Quiz about Advanced Algebra

Question 1

Given the function, which of the following correctly describes the transformations?

Accepted Answer

reflection over the x-axis, vertical compression by 1/3, horizontal shift left 1 and vertical shift down 5

Answer

reflection over the x-axis, vertical stretch by 3, horizontal shift left 1 and vertical shift down 5

Answer

reflection over the y-axis, vertical stretch by 1/3, horizontal shift left 1 and vertical shift down 5

Answer

reflection over the x-axis, vertical stretch by 1/3, horizontal shift right 1 and vertical shift down 5

Question 2

Re-write the following expressions in radical form.

$$x^{\frac{11}{2}}$$

Accepted Answer

$$\sqrt[]{x^{11}}$$

Answer

$$\sqrt[11]{x^2}$$

Answer

$$\sqrt[22]{x}$$

Answer

$$\sqrt[]{x^9}$$

Question 3

Write the expression in exponential form.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 4

Write each expression in exponential form.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 5

Rewrite in radical form.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 6

Solve for V

Accepted Answer

v=81

Answer

v=-81

Answer

v=9

Answer

v=3

Question 7

Question 7.

Accepted Answer

9

Answer

-9

Answer

7

Answer

-7

Question 8

Question 8.

Accepted Answer

1

Answer

-1

Answer

0

Answer

-2

Question 9

Question 9.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 10

Question 10.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 11

Question 11.

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 12

Calculate the z-score for a data point with a mean of 50 and a standard deviation of 10, if the data point is 60.

Accepted Answer

0.1

Answer

0.5

Answer

5.0

Answer

1.5

Question 13

A student's score on a test is 75, with a mean of 70 and a standard deviation of 5. What is the z-score for this student's score?

Accepted Answer

1

Answer

2

Answer

0.5

Answer

80

Question 14

Elise gave each member of the class a random cookie, some from recipe A and some from recipe B. Then she observed which students returned for a second cookie

What data collection method was used?

Accepted Answer

Experiment

Answer

Observational Study

Answer

Survey

Answer

Simulation

Question 15

Elise gave each member of the class a random cookie, some from recipe A and some from recipe B. Then she observed which students returned for a second cookie

What are the treatments in this scenario?

Accepted Answer

The different cookie recipes

Answer

Students A and B

Answer

Students who returned for another cookie

Answer

Elise is the treatment

Question 16

Steven observed students entering a classroom for class and recorded whether the first half of the students who arrived for class chose to sit in the front half of the room.

What data collection method was used?

Accepted Answer

Observational Study

Answer

Experiment

Answer

Survey

Answer

Simulation

Question 17

How is the graph distributed?

Accepted Answer

Skewed to the Left

Answer

Normally

Answer

Skewed to the Right

Answer

Uniform

Question 18

The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. What percentage of cars averaged less than 85 km/h?

Accepted Answer

2.5%

Answer

.15%

Answer

2.35%

Answer

18.5%

Question 19

In a normal distribution, what percentage of the data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

90%

Answer

75%

Answer

50%

Question 20

Describe the graph

Accepted Answer

skewed right

Answer

skewed left

Question 21

If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

Accepted Answer

40

Answer

35

Answer

45

Answer

50

Question 22

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the percentage of golfers that are between 30 and 46 years old.

Accepted Answer

95%

Answer

68%

Answer

94%

Answer

99.7%

Question 23

The ages of the population of people living in the Atlanta area are normally distributed with a mean of 43 and a standard deviation of 14.

The town has a population of 5,000. How many would you expect to be aged between 29 and 57?

This Standard Normal Distribution curve may help you solve this problem.

Accepted Answer

3400

Answer

1750

Answer

3860

Answer

4330

Question 24

What's the probability of the gray area?

(Mean = 55, Standard dev = 2.5)

Accepted Answer

0.8185

Answer

0.8413

Answer

0.8641

Answer

0.8389

Question 25

6.5 CLT:  Red blood cell counts of women are normally distributed with a mean of 4.577 and a standard deviation of 0.382.  What percentage of women have red blood cell counts in the normal range from 4.2 to 5.4?

Accepted Answer

82.3%

Answer

77.8%

Answer

72.6%

Answer

68%

Question 26

Find the value for
P(Z > 1.78)

Accepted Answer

0.0375

Answer

0.0376

Answer

0.0446

Answer

0.2420

Question 27

What are the x-intercepts of this function?

Accepted Answer

(1,0) and (5, 0)

Answer

(0, 3) and (0, -5)

Answer

(1, 5) and (5, 1)

Answer

(0, 1) and (0, 5)

Question 28

What is the vertex of this quadratic function?

Accepted Answer

(-2,4)

Answer

(2,4)

Answer

(4,-2)

Answer

(-4,-2)

Question 29

What is the standard form of a quadratic equation?

Accepted Answer

f(x)=ax²+bx+c

Answer

f(x)=x

Answer

f(x)=x2

Answer

f(x)=a(x-h)²+k

Question 30

What equation represents the quadratic function?

Accepted Answer

y = (x - 4)²

Answer

y = (x + 4)²

Answer

y = x² - 4

Answer

y = x² + 4

Question 31

Factor
k² -2k - 24

Accepted Answer

(k+4)(k-6)

Answer

(k+4)(k+6)

Answer

(k+6)(k-1)

Answer

(k-4)(k+6)

Question 32

What are the roots of the function
f(x)= (x - 2)(x + 3)?

Accepted Answer

x = 2 or x = -3

Answer

x = - 2 or x = 3

Answer

The are no real roots

Answer

x = 2 or x = 3

Question 33

Factor
n² + 16n + 63

Accepted Answer

(n+7)(n+9)

Answer

(n-7)(n+4)

Answer

(n+7)(n-9)

Answer

(n-3)(n-10)

Question 34

Does this exponential function model growth or decay?
y = (4/3)^x

Accepted Answer

Growth

Answer

Decay

Answer

Both

Answer

Neither

Question 35

Does this function show growth or decay?

Accepted Answer

Decay

Answer

Growth

Answer

Both

Answer

Neither

Question 36

Solve.
log(5x - 7) = log(3x + 1)

Accepted Answer

x = 4

Answer

x = 1

Answer

Infinite solutions

Answer

No solution

Question 37

Solve.
ln(x) - ln(x+4) = 0

Accepted Answer

No solution

Answer

x = 4

Answer

x = 0

Answer

Infinite solutions

Question 38

A vehicle purchased for $25,000 depreciates at a constant rate of 9%.

Determine the approximate value of the vehicle 10 years after purchase.

Accepted Answer

9735.40

Answer

59,184.09

Answer

9463.13

Answer

10560.27

Question 39

Solve for x:

7^4x-6 = 43

Accepted Answer

1.9832

Answer

1.9329

Answer

7.9329

Answer

0.9888

Question 40

Solve for x:

2^x = 50

Accepted Answer

5.6439

Answer

25

Answer

0.1772

Answer

0.1771

Question 41

Logarithms and Exponentials are what?

Accepted Answer

inverses

Answer

parallel

Answer

perpendiular

Answer

congurent

Question 42

What is the Asymptote?

Accepted Answer

x=1

Answer

x=5

Answer

x=0

Answer

y=0

Question 43

What are the transformations of this graph?

Accepted Answer

Right 1 Up 5

Answer

Right 1 Down 5

Answer

Left 1 Up 5

Answer

Left 1 Down 5

Question 44

What are the transformations of this graph?

Accepted Answer

Right 1 Up 5

Answer

Right 1 Down 5

Answer

Left 1 Up 5

Answer

Left 1 Down 5

Question 45

What is the horizontal asymptote for the graph of
f(x)=-2(3)^x+4-8 ?

Accepted Answer

y=-8

Answer

y=8

Answer

x=-8

Answer

x=-4

Question 46

Solve:

2log₆(x-8)=2

Accepted Answer

14

Answer

81/8

Answer

18

Answer

9969

Question 47

Solve:

ln(x+8) - ln (8) = 3

Accepted Answer

152.68

Answer

188.77

Answer

4.24

Answer

8.01

Question 48

What is the base in the equation

log 8 = 3?

Accepted Answer

10

Answer

8

Answer

3

Answer

1

Question 49

Rewrite log_vn = a in exponential form.

Accepted Answer

va = n

Answer

na = v

Answer

vn = a

Answer

an = v

Question 50

Expand $$\log_4\left(3xy\right)$$

Accepted Answer

$$\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\ $$

Answer

$$\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$$

Answer

$$3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$$

Answer

$$4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\ $$

Question 51

Condense into one log: $$2\log_3\left(x\right)+\log_3\left(y\right)$$

Accepted Answer

$$\log_3\left(x^2y\right)$$

Answer

$$\log_3\left(2xy\right)\ $$

Answer

$$\log_3\left(xy\right)^2$$

Answer

$$2\log_3\left(xy\right)$$

Question 52

Solve $$\log_6x+\log_69=\log_654$$

Accepted Answer

x=6

Answer

x=45

Answer

x=7

Answer

x=36

Question 53

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. Suppose f(20) = 49. Which of the following is true?

Accepted Answer

After 20 days, there are 49 ants in the colony.

Answer

After 49 days there are 20 ants in the colony.

Answer

The amount of ants times 20 is 49.

Answer

After 20 days the amount of ants remaining decreases by 49.

Question 54

Convert $$Log_5x=y$$ into Exponential Form

Accepted Answer

$$5^y=x$$

Answer

$$x^5=y$$

Answer

$$5^x=y$$

Question 55

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

Accepted Answer

4309

Answer

14327

Answer

839

Answer

7680

Question 56

Karla invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Karla earn in 15 years?

Accepted Answer

$2,706.86

Answer

$1,584.62

Answer

$2,651.39

Answer

$1,825.10

Question 57

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

Accepted Answer

$15,683.28

Answer

$15,415.94

Answer

$15,927.56

Answer

$16,109.05

Question 58

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

Accepted Answer

$2,225.54

Answer

$1,225,54

Answer

$22,255.40

Answer

$225.54

Question 59

Solve

Accepted Answer

1

Answer

0

Answer

-1

Answer

Undefined

Question 60

Solve.
e^4x=12

Accepted Answer

0.62

Answer

2.48

Answer

9.94

Answer

3

Question 61

Convert log(x)=y+2 to exponential form.

Accepted Answer

10(y+2)=x

Answer

1x=y+2

Answer

10x=y+2

Answer

x(y+2)=10

Question 62

log x - log 8 = 3

Accepted Answer

x = 8000

Answer

x = 1000

Answer

x = 800

Answer

x = 100

Question 63

An initial investment takes 12 years to double when compounded continuously. What was the annual interest rate?

Accepted Answer

5.7762%

Answer

16.521%

Answer

3.105%

Answer

27.894%

Question 64

Determine the principal, P, that must be invested at 3.5% compounded monthly, so that $500,000 will be available after 15 years.

Accepted Answer

$296,003.78

Answer

$328,684.18

Answer

$198,326.12

Answer

$401,256.71

Advanced Algebra

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