Answers Algebra 2 MP 234 CHSModeling with Periodic Functions

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Determine the domain of each piece.Domain of piece 1:[)

–5, 5

–4, –1

1, 4

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–4

–4x

= –4

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Determine the domain of each piece.Domain of piece 1:[)

–5, 5

–4, –1

1, 4

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–4

–4x

= –4

Which right prism would have the same volume as a square prism with a base area of 36 m2 and a height of 3 m?

[Image: A right triangular prism is shown. The triangle ha...]

[Image: A rectangular prism is shown. The rectangle has si...]

[Image: A triangular prism is shown. The triangle has a ba...]

Which statements about the composite figure are true? Check all that apply.

The composite figure consists of two rectangular pyramids.

The composite figure can be broken down into rectangular prisms.

The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5).

The total volume is 45 units3.

The total volume is 90 units3.

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Answer:

4.8

Which of the following shows the graph of y = –(2)x – 1?

On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5).

On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).

On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).

On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).

Which expression represents the volume of the composite figure?

(2)(4.4)(5) + (2)(4.4)(3.9)

(2)(4.4)(5) – (2)(4.4)(3.9)

(2)(4.4)(5) + (2)(4.4)(3.9)

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Answer:

105

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Complete the statements about the two cones. The volumes of the cones are equal when . If a > b, then the cross-sectional area of cone A is the cross-sectional area of cone B at every level parallel to their respective bases.

Answers:

Selection 1:a = b

Selection 2:greater than

Domain of piece 2: [)

–5, 5

–3, 3

–1, 1

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Idenify the domain for the function, f(x).

Option

Domain of piece 2: [)

–5, 5

–3, 3

–1, 1

For which value of is cot () undefined?

90º

180º

270º

450º

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Idenify the domain for the function, f(x).

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Idenify the range for the function, f(x).

Option

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Answer not available

Domain of piece 3:[]

–5, 5

1, 5

1, –3

What is the range of this function?

Option

Idenify the range for the function, f(x).

Option

Domain of piece 3:[]

–5, 5

1, 5

1, –3

What is the range of this function?

Option

Which transformations are needed to change the parent sine function to the sine function below?

vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left

vertical stretch of 2, horizontal compression to a period of , vertical shift of 2 units up, phase shift of units left

vertical stretch of , horizontal compression to a period of , vertical shift of 1 unit up, phase shift of units left

vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit down, phase shift of units left

Select the rule for each piece.Rule for piece 1:

y = –x

y = 1 – x

y = x + 1

Select the rule for each piece.Rule for piece 1:

y = –x

y = 1 – x

y = x + 1

The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. What is the life span of an appliance that has a z-score of –3?

3 months

24 months

45 months

72 months

Rule for piece 2:

y = –1

y = 0

y = 1

Rule for piece 2:

y = –1

y = 0

y = 1

A circle has a central angle measuring radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for .

3.7 cm

4.9 cm

14.3 cm

15.4 cm

Rule for piece 3:

y = –x

y = 2 – x

y = x + 2

Rule for piece 3:

y = –x

y = 2 – x

y = x + 2

What is rewritten using the power property?

e log Subscript 6 Baseline f

f log Subscript 6 Baseline e

log Subscript 6 Baseline (e times f)

log Subscript 6 Baseline (e + f)

Which of the following is the graph of ?

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.

On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

The reference angle should be , and the sign of the value should be negative.

The reference angle should be , and the cosine value for is .

The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting in the first step.

The cosine value for is , and the reference angle and quadrant should be determined by subtracting in the first step.

A triangular prism with a rectangular base is stacked on top of a rectangular prism. The rectangle has side lengths of 20 and 15 units. The rectangular prism has a height of 12. The triangular prism has a height of 16 units.

1,200 units3

4,400 units3

5,040 units3

6,000 units3

What is the formula for margin of error?

ME =

Voluntary sampling is one type of sampling method that is not probability based. This means that

each member of a population is equally likely to be chosen for the survey.

the results of the survey cannot reliably be extended and generalized.

the likelihood of a member of the population volunteering to be surveyed is not probable.

the results of the survey are not mathematically probable.

Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350. Which most restrictive level of significance would suggest that the company should raise rates? Upper-Tail Valuesa5%2.5%1%Critical z-values1.651.962.58

2.5%

10%

A gymnastics coach records the scores of a gymnast and develops the probability distribution below. What is the probability the gymnast scores a 9 or 9.5?Probability DistributionGymnastics Score: XProbability: P(X)50.025.50.0260.066.50.170.167.50.1480.188.50.189?9.50.02

0.02

0.04

0.12

0.14

A bungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. Then he falls 64.8 feet before bouncing up again. On his third descent, he falls 43.2 feet before going back up. What is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (Do not include the distance traveled up.)

234.0 ft

253.2 ft

789.8 ft

1,281.8 ft

The distribution of the values of a population is shown below, and a simple random sample is drawn from the population. Based on this information alone, can the sample be used to make inferences about the population?

No, because the population values appear to be normally distributed.

No, because the population values do not appear to be normally distributed.

Yes, because the population values appear to be normally distributed.

Yes, because the population values do not appear to be normally distributed.

The histogram below shows the estimated monthly salaries of company employees with different years of experience. How might the graph be misleading?

The scale on the y-axis overemphasizes the difference in salaries between different experience levels.

The scale on the y-axis underemphasizes the difference in salaries between different experience levels.

The scale on the x-axis overemphasizes the difference in salaries between different experience levels.

The scale on the x-axis underemphasizes the difference in salaries between different experience levels.

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

1.9 units

4.7 units

5.0 units

5.7 units

The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day?Probability DistributionDays Absent: XProbability: P(X)00.7810.1420.0330.014050.04

0.08

0.14

0.78

0.92

Which expression is equivalent to ?

log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x

log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9

3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9

3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x

For what values of x does ?

x = –3, x = 1

x = –1, x = 3

x = negative three-halves, x = 2

x = negative 2, x = three-halves

Weston completed a hypothesis test and found that he could not reject the null hypothesis. Which of the following is a valid reason for his conclusion?

The z-statistic is less than 0.

The z-statistic lies in the critical region.

The z-statistic is greater than 0.

The z-statistic lies outside the critical region.

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?