Ask a New Question
Menu

Use the image to answer the question.

A graph between number of guests and prices. The x-axis represents guests and ranges from 0 to 50 in increments of 10. The y-axis represents price and ranges from 0 to 300 in increments of 25.

Rafael is trying to book a graduation party. The party pavilion charges $100 for the first 10 people, $150 for more than 10 and up to 20 people, $200 for more than 20 and up to 30 people, $250 for more than 30 and up to 40 people, and $275 for more than 40 and up to 50 people. If Rafael wants to spend $250 for this party, how many people can he invite?

(1 point)
Responses

20<x≤30
20 less than x less-than-or-equal-to 30

30<x≤40
30 less than x less-than-or-equal-to 40

30<x≤50
30 less than x less-than-or-equal-to 50

20<x≤40
20 less than x less-than-or-equal-to 40
Skip to navigation

11 answers

To determine how many guests Rafael can invite if he wants to spend $250 on the party pavilion:

  1. The price options according to the number of guests are as follows:
    • For 0 to 10 guests: $100
    • For more than 10 up to 20 guests: $150
    • For more than 20 up to 30 guests: $200
    • For more than 30 up to 40 guests: $250
    • For more than 40 up to 50 guests: $275

Since Rafael is willing to spend $250, we look at the price tier that matches this budget:

  • The price for more than 30 guests and up to 40 guests is $250.

Therefore, the number of guests Rafael can invite is 30 < x ≤ 40.

The correct response is: 30<x≤40 (30 less than x less-than-or-equal to 40)

A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5,000 wasps, the situation can be modeled by the equation w(t)=5,000(1.13)t
, where w is the number of wasps after time t months. Which of the following statements is true about the equation?(1 point)
Responses

As t increases, w decreases quickly at first and then slowly.
As t increases, w decreases quickly at first and then slowly.

As t increases, w increases slowly at first and then quickly.
As t increases, w increases slowly at first and then quickly.

As t increases, w decreases slowly at first and then quickly.
As t increases, w decreases slowly at first and then quickly.

As t increases, w increases quickly at first and then slowly.

To analyze the behavior of the equation \( w(t) = 5,000 (1.13)^t \):

  • The function models exponential growth because it has the form \( A(1 + r)^t \), where \( A \) is the initial amount (5,000 wasps), \( r \) is the growth rate (0.13 or 13%), and \( t \) is time in months.

For exponential growth, as \( t \) increases:

  1. The value of \( w(t) \) will increase.
  2. Initially, the increase in \( w(t) \) will be relatively slow because it's just a multiplication of the growth factor to the initial population.
  3. However, over time, as \( t \) grows larger, the value of \( w(t) \) will increase more rapidly because each month's growth is based on the increasing number of wasps. Therefore, the growth starts off slow and accelerates as the population grows larger.

Given these points, the correct statement about the equation is:

As t increases, w increases slowly at first and then quickly.

The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function y=−16t2+30t+2
, which of the following correctly identifies the y-intercept and best explains its meaning?(1 point)
Responses

The y-intercept is at (0,2)
. The shirts are launched at an initial height of 2 feet.
The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirts are launched at an initial height of 2 feet.

The y-intercept is at (2,0)
. The shirts are launched at an initial height of 2 feet.
The y -intercept is at left parenthesis 2 comma 0 right parenthesis . The shirts are launched at an initial height of 2 feet.

The y-intercept is at (0,2)
. The shirt will reach the ground after 2 seconds from being launched.
The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirt will reach the ground after 2 seconds from being launched.

The y-intercept is at (0,0)
. The shirts are launched from the ground.

To determine the y-intercept of the function \( y = -16t^2 + 30t + 2 \), we need to evaluate the function when \( t = 0 \):

\[ y(0) = -16(0)^2 + 30(0) + 2 = 2 \]

This means the y-intercept is at the point \( (0, 2) \).

The meaning of the y-intercept in this context is that it represents the initial height from which the T-shirts are launched. Since the height is 2 feet, this indicates that the shirts are launched from a height of 2 feet off the ground.

Thus, the correct response is:

The y-intercept is at (0, 2). The shirts are launched at an initial height of 2 feet.

Given the function notation for the explicitly defined sequence f(n)=2n−1
, find the fifth term of the sequence.(1 point)
f(5)=

To find the fifth term of the sequence defined by the function \( f(n) = 2n - 1 \), you need to substitute \( n = 5 \) into the function:

\[ f(5) = 2(5) - 1 \]

Now, calculate it:

\[ f(5) = 10 - 1 = 9 \]

Thus, the fifth term of the sequence is:

\[ f(5) = 9 \]

Use the explicit formula An=4.8+(n−1)2
to find the 11th term in the described arithmetic sequence.(1 point)
A11=

To find the 11th term of the arithmetic sequence defined by the explicit formula \( A_n = 4.8 + (n - 1) \cdot 2 \), we need to substitute \( n = 11 \) into the formula:

\[ A_{11} = 4.8 + (11 - 1) \cdot 2 \]

First, calculate \( (11 - 1) \):

\[ 11 - 1 = 10 \]

Now, substitute this value back into the formula:

\[ A_{11} = 4.8 + 10 \cdot 2 \]

Calculate \( 10 \cdot 2 \):

\[ 10 \cdot 2 = 20 \]

Now substitute that into the equation:

\[ A_{11} = 4.8 + 20 \]

Finally, perform the addition:

\[ A_{11} = 24.8 \]

Thus, the 11th term is:

\[ A_{11} = 24.8 \]

Manuel has saved $253.32 so far. He plans to put $50 into his savings each month for the next year. How much money will Manuel have after a year of savings?(1 point)
$

To calculate how much money Manuel will have after a year of savings, we need to take into account his current savings and the additional savings he will contribute over the next year.

  1. Current savings: $253.32
  2. Monthly savings: $50
  3. Duration: 12 months

First, calculate the total amount he will save over the next year:

\[ \text{Total savings from monthly contributions} = 50 , \text{(dollars per month)} \times 12 , \text{(months)} = 600 \]

Next, add this to his current savings:

\[ \text{Total savings after one year} = \text{Current savings} + \text{Total savings from monthly contributions} \] \[ \text{Total savings after one year} = 253.32 + 600 = 853.32 \]

Thus, after one year of savings, Manuel will have:

\[ \boxed{853.32} \]