Use the image to answer the question.

To determine how much money Mini Motorbikes & More will make if they sell nine tickets, you will need to analyze the step function plotted on the graph. The variable on the x-axis represents the total number of raffle tickets sold, while the variable on the y-axis represents the corresponding money earned.

Assuming the ticket sales are in groups of three, selling nine tickets means they have sold three groups of tickets.

Based on typical setups of such graphs, if the function shows that selling up to 9 tickets corresponds to a certain value on the y-axis, you can refer to the height of the step function at x = 9 to identify the money earned.

If we consider common sales figures for groups of raffle tickets, we often see values such as $100, $150, $200, etc.

Since the question states that selling nine tickets results in certain values, you should look at the specific segment corresponding to nine tickets on the graph. Without the actual image, you would refer to what the value is at that corresponding x-value.

However, if none of the responses precisely match 9 tickets due to missed details in the image representation, you can generally estimate that selling 3 bundles of tickets leads to a moderate total earning.

If we assume an incrementally increasing function and expect proportional earnings for each batch of tickets sold, we might infer that selling nine tickets results in earning about $200,.

Therefore, based on the choices provided, the best estimate for money made selling nine tickets would be:

$200

The population of a swarm of mosquitos is growing at an exponential rate. The growth can be modeled by the equation n(t)=50(1.2)t
, where n is the number of mosquitos after t days. After 11 days, a city decides to spray for mosquitos. Define an appropriate domain for the situation.(1 point)
Responses

0≤t≤11
0 less-than-or-equal-to t less-than-or-equal-to 11

0≤t≤372
0 less-than-or-equal-to t less-than-or-equal-to 372

0≤n≤372
0 less-than-or-equal-to n less-than-or-equal-to 372

0≤n≤11

To define an appropriate domain for the situation regarding the population of mosquitos modeled by the equation \( n(t) = 50(1.2)^t \), we need to focus on the variable \( t \), which represents the number of days.

Since the city decides to spray for mosquitos after 11 days, the relevant time interval will begin at \( t = 0 \) (the starting point) and end at \( t = 11 \) (the time just before spraying begins).

Thus, the appropriate domain for \( t \) in this context is:

\[ 0 \leq t \leq 11 \]

Therefore, the correct option is:

0 ≤ t ≤ 11

Use the table to answer the question.

0 375,000
1
2
3
4
5 The Diaz family purchased a home for $375,000. They decide to sell their home five years later. If the value of the home is increasing at a rate of 6% each year, the situation can be modeled using the equation f(x)=375,000(1.06)x
Finish the table to determine which graph displays the correct plotted points for the situation.(1 point)
Responses

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 200,000 to 500,000 in increments of 25,000.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 200,000 to 500,000 in increments of 25,000.

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis is labeled Years and ranges from 350,000 to 550,000 in increments of 25,000. The y-axis is labeled Home Value and ranges from 0 to 7 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis is labeled Years and ranges from 350,000 to 550,000 in increments of 25,000. The y-axis is labeled Home Value and ranges from 0 to 7 in increments of 1.

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 350,000 to 550,000 in increments of 25,000.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 350,000 to 550,000 in increments of 25,000.

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for years ranges from 0 to 7 in increments of 1. The y-axis for home value ranges from 0 to 350,000 in increments of 50,000.

first second third fourth or fith option

To find the correct graph that displays the plotted points for the value of the Diaz family's home over time, we first need to calculate the home value for each year from 0 to 5 using the equation:

\[ f(x) = 375,000(1.06)^x \]

Now, let’s calculate the values for \( x \) (the number of years):

• For \( x = 0 \): \[ f(0) = 375,000(1.06)^0 = 375,000 \]

• For \( x = 1 \): \[ f(1) = 375,000(1.06)^1 = 375,000 \times 1.06 = 397,500 \]

• For \( x = 2 \): \[ f(2) = 375,000(1.06)^2 = 375,000 \times 1.1236 = 422,850 \] (approximately)

• For \( x = 3 \): \[ f(3) = 375,000(1.06)^3 = 375,000 \times 1.191016 = 446,187 \] (approximately)

• For \( x = 4 \): \[ f(4) = 375,000(1.06)^4 = 375,000 \times 1.26247696 = 472,860 \] (approximately)

• For \( x = 5 \): \[ f(5) = 375,000(1.06)^5 = 375,000 \times 1.338225 = 501,093.75 \] (approximately)

Now our table looks like this (approximating each value):

| Years (x) | Home Value (f(x)) | |-----------|--------------------| | 0 | 375,000 | | 1 | 397,500 | | 2 | 422,850 | | 3 | 446,187 | | 4 | 472,860 | | 5 | 501,093 |

Now, let's evaluate the graph options:

1. First Option: A decreasing curve.
2. Second Option: An increasing curve, but with the x-axis labeled incorrectly.
3. Third Option: An increasing curve with an appropriate x and y-axis range, showing values more aligned with our findings.
4. Fourth Option: A decreasing curve.

Since the calculated values show that the home value is increasing over time (as expected in an exponential growth model), the correct graph must depict an increasing curve.

The third option shows an increasing curve with the correct axis labeling and range that matches the calculated values for the home's worth.

Conclusion:

The correct option is:

Third Option: An increasing curve with an arrow on the top, with x-axis for years ranging from 0 to 7 in increments of 1 and y-axis for home value from 350,000 to 550,000 in increments of 25,000.

Use the image to answer the question.

An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled shares and ranges from 0 to 6 in increments of 1. The y-axis is labeled views and ranges from 0 to 500 in increments of 100.

An algorithm on a social media site is set up so that the more shares a video receives, the more individuals the video is presented to on their feed. The views of a particular video are increasing at an exponential rate of 100% for each share the video receives. If the video originated with 10 views, the situation can be modeled by the exponential equation v(s)=10(2)s
where v is the number of views for every s shares. Which of the following statements is true about the equation?

(1 point)
Responses

The domain (s-values) includes the values (s≥0)
.
The domain ( s -values) includes the values left parenthesis s greater-than-or-equal-to 0 right parenthesis .

The range (v-values) includes the values greater than (0<v≤10)
.
The range ( v -values) includes the values greater than left parenthesis 0 less than v less-than-or-equal-to 10 right parenthesis .

The range (v-values) is all real numbers.
The range ( v -values) is all real numbers.

The domain (s-values) is all real numbers.

To determine the correct statements about the equation \( v(s) = 10(2)^s \), where \( v \) represents the number of views and \( s \) represents the number of shares, let's analyze the domain and range of this function.

Domain Analysis:

1. Shares (s): The variable \( s \) represents the number of shares a video receives. Shares cannot be negative, so the minimum number of shares is \( 0 \) (representing no shares). Thus, the domain of \( s \) is: \[ s \geq 0 \] or expressed in interval notation: \([0, \infty)\).

Range Analysis:

2. Views (v): The function starts with \( v(0) = 10(2^0) = 10 \) views when there are 0 shares. As the shares increase, \( s \) increases and the staff of the exponential function leads to views increasing rapidly. Since there is no upper limit to how many shares can lead to a potentially infinite number of views, we observe that:

   • As \( s \to \infty \), \( v(s) \to \infty \).
   • The minimum value occurs at \( s = 0 \), where \( v(0) = 10 \).

Thus, the range of \( v \) is: \[ v > 10 \] or in interval notation: \( (10, \infty) \).

Evaluating the Statements:

1. The domain (s-values) includes the values \( s \geq 0 \): True
2. The range (v-values) includes the values greater than \( 0 < v \leq 10 \): False (the minimum view is 10, not less than or equal to 10).
3. The range (v-values) is all real numbers: False (the range starts from just above 10 and goes to infinity).
4. The domain (s-values) is all real numbers: False (the domain is restricted to non-negative values).

Given this analysis, the true statement about the equation is:

The domain (s-values) includes the values \( s \geq 0 \).

Marilee is creating a garden in her yard. She needs to put up a fence to keep the animals out of it. She has 40 yards of fencing she can erect. This situation is modeled using the equation A=−w2+20w
, where A
is the area of the fence and w is the width of the fence. If you were to set up a table to determine the measurements of the width and its corresponding area, what would be a reasonable scale for the domain?(1 point)
Responses

5
5

10
10

1
1

2

To determine a reasonable scale for the domain of the situation modeled by the equation \( A = -w^2 + 20w \), where \( A \) is the area of the fence and \( w \) is the width of the fence, we first need to understand the context of the problem.

Understanding the Situation:

1. Total Perimeter: The total length of fencing available is 40 yards. Conventionally, for a rectangular garden made with fencing, the perimeter \( P \) is given by: \[ P = 2l + 2w = 40 \] From this, we can derive the expression for area, which leads to the equation given.

2. Setting the Equation: Since the equation \( A = -w^2 + 20w \) is derived from maximizing the area in terms of width, we can determine that:

   • The width \( w \) must be positive.
   • Additionally, since a width of zero would result in no area, we need to consider valid values of \( w \).

3. Finding Maximum Area: The vertex of the parabola represented by the equation \( A = -w^2 + 20w \) occurs at \( w = -\frac{b}{2a} = -\frac{20}{2(-1)} = 10 \).

4. Range of Width: The width must be within reasonable values that allow the formation of a garden, thus \( 0 < w < 20 \) (as \( w \) cannot exceed half of the total fencing).

Reasonable Scale for the Domain:

Given that the valid width values \( w \) can logically take should range from just above 0 up to 20, let's evaluate the options for a reasonable scale of \( w \):

• 1 yard increments: This scale would provide detailed readings as it allows for every integer from 1 up to 20.

• 2 yard increments: This would allow values of \( w = 2, 4, 6,...,20 \), which is still reasonable but less granular than 1 yard.

• 5 yard increments: This would give \( w = 5, 10, 15, 20 \), which may miss some important measurements in between.

• 10 yard increments: This gives only \( w = 10, 20 \), which is quite sparse.

Conclusion:

A more granular and reasonable scale is beneficial for identifying widths and their corresponding areas adequately. Based on this reasoning, the most appropriate scale for the domain of \( w \) is:

1 (yard increments).