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Resources

Write two-variable inequalities: word problems

92

. Какие формулы не задают функцию? Ответ обоснуйте.

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y=3 x^{2}-x+1

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y=6 x+|x-3|

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y=10

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y^{2}=16

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|y-3|=5

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3 y+x-2=y-4 x+1

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x+7=0

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y=\left\{\begin{array}{l}-x^{2} \\ 3 x+1\end{array}\right.

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\frac{2 y+x+3}{5-x}=1

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y=\left\{\begin{array}{l}x^{2}, \text { если } x<-1, \\ -x, \text { если }-1 \leq x<2, \\ \frac{1}{x}, \text { если } x \geq 2 ;\end{array}\right.

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y=6 x+|x-3|

0

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y=6 x+|x-3|

1

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y=6 x+|x-3|

2

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y=6 x+|x-3|

3

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y=6 x+|x-3|

4

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y=6 x+|x-3|

5

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y=6 x+|x-3|

6

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y=6 x+|x-3|

7

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93

. Найдите значения функции в заданных точках

y=6 x+|x-3|

8

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y=6 x+|x-3|

9

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y=10

0

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y=10

1

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y=10

2

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y=10

3

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y=10

4

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94

. Определите, при каких значениях аргумента функция принимае значения

y=10

5

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y=10

6

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y=10

7

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y=10

8

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y=10

9

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y^{2}=16

0

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y^{2}=16

1

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y^{2}=16

2

Suppose you have selected a random sample of

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n=14

measurements from a normal distribution. Compare the standard normal

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z

values with the corresponding

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t

values if you were forming the following confidence intervals.

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(a)

98\%

confidence interval

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[z=2.33],[t=2.6503]:

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(b)

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99\%

confidence interval

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{:[z=2.576],[t=\square]:}

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(c)

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z

0

confidence interval

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z

1

A company’s manager estimated that the cost

C

, in dollars, of producing

n

C = 7n + 350

. The company sells each item for

\$12

. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of

n

for which the manager estimates that the company will make a profit?

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n < 70

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n < 84

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n > 70

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n > 84

For all integers

x>0

f(x)

f(x)=\frac{f(x-1)}{(-1)^x}

f(1)=1

, which of the following statement is correct for the values of

f(x)

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A) The values of

f(x)

for all even values of

x

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B) The value of

f(x)

for all odd values of

x

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C) The value of

f(x)

for all even values is

f(x)

0

and for all odd values is

f(x)

1

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D) The value of

f(x)

f(x)

0

f(x)

1

Brenna is in the orchestra at her school. Both the orchestra and the band, along with any parents who want to go, are taking a field trip to a symphony. The orchestra purchases

24

student tickets and

8

adult tickets for

\$512

. The band purchases

30

student tickets and

15

adult tickets for

\$765

. This system of equations can be used to represent the situation:

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24x + 8y = 512

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30x + 15y = 765

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Which statement is correct?

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(A) In the system of equations,

x

represents the price of an adult ticket, and

y

represents the price of a student ticket.

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(B) In the system of equations,

x

represents the total amount the band and orchestra spend on adult tickets, and

y

represents the total amount they spend on student tickets.

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(C) In the system of equations,

x

represents the total amount the band and orchestra spend on student tickets, and

y

represents the total amount they spend on adult tickets.

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(D) In the system of equations,

x

represents the price of a student ticket, and

y

represents the price of an adult ticket.

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What is the total amount of money the band and orchestra spend on student tickets?

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8

4

8

5

10

-5

\times

\times

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10

7

8

3

JH-IlijpunLFYJhEDJIOhE

1

4

3

9

22

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- (a): Your answer is ncomect.

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- (b): Your answer is incorrect.

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The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with through

9

on it. (The ball is then replaced in the machine.) The lottery board tested the machine for

25

trials and got the following results

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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}

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|0|

1

2

3

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3

2

1

2

35

3 / 2

22

2

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Fill in the table below. Round your answers to the nearest thousandth.

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(a) Assuming that the machine is fair, compute the theoretical probability of getting an odd number.

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556

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(b) From these results, compute the experimental probability of getting an odd number.

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.12

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(c) Assuming that the machine is fair, choose the statement below that is true:

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With a large number of trials, there must be no difference between the experimental and theoretical probabilities.

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With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.

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With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.

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2024

McGraw HilliC. All Rights Reserved

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7

f

-10 \leq x \leq 20

-40 \leq f(x) \leq-10

. Select each statement that must be false about

f(x)

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\begin{array}{c} f(1)=-13 \\ f(-10)=-40 \end{array}

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\square f(1)=13

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f(-9)=88

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f(5)=-40

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f(0)=0

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f(-15)=-20

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\qquad

\qquad

\qquad

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12

-2

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Skills Practice

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Probability of Compound Events

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1

-6

, a number cube is rolled and the spinner at the right is spun. Find each probability.

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1

P\left(\frac{1}{6} \operatorname{and} \frac{A}{4}=\frac{1}{24}\right.

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2

P

B

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3

P

\mathrm{D})

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4

P

4

C

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5

P

3

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6

P

(prime and consonant)

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7

. What is the probability of spinning the spinner above

3

times and getting a vowel each time?

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8

. What is the probability of rolling a number cube

3

times and getting a number less than

3

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Each spinner at the right is spun. Find each probability.

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9

\qquad

2

2

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10

P

(vowel and even)

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11

\qquad

4

1

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12

\qquad

5

and greater than

1

\qquad

6

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3

1

2

yellow marbles in a bag. Once a marble is selected, it is not replaced. Find each probability.

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13

\qquad

4

red and then yellow)

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14

P

(blue and then yellow)

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15

P

(red and then blue)

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16

. P(two yellow marbles)

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17

P

(two red marbles in a row)

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18

P

(three red marbles)

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GAMES There are

13

6

10

8

greed cards in a stack of cards turned face down. Once a card is selected, it is not replaced. Find each probability.

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19

\qquad

2

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20

\qquad

2

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21

. P(a yellow card and

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22

. P(a blue card and then a green card) then a red card)

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23

P

(two cards that are not red)

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24

. P(two cards that are neither red or green)

Two statistics teachers both believe that each has the smarter class. To put this to the test, they give the same final exam to their students. A summary of the class sizes, class means, and standard deviations is given below:

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\begin{array}{lll} n_{1}=43, & \bar{x}_{1}=82.7, & s_{1}=15.4 \\ n_{2}=52, & \bar{x}_{2}=79, & s_{2}=18.1 \end{array}

\newline

Is there evidence, at an

\alpha=0.07

level of significance, to conclude that there is a difference in the two classes? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested. Round all values to at least

4

decimal places.

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A. The value of the test statistic:

\square

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\mathrm{p}

\square

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C. Your decision for the hypothesis test:

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H_{0}

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B. Do Not Reject

H_{0}

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H_{a}

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D. Do Not Reject

H_{a}

Import favorites

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MVNU Students Ho...

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ALEKS - Jameson C...

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Trigonome tric Graphs

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Word problem involving a sine or cosine function: Problem type

2

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The average monthly temperature changes from month to month. Suppose that, for a given city, we can model the average temperature in a month with the following function.

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f(t)=60-27 \sin \left(\frac{\pi}{6} t\right)

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In this equation,

f(t)

is the average temperature in a month in degrees Fahrenheit, and

t

is the month of the year (January

=1

2

\ldots

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Find the following. If necessary, round to the nearest hundredth.

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Time for one full cycle of

f

\square

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Number of cycles of

f

\square

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Minimum average temperature in a month:

\square

\square

०

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2024

McGraw Hill LLC. All Rights Reserved.

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Type here to search

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t

0

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1

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2

21

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4

22

2024

Together, two sports clubs (A and B) have

x

A

has a members and

B

b

members. Some of the persons are members of both sports clubs. Which of the following expressions describes how many persons are members in only one of the two sports clubs?

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x+a-b

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2(a+b)-2 x

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a b-2 x

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2 \mathrm{x}-(\mathrm{a}+\mathrm{b})

\newline

\qquad

\newline

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\qquad

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8

1

-8

4

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1

2

, identify characteristics of the quadratic function and its graph.

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1

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2

\newline

3

-8

, graph the function. Compare the graph to the graph of

f(x)=x^{2}

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3

g(x)=5 x^{2}

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4

\quad k(x)=\frac{2}{3} x^{2}

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\newline

\qquad

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\qquad

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\qquad

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\qquad

3x+y=1

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y=

6x^{2}-4x-1

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(x,y)

is a solution to the system of equations shown, which of the following are

\newline

x-coordinates of the solutions?

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1

\newline

-\frac{1}{2}

\frac{5}{2}

\newline

-\frac{2}{3}

\frac{1}{2}

\newline

\frac{2}{3}

-\frac{1}{2}

\newline

\frac{2}{3}

-1

Alaina was asked whether the following equation is an identity:

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(2 x+1)^{2}-(x+1)^{2}=3(x+1)^{2}-1

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She performed the following steps:

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(2 x+1)^{2}-(x+1)^{2}

\newline

\stackrel{\text { Step } 1}{\hookrightarrow}=4 x^{2}+4 x+1-x^{2}+2 x+1

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\stackrel{\text { Step } 2}{\hookrightarrow}=3 x^{2}+6 x+2

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\stackrel{\text { Step } 3}{\hookrightarrow}=3 x^{2}+6 x+3-1

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\stackrel{\text { Step } 4}{\hookrightarrow}=3\left(x^{2}+2 x+1\right)-1

\newline

\stackrel{\text { Step } 5}{\hookrightarrow}=3(x+1)^{2}-1

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For this reason, Alaina stated that the equation is a true identity.

\newline

Is Alaina correct? If not, in which step did she make a mistake?

\newline

1

\newline

(A) Alaina is correct.

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(B) Alaina is incorrect. She made a mistake in step

1

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(C) Alaina is incorrect. She made a mistake in step

3

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(D) Alaina is incorrect. She made a mistake in step

5

A minor league hockey team has been collecting ticket sales data over the past year. At a current price of

\$ 25

per ticket, an average of

4000

seats are purchased. The team predicts that for each

\$ 1

increase in ticket price,

100

fewer tickets will be sold. Which of the following functions best models the amount of money that the hockey team expects to collect from ticket sales,

y

\$ x

increase in ticket price?

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1

\newline

y=(25+x)(4000-100 x)

\newline

y=(25-x)(4000+100 x)

\newline

y=x(4000-100 x)

\newline

y=4000(25+x)

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<

7

\newline

Mark as Complete

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5

15

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An experiment involves picking a card from the number cards

2,4,6,10

. In equation form. What is the probability model for this experiment?

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\begin{array}{l} f(x)=\square, \text { where } \\ x=2,4,6,10 \end{array}

\newline

\newline

1

1

Johnny is building birdhouses in shop class, and he has a total of

349

nails on hand. A small birdhouse requires

20

nails and a large birdhouse requires

56

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of small birdhouses

\newline

y =

the number of large birdhouses

\newline

\newline

20 + x + 56 + y < 349

\newline

20x + 56y < 349

\newline

20 + x + 56 + y \leq 349

\newline

20x + 56y \leq 349

Linda is selling handmade jewelry to earn money for camp. Bracelets sell for

\$3

and necklaces sell for

\$15

, and she needs to make at least

\$320

in revenue to cover the cost of camp.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

the number of bracelets

\newline

y =

the number of necklaces

\newline

\newline

3x + 15y \leq 320

\newline

3x + 15y > 320

\newline

3x + 15y \geq 320

\newline

3x + 15y < 320

Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least

119

kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is

17

kilometers long, and the Pinehurst Loop, which is

49

kilometers long.

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of laps on the Highland Loop

\newline

y =

the number of laps on the Pinehurst Loop

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\newline

17x + 49y > 119

\newline

49x + 17y \geq 119

\newline

49x + 17y > 119

\newline

17x + 49y \geq 119

Roger is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$2

\$1

. He can spend up to

\$8

, but not more.

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

the number of mechanical pencils Roger will buy

\newline

y =

the number of pens Roger will buy

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\newline

\newline

2x + y \geq 8

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2x + y \leq 8

\newline

x + 2y \leq 8

\newline

x + 2y \geq 8

Alice, a purchasing agent for a high-tech firm, is ordering computers for a new branch office. Laptops cost

\$750

apiece and desktop computers cost

\$410

apiece. The budget for the computers is no more than

\$22,000

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of laptops ordered

\newline

y =

the number of desktop computers ordered

\newline

\newline

750x + 410y \geq 22,000

\newline

750x \times 410y \geq 22,000

\newline

750x \times 410y \leq 22,000

\newline

750x + 410y \leq 22,000

A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least

27

passengers, the number of tourists in the group. A dinghy can seat

6

passengers and a flatboat can seat

1

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

the number of dinghies

\newline

y =

the number of flatboats

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\newline

6x + y \geq 27

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x + 6y \geq 27

\newline

6x + y \leq 27

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x + 6y \leq 27

Omar is buying soda and juice for a party and wants to spend no more than

\$45

\$2

per bottle, and juice costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

\newline

3x + 2y \leq 45

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2x + 3y \leq 45

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3x + 2y < 45

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2x + 3y < 45

32+39 x=5+6(2 x+4)+3+27 x

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The steps to show that the right-hand side of the equation is equivalent to the left-hand side are shown below. For each step, select the option below that correctly justifies it.

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\begin{array}{l} \text { Steps: } \\ 32+39 x=5+6(2 x+4)+3+27 x \\ 32+39 x=8+6(2 x+4)+27 x \\ 32+39 x=8+12 x+24+27 x \\ 32+39 x=8+24+12 x+27 x \\ 32+39 x=32+39 x \end{array}

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\newline

values over the change in

x

-values (rise/run)

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y

-axis; the beginning value of a situation

\newline

when graphed; has a constant slope

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tical Line Test

5

2

Graphs of Reciprocal Functions (Adapted from Worksheet

5

3

92

-95

\newline

3

. (a) Complete the table of values for

y=x+\frac{8}{x}-9

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(b) Plot the points and join them with a smooth curve.

\newline

\begin{tabular}{|c|c|c|c|c|c|}

\newline

x

1

3

4

5

8

\newline

y

6

-3

3

-3

-24

0

\newline

\newline

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(c) Use your graph to find the solutions of

x+\frac{8}{x}=7

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\begin{array}{c} x+\frac{2}{x}-9=7-9 \\ y=-2 \end{array}

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x=

\qquad

1

4

x=

5

\qquad

\newline

(d) The equation

(m-1) x^{2}+9 x-8=0

has no solution in the interval

0.5 \leq x \leq 7

\newline

Suggest a value of

x

0

and draw the corresponding straight line on the same grid to show that the equation has no solution in the given interval.

\newline

x^{2}+9 x-8=-2

Mrs. Fowler took her grandchildren to a baseball game, with plans to spend no more than

\$36

on snacks. An order of nachos costs

\$4

and a bag of peanuts costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of nacho orders

\newline

y =

the number of bags of peanuts

\newline

\newline

3x + 4y \leq 36

\newline

4x + 3y < 36

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4x + 3y \leq 36

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3x + 4y < 36

The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most

\$770

to purchase bats and softballs. A case of softballs has a price of

\$38

, and a bat has a price of

\$27

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

x =

the number of cases of softballs

y =

the number of bats

\newline

\newline

38x - 27y < 770

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38x \times 27y \leq 770

\newline

38x + 27y < 770

\newline

38x + 27y \leq 770

In order to raise money to attend upcoming competitions, the debate team at Belleville High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least

\$170

in revenue at tonight's game, with hot chocolate selling for

\$1

and hot apple cider selling for

\$2

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x

= the number of hot chocolates sold

\newline

y

= the number of apple ciders sold

\newline

\newline

170

\newline

B) \(2x + y \geq

170

\newline

170

\newline

D) x + \(2y \geq

170

The Dayton Playhouse wants to make at least

\$6,300

on ticket sales this year. Currently, adults' tickets cost

\$58

and children's tickets cost

\$20

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of adults' tickets sold

\newline

y =

the number of children's tickets sold

\newline

\newline

58x + 20y \geq 6,300

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20x + 58y \geq 6,300

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58 + x + 20 + y \geq 6,300

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20 + x + 58 + y \geq 6,300

Ms. Ellis, the head librarian at the Marshall County Library, can spend at most

\$3,300

to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost

\$2

each and hardback books cost

\$14

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

the number of paperback books

\newline

y =

the number of hardback books

\newline

\newline

14x + 2y \geq 3,300

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2x + 14y \geq 3,300

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2x + 14y \leq 3,300

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14x + 2y \leq 3,300

A charitable organization in Lanberry is hosting a black tie benefit for charity, and the organization's members hope to bring in at least

\$1,600

. Standard tickets are available for

\$16

each, whereas VIP tickets are offered for

\$70

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Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

the number of standard tickets

\newline

y =

the number of VIP tickets

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16x + 70y \leq 1,600

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16x + 70y \geq 1,600

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16 + x + 70 + y \leq 1,600

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16 + x + 70 + y \geq 1,600

Alana is selling handmade jewelry to earn money for camp. Bracelets sell for

\$5

and necklaces sell for

\$30

, and she needs to make at least

\$620

in revenue to cover the cost of camp.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bracelets

\newline

y =

the number of necklaces

\newline

\newline

30x + 5y \geq 620

\newline

30x \times 5y \geq 620

\newline

5x - 30y \geq 620

\newline

5x + 30y \geq 620

Logan is buying soda and juice for a party and wants to spend no more than

\$44

\$2

per bottle, and juice costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

\newline

2x + 3y \leq 44

\newline

2x + 3y < 44

\newline

3x + 2y < 44

\newline

3x + 2y \leq 44

During a special sale, all video games cost

\$28

and all movies cost

\$5

. Hansen plans to spend some or all of his

\$120

in birthday money on these movies and video games.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of video games Hansen can buy

\newline

y =

the number of movies Hansen can buy

\newline

\newline

\newline

28x + 5y \geq 120

\newline

28x + 5y \geq 120

\newline

28x - 5y \leq 120

\newline

28x + 5y \leq 120

As part of a landscaping project, Mr. Kerr is purchasing plants from a garden center. It will cost

\$36

to buy a mature tree, versus

\$8

for a young one. His target is to keep the cost under

\$1,100

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mature trees

\newline

y =

the number of young trees

\newline

\newline

36x + 8y > 1,100

\newline

36x + 8y < 1,100

\newline

8x + 36y > 1,100

\newline

8x + 36y < 1,100

Cody, the owner of a landscaping company, is ordering rakes and shovels from an equipment wholesaler. He doesn't want to spend more than

\$390

total for his purchases. He can get the rakes at a cost of

\$11

apiece and the shovels at a cost of

\$23

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of rakes ordered

\newline

y =

the number of shovels ordered

\newline

\newline

11x + 23y > 390

\newline

11x + 23y < 390

\newline

11x + 23y \geq 390

\newline

11x + 23y \leq 390

Gabby is determining the seating arrangement for her big graduation party. Circular tables can seat

10

guests and rectangular tables can seat

9

guests. Together, they must seat at least

141

guests, the number expected.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of circular tables

\newline

y =

the number of rectangular tables

\newline

\newline

10x + 9y > 141

\newline

10x - 9y > 141

\newline

10x \times 9y \geq 141

\newline

10x + 9y \geq 141

Jada is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$1

\$4

. She can spend up to

\$6

, but not more.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mechanical pencils Jada will buy

\newline

y =

the number of pens Jada will buy

\newline

\newline

4x + y \leq 6

\newline

x + 4y \leq 6

\newline

4x + y < 6

\newline

x + 4y < 6

Mrs. Hong is ordering senior portraits of her son to send to their relatives. A medium photo costs

\$12

and a large photo costs

\$34

. She wants to spend less than

\$260

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of medium photos

\newline

y =

the number of large photos

\newline

\newline

34x + 12y < 260

\newline

12x + 34y \leq 260

\newline

12x + 34y < 260

\newline

34x + 12y \leq 260

Jayla is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under

\$1,100

. A band can play for part of the time at an hourly rate of

\$120

, and a DJ can play for the remaining time at an hourly rate of

\$80

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours the band will play

\newline

y =

the number of hours the DJ will play

\newline

\newline

80 + x + 120 + y < 1,100

\newline

120 + x + 80 + y < 1,100

\newline

120x + 80y < 1,100

\newline

80x + 120y < 1,100

Jamal, a costume designer for the Dover City Opera, is making costumes for the chorus members in an upcoming performance. While costuming this group of singers, Jamal must keep costs below

\$1,400

. Male costumes cost

\$6

to make and female costumes cost

\$25

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of male costumes

\newline

y =

the number of female costumes

\newline

\newline

25x - 6y < 1,400

\newline

6x + 25y < 1,400

\newline

6x \times 25y < 1,400

\newline

25x + 6y < 1,400

Josie wants to save some low-resolution photos and some high-resolution photos on her flash drive. Each low-resolution photo takes up

2\,\text{MB}

and each high-resolution photo takes up

4\,\text{MB}

. In total, they cannot exceed the total storage space available on the drive, which is

80\,\text{MB}

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of low-resolution photos

\newline

y =

the number of high-resolution photos

\newline

\newline

2x + 4y \geq 80

\newline

4x + 2y \leq 80

\newline

2x + 4y \leq 80

\newline

4x + 2y \geq 80

The orchestra in Springdale is putting on a benefit concert for the local children's hospital. Orchestra seating costs

\$43

per ticket and balcony seating is

\$95

. The goal is to raise at least

\$6,100

for the hospital.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of orchestra seats sold

\newline

y =

the number of balcony seats sold

\newline

\newline

\newline

95x + 43y \geq 6,100

\newline

95x + 43y \leq 6,100

\newline

43x + 95y \leq 6,100

\newline

43x + 95y \geq 6,100

During the intermission of the school play, the drama class at Danville High School is offering refreshments. The goal is to make more than

\$290

in revenue tonight by selling beverages for

\$1

\$2

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of beverages sold

\newline

y =

the number of snacks sold

\newline

\newline

x + 2y > 290

\newline

1 + x + 2 + y > 290

\newline

1 + x + 2 + y < 290

\newline

x + 2y < 290

At a back-to-school sale at her favorite store, Karen can purchase any pair of pants for

\$17

and any shirt for

\$10

. Her parents tell her that she can spend at most

\$360

on these school clothes.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of pants

\newline

y =

the number of shirts

\newline

\newline

17x \times 10y \leq 360

\newline

17x + 10y \leq 360

\newline

17x + 10y \geq 360

\newline

17x \times 10y \geq 360

As part of a landscaping project, Mr. Ortega is purchasing plants from a garden center. It will cost

\$34

to buy a mature tree, versus

\$8

for a young one. His target is to keep the cost under

\$820

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mature trees

\newline

y =

the number of young trees

\newline

\newline

34x + 8y < 820

\newline

34x - 8y > 820

\newline

34x + 8y > 820

\newline

34x + 8y < 820

Brianna is knitting baby items to sell at a craft fair. She has a total of

1,280

yards of yarn to use for the items. A pair of booties uses

196

yards of yarn and a cap uses

187

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of booties Brianna can knit

\newline

y =

the number of caps Brianna can knit

\newline

\newline

187x + 196y \leq 1,280

\newline

196x + 187y \leq 1,280

\newline

187x + 196y \geq 1,280

\newline

196x + 187y \geq 1,280

Gwen wants to replace the flooring in her house with a combination of carpet and hardwood flooring, but she cannot exceed a budget of

\$4,900

. The carpet she likes has a cost of

\$9

per square foot, and the hardwood flooring she likes has a cost of

\$3

per square foot.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the amount of carpet

\newline

y =

the amount of hardwood flooring

\newline

\newline

\newline

3x + 9y \leq 4,900

\newline

9x + 3y \leq 4,900

\newline

9x + 3y \geq 4,900

\newline

3x + 9y \geq 4,900

Erik wants to save some low-resolution photos and some high-resolution photos on his flash drive. Each low-resolution photo takes up

1\,\text{MB}

and each high-resolution photo takes up

4\,\text{MB}

. In total, they cannot exceed the total storage space available on the drive, which is

1,970\,\text{MB}

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of low-resolution photos

\newline

y =

the number of high-resolution photos

\newline

\newline

\newline

4 + x + 1 + y \leq 1,970

\newline

x + 4y \leq 1,970

\newline

1 + x + 4 + y \leq 1,970

\newline

4x + y \leq 1,970