The juice is 27 and the tornadoes are 21.
What is the equation?An equation is a mathematical statement that shows that two expressions are equal by using an equal sign (=). Equations are used to find the value of an unknown variable or to show the relationship between variables.
We know that the number of the juice and the tornadoes can be x and y
We then have that;
5x + 3y = 24 ----- (1)
4x + 2y = 30 ----- (2)
Multiply equation 1 by 4 and equation 2 by 5 we have that;
20x + 12y = 96 ---- (3)
20x + 10y = 150 ----- (4)
Subtract (3) from (4)
-2y =54
y = -27
Then;
5x + 3(-27) = 24
x = 21
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What is the answer to 8 - 6n - 7
if 20km represents 20 km due east, what does -7m represent ?
The expression - 7 meters represents the 7 meters in the west direction.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
If 20km represents 20 km due east.
We know that the opposite of the east direction will be the west direction.
Then we can conclude that if the east direction represents the positive values, then the west direction represents the negative value.
Then the expression - 7 meters represents the 7 meters in the west direction.
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For Cynthia's fourth lab report, she calculated the ratio of velocities before and after the impact of a basketball bouncing on a court. This measurement is called the coefficient of restitution. She got the following four values.
0. 72
0. 75
0. 73
0. 76
The accepted value is 0. 77.
Cynthia's percent error was [blank]−−−−−−%.
Enter your answer as the number that correctly fills in the blank, rounded to two decimal places, like this: 42. 53
Cynthia's percent error in her fourth lab report was 4.38%.
Percent error is a measure of the accuracy of a numerical result, expressed as a percentage of the difference between the actual value and the calculated or measured value. It is calculated using the formula -
Percent Error = (|Actual value - Calculated value| / Actual value) * 100
In order to calculate Cynthia's percent error, we will use the formula:
Percent Error = (|Accepted Value - Measured Value| / Accepted Value) * 100%
For the mean of her four measured values (0.7325), the percent error would be:
Percent Error = (|0.77 - 0.7325| / 0.77) * 100% = 4.38%
So, the answer to be entered rounded to two decimal places is 4.38.
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(50 points) if anyone sees this can they help me out?
Classify each statement about the function f(x)=2x3+3 as true or false.
A) The domain of the function is all real numbers.
B) The range of the function is (−∞, 2).
C) The function has two x-intercepts.
D) The center of symmetry is (0, 3).
The function f(x)=(x−2)3 is transformed to g(x)=(x+1)3−2.
What transformations are performed from function f to function g?
A) Function f is translated to the left 2 units.
B) Function f is translated to the left 3 units.
C) Function f is translated up 1 units.
D) Function f is translated down 2 units.
The function f(x)=x+4−−−−√3 is transformed to f(x)=x−1−−−−√3+3.
What transformations are performed from function f to function g?
A) Function f is translated to the right 3 units.
B) Function f is translated down 1 unit.
C) Function f is translated to the right 5 units.
D) Function f is translated up 3 units
Graph this polynomial function by using its intercepts.
f(x)=x3+3x2−4x−12
Plot the points that represent the x- intercepts and y-intercept on the graph
For the first part of the question, here is my classification of each statement:
A) True. The domain of the function is all real numbers.
B) False. The range of the function is all real numbers.
C) False. The function has no x-intercepts.
D) False. The center of symmetry is (0, 0).
For the second part, the transformations performed from function f to function g are:
A) Function f is translated to the left 3 units.
For the third part, the transformations performed from function f to function g are:
A) Function f is translated to the right 3 units.
B) Function f is translated up 3 units.
For the last part, you would need to find the x and y-intercepts of the polynomial function, and plot them on the graph. The x-intercepts can be found by setting x=0 in the equation and solving for y. The y-intercept can be found by setting y=0 and solving for x. Once the intercepts are found, you can plot them on the graph and connect them to form the graph of the polynomial function.
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
A is true because any real value of x will always produce a real value of yB is not true because it would contradict option A as explained previouslyC is not true because there is only one positive real root by Descartes' Rules of Signs, so there is only one real root and two imaginary rootsD is true because the function is odd, so it is held that f(-x) = -f(x) which is true for the given functionProblem 2
A is falseB is trueC is falseD is trueProblem 3
I cannot read your problem
Problem 4
[tex]f(x)=x^3+3x^2-4x-12\\0=x^3+3x^2-4x-12\\0=x^2(x+3)-4(x+3)\\0=(x^2-4)(x+3)\\0=(x-2)(x+2)(x+3)\\x_1=-3,\,x_2=-2,\,x_3=2[/tex]
Hence, the graph of the function would have points at (-3,0) (-2,0) and (2,0).
A textbook store sold a combined total of 251 biology and psychology textbooks in a week. The number of psychology textbooks sold was 61 less than the number of biology textbooks sold. How many textbooks of each type were sold? Number of biology textbooks sold Number of psychology textbooks sold:
The number of biology textbooks sold = 156
The number of psychology textbooks sold = 95
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Let x be the number of biology textbooks sold. Then, the number of psychology textbooks sold was x - 61.
The combined total of the two types of textbooks sold was 251, so we can write an equation:
x + (x - 61) = 251
Expanding the right side:
2x - 61 = 251
Adding 61 to both sides:
2x = 312
Dividing both sides by 2:
x = 156
the number of psychology textbooks sold = x - 61
= 156 - 61
= 95
So, 156 biology textbooks were sold and 95 psychology textbooks were sold.
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A boat starts at point A. It travels a distance of 7 km on a bearing of 135° to point B. From B it
travels 12 km on a bearing of 250° to point C. Using a scale of 1 cm: 1 km, draw a diagram to
show these bearings and journeys.
The diagram that represent the distance and the journeys is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
Initial point = ADistance of 7 km on a bearing of 135° to point B. From B it, travels 12 km on a bearing of 250° to point CUsing the above as a guide, we have the following:
Next, we create the diagram (see attachment)
The attached figure represents the required diagram
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why when i calculate the uncertainty of a group of data does my uncetinty max is not greater than the actual math
The calculation of uncertainty depends on various factors, including the method used, the distribution of the data, and the number of data points. In some cases, the calculated uncertainty may be lower than the actual deviation of the data, especially if the data is not normally distributed or if the number of data points is small.
Uncertainty Calculation ExplanationIt's also important to keep in mind that uncertainty is a measure of the spread of the data, not the absolute deviation from the mean. In other words, if the data is tightly clustered around the mean, the calculated uncertainty will be low, even if the maximum deviation from the mean is relatively high.
If you think your calculated uncertainty is not accurately representing the spread of your data, you may want to consider using a different method for calculating uncertainty, or checking the underlying assumptions of the method you are using to ensure that it is appropriate for your data set.
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The uncertainty of a group of data represents the range of possible values that the data could reasonably have and is not expected to exceed the actual mathematical value of the data.
The uncertainty of a group of data is determined by factors such as measurement error and natural variability in the data & represents the range of possible values that the data could reasonably have. It is not expected to exceed the actual mathematical value of the data because the mathematical value represents the best estimate of the true value based on the available data.
The uncertainty is a measure of the limitations and potential sources of error in the data and helps to quantify the level of confidence that can be placed in the mathematical value.
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There are 13
books on a shelf. 6 of these books are new.
(a) What is the ratio of used books to all books?
(b) What is the ratio of new books to used books?
The ratio of used books to all books is 7 : 13 and the ratio of new books to used books is 6 : 7
If there are 13 books on a shelf. 6 of these books are new.
(a) The ratio of used books to all books
Number of all books = 13
Number of used books = total no. of books - no. of new books
= 13 - 6
= 7
So, ratio of used books to all books
= no. of all books : no. of total books
= 7 : 13
Thus, the ratio of used books to all books = 7 : 13
(b) The ratio of new books to used books
Number of new books = 6
Number of used books = 7
So, the ratio of new books to used books
= no. of new books : no. of used books
= 6 : 7
Thus, the ratio of new books to used books = 6 : 7
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explain in your own words why it takes more to prove that quadrilaterals are similar
Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Explaining quadrilaterals?
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.
What is quadrilateral formula?
When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.
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The complete question is -
Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.
Find the perimeter and area of
The perimeter and area of the figure are 40.8 units and 110 square units respectively.
How to determine for the perimeter and area of the figure.From the question, we have the following parameters that can be used in our computation:
The figure
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²],
where d is the distance between the points (x₁, y₁) and (x₂, y₂).
So, we have
AB = √[(8-8)² + (9-2)²] = 7
BC = √[(3-8)² + (13-9)²] = 6.4
CD = √[(-3-3)² + (9-13)²] = 7.2
DE = √[(-3+3)² + (9-13)²] = 9
EA = √[(8+3)² + (2-0)²] = 11.2
DB = √[(8+3)² + (9-9)²] = 11
Perimeter = AB + BC + CD + DE + EA.
Perimeter = 7 + 6.4 + 7.2 + 9 + 11.2
Perimeter = 40.8 units.
The figure is observed to be a trapezium ABDE and a triangle BCD.
Triangle BCD have base length DB = 11 with height from C to DB equal to 4.
Trapezium ABDE have sides AB and DE parallel to each other, and height DB = 11.
area of triangle BCD = 1/2 × 11 × 4 = 22 square units
area of trapezium ABDE = 1/2 × (7 + 9) × 11 = 88 square units
Total area ABCDE = 22 + 88
Total area = 110 square units
Hence, the perimeter and area of the figure are 40.8 units and 54 square units respectively.
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2k + 36 = 6k - 12 thx!!
Answer:
k = 12
Step-by-step explanation:
Finding the unknown value:
To find the value of 'k', isolate k
First subtract 36 from both sides.2k + 36 = 6k - 12
2k = 6k - 12 - 36
2k = 6k - 48
Subtract 6k from both sides2k - 6k = -48
- 4k = -48
Now, divide both sides by (-4)k = -48 ÷ (-4)
k = 12
If a battery has a radius of 4 millimeters and a height of 32 millimeters, approximately what is the area of the surface to be covered by the label? Use 3.14 for and round to the nearest hundredth.
The area of the surface to be covered by the label = 904.32 mm²
We know that the formula for the surface area of cylinder is:
A = 2πrh + 2πr²
where r is the radius of the cylinder and h is the height of the cylinder
Here, the dimensions of the cylindrical battery:
radius r = 4 millimeters
height h = 32 millimeters
Using the above formula of surface area of cylider, the area of the surface to be covered by the label would be,
A = 2πrh + 2πr²
A = 2πr(h + r)
A = 2π × 4 × (32 + 4)
A = 2 × 3.14 × 4 × 36
A = 904.32 mm²
Therefore, the required area is 904.32 mm²
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The width of a rectangle is double the length. If the perimeter of the rectangle is 120 feet, find the length
Answer:
20
Step-by-step explanation:
lets say width is 2x and the length is x
2x+x+2x+x=120
6x=120
x=20
thus, your answer is 20
A car is purchased under the following conditions. There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.
If the customer paid $14 000, what was the original purchase price of the car before any of the discounts and taxes?
Please explain. p.s I know that the answer is $15 224, but I still need an explanation
thanks. :)
The original purchase price of the car before any of the discounts and taxes is,
⇒ $15,024
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.
Here, the customer paid $14 000.
Now, Let the original price = x
Hence, We can formulate;
⇒ x - (12% of x) - 5% of x + 10% of x = 14,000
⇒ x - 12x/100 - 5x/100 + 10x/100 = 14,000
⇒ (100x - 12x - 5x + 10x) / 100 = 14,000
⇒ 93x/100 = 14,000
⇒ 93x = 1400000
⇒ x = $15,024
Thus, The original purchase price of the car before any of the discounts and taxes is,
⇒ $15,024
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a new table needs to be added to the sports physical therapy database to track which sports the patients are playing. this data will be used to analyze the results of the therapies. assuming that many patients play multiple sports, how would you design the table?
To design the table, you could create a "Sports" table and a "Patient-Sport" table with the following fields:
Sports table: Patient-Sport table:
SportID (primary key) PatientID (foreign key)
SportName SportID (foreign key)
What do you mean by database?A database is a collection of organized data stored and retrieved electronically. It is designed to allow efficient storage, retrieval, manipulation, and management of large amounts of data. Databases can be used to store information such as text, numbers, images, and other media. The data in a database is typically organized into tables, which are made up of rows and columns. Each row represents a single record, and each column represents a field of information within that record. There are many different types of databases, including relational databases, NoSQL databases, and in-memory databases, and they are used in a wide range of applications, such as online retail, finance, healthcare, and more.
The Patient-Sport table is used to connect the patient to the sport they are playing. This allows for multiple sports to be assigned to a single patient. In this way, you can track the sports played by each patient, while still maintaining the relationships between the patient and their data in the other tables.
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Fill in the blanks below in order to justify
whether or not the mapping shown
represents a function.
Set A
7
3
6
Set B
The mapping diagram above
8
represents
since for each number
Set A (the output) there
are multiple mappings ◆
5
-3
a function
in
The mapping above represents a function, since each number in Set A is mapped to only one number in Set B.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For the relation in this problem, we have that:
Input of 7 is mapped to an output of 2.Input of 0 is mapped to an output of 2.Input of 8 is mapped to an output of -4.As there are no repeated inputs, the relation represents a function.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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There are 70 students in a speech contest yesterday 1/5 of them gave their speeches today 2/7 of the remaining students gave their speeches how many students still haven't got their speeches
Step-by-step explanation:
You would need to start by finding how many students is 1/5 of them
So to find this out you would take 70 and divided it by 5
So 70/5 = 14
Take 70 and subtract 14 to get 56
Next find what 1/7 is
So 56/7 = 8
But because it’s 2 sevenths take the 1/7 and multiply by 2
8 x 2 = 16
So
Take the 56 and subtract 16 to get 40
To find the fraction form it would be
40/70 students
Just simplify now
4/7
Step-by-step explanation:
day 1
70*1/5= 14
70-14 = 56
day 2
2/7 * 56= 16
16+14 = 30.
Remaining students = 70 - 30 = 40
Find the surface area of the prism.
22 cm
7.5 cm
5.5 cm
i'm to lazy to bored trying to do my work and I'm also very dumm
Calculate the slope based on the table below:
The slope of the points in this table is equal to 2.
How to calculate the slope based on the table?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (-2, -1).Points on y-axis = (-3, -1).Substituting the given points into the slope formula, we have the following;
Slope, m = (-1 + 3)/(-1 + 2)
Slope, m = 2/1
Slope, m = 2.
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WILL GIVE BRAINLIEST!! Give an example of a system of two linear equations in two variables with 0, 1, or infinitely many solutions. Explain how you can determine whether this system has 0, 1, or infinitely many solutions without graphing. What does this reveal about the relationship between the lines on the graph?
Write at least 150–300 words please
The solution of a system of equations can be determined by dividing the coefficients of variables.
What are system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Solution of system of equations :-
Let the two system of equations be
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
1) Unique solution or one solution :-
The solution of the system of equations will be unique when,
a₁ / a₂ ≠ b₁ / b₂
2) Infinite solutions :-
The solution of the system of equations will have infinitely many solutions when,
a₁ / a₂ = b₁ / b₂ = c₁ / c₂
3) No solution :-
The solution of the system of equations will have no solutions when,
a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂
Hence, the solution of a system of equations can be determined by dividing the coefficients of variables.
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Which among the following is the smallest 4- Digit number is divisible by 6,8 and 9
a} 2012 b}2160 c}2088 d}1008
Keisha bought 12 pounds of sugar for $7. How many pounds of sugar did she get per dollar?
Answer:
1.71 pounds of sugar per dollar.
Step-by-step explanation:
To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:
12 ÷ 7 = 1.71
So, Keisha got 1.71 pounds of sugar per dollar.
If you are on an island and there are already 375 inhabitants, and
for every footprint there is one eyeball, for every 32 pineapples there
are 40 ducks, for every 2 hands there is one inhabitant, for every
palm tree there are 12 pineapples, for every hand there is one
eyeball, for every lizard there are 4 footprints, for every 30 palm
trees there is one wave, for every 2 turtles there is 1 anchor, for
every palm tree there are 8 cacti, for every 120 anchors there is one
wave, for every 0.5 lizards there are 20 ducks, for every 20 turtles
there are 30 pineapples, for every 5 waves there are 3 canoes. How
many cacti are there on the island? Show your work!
Answer:
3000
Step-by-step explanation:
8 x 375 = 3000
8. f(x) = -x^4 + 2x²-x-2
Domain:
Range:
Rel. Maximum(s):
Rel. Minimum(s):
End Behavior: As x→∞, f(x)→
As x→→→∞0. f(x)→
Inc. Intervals:
Dec. Intervals:
Domain is all real numbers and Range is all real numbers less than or equal to -2.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x) = -x⁴+ 2x²-x-2
Domain is all real numbers.
Range is all real numbers less than or equal to -2.
Relative Maximum is the function does not have any relative maximums.
Relative Minimum(s): The function does not have any relative minimums.
End Behavior as x approaches infinity, f(x) approaches negative infinity. This can be seen by observing that the leading term in f(x),
-x⁴ grows much faster than the other terms as x increases, so the overall value of f(x) becomes more and more negative as x approaches infinity.
Hence, Domain is all real numbers and Range is all real numbers less than or equal to -2.
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Simplify the expression 12p-8p,4p(3-2)
The value of the expression is A = 4p ( 3 - 2 ) = 4p
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 12p - 8p be equation (1)
On simplifying the equation , we get
Taking the common factor as 4p in the expression , we get
A = 4p ( 3 - 2 )
On further simplification , we get
A = 4p
Therefore , the value of A is 4p
Hence , the expression simplified is 4p
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The __ of the __ between the mean of the data set and the individual numbers in the data set
(mean absolute deviation)
The missing words in the statement are mean and absolute deviation respectively.
What is mean absolute deviation (MAD)The mean absolute deviation (MAD) is a measure of the average magnitude of the differences between individual values in a data set and the mean of the data set. It is calculated by first finding the absolute value of the difference between each data point and the mean, summing these absolute values, and then dividing by the number of data points. The resulting value provides a measure of the "typical" or average deviation of individual data points from the mean, without considering the direction of the deviation (positive or negative). The mean absolute deviation is often used as a summary statistic for data that is not normally distributed or when the variance or standard deviation are not meaningful.
The mean of the absolute deviation between the mean of the data set and the individual numbers in the data set is referred to as the mean absolute deviation (MAD).
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The difference of the data between the mean of the data set and individual numbers in the data set is called the deviation.
What is mean absolute deviation?Mean Absolute Deviation (MAD) is a measure of the average distance between the values in a dataset and the mean of that data set. It is calculated by finding the absolute difference between each value and the mean, summing them, and dividing by the total number of values. MAD is commonly used as a way to describe the variability or dispersion of a set of data.
In other words, the mean absolute deviation (MAD) is the average distance between each data value and the mean of the data set.
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Fimd the explicit formula.
-4,-12,-36,-108
The explicit formula for the given geometric series will be [tex]a_n = -4(3)^{n-1}[/tex].
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.
Given that the geometric series is -4,-12,-36,-108. The formula for the nth term of the geometric progression will be written as:-
[tex]a_n = a_1(r)^{n-1}\\[/tex]
Here, r is the common ratio of the series. The value of the common ratio is r = -12 / -4 = 3.
The formula will be:-
[tex]a_n = a_1(r)^{n-1}\\[/tex]
[tex]a_n = -4(3)^{n-1}\\[/tex]
Therefore, the formula for the nth term will be [tex]a_n = -4(3)^{n-1}\\[/tex].
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Aled and Gareth went on holiday to France.
The total cost of the holiday was £660.
• Aled’s mother paid 1/3 of the total cost.
• Aled and Gareth shared the remaining cost in the ratio 1:9 .
Calculate how much each person paid towards the cost of the holiday.
Answer:
Aled's mother paid £220.
Aled paid £44.
Gareth paid £396.
Step-by-step explanation:
1-(1/3)= 2/3 [fraction of amt. Aled and Gareth paid]
£660×(2/3)= £440 [amt. Aled and Gareth paid]
total units= 1+9
= 10
10 units= £440
1 unit= £440÷10
= £44
9 units= £44×9
= £396
£660×(1/3)= £220
Can anyone do this math problem please?
Jeremy should choose Model A.
How to determine the model to chooseFrom the question, we have the following parameters:
The capacity of A is twice the backpackB, is 15 L more than his daypack. 18 + Model A = 28 + Model BThese mean that:
Model A = 2 * Backpack (x)
Model B = 15 + Backpack (x)
18 + Model A = 28 + Model B
As equations, we have
A = 2x
B = 15 + x
18 + A = 28 + B
So, we have
18 + 2x = 28 + 15 + x
Evaluate
x = 25
So, we have
A = 2 * 25 = 50
B = 15 + 25 = 40
Hence, he should choose model A
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Triangle HIJ is similar to triangle KLM. Find the measure of side MK. Round your answer to the nearest tenth
The measure of side MK is 103.3.
To find the length of side MK, we need to use the concept of similar triangles. Similar triangles have the same shape but may be different sizes. In this case, the ratio of corresponding sides is the same.
Now, we can use the fact that the ratio of corresponding sides is the same for both triangles:
JI/JH = ML/MK
16/29 = 57/x
cross-multiply the expression, we get
16x = 57 × 29
x = (57 × 29)/16
x = 103.3125
Therefore the measure of side MK is 103.3 to the nearest tenth place.
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