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Question
There are 168 members in an orchestra, and 38
of them play the violin. If each non-violin member practices 40 hours each week, how many hours do all of the violinists practice if they only practice25
of the amount of time?(3 points)
Step 1: Determine how members play the violin.

violinists

Step 2: Determine how much time each violinist spends practicing each week.

hours

Step 3: Use the answers from steps 1 & 2 to determine the total time spent practicing by all violinists.

hours

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7 answers

To solve the problem step by step, we'll follow the instructions provided in each step.

Step 1: Determine how many members play the violin.

There are 168 members in total, and 38 of them play the violin.

Number of violinists = 38

Step 2: Determine how much time each violinist spends practicing each week.

Each non-violin member practices for 40 hours each week. To find out how much time each violinist practices, we need to calculate 25% of that amount:

  • Practice time for non-violin members = 40 hours

Now we calculate 25% of this time for the violinists:

\[ \text{Practice time for violinists} = 40 , \text{hours} \times 0.25 = 10 , \text{hours} \]

Step 3: Use the answers from steps 1 & 2 to determine the total time spent practicing by all violinists.

Now that we know there are 38 violinists and each practices for 10 hours:

\[ \text{Total practice time for all violinists} = \text{Number of violinists} \times \text{Practice time for each violinist} \]

\[ \text{Total practice time} = 38 \times 10 = 380 , \text{hours} \]

Final Answers:

  1. Number of violinists: 38
  2. Time each violinist spends practicing each week: 10 hours
  3. Total time spent practicing by all violinists: 380 hours
5 of 75 of 7 Items

Question 1
The regular price of a novel is $24.95. It is currently on sale for $14.97. Complete the proportion to determine the percent of change.(2 points)
Drop target 1
Drop target 2
Question 2
What is the percent of change in this situation?(1 point)

% Round the answer to the nearest whole percent.
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To complete the questions regarding the percent of change in the price of the novel, we will follow the steps.

Question 1: Complete the proportion to determine the percent of change.

The percent of change can be calculated using the formula:

\[ \text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \]

In this case:

  • Old Value (regular price) = $24.95
  • New Value (sale price) = $14.97

Substituting the values into the formula, we get:

  1. Drop target 1: \( \text{New Value} - \text{Old Value} = 14.97 - 24.95 \)
  2. Drop target 2: \( \frac{14.97 - 24.95}{24.95} \times 100 \)

Thus, we have:

\[ \text{Percent Change} = \frac{14.97 - 24.95}{24.95} \times 100 \]

Question 2: Calculate the percent of change in this situation.

Now we need to calculate the actual percent change:

  1. Calculate the difference: \[ 14.97 - 24.95 = -9.98 \]

  2. Place this value in the formula: \[ \text{Percent Change} = \frac{-9.98}{24.95} \times 100 \]

  3. Perform the calculation: \[ \text{Percent Change} = \frac{-9.98}{24.95} \approx -0.400801 \]

  4. Convert it to a percentage: \[ -0.400801 \times 100 \approx -40.08% \]

Rounding to the nearest whole percent gives us:

Percent Change: -40%

Summary of the Answers:

  1. For the proportion: \( \text{Drop target 1} = 14.97 - 24.95 \) and \( \text{Drop target 2} = \frac{14.97 - 24.95}{24.95} \times 100 \)
  2. The percent of change in this situation is: -40%.
6 of 76 of 7 Items

Question 1
You are participating in a 5K run which is 3.1 miles. If there are 5,280 feet in one mile, complete the proportion to determine how many feet are in the 5K.



(1 point)
Drop target 1
Drop target 2
Drop target 3
Question 2
How many feet are in the 5K?(1 point)
feet (Enter your response without commas.)
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To solve the problems regarding the 5K run (which is 3.1 miles) and convert miles to feet, we will proceed as follows:

Question 1: Complete the proportion to determine how many feet are in the 5K.

We know that:

  • 1 mile = 5,280 feet

To find the total number of feet in 3.1 miles (5K), we can set up a proportion in the following way:

  1. Drop target 1: \(3.1 , \text{miles}\)
  2. Drop target 2: \(5,280 , \text{feet}\)
  3. Drop target 3: \(X , \text{feet}\)

The proportion could be expressed as:

\[ \frac{3.1 , \text{miles}}{X , \text{feet}} = \frac{1 , \text{mile}}{5,280 , \text{feet}} \]

In this case, the proportion setup means \(X\) equals the number of feet in 3.1 miles.

Question 2: How many feet are in the 5K?

Now, we need to calculate the total feet in 3.1 miles. We can do this by multiplying the number of miles by the number of feet in a mile:

\[ X = 3.1 , \text{miles} \times 5,280 , \text{feet/mile} \]

Calculating this gives us:

\[ X = 3.1 \times 5,280 \]

\[ X = 16,368 , \text{feet} \]

Final Answers:

  1. Proportion setup:

    • Drop target 1: \(3.1\)
    • Drop target 2: \(5,280\)
    • Drop target 3: \(X\)

  2. Feet in the 5K: 16368 (Enter without commas)

7 of 77 of 7 Items

Question 1

Lynley draws the quadrilateral on the left and then uses a scale factor to create the quadrilateral on the right. Determine the correct pairs of corresponding sides. Choose 2.

(2 points)
Responses

4 units corresponds to 5 units
4 units corresponds to 5 units

4 units corresponds to 7.5 units
4 units corresponds to 7.5 units

5 units corresponds to 7.5 units
5 units corresponds to 7.5 units

6 units corresponds to 4 units
6 units corresponds to 4 units

6 units corresponds to 5 units
6 units corresponds to 5 units

6 units corresponds to 7.5 units
6 units corresponds to 7.5 units
Question 2
Determine the scale factor she used to create the second quadrilateral.(1 point)
Responses

0.67
0.67

1.25
1.25

1.5
1.5

1.875
1.875
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To determine the correct pairs of corresponding sides and the scale factor used to create the second quadrilateral, let’s evaluate both questions step by step.

Question 1: Determine the correct pairs of corresponding sides.

To identify the corresponding sides between two quadrilaterals, it is essential to compare the lengths of each side in the original quadrilateral to the lengths of the sides in the scaled version. Since I do not have the diagram to refer to, I will explain how you can approach identifying the pairs.

  1. 4 units corresponds to 5 units: Determine if this is a valid corresponding pair. For example, if one side is 4 units in the original and it's scaled to 5 units in the new quadrilateral, then it's a match.
  2. 4 units corresponds to 7.5 units: Similarly, compare if a side of 4 units from the original is matched with a side of 7.5 units in the scaled version.
  3. 5 units corresponds to 7.5 units: Check if the original 5-unit side matches with a 7.5-unit side in the new quadrilateral.
  4. 6 units corresponds to 4 units: Assess if a side of 6 units in the first matches with 4 units in the second quadrilateral.
  5. 6 units corresponds to 5 units: Check if this is a valid correlation.
  6. 6 units corresponds to 7.5 units: Finally, determine if a 6-unit side in the original quadrilateral corresponds to 7.5 in the scaled quadrilateral.

Without the actual measurements from the figure:

  • To select the correct pairs, look for proportionality. The pairs should fit within the same scale factor.

Question 2: Determine the scale factor.

To calculate the scale factor, use the formula:

\[ \text{Scale Factor} = \frac{\text{Length of side in scaled quadrilateral}}{\text{Length of corresponding side in original quadrilateral}} \]

For example:

  • If a side in the original quadrilateral is \(x\) and the corresponding side in the scaled version is \(y\), then the scale factor \(k\) can be calculated for each corresponding pair.

Once you have collected pairs, simply calculate each one and find the common scale factor among them.

Let’s consider an example:

  1. If original side = 4 units and scaled side = 5 units: \[ k = \frac{5}{4} = 1.25 \]

  2. If original side = 6 units and scaled side = 7.5 units: \[ k = \frac{7.5}{6} = 1.25 \]

If multiple pairs agree with a scale factor of 1.25, then that would be the factor used for the scaling.

Final Steps to Determine Answers:

  1. Select two pairs of corresponding sides based on comparison and proportionality from the options provided.
  2. Calculate or identify the scale factor based on the selected corresponding sides, choosing from the list provided (0.67, 1.25, 1.5, 1.875).

If you can identify the correct corresponding sides based on the properties given or the images in front of you, use those to find the correct scale factor.