10. manufacturing a machinist can produce 114 parts in 6 minutes. at this rate, how many parts can the machinist produce in 15 minutes?
11. recipes a recipe that makes 8 jumbo blueberry muffins calls for 1 1/2 teaspoons of baking powder. how much baking powder is needed to make 3 dozen jumbo muffins?
estimate the unit rate for each item. justify your answers.
12. $299 for 4 tires
13. 3 yards of fabric for $13.47
14. utilities use the table that shows the average monthly electricity and water usage.
a. which family uses about twice the amount of electricity per person than the other two families? explain your reasoning.
b. which family uses the least amount of water per person? explain your reasoning.
| family name | family size | electricity (kilowatt - hours) | water (gal) |
|--|--|--|--|
| melendez | 4 | 1,560 | 3,500 |
| barton | 6 | 2,130 | 6,400 |
| stiles | 2 | 1,490 | 2,500 |

Question

Accepted Answer

### 10.
# Explanation:
## Step1: Find the production rate per minute
The machinist produces 114 parts in 6 minutes. The rate $r$ (parts per minute) is found by dividing the number of parts by the number of minutes. So $r=\frac{114}{6}=19$ parts per minute.
## Step2: Calculate parts produced in 15 minutes
To find the number of parts $n$ produced in 15 minutes, we multiply the rate $r$ by the time $t = 15$ minutes. So $n=r	imes t=19	imes15 = 285$ parts.
# Answer:
285

### 11.
# Explanation:
## Step1: Convert 3 dozen to number of muffins
Since 1 dozen is 12, 3 dozen is $3	imes12 = 36$ muffins.
## Step2: Find the amount of baking - powder per muffin
The recipe for 8 muffins calls for $1\frac{1}{2}=\frac{3}{2}$ teaspoons of baking powder. The amount of baking powder per muffin $b$ is $b=\frac{\frac{3}{2}}{8}=\frac{3}{2}	imes\frac{1}{8}=\frac{3}{16}$ teaspoons per muffin.
## Step3: Calculate baking - powder for 36 muffins
The amount of baking powder $B$ needed for 36 muffins is $B = b	imes36=\frac{3}{16}	imes36=\frac{3	imes36}{16}=\frac{108}{16}=\frac{27}{4} = 6.75$ teaspoons.
# Answer:
6.75 teaspoons

### 12.
# Explanation:
## Step1: Calculate the unit rate
To find the unit rate (cost per tire), divide the total cost by the number of tires. The unit rate $u$ for 4 tires costing $299$ is $u=\frac{299}{4}=74.75$ dollars per tire.
# Answer:
$74.75$ per tire

### 13.
# Explanation:
## Step1: Calculate the unit rate
To find the unit rate (cost per yard of fabric), divide the total cost by the number of yards. The unit rate $u$ for 3 yards of fabric costing $13.47$ is $u = \frac{13.47}{3}=4.49$ dollars per yard.
# Answer:
$4.49$ per yard

### 14a.
# Explanation:
## Step1: Calculate electricity consumption per person for each family
For Melendez family: $\frac{1560}{4}=390$ kilowatt - hours per person.
For Barton family: $\frac{2130}{6}=355$ kilowatt - hours per person.
For Stiles family: $\frac{1490}{2}=745$ kilowatt - hours per person.
## Step2: Compare the values
We can see that $745\approx2	imes355$ and $745$ is approximately twice of $355$. So the Stiles family uses about twice the amount of electricity per person than the Barton family.
# Answer:
The Stiles family.

### 14b.
# Explanation:
## Step1: Calculate water consumption per person for each family
For Melendez family: $\frac{3500}{4}=875$ gallons per person.
For Barton family: $\frac{6400}{6}\approx1066.67$ gallons per person.
For Stiles family: $\frac{2500}{2}=1250$ gallons per person.
## Step2: Compare the values
Since $875<1066.67<1250$, the Melendez family uses the least amount of water per person.
# Answer:
The Melendez family.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

10.

Step1: Find the production rate per minute

Step2: Calculate parts produced in 15 minutes

Step1: Convert 3 dozen to number of muffins

Step2: Find the amount of baking - powder per muffin

Step3: Calculate baking - powder for 36 muffins

Step1: Calculate the unit rate

Answer:

11.