9. error analysis find the error in the work below. then show the correct calculation.
$\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6 = 8 \times \frac{1}{12} = \frac{8}{12} = \frac{1}{3}$
10. a scientist measured the amount of rainfall during the afternoon. it rained 0.43 inches each hour. what was the total amount of rainfall in 3 hours?
11. a giraffe can run at a speed of 32 miles per hour. which animal listed in the chart has a speed that is $\frac{15}{16}$ of the speed of a giraffe? explain how you found your answer.
| animal | speed (in miles per hour) |
| ---- | ---- |
| car | 30 |
| cheetah | 70 |
| jackal | 25 |
12. if a frilled lizard is 90 centimeters long, how long is the tail?
(the frilled lizards tail is $\frac{2}{3}$ of its length.)
13. higher order thinking eric has 240 coins in his collection. $\frac{11}{20}$ of the coins are pennies. $\frac{4}{20}$ of the coins are nickels. the rest of the coins are quarters. how many of the coins are quarters? explain how you found your answer.

Question

Accepted Answer

### Question 10:
# Explanation:
## Step1: Identify the formula for total rainfall
The total rainfall is the rate of rainfall per hour multiplied by the number of hours. The formula is $ \text{Total Rainfall} = \text{Rate} \times \text{Time} $.
## Step2: Substitute the given values
The rate is $ 0.43 $ inches per hour and the time is $ 3 $ hours. So we calculate $ 0.43\times3 $.
## Step3: Perform the multiplication
$ 0.43\times3 = 1.29 $

# Answer:
The total amount of rainfall in 3 hours is $ 1.29 $ inches.

### Question 11:
# Explanation:
## Step1: Calculate $ \frac{15}{16} $ of the giraffe's speed
The giraffe's speed is $ 32 $ miles per hour. We need to find $ \frac{15}{16} \times 32 $.
## Step2: Simplify the multiplication
$ \frac{15}{16} \times 32 = 15\times2 = 30 $ (because $ 32\div16 = 2 $)
## Step3: Compare with the given speeds
Looking at the table, the car has a speed of $ 30 $ miles per hour, which matches our calculation.

# Answer:
The car has a speed that is $ \frac{15}{16} $ of the speed of a giraffe because $ \frac{15}{16}\times32 = 30 $ miles per hour, which is the speed of the car.

### Question 12:
# Explanation:
## Step1: Identify the formula for the tail length
The tail length is $ \frac{2}{3} $ of the lizard's total length. The formula is $ \text{Tail Length} = \frac{2}{3} \times \text{Total Length} $.
## Step2: Substitute the given values
The total length is $ 90 $ centimeters. So we calculate $ \frac{2}{3}\times90 $.
## Step3: Perform the multiplication
$ \frac{2}{3}\times90 = 2\times30 = 60 $ (because $ 90\div3 = 30 $)

# Answer:
The length of the frilled lizard's tail is $ 60 $ centimeters.

### Question 13:
# Explanation:
## Step1: Find the fraction of coins that are quarters
First, find the sum of the fractions of pennies and nickels. The fraction of pennies is $ \frac{11}{20} $ and the fraction of nickels is $ \frac{4}{20} $. So the sum is $ \frac{11}{20}+\frac{4}{20}=\frac{15}{20} $.
The fraction of quarters is $ 1 - \frac{15}{20}=\frac{5}{20}=\frac{1}{4} $.
## Step2: Calculate the number of quarters
The total number of coins is $ 240 $. So we find $ \frac{1}{4}\times240 $.
## Step3: Perform the multiplication
$ \frac{1}{4}\times240 = 60 $

# Answer:
The number of quarters is $ 60 $.

### Question 9 (Error Analysis):
# Explanation:
## Step1: Identify the correct method for multiplying fractions
When multiplying $ \frac{8}{12}\times6 $, we can simplify $ \frac{8}{12} $ to $ \frac{2}{3} $ first, or multiply $ 8\times6 $ and then divide by $ 12 $.
## Step2: Analyze the error in the given work
The given work has an error in the step $ \frac{8}{12}\times6 = 8\times\frac{1}{12}\times6 $ (this step is incorrect in the way it's simplified, but the main error is in the subsequent steps). The correct calculation should be $ \frac{8}{12}\times6=\frac{8\times6}{12}=\frac{48}{12} = 4 $. The given work incorrectly simplifies $ 8\times\frac{1}{12}\times6 $ as $ 8\times\frac{1}{2} $ (wrong simplification) and then gets $ \frac{8}{2}=\frac{8}{12}=\frac{1}{3} $ which is a series of errors.
## Step3: Show the correct calculation
$ \frac{8}{12}\times6=\frac{8\times6}{12}=\frac{48}{12} = 4 $ or simplify $ \frac{8}{12} $ to $ \frac{2}{3} $, then $ \frac{2}{3}\times6 = 4 $.

# Answer:
The error is in the incorrect simplification and calculation steps. The correct calculation is $ \frac{8}{12}\times6 = \frac{8\times6}{12}=4 $ (or $ \frac{2}{3}\times6 = 4 $).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 10:

Step1: Identify the formula for total rainfall

Step2: Substitute the given values

Step3: Perform the multiplication

Step1: Calculate \( \frac{15}{16} \) of the giraffe's speed

Step2: Simplify the multiplication

Step3: Compare with the given speeds

Step1: Identify the formula for the tail length

Step2: Substitute the given values

Step3: Perform the multiplication

Answer:

Question 11: