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Question

Question
Which two ratios form a proportion?(1 point)
Responses

204
and 15
20 fourths and 1 fifth

420
and 15
4 over 20 and 1 fifth

420
and 25
4 over 20 and 2 fifths

204
and 25
20 fourths and 2 fifths
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Answer 1

To determine which two ratios form a proportion, we must check if the cross-products are equal. In other words, for two ratios \( \frac{a}{b} \) and \( \frac{c}{d} \), they form a proportion if \( a \times d = b \times c \).

Let's analyze the given pairs:

1. 204 and 15

   • Not clear, let’s skip this.

2. 20 fourths and 1 fifth

   • This can be expressed as:
     • \( 20 \div 4 = 5 \) (so "20 fourths" = 5)
     • \( 1 \div 5 = 0.2 \) (so "1 fifth" = 0.2)
   • The ratio is \( 5:0.2 \).

3. 420 and 15

   • Again, not clear, let’s skip this.

4. 4 over 20 and 1 fifth

   • Expressing these as fractions:
     • \( \frac{4}{20} = \frac{1}{5} \)
     • Ratio = \( \frac{1}{5} \)

5. 420 and 25

   • Not as clear. Let’s check.

6. 4 over 20 and 2 fifths

   • \( \frac{4}{20} = \frac{1}{5} \) and \( 2 \div 5 = 0.4 \).

7. 204 and 25

   • Not clear, let’s skip.

8. 20 fourths and 2 fifths

   • \( 20 \div 4 = 5 \) and \( 2 \div 5 = 0.4 \).

So, out of the options after analyzing, we check the pairs:

• Out of 4 over 20 and 1 fifth is equal, therefore it forms a proportion as:

\[ 4 \times 5 = 20 \] \[ 20 \times 1 = 20 \]

Thus, the correct option is 4 over 20 and 1 fifth forming a proportion.

Answer 2

2 of 182 of 18 Items
Question 1
Madison is buying bulky candy for a dance company fundraiser. She buys 1000 candy bars for $350. What is the unit cost per candy bar?

Which process will you use to solve this problem?

(1 point)
Responses

1000÷350
1000 divided by 350

350÷1000
350 divided by 1000

1000×350
1000 times 350

1000−350
1000 minus 350
Question 2
What is the unit cost per candy bar?(1 point)
The unit price is $
per candy bar
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Answer 3

To determine the unit cost per candy bar, you need to find the cost of one candy bar by dividing the total cost by the total number of candy bars.

Question 1:

Which process will you use to solve this problem?

• The correct option is: 350 ÷ 1000 (350 divided by 1000)

Question 2:

What is the unit cost per candy bar? Now, let's calculate it:

• Total cost = $350
• Number of candy bars = 1000

The unit cost per candy bar can be calculated as follows:

\[ \text{Unit cost} = \frac{\text{Total cost}}{\text{Number of candy bars}} = \frac{350}{1000} = 0.35 \]

Thus, the unit price is $0.35 per candy bar.

Answer 4

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Question 1
A hiker ascended 34
of a kilometer in 116
of an hour. What was the mountain hiker's ascent rate in kilometers per hour?



What process will you use to solve this problem?

(1 point)
Responses

34−116
3 fourths minus 1 over 16

34×116
3 fourths times 1 over 16

34÷116
3 fourths divided by 1 over 16

116÷34
1 over 16 divided by 3 fourths
Question 2
What was the mountain hiker's ascent rate in kilometers per hour?(1 point)
kilometers per hour
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Answer 5

To find the ascent rate in kilometers per hour for the hiker, you need to divide the distance ascended by the time taken.

Question 1:

What process will you use to solve this problem?

• The correct option is: 34 ÷ 116 (3 fourths divided by 1 over 16)

This reflects finding how many kilometers per hour by dividing the distance (in kilometers) by the time (in hours).

Question 2:

Now, let's calculate the ascent rate:

1. Distance ascended: \( \frac{3}{4} \) kilometers
2. Time taken: \( \frac{1}{16} \) hours

To find the ascent rate, we perform the division:

\[ \text{Ascent rate} = \frac{\frac{3}{4}}{\frac{1}{16}} \]

To divide by a fraction, we multiply by its reciprocal:

\[ \text{Ascent rate} = \frac{3}{4} \times \frac{16}{1} = \frac{3 \times 16}{4 \times 1} = \frac{48}{4} = 12 \text{ kilometers per hour} \]

Thus, the mountain hiker's ascent rate is 12 kilometers per hour.

Answer 6

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Question 1
Three dozen muffins cost $9.00. Determine the cost per muffin.

What process will you use to solve this problem?

(1 point)
Responses

9÷3
9 divided by 3

9÷12
9 divided by 12

9÷(3×12)
9 divided by open paren 3 times 12 close paren

9÷3×12
9 divided by 3 times 12

12÷3×9
12 divided by 3 times 9
Question 2
What is the cost per muffin?(1 point)
$
per muffin
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Answer 7

To determine the cost per muffin, you need to divide the total cost by the total number of muffins.

Question 1:

What process will you use to solve this problem?

• The correct option is: 9 ÷ (3 × 12) (9 divided by open paren 3 times 12 close paren)

This is because you need to first calculate the total number of muffins (which is 3 dozen, or \(3 \times 12\)) and then divide the total cost ($9) by that number.

Question 2:

Now, let's calculate the cost per muffin:

1. Total cost: $9.00
2. Total number of muffins: \(3 , \text{dozen} = 3 \times 12 = 36 , \text{muffins}\)

Now, calculate the cost per muffin:

\[ \text{Cost per muffin} = \frac{\text{Total cost}}{\text{Total number of muffins}} = \frac{9}{36} \]

Now simplify \( \frac{9}{36} = \frac{1}{4} = 0.25 \).

Thus, the cost per muffin is $0.25 per muffin.

Answer 8

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Question
Which THREE equations represent non-proportional relationships?(1 point)
Responses

y=23x
y is equal to 2 thirds x

y=−15x
y is equal to negative 15 x

y=4.08x
y is equal to 4 point 0 8 x

y=5x−9
y is equal to the fraction with numerator 5 and denominator x minus 9

y=10x+10
y is equal to 10 x plus 10

y=x2
y is equal to x squared
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Answer 9

To determine which equations represent non-proportional relationships, we need to understand that a proportional relationship can be expressed in the form \(y = kx\), where \(k\) is a constant. Non-proportional relationships either have a constant added or subtracted (which results in a y-intercept different from zero), or involve other non-linear functions.

Let's analyze the provided equations:

1. \(y = \frac{2}{3}x\): This is a proportional relationship (the y-intercept is 0).

2. \(y = -15x\): This is also a proportional relationship (the y-intercept is 0).

3. \(y = 4.08x\): This is a proportional relationship (the y-intercept is 0).

4. \(y = 5x - 9\): This is non-proportional because of the \(-9\) (the y-intercept is not 0).

5. \(y = 10x + 10\): This is non-proportional because of the \(+10\) (the y-intercept is not 0).

6. \(y = x^2\): This is non-proportional because it is a quadratic equation (not a linear relationship).

Summary

The three equations that represent non-proportional relationships are:

• \(y = 5x - 9\)
• \(y = 10x + 10\)
• \(y = x^2\)

So the final answer is:

1. \(y = 5x - 9\)
2. \(y = 10x + 10\)
3. \(y = x^2\)