name:______________________________ homeroom:_____________________ day 2 - please show your thinking! you might need to do it on another piece of paper. measurement andrea is buying a rectangular rug that is 3 feet wide by 4 feet long. what is the total area that the rug will cover? a) 12 square feet b) 14 square feet c) 24 square feet d) 28 square feet if you have a triangle and one angle is 60 degrees and the second angle is 90 degrees, what is the measurement of the third angle? geometry draw an acute angle. true or false? an acute angle is less than 90 degrees.______ an isosceles triangle has three equal sides.______ an equilateral triangle has all acute angles.______ statistics the 5th grade students received the following scores on their spelling test 88, 83, 98, 65, 76, 92 determine the following: mean______ median______ mode______ range______ on the back, create a stem and leaf plot to show the above data. word problems bobby wanted to read his book every night. he wants to finish it in three nights. the book has 677 pages. bobby reads 137 pages the first night and 250 the third night. how many pages did bobby read on the second night to get the book finished? bonus: create a word problem about lunches served in the cafeteria.see if a family member can correctly solve it using the four square method (you are now the teacher; dont give them the answer just give them clues).

Question

Accepted Answer

### Measurement - Rug Area
# Explanation:
## Step1: Recall area formula for rectangle
The area $ A $ of a rectangle is given by $ A = \text{length} \times \text{width} $.
## Step2: Substitute values
Given length $ = 4 $ feet and width $ = 3 $ feet. So, $ A = 4 \times 3 $.
## Step3: Calculate the product
$ 4 \times 3 = 12 $ square feet.
# Answer: a) 12 square feet

### Measurement - Triangle Angle
# Explanation:
## Step1: Recall triangle angle sum property
The sum of the interior angles of a triangle is $ 180^\circ $.
## Step2: Let the third angle be $ x $
We know two angles: $ 60^\circ $ and $ 90^\circ $. So, $ 60 + 90 + x = 180 $.
## Step3: Solve for $ x $
$ 150 + x = 180 $, so $ x = 180 - 150 = 30^\circ $.
# Answer: $ 30^\circ $

### Geometry - Acute Angle Drawing
# Explanation:
An acute angle is an angle less than $ 90^\circ $. To draw it:
1. Draw a straight line (one side of the angle).
2. Place the center of the protractor on the endpoint of the line.
3. Mark a point at, say, $ 45^\circ $ (any angle less than $ 90^\circ $) on the protractor.
4. Draw a line from the endpoint to the marked point. This forms an acute angle.
# Answer: (A rough sketch: a small angle, e.g., $ 45^\circ $, between two lines)

### Geometry - True/False 1
# Explanation:
By definition, an acute angle is an angle whose measure is less than $ 90^\circ $.
# Answer: True

### Geometry - True/False 2
# Explanation:
An isosceles triangle has at least two equal sides, while an equilateral triangle has three equal sides. So, an isosceles triangle does not necessarily have three equal sides.
# Answer: False

### Geometry - True/False 3
# Explanation:
An equilateral triangle has all sides equal, so all angles are equal. The measure of each angle in an equilateral triangle is $ \frac{180^\circ}{3}=60^\circ $, and $ 60^\circ $ is less than $ 90^\circ $ (so acute). Thus, all angles are acute.
# Answer: True

### Statistics - Mean
# Explanation:
## Step1: Recall mean formula
Mean $ = \frac{\text{Sum of all values}}{\text{Number of values}} $.
## Step2: Calculate sum of scores
Scores: $ 88, 83, 98, 65, 76, 92 $. Sum $ = 88 + 83 + 98 + 65 + 76 + 92 $.
$ 88 + 83 = 171 $, $ 171 + 98 = 269 $, $ 269 + 65 = 334 $, $ 334 + 76 = 410 $, $ 410 + 92 = 502 $.
## Step3: Divide by number of values (6)
Mean $ = \frac{502}{6} \approx 83.67 $ (or as a fraction $ \frac{251}{3} $).
# Answer: Approximately $ 83.67 $ (or $ \frac{251}{3} $)

### Statistics - Median
# Explanation:
## Step1: Arrange scores in order
Scores in order: $ 65, 76, 83, 88, 92, 98 $.
## Step2: Find the middle value(s)
There are 6 values (even number), so median is the average of the 3rd and 4th values.
3rd value: $ 83 $, 4th value: $ 88 $.
## Step3: Calculate average
Median $ = \frac{83 + 88}{2} = \frac{171}{2} = 85.5 $.
# Answer: $ 85.5 $

### Statistics - Mode
# Explanation:
Mode is the value that appears most frequently. In the scores $ 88, 83, 98, 65, 76, 92 $, each score appears only once. So, there is no mode (or all values are modes with frequency 1).
# Answer: No mode (or each score is a mode with frequency 1)

### Statistics - Range
# Explanation:
## Step1: Recall range formula
Range $ = \text{Maximum value} - \text{Minimum value} $.
## Step2: Identify max and min
Maximum value: $ 98 $, Minimum value: $ 65 $.
## Step3: Calculate range
Range $ = 98 - 65 = 33 $.
# Answer: $ 33 $

### Statistics - Stem and Leaf Plot
# Explanation:
For the scores $ 88, 83, 98, 65, 76, 92 $:
- Stem (tens place): 6, 7, 8, 9.
- Leaves (units place):
  - Stem 6: 5 (from 65)
  - Stem 7: 6 (from 76)
  - Stem 8: 3, 8 (from 83, 88)
  - Stem 9: 2, 8 (from 92, 98)

So the stem - and - leaf plot is:

| Stem | Leaf |
|------|------|
| 6    | 5    |
| 7    | 6    |
| 8    | 3, 8 |
| 9    | 2, 8 |

# Answer: (The stem - and - leaf plot as above)

### Word Problems - Bobby's Reading
# Explanation:
## Step1: Let pages read on second night be $ x $
Total pages $ = $ pages read first night $ + $ pages read second night $ + $ pages read third night.
## Step2: Substitute values
$ 677 = 137 + x + 250 $.
## Step3: Solve for $ x $
First, $ 137 + 250 = 387 $. Then, $ 677 - 387 = x $. So, $ x = 290 $.
# Answer: 290 pages

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Measurement - Rug Area

Step1: Recall area formula for rectangle

Step2: Substitute values

Step3: Calculate the product

Step1: Recall triangle angle sum property

Step2: Let the third angle be \( x \)

Step3: Solve for \( x \)

Answer:

Measurement - Triangle Angle