The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.
The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.
So, in the equation y = rx, the value of r is the constant of proportionality.
In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.
For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.
In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.
In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.
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The planet Neptune orbits the Sun. Its orbital radius is 30.1 (AU)
Assuming Neptune's orbit is circular, what is the distance it travels in a single orbit around the Sun?
Give your answer in terms of π
in a sequence the first term is 4 and the common difference is 3
Answer:a=3, d=common difference=3, a2=7, a3=9
Step-by-step explanation:
firstly we have given a,d (using the arithmetic progression formula)
( an=a+(n-1) )
so we have made a sequence a2=a+d=7
a3=a+2d=9
Which residual plot shows that the line of best fit is a good model?
A residual plot that shows clear patterns or trends in the residuals suggests that the line of best fit is not a good model.
Here are some characteristics of a residual plot that suggest that the line of best fit is a poor model,
The residuals show a clear pattern or trend, such as a curve or a U-shape.
The residuals are not evenly distributed above and below zero.
There are one or more outliers or extreme values that stand out from the rest of the data.
The variability of the residuals changes across the range of the predictor variable.
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Compact fluorescent light (CFL) bulbs reduce energy waste. The amount of energy
waste that is reduced each day in a certain community can be estimated by -b² + 8b
where b is the number of bulbs. Divide by b to find the average amount of energy
saved per CFL bulb.
A, B & C form the vertices of a triangle, where ∠CAB = 90°.AB = 10.5 m and AC = 5.2 m.
Evaluate ∠CBA, giving your answer rounded to 3 SF.
Answer: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of side BC can be found using the Pythagorean Theorem:
BC^2 = AB^2 + AC^2
BC^2 = 10.5^2 + 5.2^2
BC^2 = 110.25 + 27.04
BC^2 = 137.29
BC = √137.29
BC ≈ 11.68 m
Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:
∠CBA = cos^-1 (BC / AB)
∠CBA = cos^-1 (11.68 / 10.5)
∠CBA ≈ 68.194°
Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.
Step-by-step explanation:
what is the missing
equivalent ratio of 4 : 2 = 10: _
Answer:
4 : 2 = 10 : 5.
Step-by-step explanation:
Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)
How does the distance change during the last section of tom’s journey? What does this mean? Explain your reasoning
The distance is decreasing with time meaning that the object is going back to the starting point.
What does it mean when distance decreases with time?When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.
Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.
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Linda wants new carpeting for her bedroom her bedroom is a 75m by 50m rectangle if carpeting cost AED 12 per square meters how much will it cost to lay carpet for her entire bedroom?
(please answer as soon as possible i need this answer) thank you
If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.
Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:
Area = length x width = 75 meters x 50 meters = 3750 square meters
Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:
Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter
Multiplying the area by the cost per square meter gives us:
Total cost = AED 45,000
Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
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in
2. The park charges $24 to enter and
$0.45 per ticket. Write an algebraic
expression to represent the total
amount spent by a guest.
Answer:
C = $24 + 0.45x
Step-by-step explanation:
If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is
C = $24 + 0.45x
POINTS UP FOR GRABS!!!!
The ordinary numbers for the expressions will be
a. 3.25*10⁴ = 32500
b. 6.04*10⁻³= 0.00604
c. 2400000 = 2.4*10⁶
d. 0.00147 = 1.47*10⁻³
What are expressions exactly?
In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.
Now,
Given expressions/Numbers are a. 3.25*10⁴ then ordinary form is
3.25*10000
=32500
b. 6.04*10⁻³ then ordinary numbers is
=6.04/1000
=0.00604
c. 2400000 then standard from is
=2.4*1000000
=2.4*10⁶
d. 0.00147 then standard form is
=1.47/1000
=1.47*10⁻3
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6. A group of students decide to chip in $2.50
each to buy a gift for their teachers. If
5 more students join the group, they each
would have to pay $0.50 less. How much do
they plan to spend on the gift?
Let's call the original number of students in the group "n". Each student contributed $2.50, so the total amount the original group of students collected is $2.50 * n.
When 5 more students join the group, the new total number of students is n + 5, and each student contributes $2.50 - $0.50 = $2.00. So the total amount the new group collects is $2.00 * (n + 5) = $2.00n + $10.
Since the total amount collected remains the same, we can set the two expressions for the total amount equal to each other:
$2.50n = $2.00n + $10
Solving for n, we have:
$0.50n = $10
n = 20
So, there were originally 20 students in the group. To find out how much they plan to spend on the gift, we can multiply the original number of students by the original contribution amount:
$2.50 * 20 = $50.00
Therefore, the students plan to spend $50.00 on the gift.
Find the sum of each infinite geo sequence WILL MARK BRANLIEST
48, 24, 12, ...
Answer:
S∞ = 96
Step-by-step explanation:
What is the perimeter of the parallelogram?
A 12
B 15
C 30
D 44
Answer:
C. P = 30
Step-by-step explanation:
Parallelogram opposite (or parallel) sides are equal,
so:
2x = x + 2
5y - 9 = 2y + 3
For x:
2x = x + 2
2x - x = 2
x = 2
For y:
5y - 9 = 2y + 3
5y - 2y = 3 + 9
3y = 12
y = 4
the smallest sides are equal 2x and x + 2 => 2 * 2 = 4
the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11
P = 2 * (a + b)
P = 2 * (4 + 11)
P = 2 * 15
P = 30
5. Pilihan ganda5 menit1 ptQ. An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle? Leave your answer in radical form.Pilihan jawaban30√3 m10√3 m5√3 m30 m
If an equilateral triangle has an altitude of 15 meters, then the perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex] meters
The altitude of the equilateral triangle = 15 meters
The equilateral triangle is the triangle with equal side. The interior angle of the equilateral triangle will be 60 degrees. Number of vertices and edges will be three . The line of symmetry is 3
The altitude of of the equilateral triangle h = [tex]\sqrt{3}[/tex]a /2
Where h is the altitude of the equilateral triangle
a is the side of the equilateral triangle
Then the equation will become
15 = [tex]\sqrt{3}[/tex] a /2
[tex]\sqrt{3}[/tex]a = 15 × 2
Multiply the terms
[tex]\sqrt{3}[/tex]a = 30
Move [tex]\sqrt{3}[/tex] to the right hand side of the equation
a = 30 / [tex]\sqrt{3}[/tex]
a = 10[tex]\sqrt{3}[/tex] meters
The perimeter of the equilateral triangle = 3 × 10[tex]\sqrt{3}[/tex]
= 30[tex]\sqrt{3}[/tex] meters
Therefore, perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex]
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You type 170 words per minute. How many minutes does it take you to type 3400 words?
Answer:
Step-by-step explanation:
3400/170 = 20 minutes.
Answer:
20 minutes
Step-by-step explanation:
3400 words / 170 wpm
20 minutes
What is the probability of choosing a green in 4 red marbles, 10 blue marbles, 7 green marbles, 6 yellow marbles
What is the probability of me choosing a green???
simplify (4x+5y)(2x-3y)+3xy
Answer: 8x^2 + xy - 15y^2
Step-by-step explanation:
first do the FOIL method than add 3xy to the equation after
Answer:
[tex]8x^2+xy-15y^2[/tex]
Step-by-step explanation:
[tex](4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2[/tex]
A fruit Juice blend is made by mixing the juice of oranges and apples in the ratio 7:5 If 168 litres of orange juice is used How much litres of Apple juice must be used ?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:
168 × 0.714285714 = 120Why do we multiply by 0.714285714?We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.
Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.
what is 13 over 16 as a decimal rounded to the nearest tenth
13/16 as a decimal rounded to the nearest tenth is 0.8.
A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.
To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).
If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.
Therefore, we leave the tenths place as is, and the final answer is 0.8.
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ABCD is a kite with AB = BC and AD = DC = AC, the size of
The size of angle BCA is 45 degrees
What is Kite figure?A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.
Where the two uneven sides meet, the two angles are equal. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.
Given:
From the Figure we can see that
AB = BC and AD = DC = AC
and, ABC = 90 degrees
Now, In triangle ABC using Angle sum Property
A + B + C = 180
So, A + 90 + C = 180
A + C = 90
As, AB = BC
Then, 2C = 90
C = 45
Hence, the angle is 45 degrees
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The Question attached here seems to be incomplete/ inappropriate. The complete Question is:
ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle BCA
the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months. oil costs $0.45 per gallon and increases at a rate of $0.05 every six months. how many years will it take for them to be equal in price?
The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.
To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.
We can start with the initial prices and solve for the time when they are equal:
$2.27 - 0.03t = 0.45 + 0.05t
where t represents the time in years.
Solving for t, we get:
$2.27 - 0.03t = 0.45 + 0.05t
$1.82 = 0.08t
t = 22.5
Since t is in months, we have to divide by 12 to convert it to years:
t = 22.5 / 12 = 1.875
So the price of gasoline and oil will be equal in price after approximately 4 years.
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Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6} if you roll the die once, calculte the following probabilities. Write you answers in fraction form and in lowest terms (e. G. 1/4) a) the probability of getting a 6 is. B) the probability of getting an even number is. C) the probability of getting a number greater than 2 is
The probability for the sample space of a fair die rolled out {1, 2, 3, 4, 5, 6} with different conditions are :
a. Probability of getting 6 = 1/6
b. Probability of an even number on a die = 1/2
c. Probability of number more than 2 = 2/3.
Sample space is equal to {1, 2, 3, 4, 5, 6}
Number of times die rolled out = only once.
Total number of outcomes = 6
Probability = ( Number of favourable outcomes ) / ( Total outcomes )
Required probability in fraction form with lowest terms:
a. Probability of getting 6
Favourable outcomes ={ 6 }
Number of favourable outcomes = 1
Probability of getting 6 = 1 / 6
b. Probability of getting an even number
Favourable outcomes = { 2, 4, 6 }
Number of favourable outcomes = 3
Probability = 3 / 6
= 1 / 2
c. Probability of getting number greater than 2
Favourable outcomes = { 3, 4, 5, 6 }
Number of favourable outcomes = 4
Probability = 4 / 6
= 2 / 3
Therefore, the required probability as per the mentioned conditions are:
a. Probability of getting 6 = 1/6
b. Probability of even number = 1/2
c. Probability of number greater than 2 = 2/3.
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Write an exponential function in the form y=ab x that goes through points ( 0 , 12 ) and ( 2 , 300 )
The exponential function that goes through points (0,12) and (2,300) is [tex]y = 12(5)^x[/tex].
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The coordinate points are (0,12) and (2,300).
The exponential function has form [tex]y=ab^x[/tex].
So, the x values are 0,2 and y values are 12,300.
Substitute the first x and y values in the equation -
[tex]12=ab^0[/tex]
a = 12 ...... equation (1)
Substitute the second x and y values in the equation -
300 = ab² ...... equation (2)
Substitute the value of equation (1) in equation (2) -
300 = (12)b²
b² = 300 / 12
b² = 25
b = √25
b = 5
Substitute the values of a and b in exponential function -
[tex]y = 12(5)^x[/tex]
Therefore, the exponential function is [tex]y = 12(5)^x[/tex].
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selecting christmas presents if a person can select presents from presents under a christmas tree, how many different combinations are there?
Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations
When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.
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Sophie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $127 for parts. The total was $227. Write and solve an equation which can be used to determine
x, the cost of the labor per hour.
Answer:
Step-by-step explanation:
(227-127)/4=x
"/" means divide.
Multiply out the brackets and then simplify: 12(-10x+5y)
Eric owes his brother $17. He recently got some money for his birthday and plans to use some of it to pay his brother back. Use the variable to represent the amount of money Eric got for his birthday, and use this variable to write an expression for the amount of money Eric will have left after he pays his brother back. Choose the expression for the amount of money Eric has after he pays his brother back.
A. 17-x
B. x-17
C. 17x
D. x+17
The expression for the amount of money Eric has after he pays his brother back is x- 17.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given:
Eric owes his brother $17.
let x be the amount of money Eric got for his birthday.
If Eric gave the money back to his brother then he left with
= x - 17
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Pls answer! Lots of points! Question down below!
The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.
What is a rectangle?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
The number of lines along the length is 11.
The length of the frame is 10 units.
The number of lines along the width is 8.
The width of the frame is 7 units
The dimension of an object is length × width.
The dimension of the frame is 10 units × 7 units.
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80% of a number is x. What is 100% of the number? Assume x>0
100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.
To convert a percentage to a decimal, divide the percentage by 100.
So, if 80% of the number is x, then:
x ÷ 0.8 = the number
In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).
Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.
So, 100% of the number is:
the number x ÷ 0.8 × 1 = the number
In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.
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Electric utility poles in the form of right cylinders are made out of wood that costs $25.81 per cubic foot. Calculate the cost of a utility pole with a radius of 0.5 ft and a height of 25 ft. Round your answer to the nearest cent.
The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:
π * 0.5^2 * 25 = 19.63 cubic feet
So the cost of the utility pole would be 19.63 * $25.81 = $509.24
Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.
