Question

week 1 instructions: choose 4 questions to answer each day. if you’re feeling daring, answer all 5!

day 1:

• write the following number in expanded form, and in words: 3 456 789
• find the mean of the following set of numbers: 21, 27, 29, 30, 22, 24
• find the difference? ( \begin{array}{r} 489.3 \\ -26.5 \\ hline end{array} )
• graph the number pattern. state the pattern rule. (table with term 1–5, number values)
• at the store, a designer handbag is 40% off. it’s original cost was $750. what is the discounted price?

day 2:

• describe the image below. what does it tell us? (number line with a dot)
• determine the missing angle measure (x). (angle diagram)
• if the pattern continues to increase by the same number, how many dots will be in the 8th term? (dot patterns: 1, 2, 3, 4, 5 with dots)
• solve for the following: ( \frac{4}{9} + \frac{4}{4} )
• create a proper factor tree for the number 98. (tree image)

day 3:

• draw any and all the lines of symmetry within the shape below. (triangle with a line)
• create a 8 digit number using the table. then, answer the questions. (table image)
• list the number of: pairs of parallel sides, equal sides (trapezoid image)
• fill out the input/output table. (table image)
• sam deposits $2500 into a 3% per annum simple interest account. how much money will he have in total after 4 years? (image of a person at a bank)

Explanation:

Let's solve the "Find the mean of the following set of numbers: 21, 27, 29, 30, 22, 24" problem.

Step1: Recall the formula for the mean

The mean (average) of a set of numbers is calculated by the sum of the numbers divided by the count of the numbers. The formula is $\text{Mean} = \frac{\sum_{i = 1}^{n} x_{i}}{n}$, where $x_{i}$ are the individual numbers and $n$ is the number of terms.

Step2: Calculate the sum of the numbers

First, we add up all the numbers: $21 + 27 + 29 + 30 + 22 + 24$. Let's compute that:
$21+27 = 48$; $48 + 29 = 77$; $77+30 = 107$; $107 + 22 = 129$; $129+24 = 153$.

Step3: Determine the number of terms

There are 6 numbers in the set, so $n = 6$.

Step4: Calculate the mean

Now we divide the sum by the number of terms: $\text{Mean} = \frac{153}{6}$.

Simplifying $\frac{153}{6}$, we can divide numerator and denominator by 3: $\frac{153\div3}{6\div3}=\frac{51}{2} = 25.5$.

Answer:

The mean of the set of numbers is $25.5$.