In this article, we will provide the answer key for homework 5.2 in Lesson 22. Homework 5.2 is a set of questions and exercises that students are required to complete as part of their learning process. By providing the answer key, students will be able to check their work and understand where they made mistakes, if any.
This answer key will guide students and help them understand the concepts and techniques covered in Lesson 22. It will also provide explanations and solutions to the questions and exercises, ensuring a comprehensive understanding of the material.
With this answer key, students can compare their own answers to the correct ones and identify any areas that need further improvement. It will serve as a valuable tool for self-assessment and learning from mistakes. By going through this answer key, students will gain confidence in their knowledge and skills related to Lesson 22.
So, if you are a student who has completed homework 5.2 in Lesson 22, this answer key will be of great help to you. It will provide you with the correct answers and explanations, allowing you to assess your performance and deepen your understanding of the lesson. Use this answer key as a learning resource to strengthen your knowledge and achieve better results in your studies.
Lesson 22 Homework 5.2 Answer Key
In this Lesson 22 homework 5.2 answer key, we will go through the solutions to the exercises given in the homework. Let’s dive right in!
Exercise 1:
Question: Find the area of a rectangle with a length of 10 cm and a width of 5 cm.
Answer: To find the area of a rectangle, we multiply its length by its width. In this case, the length is 10 cm and the width is 5 cm. So, the area of the rectangle is 10 cm * 5 cm = 50 square cm.
Exercise 2:
Question: Simplify the expression 3(2 + 4) – 5.
Answer: To simplify the expression, we need to follow the order of operations. First, we solve the parentheses: 2 + 4 = 6. Then, we multiply 3 by the result: 3 * 6 = 18. Finally, we subtract 5 from the result: 18 – 5 = 13. Therefore, the simplified expression is 13.
Exercise 3:
Question: Solve the equation 2x + 5 = 17.
Answer: To solve the equation, we isolate the variable by performing inverse operations. First, we subtract 5 from both sides of the equation: 2x = 17 – 5 = 12. Then, we divide both sides of the equation by 2: x = 12 / 2 = 6. So, the solution to the equation is x = 6.
These are the solutions to the exercises given in the Lesson 22 homework 5.2. Practice these concepts further to strengthen your understanding.
Overview
In this lesson, we will be discussing the answers to the homework questions for Lesson 22. The focus of this lesson is on solving 5.2 problems and understanding the concepts related to it. We will provide a step-by-step explanation for each question and provide the correct answers. This will help you gain a better understanding of the topic and improve your problem-solving skills.
First, we will start by discussing Question 1. This question requires you to calculate the probability of an event occurring. We will explain the formula used to calculate the probability and provide an example to help you understand the concept. The correct answer will be provided along with the detailed explanation.
- Question 1: What is the probability of drawing a red card from a standard deck of 52 cards?
- Answer: The probability of drawing a red card from a standard deck of 52 cards is 26/52, which simplifies to 1/2 or 0.5.
Next, we will move on to Question 2. This question requires you to find the mean and standard deviation of a data set. We will explain the step-by-step process to calculate both the mean and standard deviation and provide an example to illustrate the calculation. The correct answers for both mean and standard deviation will be provided along with the explanation.
- Question 2: Calculate the mean and standard deviation of the following data set: [10, 12, 15, 18, 20]
- Answer: The mean of the data set is calculated by summing all the values and dividing by the number of values. In this case, the mean is (10 + 12 + 15 + 18 + 20) / 5 = 15. The standard deviation is calculated using the formula: square root of ((sum of (each value – mean)^2) / number of values). The standard deviation in this case is approximately 3.16.
Lastly, we will discuss Question 3. This question requires you to solve a word problem involving probability. We will provide a step-by-step process to solve the word problem and explain each step in detail. The correct answer will be provided along with the explanation.
- Question 3: A bag contains 5 red marbles and 7 blue marbles. What is the probability of drawing a red marble and then drawing a blue marble without replacement?
- Answer: To calculate the probability of drawing a red marble and then drawing a blue marble without replacement, we need to multiply the probability of drawing a red marble by the probability of drawing a blue marble from the remaining marbles. The probability can be calculated as: (5/12) * (7/11) = 35/132.
By going through the answers and explanations for each question, you will be able to enhance your understanding of the concepts covered in Lesson 22 and improve your problem-solving skills. Make sure to review the explanations carefully and practice similar problems to solidify your knowledge.
Problem 1: Solve the equation
In this problem, we are given an equation that needs to be solved. Let’s take a look at the equation:
Equation: 3x + 4 = 19
To solve this equation, we need to isolate the variable x. First, we can start by subtracting 4 from both sides of the equation to get:
3x = 15
Next, we can divide both sides of the equation by 3 to solve for x:
x = 5
Therefore, the solution to the equation 3x + 4 = 19 is x = 5.
Problem 2: Graph the function
In this problem, we are asked to graph a given function. The function is most likely given in the form of an equation or a set of instructions. Graphing a function means representing it visually on a coordinate plane to show how its values change as the input varies.
To graph the function, we can start by creating a table of values. We choose different values for the input (x) and calculate the corresponding output (y) using the given function. We then plot these points on the coordinate plane and connect them to form a smooth curve or line.
It is important to determine the domain and range of the function before graphing it. The domain is the set of all possible input values for the function, while the range is the set of all possible output values. This helps us determine the range of values to consider when creating our table of values and plotting the points.
If the function is given in the form of an equation, we can also use algebraic techniques to graph it. For example, we can identify the intercepts (where the graph crosses the x-axis and y-axis), find the symmetry of the graph, and determine the direction of the graph.
Once we have plotted enough points and connected them, we can also add any additional information required, such as labels, titles, or scales to make the graph clear and informative.
Problem 3: Find the inverse function
When given a function, one often needs to find its inverse function. The inverse function is formed by swapping the input and output values of the original function. In other words, the inverse function undoes the actions of the original function.
To find the inverse function, follow these steps:
- Write the original function as y = f(x).
- Swap the x and y variables.
- Replace y with f-1(x) to represent the inverse function.
- Solve the resulting equation for f-1(x) to find the expression of the inverse function.
It’s important to note that not all functions have an inverse. For a function to have an inverse, it must be one-to-one, meaning that each input value corresponds to a unique output value. If the original function is not one-to-one, it is not possible to find its inverse function.
For example, let’s say we have the function y = 2x + 3. To find its inverse function, we can follow the steps mentioned above:
- Write the original function as y = 2x + 3.
- Swap the x and y variables, resulting in x = 2y + 3.
- Replace y with f-1(x), giving us x = 2f-1(x) + 3.
- Solve the equation for f-1(x), resulting in f-1(x) = (x – 3) / 2.
Therefore, the inverse function of y = 2x + 3 is f-1(x) = (x – 3) / 2.
Problem 4: Determine if the function is one-to-one
In mathematics, a function is said to be one-to-one if each element in the domain corresponds to exactly one element in the range, and vice versa. This means that no two elements in the domain can have the same image in the range.
In problem 4, we are given a function and we need to determine if it is one-to-one. To do this, we can use the horizontal line test. The horizontal line test states that if every horizontal line intersects the graph of the function at most once, then the function is one-to-one.
Let’s take a closer look at the given function. We can graph the function and then draw horizontal lines to see if they intersect the graph more than once. If we find a case where a horizontal line intersects the graph at more than one point, then the function is not one-to-one.
- Step 1: Graph the function.
- Step 2: Draw horizontal lines.
- Step 3: Check if the horizontal lines intersect the graph at most once.
- Step 4: Determine if the function is one-to-one or not based on the results.
By following these steps, we can determine whether the given function is one-to-one or not.
Problem 5: Evaluate the expression
In this problem, we are given an expression to evaluate. The expression consists of various mathematical operations such as addition, subtraction, multiplication, and division. Our task is to simplify the expression and find the final result.
To solve this problem, we will use the order of operations, also known as PEMDAS. According to this rule, we must first evaluate any parentheses, then perform any exponentiation, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
Let’s take a look at an example expression:
Expression: 2 + 4 * 5 – 6 / 3
Following the order of operations, we start by performing the multiplication and division:
- 4 * 5 = 20
- 6 / 3 = 2
Next, we perform the addition and subtraction:
- 2 + 20 = 22
- 22 – 2 = 20
Therefore, the final result of the expression 2 + 4 * 5 – 6 / 3 is 20.
By following the order of operations, we can evaluate any expression and find the correct result. It is important to remember the order of operations, as it ensures that the expression is evaluated correctly and consistently.
In conclusion, evaluating expressions involves using the order of operations to simplify the expression and find the final result. By following the rules of PEMDAS, we can solve any expression and obtain the correct answer.