The larger leg of a right triangle is 3 cm longer than it’s smaller leg. How many centimeters long is the smaller leg?

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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Answer: 18x + 12

Step-by-step explanation:

3 ( 6x + 4 )

3 x 6x = 18x

3 x 4 = 12

18x + 12

Answer:

It is not possible... I think so

When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.

Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.

We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:

Using the formula V = \(Pe^rt\)

Principal (P) = $48,800.00

Annual Rate (R) = 3.1%

Compound (n) = Compounding Continuously

Time (t in years) = 13 years

Result:

V = $73,019.78

V = P + I where

P (principal) = $48,800.00

I (interest) = $24,219.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.1/100

r = 0.031 rate per year,

Solving the equation for V:

V = \(Pe^rt\)

V = \(48,800.00(2.71828)^(0.031)(13)\)

V = $73,019.78

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Answer:

Elijah is 8.

Step-by-step explanation:

8 x 5 = 40 (Jackie is 40)

40 + 8 is 48!

Answer:

97.9% sure its 8

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

Using quadratic formula, we can solve this equation as:

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

Answer:
the length of the rectangle is y - 3.

Step-by-step explanation:

To find the length of the rectangle, we need to use the formula for the area of a rectangle:

Area = length x width

We are given the area of the rectangle as y^2 + 2y - 15 and the width as y + 5.

Let's substitute these values into the formula:

y^2 + 2y - 15 = length x (y + 5)

Now, we can solve for the length by dividing both sides by y + 5:

length = (y^2 + 2y - 15) / (y + 5)

We can simplify this expression by factoring the numerator:

length = [(y + 5)(y - 3)] / (y + 5)

The (y + 5) term in the numerator and denominator cancel out, leaving us with:

length = y - 3

Therefore, the length of the rectangle is y - 3.

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer:

\(m=\dfrac{6}{11}\)

Step-by-step explanation:

We need to find the slope of the line that goes through following 2 points (4, 9) and (-7,3).

The formula of slope that goes through (x₁,y₁) and (x₂,y₂) is given by :

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Putting all the values, we get :

\(m=\dfrac{3-9}{(-7)-4}\\\\m=\dfrac{6}{11}\)

So, the slope of the line is \(\dfrac{6}{11}\).

Answer:

144? or 126 sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

15

Step-by-step explanation:

For every 20 students, 3 will say that fruit is their favorite snack. So, if we multiply the number of students by 5, we multiply the number of students that say fruit is their favorite snack by 5 too. So, 15 students will say that fruit is their favorite snack.

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

The probabilities for this problem are given as follows:

a) Moderate to high, given that it is an aerospace company: p = 4/9 = 0.4444.

b) Moderate to high, given that it is a food retailer: p = 6/11 = 0.5455.

c) As the probabilities are different, the company type is independent of the level of risk of the firm's stock.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability is given as follows:

p = 8/18

p = 4/9.

For item b, the outcomes are given as follows:

Hence the probability is given as follows:

p = 30/55

p = 6/11.

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Given:

The APR is 18.99%

Find-:

What is the periodic interest rate for an account that is billed monthly?

Explanation-:

The APR is calculated by dividing the APR by the number of periods it is to be converted to.

If, for instance, a monthly periodic rate is needed, divide APR by 12 as there are 12 months in a year.

So, the billed monthly are:

The monthly bill is 1.58%

Answer: -102

Step-by-step explanation: First we do 9-3 = 6, then add -6 which cancels each other out, so all we have left is -102.

Hope this helps! :)

Answer:

-102

Step-by-step explanation:

(+9) - (+3) = +6

(-6) = -6

+ (-102) = -102

so, +6 -6 -102 = -102

Answer:

Step-by-step explanation:

You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and

plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy

the guitar? Explain your answer.

15 hours × 3 weeks × $9 per hour

15 × 3 × 9 =

45 × 9 = 405$

The answer is YES

Answer:

Among the four choices, \((x + 5)\) is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let \(a\) denote some constant. A linear factor of the form \((x - a)\) is a factor of a polynomial \(f(x)\) if and only if \(f(a) = 0\) (that is: replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(a\!\) would give this polynomial a value of \(0\).)

For example, in the second linear factor \((x - 2)\), the value of the constant is \(a = 2\). Verify that the value of \(f(2)\) is indeed \(0\). (In other words, replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(2\) should give this polynomial a value of \(0\!\).)

\(\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}\).

Hence, \((x - 2)\) is indeed a linear factor of polynomial \(f(x)\).

Similarly, it could be verified that \((x - 5)\) and \((x + 2)\) are also linear factors of this polynomial function.

Rewrite the first linear factor \((x + 5)\) in the form \((x - a)\) for some constant \(a\): \((x + 5) = (x - (-5))\), where \(a = -5\).

Calculate the value of \(f(5)\).

\(\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}\).

\(f(5) \ne 0\) implies that \((x - (-5))\) (which is equivalent to \((x + 5)\)) isn't a linear factor of this polynomial function.

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer:

Users who park at the selected trailheads and​ cross-country ski lots. ; Convenience sampling

Step-by-step explanation:

A) The population of interest:

The population of interest should include the concerned individuals which would be those who park at the selected trailheads and cross-country ski lots.

B) By sampling the first 50 users encountered at each fee areas shows that the researcher prioritizes ease or convenience while choosing samples from a population. The first 50 fee users represents the most easily accessible users. Hence, the reason the adopted sampling method is called convenience sampling.

The dimensions of the rectangle are  (2x + 7y) and (2x - 7y)

The formula for calculating the area of a square is expressed as:

A = L^2

Given the area of a square expressed as 16x^2 + 24x + 9

Factorize 16x^2 + 24x + 9

16x^2 + 24x + 9

=  16x^2 + 12x + 12x + 9

= 4x(4x+3) + 3(4x+3)

= (4x+3)^2

Hence the lngth of each side of the square is 4x+3

For the funciton 4x^2 − 49y^2

On factoring completely

4x^2 − 49y^2

= (2x)^2 - (7y)^2

= (2x + 7y)(2x - 7y)

Hence the dimension of the rectangle are  (2x + 7y) and (2x - 7y)

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The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer: A

Step-by-step explanation: So, first of all, this is a linear graph, which is represented by the equation y = mx + b.

b = y-intercept. The y-intercept is the point in which the line crosses the y axis. Assuming this graph has units that go up by 1, the y- intercept for this line is 2, which eliminates choices B and C.

This graph is going down, which means it is negative, so the format should be -mx + b, which is answer choice A. Hope this helps! :)

Answer:

a=6

Step-by-step explanation:

I did guess and check so in the calculator, I started from ten and realized that was way too high and eventually got to the answer, 6.

Answer:

6

Step-by-step explanation

∛a^3 = ∛216

∛216 = 6

Answer:

50% Increase

Step-by-step explanation:

336 - 224 = 112

112 / 224 = 0.5

A 50% Increase of 224 = 336

Answer:

i

Step-by-step explanation: