Aaron has a budget of $100 per month to spend on lunch. He made a table showing the total amount of lunch money he will have left after the given number of lunches.

Number of lunches 0 5 10 15
Total amount of lunch money left ($) 100 75 50 25
Which equation, in standard form, represents the relationship between the number of lunches, x, and the amount of lunch money Aaron will have left, y?

x + 5y = 100

100x + y = 5

x + 100y = 5

5x + y = 100

Answer and explanation;

If we choose two whole numbers; 8 and 10

We want to divide certain numbers by 8 and 10 to get 9 remainder 5.

In this case; 77 divided by 8 is equal to 9 rem 5

and 95 divided by 10 is equal to 9 rem 5

To justify which is greater, we use decimal division;

= 77 divided by 8 we get 9.625 ( 77 ÷ 8 = 9.625)

and

= 95 divided by 10 is equal to 9.5 (95 ÷10 = 9.5)

Therefore; the first case is greater since 9.625 is greater than 9.5

That is; 9 rem 5 got after dividing 77 by 8 is greater than 9 rem 5 got after dividing 95 by 10.

The pattern of rule n-4 can consist of several numbers depending on the value of n (integer, whole number, natural number or prime number)

Algebraic expressions in mathematics are a combination of coefficients, numbers, variables, constants and arithmetic operations such as addition, subtraction, multiplication, and division.

The main composition of algebraic expressions are:

• 1. phrases

algebraic forms separated by arithmetic operations

consists of one phrase (monomial) to many phrases (polynomial)

• 2. variable

is a value that can be changed, can be in the form of letters, for example, x, y, a, b, etc.

• 3. constants

is a fixed value, can be a number

• 4. arithmetic operations

operations [tex]{\displaystyle \boxed {+}, \boxed {-}, \boxed {:}, \boxed {x}}[/tex]

Numbers in mathematics can be divided into several terms

numbers consist of positive, negative and 0 numbers

numbers consisting of positive numbers, starting with number 1

a number consists of positive numbers and zeros

numbers that can only be divided by numbers themselves and the number 1

And examples of other numbers such as imaginary numbers, real numbers, rational numbers, etc.

Integers themselves consist of

the number to the right of the number 0 is 1,2,3 ...

the numbers to the left of the zeros are -1, -2, -3 ...

n-4 is an algebraic form

the pattern is generated from rule = (n-4)

There are several possible values ​​of n that can be entered to form a pattern

pattern = -7, -6, -5, -4, -3, -2, -1, ...

pattern = -3, -2, -1, ...

pattern = -4, -3, -2, -1, ...

pattern = -2, -1,1,3, ....

Express 0.000431 L answer as an integer

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type of number

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Classify the number as a natural, whole, integer, rational, or irrational.

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Keywords: natural, whole, integer, prime, number

The pattern of the rule [tex]\left( {n - 4} \right)[/tex] is [tex]\boxed{ - 4, - 3, - 2, - 1 \ldots {\text{ and }} - 3, - 2, - 1,0 \ldots }.[/tex]

Further explanation:

Given:

The rule is [tex]\left( {n - 4} \right).[/tex]

Explanation:

If n takes the value of natural numbers.

Substitute 1 for [tex]n[/tex] in [tex]\left( {n - 4} \right).[/tex]

[tex]\begin{aligned}n - 4&= 1 - 4\\&=- 3\\\end{aligned}[/tex]

Substitute 2 for [tex]n[/tex] in [tex]\left( {n - 4} \right).[/tex]

[tex]\begin{aligned}n- 4&= 2 - 4\\&= - 2\\\end{aligned}[/tex]

If [tex]n[/tex] takes the value of whole numbers.

Substitute 0 for [tex]n[/tex] in [tex]\left( {n - 4} \right).[/tex]

[tex]\begin{aligned}n - 4&= 0 - 4\\&= - 4\\\end{aligned}[/tex]

The pattern of the rule [tex]\left( {n - 4} \right)[/tex] is [tex]\boxed{ - 4, - 3, - 2, - 1 \ldots {\text{ and }} - 3, - 2, - 1,0 \ldots }.[/tex]

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Number System

Keywords: numbers, rule, n-4, create, pattern, irrational numbers, rational numbers, adding, subtracting, multiplication, division, decimal expansion, natural numbers

The two fractions with a difference of 1/5 but with neither denominator equal to 5 are; 4/10 and 2/10

Two fractions that can give a difference of 1/5 are;

2/5 and 1/5

However, we are told that the denominator of both fractions must not be 5.

This means we have to multiply both numerator and denominator by the same number so that the denominator is no longer 5.

From multiplication law of equality of fractions, when we multiply the numerator and denominator of a fraction by the same number, the result is equal to the initial fraction.

Thus, let us multiply both numerator and denominator by 2 to get;

4/10 and 2/10

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The total number of people in the pie chart will be 40.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

108° → 12 people.

Per degree people or the ratio of degree to people will be,

1° → 12/108 people

In a circle, there is 360° thus multiply by 360 on both sides,

360° = 12/108 x 360 = 40 people

Hence "The total number of people in the pie chart will be 40.".

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To find the equivalent number of calories per serving based on that a can of juice contains 175 calories for 2.5 servings, divide 175 by 2.5 to get 70 calories per serving. Any amount other than 70 calories per serving would not be equivalent.

The question is asking to find an equivalent number of calories per serving based on the information that a can of juice contains 175 calories per 2.5 servings. To calculate the calories per serving, we divide the total number of calories by the number of servings, so:

Calories per serving = Total calories ÷ Number of servings = 175 calories ÷ 2.5 servings = 70 calories per serving.

Now, let's say we have several options that represent the number of calories per serving:

From this list, every option except for the first one (70 calories per serving) is not an equivalent number of calories per serving as our calculated 70 calories per serving.

The number of teams Ms.Morris can make would be 5-students groups.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that there are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team.

If Ms. Morris wants to divide all the students in 3, 4 or 5 equal teams, then apply a division to know the number of students per group.

If she makes 3-students groups, it would be;

25/3

If she considers 4-students groups, then it would be;

25/4

Thus, it can be seen that she cannot divide a students in parts to have equal groups.

Therefore, she has to make 5-students groups,

25/5 = 5

This means that she can make groups of 5 students each, and she would have equal groups.

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Answer: 1/20 :)

Step-by-step explanation: I did this and got full points heres for each question.

1. 5/21

2. 3/40

3. 33/56

4. 1/20 of a foot

5. 2/5 of the book

The total number of dogs and cats in the animal shelter is 25. We get this by dividing the number of puppies, which represent 28% of the population, by 0.28.

To figure out the total dog and cat population in the animal shelter, we need to use the information given to us: the puppies, which make up 28% of the total population, number 7. To get the full population, we need to think of these 7 puppies as representing 28%. The way to get the total is to divide the number of puppies by the percentage they represent. Express 28% as a decimal and divide:

7 / 0.28 = 25

So there are 25 dogs and cats in the animal shelter.

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To calculate the total length of six pipes each of 9 1/3 inches long, multiply the length of one pipe by the number of pipes. By doing so, we find that the row of pipes would be approximately 56 inches long.

The question asks how long a row of six pipes would be if each pipe was 9 1/3 inches long. To figure this out, you multiply the length of one pipe by the number of pipes. In this case, that would be 9 1/3 inches times six pipes.

To simplify the calculation, convert the fraction 1/3 to a decimal. 1/3 is approximately 0.333, and adding that to 9 makes 9.333 inches. Now that we have a decimal, we can multiply: 9.333 inches per pipe times 6 pipes equals approximately 56 inches.

Therefore, a row of six pipes each of 9 1/3 inches long would be approximately 56 inches long.

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we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the amount in interest

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=?\ years\\ P=\$1,300\\ I=\$299\\r=0.0575[/tex]

substitute in the formula above  and solve for t

[tex]299=1,300(0.0575)(t)[/tex]

[tex]t=299/[1,300(0.0575)][/tex]

[tex]t=4\ years[/tex]

therefore

the answer is

[tex]4\ years[/tex]

Bonita's money was in the account for approximately 5 years.

Step 1: Define Variables and Formula

Let:

The formula for simple interest is:

I = P × r × t

Step 2: Apply the Formula to Known Values

We are given the values for I, r, and P (we can solve for P using the given information). Let's plug these values into the formula:

$299 = P × 0.0575 × t

Step 3: Solve for the Unknown (t - Number of Years)

Step 4: Find the Principal Amount (P)

The total amount Bonita received when closing the account is the principal amount (P) plus the interest earned (I). We can represent this as:

Step 5: Solve for the Number of Years (t)

Now that we know P, we can plug it back into the equation along with the interest rate (r) to solve for t:

Step 6: Round the Answer (Nearest Whole Year)

The question asks for the number of years rounded to the nearest whole year. Since the decimal part (0.49) is closer to 0 than 1, we round down.

It will not have any possible solutions

Step-by-step explanation:

this would actually have some solutions because

y=3.5x−3.5

Step: Substitute 3.5x−3.5 for y in y=−3.5x+3.5:

y=−3.5x+3.5

3.5x−3.5=−3.5x+3.5

3.5x−3.5+3.5x=−3.5x+3.5+3.5x(Add 3.5x to both sides)

7x−3.5=3.5

7x−3.5+3.5=3.5+3.5(Add 3.5 to both sides)

7x=7

7x

7

=

7

7

(Divide both sides by 7)

x=1

Step: Substitute 1 for x in y=3.5x−3.5:

y=3.5x−3.5

y=(3.5)(1)−3.5

y=0(Simplify both sides of the equation)

x=1 and y=0

Answer: 3.4875

Step-by-step explanation:

Here, According to the question,

Total amount is $23.25

[tex]100\% = 23.25[/tex]

⇒[tex]1\% = \frac{23.25}{100}[/tex]

⇒[tex]1\%= \frac{0.95}{8}[/tex]

⇒ [tex]15\%= 15\times \frac{0.95}{8}[/tex] ( By multiplying 15 on both sides)

⇒ [tex]15\%= \frac{14.25}{8}[/tex]

⇒  [tex]15\%= 3.4875 [/tex]

Thus, 15% of $23.25 is $3.4875

Answer: F) $5

Step-by-step explanation:

Monthly charge for cable bill payed be Danielle= $69

Last month, her total bill= $104

Therefore, amount she paid for movies = $104-$69= $35

Thus, amount she paid for  7 movies on demand = $35

⇒ The monthly charge ,every time she watches a movie on demand

=[tex]\frac{\$35}{7}=\$5[/tex]

Therefore, The monthly charge ,every time she watches a movie on demand=$5.

In  order to raise $100, Bo should charge $5 for each game. In mathematics, "at least one" refers to one or more.

He provided the least amount of money of any donor, whether in size, quantity, degree, etc. lowest in importance, standing, or consideration. noun. The smallest possible quantity, degree, or other attribute.

In mathematics, "at least one" refers to one or more. It is frequently employed when existence can be proved but there is no way to know how many possible solutions there are.

Given ,

Let x represent the lowest price per video game.

The number of games available is 23.

Selling video games will need to raise $100 as the minimum amount.

The necessary inequality follows:

total number of games need minimum sum

i.e.[tex]23x\geq 100[/tex]

23 divided by both sides gives us

[tex]x\geq 4.24782608696[/tex]≈5

So, in order to raise $100, Bo should charge $5 for each game.

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