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Interpret the following linear function model with the given context. Leslie wants to throw a birthday party at their local bowling alley. The space is $100 to rent with an additional charge of $15 per person attending. This scenario of total cost is modeled by the linear function b(x)=100+15x

. Leslie gets a bill of $550 at the end of the evening. In addition to Leslie and Steve, how many other people attended this birthday party?(1 point)
Responses

32
32

30
30

28
28

37

5 answers

To find out how many additional people attended Leslie's birthday party, we can use the given linear function model for total cost:

\[ b(x) = 100 + 15x \]

where:

  • \( b(x) \) is the total cost,
  • \( 100 \) is the initial space rental fee,
  • \( 15 \) is the cost per person, and
  • \( x \) is the number of people attending.

Leslie received a bill of $550, so we can set the equation:

\[ 100 + 15x = 550 \]

Now, we can solve for \( x \):

  1. Subtract 100 from both sides: \[ 15x = 550 - 100 \] \[ 15x = 450 \]

  2. Divide both sides by 15: \[ x = \frac{450}{15} \] \[ x = 30 \]

Since the problem states that Leslie and Steve are attending, we have to add them to the number of additional people:

  • Total attendees, \( x \), is 30.
  • Given that Leslie and Steve are 2 people, the number of other people attending will be: \[ 30 - 2 = 28 \]

Therefore, the number of other people who attended the birthday party is 28.

Report the longest possible length with the appropriate level of precision for a measurement of 34.2 meters.(1 point)
Responses

34.25
34.25

33.7
33.7

35.25
35.25

29.2

When reporting the longest possible length with the appropriate level of precision for a measurement of 34.2 meters, we need to consider the precision of the original measurement.

The measurement of 34.2 meters has one decimal place, indicating a precision of 0.1 meters. The longest possible length while maintaining this level of precision would be 34.2 meters plus the maximum uncertainty allowed by the precision.

Thus, the longest possible length is: \[ 34.2 , \text{meters} + 0.05 , \text{meters} = 34.25 , \text{meters} \]

Therefore, the correct response is 34.25.

Which response represents the longest possible length and width of the rectangle with the appropriate level of precision?

(1 point)
Responses

3.3 and 4.7 inches
3.3 and 4.7 inches

3.8 and 5.2 inches
3.8 and 5.2 inches

3.85 and 5.25 inches
3.85 and 5.25 inches

3.95 and 5.35
3.95 and 5.35

To determine the longest possible length and width of a rectangle with the appropriate level of precision, we first need to consider the precision of the given measurements.

When reporting dimensions, the precision is typically determined by the least precise measurement, which would need to be used when making calculations involving those dimensions.

Here’s the level of precision for each pair of measurements provided:

  1. 3.3 and 4.7 inches: Both have one decimal place.
  2. 3.8 and 5.2 inches: Both have one decimal place.
  3. 3.85 and 5.25 inches: Both have two decimal places.
  4. 3.95 and 5.35 inches: Both have two decimal places.

To find the longest possible dimensions at the correct level of precision:

  • The pairs 3.85 and 5.25 inches and 3.95 and 5.35 inches provide two decimal places, which is more precise than the measurements with just one decimal place.

To maintain this level of precision, we can assert the longest possible values include these pairs.

Among the options:

  • 3.95 and 5.35 inches are numerically larger than 3.85 and 5.25 inches.

Therefore, the correct response representing the longest possible length and width of the rectangle with the appropriate level of precision is:

3.95 and 5.35.