7 curtis wants to build a model of a 180 - meter tall building. he will be using a scale of 1.5 centimeters = 3.5 meters. how tall will the model be? round your answer to the nearest tenth. 8 there are 10 cups of oatmeal in the box of quaker oatmeal. if each serving is 1/3 of a cup, how many servings are in the box? a. 3 b. 30 c. 300 d. 10 9 a small rectangle has a width of 4 ft. and a length of 10 ft. a larger, similar rectangle has a length of 12 ft. what is the perimeter of the larger rectangle? 10 jessica bakes 112 muffins in 7 batches. how many muffins does each batch contain? 11 a meteorologist reports that the ratio of snowfall in january to total snowfall during the average winter is 2 to 5. if 34 inches have fallen in january of the current year, find the predicted total snowfall for the entire winter 12 triangle hjk is similar to triangle lmn. which proportion can be used to calculate the length of lm in centimeters? a 7.5/11.25 = lm/4.5 b 6/7.5 = lm/9 c 11.25/lm = 4.5/7.5 d 9/lm = 6/4.5

Question

Accepted Answer

### 7
# Explanation:
## Step1: Set up proportion
Let $x$ be the height of the model. The proportion is $\frac{1.5}{3.5}=\frac{x}{180}$.
## Step2: Cross - multiply
$3.5x = 1.5	imes180$.
## Step3: Solve for $x$
$x=\frac{1.5	imes180}{3.5}=\frac{270}{3.5}\approx77.1$ centimeters.
# Answer:
$77.1$ centimeters

### 8
# Explanation:
To find the number of servings, divide the total amount of oatmeal by the amount per serving. The total amount of oatmeal is 10 cups and each serving is $\frac{1}{3}$ of a cup. So we calculate $10\div\frac{1}{3}$.
## Step1: Use division rule for fractions
$10\div\frac{1}{3}=10	imes3$.
## Step2: Calculate result
$10	imes3 = 30$.
# Answer:
b. 30

### 9
# Explanation:
Since the rectangles are similar, the ratios of their corresponding sides are equal. Let the width of the larger rectangle be $w$. We have $\frac{10}{12}=\frac{4}{w}$, so $10w = 4	imes12$, and $w=\frac{4	imes12}{10}=4.8$ ft.
## Step1: Calculate perimeter formula
The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l = 12$ ft and $w = 4.8$ ft.
## Step2: Substitute values
$P=2(12 + 4.8)$.
## Step3: Calculate result
$P=2	imes16.8=33.6$ ft.
# Answer:
$33.6$ ft

### 10
# Explanation:
To find the number of muffins in each batch, divide the total number of muffins by the number of batches.
## Step1: Perform division
$112\div7 = 16$.
# Answer:
16 muffins

### 11
# Explanation:
Let the total snow - fall be $x$ inches. Set up a proportion using the given ratio. The proportion is $\frac{2}{5}=\frac{34}{x}$.
## Step1: Cross - multiply
$2x=34	imes5$.
## Step2: Solve for $x$
$x=\frac{34	imes5}{2}=85$ inches.
# Answer:
85 inches

### 12
# Explanation:
For similar triangles, the ratios of corresponding sides are equal. In similar triangles $	riangle HJK$ and $	riangle LMN$, the ratio of the hypotenuses is equal to the ratio of the corresponding legs.
## Step1: Identify corresponding sides
The ratio of the hypotenuse of $	riangle HJK$ to the hypotenuse of $	riangle LMN$ is equal to the ratio of the leg $HJ$ to the leg $LM$. So $\frac{7.5}{11.25}=\frac{4.5}{LM}$. Cross - multiplying gives $\frac{7.5}{11.25}=\frac{LM}{4.5}$ is incorrect. The correct proportion for finding $LM$ is $\frac{11.25}{LM}=\frac{7.5}{4.5}$ or $\frac{LM}{4.5}=\frac{11.25}{7.5}$.
# Answer:
C. $\frac{11.25}{LM}=\frac{7.5}{4.5}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

7

Step1: Set up proportion

Step2: Cross - multiply

Step3: Solve for $x$

Step1: Use division rule for fractions

Step2: Calculate result

Step1: Calculate perimeter formula

Step2: Substitute values

Step3: Calculate result

Answer:

8