Question

1. complete the equivalent forms of the ratio.

using hundredths
in words\tas a fraction\tas a percent\tas a decimal
sixty - five hundredths\t$\frac{65}{100}$\t65%\t0.65
using tenths and hundredths
as the sum of two fractions\tas the sum of two percents\tas the sum of two decimals
$\frac{6}{10}+\frac{5}{100}$\t60% + 5%\t0.6 + 0.05

1. use the number line to create a data set with 12 values that has a range of 11, a mode of 4, and that is right - tailed.

cuny start quantitative reasoning, class 2

Explanation:

Step1: Understand the requirements

We need a data set of 12 values with range 11, mode 4, and right - tailed (more values on the right side of the mode or a longer tail on the right). Range is maximum - minimum = 11. Let's choose minimum value first. Let's take minimum value as 4 (since mode is 4, it's a good start). Then maximum value = 4+11 = 15.

Step2: Ensure mode is 4

Mode is the most frequent value. So we need to have more 4s than any other number. Let's have 4 appear, say, 4 times.

Step3: Build the right - tailed data set

We want a right - tailed distribution, so we will have more values towards the higher end. Let's construct the data set:

• Minimum value: 4 (appears 4 times: 4, 4, 4, 4)
• Then we add values greater than 4, gradually increasing towards the maximum (15). Let's choose values: 5 (2 times), 6 (2 times), 7 (1 time), 8 (1 time), 9 (1 time), 15 (1 time). Wait, let's check the count: 4 (4) + 5 (2)+6 (2)+7 (1)+8 (1)+9 (1)+15 (1)=4 + 2+2 + 1+1+1+1 = 12. Wait, but maximum should be 15 (since 4 + 11=15). Let's adjust. Wait, if minimum is 4, maximum is 15, range is 15 - 4 = 11 (good). Let's make the data set more right - tailed. Let's have: 4, 4, 4, 4, 5, 5, 6, 7, 8, 9, 10, 15. Wait, count: 4 (4) + 5 (2)+6 (1)+7 (1)+8 (1)+9 (1)+10 (1)+15 (1)=4+2 + 1+1+1+1+1+1 = 12. Range: 15 - 4 = 11 (good). Mode: 4 (appears 4 times, more than any other number). And it's right - tailed because most of the non - mode values are on the right side of 4. Another possible data set: 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 15. Wait, count: 4 (4)+5 (1)+6 (1)+7 (1)+8 (1)+9 (1)+10 (1)+11 (1)+15 (1)=4 + 1+1+1+1+1+1+1+1=12. Range: 15 - 4 = 11. Mode: 4. And it's right - tailed as values increase towards 15.

Answer:

A possible data set is \(\{4, 4, 4, 4, 5, 5, 6, 7, 8, 9, 10, 15\}\) (Note: There are other valid data sets as well, as long as they meet the range, mode, and right - tailed criteria)