6. (36, 48) five eighths of the rocks in the box were metamorphic. the rest were igneous.
a. what fraction of the rocks were igneous?
b. what was the ratio of igneous to metamorphic rocks?
c. what percent of the rocks were metamorphic?
7. (40) refer to the figure at right to answer a and b.
a. name two pairs of vertical angles.
b. name two angles that are supplemental to ∠rps.
* 8. (51) a. write six hundred ten thousand in scientific notation.
b. write 1.5 × 10⁴ in standard form.
* 9. (45, 50) connect from goal line to goal line a football field is 100 yd long. one hundred yards is about how many meters? use a unit multiplier to make the conversion and round the answer to the nearest meter. (1 meter ≈ 1.1 yd)
10. (43, 48) a. write ¹⁄₆ as a decimal number rounded to the nearest hundredth.
b. write ¹⁄₆ as a percent.
11. (51) how many pennies equal one million dollars? write the answer in scientific notation.
12. (51) compare: 11 million ○ 1.1 × 10⁶
13. (27) which even two - digit number is a common multiple of 5 and 7?
the figure shows the dimensions of a window. refer to the figure to answer problems 14 and 15.
* 14. (29) estimate what is the approximate perimeter of the window in feet?
* 15. (29) estimate what is the approximate area of the window in square feet?

Question

Accepted Answer

### Problem 6 (assuming we solve part a first)
# Explanation:
## Step1: Define total as 1
Let the total fraction of rocks be $ 1 $ (since the sum of fractions of all types of rocks should be 1).
## Step2: Find fraction of metamorphic (assuming five eighths are metamorphic? Wait, the original text: "Five eighths of the rocks in the box were metamorphic. The rest were igneous." So to find igneous, subtract metamorphic from 1.
Fraction of igneous $ = 1 - \frac{5}{8} = \frac{8 - 5}{8} = \frac{3}{8} $
# Answer:
$\frac{3}{8}$

### Problem 7a
# Brief Explanations:
Vertical angles are opposite angles formed by two intersecting lines. In the figure with lines intersecting at $ P $, $ \angle QPT $ and $ \angle RPS $ are vertical angles, and $ \angle QPR $ and $ \angle TPS $ are another pair.
# Answer:
$ \angle QPT $ and $ \angle RPS $, $ \angle QPR $ and $ \angle TPS $ (or other valid pairs based on the figure)

### Problem 8a
# Explanation:
## Step1: Write the number in digits
Six hundred ten thousand is $ 610000 $
## Step2: Convert to scientific notation
Scientific notation is $ a \times 10^{n} $ where $ 1 \leq a < 10 $ and $ n $ is an integer. For $ 610000 $, we move the decimal 5 places to the left to get $ a = 6.1 $, so it's $ 6.1 \times 10^{5} $
# Answer:
$ 6.1 \times 10^{5} $

### Problem 8b
# Explanation:
## Step1: Expand $ 10^{4} $
$ 10^{4}=10000 $
## Step2: Multiply by 1.5
$ 1.5\times10000 = 15000 $
# Answer:
$ 15000 $

### Problem 9
# Explanation:
## Step1: Set up the unit multiplier
We know $ 1 $ meter $ \approx 1.1 $ yd, so to convert yards to meters, we use the multiplier $ \frac{1\ \text{meter}}{1.1\ \text{yd}} $
## Step2: Multiply the length in yards by the multiplier
Length $ = 100\ \text{yd} $, so meters $ = 100\times\frac{1}{1.1}\approx\frac{100}{1.1}\approx90.91\approx91 $ (rounded to nearest meter)
# Answer:
$ 91 $ meters

### Problem 10a
# Explanation:
## Step1: Divide 1 by 6
$ \frac{1}{6}=1\div6\approx0.1666\cdots $
## Step2: Round to nearest hundredth
Look at the thousandth place (6), which is more than 5, so round up the hundredth place: $ 0.17 $
# Answer:
$ 0.17 $

### Problem 10b
# Explanation:
## Step1: Convert fraction to decimal (as in 10a: $ \frac{1}{6}\approx0.1666\cdots $)
## Step2: Multiply by 100 to get percent
$ 0.1666\cdots\times100\approx16.67\% $
# Answer:
$ 16.67\% $ (or $ 16\frac{2}{3}\% $)

### Problem 11
# Explanation:
## Step1: Convert one million dollars to pennies
1 dollar = 100 pennies, 1 million dollars = $ 1000000 $ dollars. So pennies $ = 1000000\times100 = 100000000 $
## Step2: Convert to scientific notation
$ 100000000 = 1\times10^{8} $
# Answer:
$ 1\times10^{8} $ pennies

### Problem 12
# Explanation:
## Step1: Convert 11 million to scientific notation
11 million $ = 11000000 = 1.1\times10^{7} $
## Step2: Compare with $ 1.1\times10^{6} $
Since $ 7 > 6 $, $ 1.1\times10^{7}>1.1\times10^{6} $, so $ 11\ \text{million} > 1.1\times10^{6} $
# Answer:
$ > $

### Problem 13
# Explanation:
## Step1: Find LCM of 5 and 7
LCM of 5 and 7 (coprime) is $ 5\times7 = 35 $
## Step2: Find even two - digit multiple
Multiples of 35: 35, 70, 105,... 70 is even and two - digit.
# Answer:
$ 70 $

### Problem 14
# Explanation:
## Step1: Convert inches to feet (1 foot = 12 inches)
Length: $ 47\frac{1}{2}=\frac{95}{2} $ inches, in feet: $ \frac{95}{2}\div12=\frac{95}{24}\approx3.96 $ feet
Width: $ 35\frac{1}{2}=\frac{71}{2} $ inches, in feet: $ \frac{71}{2}\div12=\frac{71}{24}\approx2.96 $ feet
## Step2: Calculate perimeter of rectangle ($ P = 2(l + w) $)
$ P\approx2(3.96 + 2.96)=2\times6.92 = 13.84\approx14 $ feet (approximate)
# Answer:
Approximately $ 14 $ feet (or more precise calculation: $ 47.5\div12\approx3.96 $, $ 35.5\div12\approx2.96 $, $ P = 2(3.96 + 2.96)=13.84\approx14 $)

### Problem 15
# Explanation:
## Step1: Convert inches to feet
Length: $ 47.5\div12\approx3.96 $ feet, Width: $ 35.5\div12\approx2.96 $ feet
## Step2: Calculate area of rectangle ($ A=l\times w $)
$ A\approx3.96\times2.96\approx11.72\approx12 $ square feet (approximate)
# Answer:
Approximately $ 12 $ square feet (or more precise: $ 3.96\times2.96 = 11.7216\approx12 $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 6 (assuming we solve part a first)

Step1: Define total as 1

Step2: Find fraction of metamorphic (assuming five eighths are metamorphic? Wait, the original text: "Five eighths of the rocks in the box were metamorphic. The rest were igneous." So to find igneous, subtract metamorphic from 1.

Step1: Write the number in digits

Step2: Convert to scientific notation

Answer:

Problem 7a