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| Section | Objectives |
|---|---|
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
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NEW QUESTION # 62
A person makes down quilts to sell.
The graph shows the functions that model the cost and revenue.
How many down quilts need to sell to break even/start making a profit?
Answer: D
Explanation:
This question asks us to interpret a graph showing cost and revenue.
In Applied Algebra, the break-even point is where:
" Revenue " = " Cost "
On a graph, this happens where the revenue line and the cost line intersect.
From the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The break-even point occurs where these two lines cross.
Looking carefully at the graph, the two lines intersect at approximately:
x=6
The horizontal axis represents the number of units, meaning the number of down quilts sold.
So the person needs to sell about:
6 " quilts "
to break even.
After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.
NEW QUESTION # 63
In the graph showing the number of new customer accounts, the horizontal axis shows the number of weeks since the beginning of winter and the vertical axis shows the number of new customer accounts. More customer accounts are opened during snowy weeks than during weeks without snow.
When was it likely snowy?
Answer: B
Explanation:
This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions.
Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.
NEW QUESTION # 64
A researcher collected data on the average selling price for tickets to a concert over time. The results are shown in the scatterplot. A regression function is graphed with r
2=0.56. The predicted average selling price for tickets after 10.8 days is $167.20.
Is this prediction appropriate?
Answer: C
Explanation:
The regression model has r2=0.56, which indicates a moderate fit. A moderate fit is not as reliable as a strong fit, but it can still be used for limited prediction when the extrapolation is close to the observed data. The prediction is made at x=10.8 days. This value is slightly beyond the maximum observed x-value, so the prediction is an extrapolation. For a moderate fit, the x-value should remain within about 25% of the range beyond the maximum value. In this case, x=10.8 is within that acceptable range, so the prediction is appropriate. Therefore, the correct answer is B.
NEW QUESTION # 65
A cart is being loaded with boxes, and each box has the same weight. After 4 boxes are loaded, the total weight of the boxes and cart is 116 pounds. After 9 boxes are loaded, the total weight is 161 pounds.
What is the weight of each box?
Answer: A
Explanation:
This situation can be modeled with a linear relationship because each box has the same weight.
We are given:
4 " boxes " #116 " pounds "
and
9 " boxes " #161 " pounds "
The weight increases because more boxes are added.
First, find the change in total weight:
161-116=45
Then find the change in the number of boxes:
9-4=5
Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:
45/5=9
So each box weighs:
9 " pounds "
Check:
If each box weighs 9 pounds, then adding 5 more boxes adds:
5(9)=45
116+45=161
This matches the given information.
NEW QUESTION # 66
The number of property sales in a region this year is expected to be 6 less than the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 330?
Answer: D
Explanation:
We are told that this year's number of property sales is 6 less than last year's number of property sales.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 6 less than last year's sales, the function rule is:
H(x)=x-6
The question says that the number of properties sold last year was:
x=330
Substitute 330into the function:
H(330)=330-6
H(330)=324
So the notation that correctly represents the number of property sales this year is:
H(330)=324
This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.
NEW QUESTION # 67
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