Yes, the statement is true. If a proportional relation has the point (1, r), then r is the unit rate.
Is the statement true or false?Here we have the following statement:
"The point (1, r) on the graph of a proportional relationship shows the unit rate r."
First, remember that a proportional relationship between two variables x and y can be written as:
y = k*x
There k is what we call the constant of proportionality or the unit rate.
If we evaluate that equation in x = 1, we will get:
y = k*1
y = k
Then we have the point (1, k).
In this case, we know that our proportional relation has the point (1, r), comparing this with the case above, we can see that r is the unit rate of the proportional relation.
So the statement is true.
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Brian has 64 flowers for a big party decoration. In addition, he is considering buying flower arrangements that have 18 flowers each. All of the arrangements cost the same. Brian can buy up to 5 arrangements given the amount of money he has. Let x represents the number of flower arrangements Brian buys. Write a function rule to describe how many flowers Brian will have based on the number of arrangements he buys. Find a reasonable range for the function.
The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].
Let the number of flowers which is to be calculated be x,
now we know that she already have 64 flowers and that each arrangement will have 18 flowers.
Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.
Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes [0,5] .
To find the range we will put the value of domain in the given function.
when x = 0 ,
f(0) = 64
when x = 5,
f(5) = 154
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Factor the quadratic expression
4a²+27a+18
The factors of given quadratic expression are (4a+3) and (a+6).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given quadratic expression is 4a²+27a+18.
By splitting middle term method, we get
4a²+3a+24a+18
= a(4a+3)+6(4a+3)
= (4a+3)(a+6)
Therefore, the factors of given quadratic expression are (4a+3) and (a+6).
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PLEASE HELP!
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350-pound delivery to contain? Round your answer to the nearest tenth of a pound.
There are 23.33 pounds of defective nails should the manager expect the 350-pound delivery to contain.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails.
And, The manager found that 0.3 pounds of nails in the sample were defective.
Since, The manager found that 0.3 pounds of nails in the sample were defective.
Hence, Amount of pounds of defective nails should the manager expect the 350-pound delivery to contain is,
⇒ 350 × 0.3 / 4.5
⇒ 23.33 pounds
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Find the x-intercept and y-intercept
from the following linear equation:
X + 4y = -56
x - intercept ()
y - intercept ()
Answer:
x-intercept: (-56, 0)
y-intercept: (0, -14)
Step-by-step explanation:
The x-intercept is the point at which the line crosses the x-axis, so when y=0. To find the x-intercept, substitute y=0 into the given equation:
[tex]\begin{aligned}y=0\implies x+4(0)&=-56\\x+0&=-56\\x&=-56\end{aligned}[/tex]
Therefore, the x-intercept of the given linear equation is:
(-56, 0)The y-intercept is the point at which the line crosses the y-axis, so when x=0. To find the y-intercept, substitute x=0 into the given equation:
[tex]\begin{aligned}x=0\implies 0+4y&=-56\\4y&=-56\\y&=\dfrac{-56}{4}\\y&=-14\end{aligned}[/tex]
Therefore, the y-intercept of the given linear equation is:
(0, -14)Write an inequality with the solution x > or equal to 4. The inequality should have the variable on both sides, a fractional coefficient of the variable on the left side, and a fraction anywhere on the right side.
The inequality equation ( x ≥ 4 ) is given as ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x ≥ 4 be equation (1)
On simplifying the equation , we get
Divide by 4 on both sides of the equation , we get
( x / 4 ) ≥ 1
Adding x on both sides of the equation , we get
x + ( x/4 ) ≥ 1 + x
Now , adding ( 1/4 ) on both sides of the equation , we get
x + ( 1/4 ) + ( x/4 ) ≥ 1 + x + ( 1/4 )
On simplifying the equation , we get
( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Therefore , the value of A is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Hence , the inequality equation is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
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One angle of a triangle meaure 140°. The other two angle are in a ratio of 3:5. What are the meaure of thoe two angle
One angle of a triangle measure 140°. The other two angles are in a ratio of 3:5.The smaller angle would measure 84°, and the larger angle would measure 56°. This can be found through the use of basic trigonometry.
A triangle is a three-sided polygon with three angles that add up to 180°. Since one of the angles is already known, the remaining two angles can be calculated by subtracting 140° from 180°, which equals 40°. This 40° can then be divided by the ratio 3:5, which is 8° and 32°.
If 8° is the smaller angle, then 32° must be the larger angle. To convert 8° and 32° to the final answer of 84° and 56°, 8° must be multiplied by 10 and 32° must be multiplied by 5. This gives a total of 84° and 56° for the other two angles.
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One angle of a triangle measures 140°. The other two angles are in a ratio of 3:5. What are the measures of that two angles?
What is the domain of √?
The domain of √ (square root) is all non-negative real numbers.
The domain of a function represents the set of all input values that can be used in the function without resulting in an undefined or meaningless output.
The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number.
This is because in order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. Therefore, any real number greater than or equal to zero can be used as the input for the square root function, making its domain all non-negative real numbers.
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Solve this problem?
step by step
The value of x is 9.32 after solving using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagram has 4 corners namely - A, B, C and D.
Draw a perpendicular through B.
The intersecting point at line AD is named as E.
It can be seen in figure that EDCB is a rectangle and falls under the category of parallelogram.
So, angle ADC = angle DEB = angle AEB = 90° .
Now, side BC = ED = 5.
So, side AE = 18 - 5 = 13.
Here, it can be seen that triangle ABE is a right-angled triangle.
So, to get the measurement of side BE, apply the Pythagoras theorem -
c^2 = a^2 + b^2
Where, a is perpendicular, b is base and c is hypotenuse.
So, according to the diagram -
(16)^2 = (13)^2 - (BE)^2
(BE)^2 = (16)^2 - (13)^2
(BE)^2 = 256 - 169
(BE)^2 = [tex]\sqrt{87}[/tex]
(BE)^2 = 9.32
Now, as EDCB is a rectangle so, side BE = side CD.
Therefore, the value for side CD = x = 9.32.
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Write the ratio of the first measurement to the second measurement. Compare in inches.
Answer:
when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch
Sydney says that if all of the side lengths of a cube are doubled, the volume of the cube will also double. Is she correct? Explain.
Answer:
no, it's not correct
Step-by-step explanation:
volume or the cube = L³
so if we doubled the side lengths
They would be 2L
then the volume= (2L)³ = 8L³
so that would make the volume 8 times the first value not double
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497
The probability is 0.4444.
What is probability?Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.
The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.
For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.
Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.
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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).
PLEASE SOMEONE ANSWER THIS ASAP I NEED YOUR HELP:
PQR is a non-right-angled triangle. QR is 5.1cm, RP is 7.8cm and PQ is 6.2cm. Find the area of PQR
Using Heron's formula the area of the triangle is 15.78cm²
What is Heron's FormulaHeron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:
Area = √s(s-a)(s-b)(s-c)
Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:
s = (a + b + c)/2
Let's define the variables as;
a = 5.1b = 7.8c = 6.2s = (5.1 + 7.8 + 6.2) / 2
s = 9.55cm
The area can be calculated as;
A = √s(s - a)(s - b)(s - c)
A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)
A = 15.78cm²
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A recipe for 3 people uses 150 g of flour. How much flour is needed to
make the same recipe for 6 people? Give your answer in grams (g).
600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.
Given that a recipe for 3 people uses 150 g of flour.
We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.
So if the number of people will increase so the quantity of flour will be needed more.
The flour needed to make the recipe for 1 people is = 150/3 = 50 g.
The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.
Hence 600 g flour is needed to make the same recipe for 6 people.
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Q 23
Regina writes the expression y + 9
Which expression is equivalent to the one Regina writes?
A) (9. 3 • 4) + y
B 9+ y (3 = 4)
© (y + 9)(3 = 4)
None of these
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression.
The expression written by Regina is y + 9, which means adding nine to some number y. None of the given expressions are equivalent to this expression. In order for two expressions to be equivalent, they must have the same value when the same values are plugged into them. For example, if y is equal to 5, then y + 9 would be equal to
14, while (9. 3 • 4) + y
would be equal to
27, (9+ y (3 = 4))
would be equal to 17, and
(y + 9)(3 = 4)
would be equal to 21. As these values are not equal, the given expressions are not equivalent to the one written by Regina.
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b) Sita had.50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get?
Answer:
4 sweets each
Step-by-step explanation:
50 sweets to begin with and eats 10 , so 50 - 10 = 40 left
she then gives 8 to her brother , leaving 40 - 8 = 32 sweets
she then shares 32 equally among her 8 friends , so
32 ÷ 8 = 4
that is each friend got 4 sweets
Simplify the following: (3 + 10i) - (-9 - 4i)
*PLEASE INCLUDE EXPLANATION
Answer:
12+14i
Step-by-step explanation:
For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.
You will get 9+4i
Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.
12+14i
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This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A
BCDF
Frequency
5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p=[?]
Enter a decimal rounded to the nearest hundredth.
Answer:
85.71% probability
Step-by-step explanation:
30 of 35 of the students are in abc range so take 35/100% or 0.35 and go 30/0.35 and you get 85.71%
20. Kim works on commission. If her monthly earnings for the first
four months of the year were $1625, $960, $1235, and $1420,
estimate what her annual earnings will be.
A) $14,240 B) $15,390 C) $15,720 D) $16,150 E) $16,280
O A
OB
OC
OD
ΟΕ
Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720
What is statistics?Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.
What is mean of the data?The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.
salary for four months = $1625, $960, $1235, and $1420.
Average = ($1625 + $960+ $1235+$1420) /4 = $1310
for whole year = $1310 * 12 = $15,720
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Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4. 20.
Write and solve an equation to find the original price of the charging cord, x
The equation to find the original price of the charging chord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
Let the price of the phone case is x.
And the price of the charging cord is y.
Discounted price for phone case: 15% of x = 0.15x
Discounted price for charging cord = 0.15y
Now, according to the question, the total discount is $4. 20
⇒0.15x + 0.15y = 4.20
⇒0.15 * 18 + 0.15y = 4.20
⇒2.7 + 0.15y = 4.20
⇒0.15y = 4.2 - 2.7
⇒y = 1.5/0.15
⇒y = $10
Therefore the equation to find the original price of the cord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.
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What is the difference between a problem and an algorithm?
A problem is just a function or even a mapping of inputs to outputs. An algorithm is a recipe for solving a problem with concrete and unambiguous steps.
What is algorithm?In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions used to solve a class of specific problems or perform a computation.
Algorithms are data calculation and processing specifications. More advanced algorithms can use conditionals to divert code execution through various paths (referred to as automated decision-making) & deduce valid inferences (referred to as automated reasoning), eventually achieving automation.
Alan Turing used metaphorical terms like "memory", "search," and "stimulus" to describe machines.
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A grocery store has increased its prices over time. The price per pound of apples in 2016 was $0.45. Today, the price per pound of apples is $0.85.
What is the equation of the line that would represent the price increase per pound of apples over time?
Answer:
C = 0.06x + 0.45
Step-by-step explanation:
Today is 2023
So, from 2016 to 2023, it has been 7 years.
0.85 - 0.45 = $0.40
So, $0.40 is the increase in 7 years
0.40 / 7 = $0.06
So, $0.06 is the change per year
Let C represent the total cost and x represent the number of years and we have
C= 0.06x + 0.45
253 x 804 =
Solve by using standard algorithms
Answer:
203412
Step-by-step explanation:
253
*804
___
16
40
32
20
12
______
203412
This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.
slope intercept form of y + 6 = (x - 4)
3.) In a proportional relationship, y=2 when x = 8. Which of the following equations would describe this relationship? (1) y=1/4x (2) y = 4x (3) y=x-6 (4) y =1/2x-2
The correct option is y=1/4x.Because it holds the directly proportional relationships.
What is directly proportional?Two values x and y are said to be directly proportional to each other when the ratio x:y always remains the same. Directly proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.
How do you find if an equation is a proportional relationship?A relationship is proportional if each pair of data values are related in the same way by multiplying by a factor. You can recognize a proportional relationship by looking at data.When two quantities x and y are in direct proportion then they are written as x ∝ y. Symbol “∝” stands for 'is proportional to'.
NOW we find
according to directly proportion
y∝x
y=kx
y/x=k
2/8 =k
1/4 =k
Now we get
y = 1/4x
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Kylie ran 7/10 of a mile and walked 2/5 of a mile. How much farther did Kylie run than walk?
Write your answer as a fraction or as a whole or mixed number.
The farther distance run by Kylie is 3 /10 miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kylie ran 7/10 of a mile and walked 2/5 of a mile. The distance will be calculated as,
Distance = ( 7/10 ) - ( 2 / 5)
Distance = ( 7 - 4 ) / 10
Distance = 3 / 10 miles
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5)48 I need help I suck at math
On solving the question resultant answer from the given data we have algebraic expression 5/48 could be 0.10
what is an algebraic expression ?Algebraic expression can be defined as the combination of constants , variables and operators. Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
So, the given expression , 5/48
5/48 = 0.10
The resultant answer from the given expression 5/48 could be 0.10
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The correct question is -
Solve the equation.
p= −6p=48
Please help I suck at math
I need help on these questions. They confuse me.
The graphic solution for each system of equations is given as follows:
20. (5/3, 28/3).
21. (0.205, 3.846).
22. (-1/2, -5/2).
23. (-4.615, 7.462).
How to solve a system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.
For this problem, the systems are composed by functions of the first degree, hence they are linear functions.
For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.
Each system is traced on a different color, as follows:
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How to do elimination with 3 equations?
Elimination is a method of solving a system of equations using addition or subtraction to eliminate one of the variables.
Here we will use the elimination method to solve a system of three equations with three variables.
Let's say we have three equations with three variables x, y and z.
Equation 1: ax + by + cz = d
Equation 2: ex + fy + gz = h
Equation 3: ix + jy + kz = l
We will start by multiplying the first equation by a number that will make the coefficients of y in the two equations the same.
Let's say we choose to multiply the first equation by -f, so that we get:
-fax -fby -fcz = -fd
Now we add the two equations to eliminate y:
ax + by + cz + (-fax -fby -fcz) = d -fd
ax -fax + by -fby + cz -fcz = d -fd
(a -f)x + (b -f)y + (c -f)z = d -fd
Now we can multiply the second equation by a number that will make the coefficients of z in the two equations the same. Let's say we choose to multiply the second equation by -k, so that we get:
-kex -kfy -kgz = -kh
Now we add the two equations to eliminate z:
(a -f)x + (b -f)y + (c -f)z + (-kex -kfy -kgz) = d -fd -kh
(a -f)x + (b -f)y + (c -f)z -kex -kfy -kgz = d -fd -kh
(a -f -k)x + (b -f -k)y = d -fd -kh
We can now solve this equation for x:
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
Now we can substitute this expression for x in any of the original equations and solve for y:
Let's choose to substitute in the first equation:
ax + by + cz = d
(d -fd -kh - (b -f -k)y) / (a -f -k) + by + cz = d
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
Now we can substitute this expression for y in any of the original equations and solve for z:
Let's choose to substitute in the second equation:
ex + fy + gz = h
e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) + gz = h
gz = h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
Now we have
x = (d -fd -kh - (b -f -k)y) / (a -f -k)
y = (d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k) -cz) / (b -f -k)
z = (h -e(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k)) -f(d -fd -kh - (a -f -k)(d -fd -kh) / (b -f -k))) / g
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Williamston Daily is a new daily newspaper. When they first started printing three years ago they had 5900 home delivery subscribers. The number of subscribers increases by 66 every month. Write an equation that expresses the number of subscribers B in terms of n, the number of months the paper has been printed.a.B
this is a question of set of equations and solution is as follows,
Williamston Daily newspaper started printing newspaper.
Three years ago they had 5900 subscribers.
every month there is an increase of 66 new subscribers.
n is the number of months the paper has been printed.
so, the linear model will be
B= early subscriber + number of month × increments
B= 5900 + n × 66
B= 66 n + 5900
Example - subscribers after 3 months,
n = 3
= 66 x 3 +5900
= 198 + 5900
= 6000
set of equations
A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Linear equations
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
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a salesman goes to Murano and buys three dozen vases paying €16.25 each. During transport if they break me 9. How much did each remaining vase sell for if he earned €360
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
what is unitary method ?
The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
A salesperson purchases three dozen vases (12 * 3 = 36),
at a cost of 36 * €16.25 (or $585),
with seventeen remaining.
The cost of selling each remaining vase is € 585 / 17
= € 34.41.
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
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