The explicit rule for the remaining train sets after 'n' months is represented by the formula T(n) = 35 - 3n, where T(n) is the total number of train sets, and 'n' is the number of months.
Explanation:The explicit rule for the number of train sets a store has after ‘n’ months, given that the store starts with 35 train sets and sells 3 each month, can be represented by a linear equation. The initial amount of train sets is the starting point, and the number of sets sold each month is the rate of change.
The explicit rule for the number of train sets the store has after 'n' months can be represented by the linear function:
\[ T(n) = 35 - 3n \]
Here, \( T(n) \) represents the number of train sets after 'n' months, 35 is the initial number of train sets, and 3n represents the number of train sets sold each month. The negative coefficient (-3) indicates the decrease in the number of train sets each month. By plugging in different values for 'n', you can determine the number of train sets the store will have at any given month.
This is reflected in the equation:
T(n) = 35 - 3n
where T(n) represents the total number of train sets after n months, and n is the number of months that have passed.
What is the domain and range of f(x)=3x?
The required domain and range of the f(x) = 3x is (-∞, +∞) and (-∞, +∞) respectively.
What is a domain?The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
The function f(x) = 3x is a linear function where the output (the range) is directly proportional to the input (the domain).
The domain of this function is the set of all real numbers because we can substitute any real number for x and get a valid output.
The range of the function is also the set of all real numbers because we can get any real number as the output by multiplying a real number by 3. Therefore, the range of the function is also all real numbers.
In interval notation, we can represent the domain and range as follows,
Domain: (-∞, +∞)
Range: (-∞, +∞)
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A number, one-third of that number , and one-fourth of that number are added. The result is 19 what is the original number
Graph the ellipse with equation x squared divided by nine plus y squared divided by sixteen = 1
Here is the picture of the answer above
The Sanders family and the Wright family each used their sprinklers last summer. The Sanders family's sprinkler was used for 20 hours. The Wright family's sprinkler was used for 35 hours. There was a combined total output of 1025L of water. What was the water output rate for each sprinkler if the sum of the two rates was 40L per hour?
The water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
Let the water output rate as "x" liters per hour and the water output rate for the Wright family's sprinkler as "y" liters per hour.
Given that the combined total output of water from both sprinklers was 1025L, we can set up the following equation:
20x + 35y = 1025
We also know that the sum of the two rates is 40L per hour:
x + y = 40
x = 40 - y
Substituting this value of x into the first equation:
20(40 - y) + 35y = 1025
800 - 20y + 35y = 1025
15y = 225
y = 15
Substituting this value of y back into the second equation:
x + 15 = 40
x = 25
Therefore, the water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
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To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 6% of $3700. How much will she pay?
Twenty-seven minus 1.5 of a number (x) is not more than 36. What is the number?
The school theater department made $2142 and the department sold the same number of tickets each night and each ticket cost $7. How many tickets did the theater department sell each night?
You should get your answer of 306 :)
[tex]\sqrt[7]{2142}[/tex]
^online division .-.
Translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width
The required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
Given that,
To translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width."
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here, the given string, “the perimeter of a rectangle is equal to 2 times the length plus twice the width" can be translated in the mathematical form is,
Perimeter = 2 * length + 2 * width.
Thus, the required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
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A bicycle shop advertised all mountain bikes were priced at 1/4 discount.
What is the constant of proportionality in the equation y = 2.5x?
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]
where
k is the constant of proportionality
In this problem we have
[tex]y=2.5x[/tex]
so
the constant of proportionality k is equal to
[tex]k=2.5[/tex]
therefore
the answer is
[tex]k=2.5[/tex]
The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]
Further explanation:
The relation is defined as the relationship between the input values and output values.
The x coordinates are the domain of the function and the y coordinates are the range of the function.
Given:
The equation is [tex]y = 2.5x.[/tex]
Explanation:
The proportionality equation can be expressed as follows,
[tex]y \propto x[/tex]
The value of [tex]y[/tex] changes as [tex]x[/tex] changes. If the value of [tex]x[/tex] increases then the value of y is also increasing.
The equation can be expressed as follows,
[tex]y = kx[/tex]
The inversely proportional relationship can be expressed as,
[tex]y \propto \dfrac{1}{x}[/tex]
Here, [tex]k[/tex] is the proportionality constant.
The given equation is [tex]y = 2.5x.[/tex]
The y is the independent variable and [tex]x[/tex] is the dependent variable.
The proportionality constant is 2.5.
The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]
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3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Ratio and proportion
Keywords: proportional, directly proportional, constant, proportionality equation, y=0.41x, constant of proportionality.
A friend is planning a trip to Alaska. He purchased a coat that is recommended for outdoor temperatures from −15°F−15°F negative 15 degrees cap f to 45°F
The question is about the temperature range of a coat and its ability to withstand extreme temperatures.
Explanation:The subject of this question is Physics, as it involves understanding the temperature range of a coat and its ability to withstand extreme temperatures.
Given that the coat is recommended for temperatures from -15°F to 45°F, it means that the coat is designed to provide sufficient insulation and protection within this temperature range. The negative symbol in -15°F indicates that it is below freezing point.
This suggests that the coat is designed to keep the wearer warm in sub-freezing temperatures, down to -15°F, and up to 45°F. It is important to note that the recommended temperature range may vary depending on individual tolerance, activity level, and wind chill factors.
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A normal distribution has a mean of µ = 100 with σ = 20. if one score is randomly selected from this distribution, what is the probability that the score will have a value between x = 90 and x = 120?
The table shows the amount of money in your bank account over a period of 5 weeks. The account does not pay interest. You plan to keep saving at the same rate until you have $650 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?
Answer:
35*n+100=650
Step-by-step explanation:
I got the question right on TTM
passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?
Answer:
Equation of line , 5x + 3y = 0
Step-by-step explanation:
The slope of a line passing through points (x₁,y₁) and (x₂,y₂) is given by [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here points are given by (-3,0) and (-6,5)
Slope[tex]=\frac{5-0}{(-6)-(-3)}=\frac{-5}{3}[/tex]
The slope of parallel lines are same. So slope of required line [tex]=\frac{-5}{3}[/tex]
Equation of a line with slope m passing through origin is given by
y =mx
So equation of line, [tex]y=\frac{-5}{3}x\\\\3y=-5x\\\\5x+3y=0[/tex]
Equation of line , 5x + 3y = 0
Answer: -5x -3y = 0
Step-by-step explanation:
took on edmentum/plato and got it right. enjoy :)
5/8 of the 64 musicians in a music contest are guitarist. Some of the guitarist play jazz solos, and the rest play classical solos. The ratio of the number of guitarist playing jazz solos to the total number of guitarist in the contest is 1:4. How many guitarist play classical solos in the contest?
Recall that a prime number is a natural number whose only factors are itself and 1 (for example, 2, 3, 5, . . . ). the goldbach conjecture, posed in 1742, claims that every even number greater than 2 can be expressed as the sum of two primes. for example, 4 = 2 + 2, 6 = 3 + 3, and 8 = 5 + 3. a deductive proof of this conjecture has never been found. test the conjecture for at least 10 even numbers and present an inductive argument for its truth. do you think the conjecture is true? why or why not?
Prime Number is a number whose only factors are itself and one. For example 1,3,5,7,11,13,17,19,23… Now consider the following arguments : Every even number greater than 2 can be expressed as sum of two primes. Now consider the following premises:
Premise 1 : 4 = 2 + 2
Premise 2 : 10 = 5 + 5
Premise 3 : 12 = 5 + 7
Premise 4 : 16 = 5 + 11
Premise 5 : 18 = 5 + 13
Premise 6 : 22 = 11 + 11
Premise 7 : 30 = 7 + 23
Premise 8 : 32 = 3 + 29
Premise 9 : 40 = 3 + 37
Premise 10 : 52 = 5 + 47
Premise 11 : 100 = 3 + 97
Conclusion : every whole number is sum of two prime numbers.
All 11 cases are different, yet the rule applies to all. This outcome offers a strong inductive argument in favor of the conclusion or rule specified. It can be strengthened by additional cases that confirm the rule. Conjecture specified will be true because each number can be specified as sum of two primes. As each whole number will have difference os 1, 2, 3, 5, or 7 between the number and the nearest prime number. Consider the following example :
34 = 31 + 3
36 = 33 + 3
Hence the conjecture “Every number greater than two can ve expressed as the sum of two primes” is true.
A two year degree that focuses on natural science, engineering, and mathematics is called an
Associate of science
Answer:
Assosiate in science
Step-by-step explanation:
An Associate of Science (AS) is a 2-year degree offered by most community colleges. Most AS degrees are transfer degrees and provide an academic foundation, but not specific career training. The A.S. degree is intended for students planning to pursue a bachelor’s degree in the areas of math or science.
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How do I write 18,801,310 in expanded form using exponents
Expanded form of a certain number involves writing out the place Number value of each digit in the number. The expanded Form of 18,801,310 is [tex] (1 \times {10}^{7} ) + (8 \times {10}^{6} ) + (8 \times {10}^{5} ) + (0 \times {10}^{4} ) + (1 \times {10}^{3} ) + (3 \times {10}^{2} ) + (1 \times {10}^{1} ) + (0 \times {10}^{0} ) [/tex]
[tex]1 = 10 \: million \: place \: = 1 \times 10000000 = 1 \times {10}^{7} [/tex][tex]8 \: = 1 \: million \: place \: = 8 \times 1000000 = 8 \times {10}^{6} [/tex][tex]8 = 100 \: thousand \: place \: = 8 \times 100000 = 8 \times {10}^{5} [/tex][tex]0 = 10 \: thousand \: place \: = 0 \times 10000 = 1 \times {10}^{4} [/tex][tex]1 = 1 \: thousand \: place \: = 1 \times 1000 = 1 \times {10}^{3} [/tex][tex]3 = 1 \: hundred \: place \: = 1 \times 100 = 1 \times {10}^{2} [/tex][tex]1 = 10s \: place \: = 1 \times 10 \: = 1 \times {10}^{1} [/tex][tex]0 = 0 \times {10}^{0} [/tex]Hence,
[tex]18,801,310 = (1 \times {10}^{7} ) + (8 \times {10}^{6} ) + (8 \times {10}^{5} ) + (0 \times {10}^{4} ) + (1 \times {10}^{3} ) + (3 \times {10}^{2} ) + (1 \times {10}^{1} ) + (0 \times {10}^{0} )[/tex]
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What is greater 3.26 or 3 5/8
Gina wrote the number 43,628. Then she used the same digits to write a new number. In the new number, she moved the digit 6 one place to the left. Which is the value of 6 in Gina's new number?
Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin determines about how many times the spinner will land on red or green, and his work is shown below.
Kevin's spinner will land on red or green approximately 72 times out of 180 spins since the probability of landing on red or green per spin is 0.4.
Explanation:The student's question involves determining the expected number of times a spinner will land on specific colors, given that the spinner is spun a large number of times. In this scenario, Kevin has a spinner with 10 equal sections with 2 sections of each color - red, blue, green, yellow, and purple. When Kevin spins the spinner 180 times, he wants to figure out how many times it will land on red or green.
Since there are 2 sections each of red and green out of a total of 10, the probability of landing on either red or green for a single spin is P(red or green) = P(red) + P(green) = 2/10 + 2/10 = 4/10 = 0.4. To find the expected number of times the spinner will land on red or green after 180 spins, we simply multiply the total number of spins by the probability of landing on red or green: 180 spins * 0.4 = 72 spins. Therefore, we can expect the spinner to land on red or green approximately 72 times out of 180 spins.
A salesperson's weekly paycheck is 15% less than a second salesperson's paycheck. The two paychecks total $1425. Find the amount of each paycheck.
George is at a trade show and is trading cards. He started the day with 50 cards, traded 5 of his cards for 1 of Billy's cards, traded 2 of his cards for 7 of Eloise's cards, and then traded 6 of his cards for 6 of Migel's cards. How many cards does he have at the end of the day?
When a day of the week is randomly selected it is a saturday?
find two possible factors for the estimated product 2,800
How does a "for every" statement show a ratio comparison?
Which fraction has a terminating decimal as it's the small expansion?
A) 1/3
B) 1/5
C) 1/7
D) 1/9
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt?
Answer:
Step-by-step explanation:
A & B
(201)3 is equivalente to: (11)10; (10010)2; (11)16; (23)8
It costs $2.80 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 170% of the cost. The sandwich sells for $ .