The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.
How many chickens and pigs he saw?Let
Number of chickens = x
Number of pigs = y
x + y = 53
2x + 4y = 138
From (1)
x = 53 - y
Substitute x = 53 - y into (2)
2x + 4y = 138
2(53 - y) + 4y = 138
106 - 2y + 4y = 138
- 2y + 4y = 138 - 106
2y = 32
divide both sides by 2
y = 32/2
y = 16
Substitute y = 16 into
x + y = 53
x + 16 = 53
x = 53 - 16
x = 37
Therefore, there are 37 chickens and 16 pigs respectively.
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math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.
How to explain the informationIn this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.
By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.
Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.
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14 minus 25% algebraic expression
The value of the expression is 13. 75
What is an algebraic expression?An algebraic expression is described as an expression that is known to consist of certain variables, terms, their coefficients, factors and also their constants.
Algebraic expressions are also known to be made up of some arithmetic operations such as;
BracketParenthesesDivisionMultiplicationSubtractionAdditionFrom the information given, we have that;
14 minus 25%
This is represented as;
14 - 25%
Find the percent
14 - 25/100
Divide the values
14 - 0.25
13. 75
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Which is a Function or
Not a function
The relation that is not a function is relation 3, and the other 3 are functions.
Which are functions and which aren't?A relation is a function if each point on its domain is mapped into a single point in the range.
So if you see an input that is mapped into two different outputs, then it is not a function.
Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.
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Kevin has money in two savings accounts. One rate is 8% and the other is 12%. If he has $450 more in the 12% account and the total interest is $176, how much is invested in each savings account?
Answer:
8%: $61012%: $1060Step-by-step explanation:
You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.
SetupLet x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...
0.08(x -450) +0.12(x) = 176
Solution0.20x - 36 = 176 . . . . . simplify
0.20x = 212 . . . . . . add 36
x = 1060 . . . . . . divide by 0.2
x -450 = 610
The 8% account had $610 invested; the 12% account had $1060 invested.
can someone help me on number 1
The segments AB and CD on item 1 are classified as follows:
Perpendicular.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.The slope of segment AB is given as follows:
m = (3 - 13)/(0 - (-2))
m = -10/2
m = -5.
The slope of segment CB is given as follows:
m = (3 - 0)/(10 - (-5))
m = 3/15
m = 1/5.
The multiplication of these slopes is given as follows:
-5 x 1/5 = -1.
As the multiplication of the slopes is of -1, the segments are perpendicular.
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Anwer fast due tomorrow show work
Answer:45.3 miles/h
Step-by-step explanation
let 'x' be the speed of the car.
60 × 2/3 = 120/3 = 40
30 × 1/5 = 151/5
151/5 /40 = x / 60
151 / 200 = x / 60
=> x = (151×60) / 200
=> x = 45.3
solution to the system of equations y = 2x -1 and y = x + 3
The solution to the system of equations, y = 2x -1 and y = x + 3 is: x = 4 and y = 7.
How to Find the Solution to a System of Equations?Given the system of equations as:
y = 2x - 1 ---> eqn. 1
y = x + 3 --> eqn. 2
Substitute y for (x + 3) into equation 1:
x + 3 = 2x - 1
Combine like terms:
x - 2x = -3 - 1
-x = -4
x = 4
Substitute x = 4 into equation 1:
y = 4 + 3
y = 7
The solution is: x = 4 and y = 7.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer choices
Only child
Have chores
Have a sibling
Does not have chores
Answer:
only child
Step-by-step explanation:
Y varies inversely as x. If x = 8 then y = 6. FInd y when x = 2.
Y=
Answer: If y varies inversely as x, then:
y = k/x
where k is a constant of proportionality. To find k, we can use the initial condition that y = 6 when x = 8:
6 = k/8
Solving for k, we get:
k = 48
Now we can use this value of k to find y when x = 2:
y = 48/2 = 24
Step-by-step explanation:
How would you describe what this transformation looks like when preformed on a coordinate plane
The description of function transformations and an example is highlighted below
Describing the transformation of the functionsTo describe the transformation of the functions, we need to identify the image and the preimage of the functions to be transformed
Take for instance the function is y = x² transformed to the function y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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A student said that to
write a percent as a fraction, write the
number that comes before the percent
symbol over a denominator of 100. Is the
student correct? Justify your conclusion.
Answer:
Step-by-step explanation:
Yes, the student is correct. To write a percent as a fraction, we can write the number before the percent symbol as the numerator and 100 as the denominator. For example, 25% can be written as 25/100, which can be simplified to 1/4. This is because percent means "per hundred," so 25% means 25 per hundred, which can be expressed as a fraction with a denominator of 100.
Help me, please my friends. I need the assistance
The area of a rectangle is 14x² + 19x - 3 square units.
The degree of 4x² + 3y - 6x⁴y + 4 is 5.
The number of terms of 4x² + 3y - 6x⁴y + 4 is 4.
Adding, subtraction or multiplying two polynomials always results in another polynomial.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (7x - 1) × (2x + 3)
Area of rectangle = 14x² + 21x - 2x - 3
Area of rectangle = 14x² + 19x - 3 square units.
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Which is NOT personally liable for any losses or damages? Group of answer choices Shareholders in a public corporation, Owner of a sole proprietorship, Shareholders in a corporation, Partners in a partnership
The option which is not personally liable for any losses or damages is Shareholders in a public corporation, the correct answer is A.
We are given that;
Four options of damages
Now,
Shareholders in a public corporation are not personally liable for any losses or damages caused by the corporation, because they have limited liability. This means that they can only lose the amount they invested in the corporation, and their personal assets are protected from creditors or lawsuits12.
Owner of a sole proprietorship, shareholders in a private corporation, and partners in a partnership are all personally liable for any losses or damages caused by their business activities, unless they have some form of liability insurance or protection12. This means that they can be sued for their personal assets if the business cannot pay its debts or obligations.
Therefore, by unitary method the answer will be Shareholders in a public corporation
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seventeen more than a number is negative twenty-three
The number that represents the phrase is -40.
Let's use algebra to solve the problem.
If we let "a number" be represented by the variable x, we can write the first part of the sentence as "Seventeen more than a number" which can be written as:
x + 17
The problem also says that this expression is equal to negative twenty-three.
We can write that as:
x + 17 = -23
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 17 from both sides:
x + 17 - 17 = -23 - 17
x = -40
Therefore, the number is -40.
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Question is below ⬇️.
The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.
What is the missing statement about the trapezoid?
The base angles of isosceles trapezoids are congruent.
In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.
Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.
In the given diagram, we will identify the base angles as follows;
∠TPR ≅ ∠ TAR
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Solve the question below:
Answer:
x = 15
Step-by-step explanation:
3x+1+4x-3 = 103
7x = 105
x = 15
a + b = 10 a - b = 2 Solve the system of equations. Responses
The solution to the given system of equations is a = 6, b = 4.
The system of equations is given as follows:
a + b = 10 .....(i)
a - b = 2 .....(ii)
To solve this system of equations, we can use the method of elimination.
Adding the two equations, we get:
(a + b) + (a - b) = 10 + 2
2a = 12
a = 6
Substituting a = 6 into one of the equations, we get:
6 - b = 2
b = 4
Therefore, the solution to the system of equations is:
a = 6, b = 4.
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The illustration represents the number 3. Which improper fraction does it also represent?
please help me its due in a little bit!!
the diamter is 37 m find its nearest whole number
The area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.
Given that a circle has a diameter of 37 m, we will find the circumference of and the area of the circle,
Radius = diameter /2
Radius = 18.5 m
Circumference = π × diameter
= 3.14 × 37
= 116.18 m
Area = π × radius²
= 3.14 × 18.5²
= 1074.6 m²
Hence, the area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.
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Lee watches TV for 3 hours per day. During that time, the TV consumes 250 watts per hour. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Lee's TV costs $4.05 to operate for a month of 30 days.
To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.
First, let's find out how many watts Lee's TV consumes in a day:
250 watts/hour x 3 hours/day = 750 watts/day
To convert this to kilowatts, we divide by 1000:
750 watts/day ÷ 1000 = 0.75 kilowatts/day
Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:
0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours
Finally, we can calculate the cost of operating the TV for a month:
22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05
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Quiz: Measures of Center and Spread
Question 1 of 10
If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B.
A. True
B. False
The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.
The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.
A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.
Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.
Hence, the given statement is true.
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
Which of the following choices is a linear function? NEED HELP ASAP!
Answer: f(x)=x-2
Step-by-step explanation:
Linear function means a straight line so graph each one to find which is a straight line
A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.
A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 6 to 10 that stops at 3, for 11 to 15 that stops at 5, for 16 to 20 that stops at 6, and for 21 to 25 that stops at 1. There is no shaded bar for the 1 to 5 interval.
Which of the following best describes the spread of the data?
Explain its meaning in this situation.
The data has a possible range of 19, which is a wide spread. This might mean that the most common number of water-skiing trips is 10.
The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
The data has a possible range of 6, which is a narrow spread. This could mean that most of the students have taken a similar number of water-skiing trips.
The data has a range of 6, which is a narrow spread. This might mean that the most common number of water-skiing trips was 6.
Answer:
(b) The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
Step-by-step explanation:
You want the best description of the spread of data shown in the histogram.
SpreadThe least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...
range = max - min = 25 -6 = 19
This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.
__
Additional comment
The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)
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I need help with this please
Answer:
Multiply row 1 by 1/7
The resulting matrix is
[tex]\begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]
Step-by-step explanation:
Original matrix is
[tex]\begin{pmatrix}7&-4&8\\ -12&7&-13\end{pmatrix}[/tex]
Multiplying any one row by a nonzero scalar is a valid matrix operation. This will not affect the final solution of the matrix
So all we have to do is to multiply row 1 by 1/7 and you get a 1 in row 1, column 1
[tex]R_1 \times \dfrac{1}{7} \longrightarrow \begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]
A rectangular room is 28 feet by 32 feet.
A scale drawing of the room has a perimeter is 12 inches.
What is the length of the shorter side of the room on the scale drawing?
50 POINTS PLSSSS!!!!!
The length of the shortest side is 0.28ft
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
Scale factor = dimension of new shape / dimension of old shape
Perimeter of new rectangle = 12 inches = 1 feet
perimeter of the old = 2(28+32)
= 100feet
scale factor = 1/100
therefore the dimension of the shortest length is
1/100 = x/28
100x = 28
x = 28/100
x = 0.28ft
The shortest length of scale drawing is 0.28feet.
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13.5.6 Check Your Understanding Complete the statements. The graph of y = (x + 3)² is a [DROP DOWN 1] of the graph y = C with the graph of y = (x+3)2, it is shifted [DROP DOWN 2] 3 units. When building a table of values to 2 For the graph y = X to coincide model the function y = (x+3)2, this shift can be found by [DROP DOWN 3] 3 to/from each [DROP DOWN 4] for each corresponding [DROP DOWN 5].
The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.
Describing the transformation of the functionsThe equation of the function is given as
y = x²
The transformed function is
y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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I REALLY NEED THIS TO PASS SOMEONE PLEASE TRY AND HELP
solve this triangle. Round to the nearest tenth
Answer:
Im pretty sure its the third one
Step-by-step explanation:
It all depends on the square root to find the nearest tenth and rounding it all up.
Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q
A point that represent a striking deviation in the box plot above include the following: C. P.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 24.First quartile (Q₁) = 26.Median (Med) = 28.Third quartile (Q₃) = 29.Maximum (Max) = 30.In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).
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i need help with this, please anyone I am so scared of failing. Please explain throughly,
thank you so much.
Check the picture below.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ triangle }{\cfrac{1}{2}(26)(17)}~~ + ~~\stackrel{ rectangle }{(26)(9)}}\implies 221+234\implies \text{\LARGE 455}[/tex]