39 and the cost of a mango in the first market day was Ksh. 63.
(iii) Calculation of the total amount of money realized for the sales:
On the second market day, Fatuma bought 15 oranges and 20 mangoes.
Cost of 15 oranges = 15(1.2x) = 18x
Cost of 20 mangoes = 20(3/4y) = 15y
Total cost of fruits bought on the second market day = 18x + 15y = 18(39) + 15(63) = Ksh. 1629
Profit earned on 15 oranges at 10% = 1.1(1.2x)(15) - (1.2x)(15) = 0.18x(15) = 2.7x
Profit earned on 20 mangoes at 15% = 1.15(3/4y)(20) - (3/4y)(20) = 0.15y(20) = 3y
Total profit earned = 2.7x + 3y
Total amount of money realized for the sales = Total cost + Total profit
= Ksh. 1629 + 2.7x + 3y.
Step-by-step explanation: