Algebra II Semester 2 Final (not finished)

The graph of an exponential model in the form y=a x b to the x passes through the points (2,3) and (3,9). Which point is also located on the graph?

(1,1) (b)

What if f(-12), given that f(x)= -third√x-5 +8

(b) 11

Multiply (2√12 - √75)√ 3

-3 (a)

Which of the following are measures of the angle shown? Select all that apply.

-390° (b) and 330° (d)

A game at the fair involves balls numbered 1 to 18. You can win a prize if you correctly chose the 5 numbers that are randomly drawn. What are your approximate chances of winning?

.0001 (a)

Half of a class took Form A of a test and half took Form B . Of the students who took form b, 39% passed. What is the probability that a randomly chosen student took form b and did not pass

.305 (c)

The probability that a machine part is defective is .1. Find the probability that no more than 2 out of 12 tested are defective.

.89 (c)

Evaluate the expression x²-4x+1 when x=2+√3

0 (c)

solve (third√13x-1) -4 =x-5

0,5,-2

The probability that a newborn baby at a certain hospital is male is 50% What is the probability that exactly 2 out of 3 babies born in the hospital on any day are male?

0.375 (a)

What is the area in square unites of the triangle w one vertex at the origin and defined by the vectors <-3,-5> and <2,-4>?

11 (d)

simplify (4+√6)/(3-3√6)

12+15√6

Tom delivers papers on a rural route from his car. If he throws a paper from a height of 4.5ft, and it lands 20ft from the car, at what angle of depression, did he throw the paper to the nearest tenth of a degree?

12.7°

An angle has a reference angle of 35° and its terminal side lies in Quadrant II. What are the possible positive measure and negative measure for the angle?

145°,-215° (d)

simplify (16b to the -2) to the -1/2

16

Which of the following is equivalent to the expression log (a²b²/c³)?

2 log a+2 log b- 3 log c (c)

A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf lands on the rectangle lands within the section shaped like a trapezoid?

2/3 (d)

fourth √234⁴

234

A chef randomly chooses 5 apples from a case of 24 apples. Which best represents the number of ways the chef can make the selection?

24C5 (b)

A chef randomly choses 5 apples from a case of 24 apples. Which best represents the number of ways the ched can make the selection?

24C5 (b)

For which value of A does the equation Ax²-4x+4y²+7y+100=0 represent a ellipse?

25 (c)

A student invests $500 dollars with a 2.5% interest rate. How much time will it take for the student to double their investment when compounding continuously? A=Pert

28 years

√10.1

3.2

There are 5 red tiles and 5 blue tiles with the letter A in a bag. There are also 6 red tiles and 4 blue tiles with the letter B in the bag. What is the probability that a randomly selected tile is blue or has the letter B?

3/4 (c)

A brand of light bulbs has a mean lifetime of 1,500 hours and a standard deviation of 150 hours. A sample of 100 light bulbs gave a mean lifetime of 1,400 hours. What is the margin of error for the sample?

30 (a)

if cotθ= tan60°, what is θ?

30° (a)

A bookstore classifies its books by reader group, type of book, and cost. What is the probability that a book selected at random is a child's book, given that is costs $15?

315/575 (c)

solve (third √2x)=4

32

What data value is greater than approximately 80% of the distribution?

36.1 (c)

log substrip3 81

4

Convert 720° to radians.

4pi

simplify root 2 times (2 times root.125 + root18)

7

Which of the following are parameters? Select all that apply.

75% of the students at North High School voted for Lucy, the total collected at a fund-raiser was $5,281 ; (a and b)

In matrix V, the entries are the number of loaves of bread at a bakery. Column 1 lists wheat bread, column 2 lists rye bread, row 1 lists small loaves, and row 2 lists large loaves. What does the number in position v₂₂ represent?

9 large rye loaves (a)

Which of the following pairs of events are independent? Select all that apply.

Draw a 3 of spades from a standard deck of 52 cards, replace it, then draw a 5 of hearts , Roll a 2 on number cube and spin a 3 on a spinner, and events A and B, where P(A)= 0.1, P(B)= 0.5, and P(A and B)= 0.05 (b,d,f)

Which of the following is an example of a statistical experiment?

More streetlights are installed on one street and people are then asked if they like the change (b)

Which of the following are true if events A and B are independent?

P(A|B)= P(A), P(B

Which of the following are true if events A and B are independent?

P(A|B)= P(A), P(B|A)=P(B); (a and f)

It is meaningless to compare Keenan's and Rachel's scores directly, because they each took a different exam. Which of the following describes a valid way to use statistics to compare Keenan's score on his exam with Rachel's score on her exam?

Rachel did better than Keenan because her z score was greater than Kennan's (c)

Which of the statements about the ellipse represented by the equation (x+6)²/36 + (y+8)²/4 =1 are true? Select all that apply.

The co-vertices are (-6,-10) and (-6,-6) and the horizontal axis is 12 units long; (c and d)

Consider the vector v=<1,2>. Which statements about the scalar product -2v are true? Select all that apply

The component from of -2v is <-2,-4>, The magnitude of -2v is 2 times the magnitude of v , and the direction of -2v is the opposite direction of v; (a,b and c)

simplify root a to the 6th over b to the 10th

a to the 3th over b to the 5th

the function f(x)=400(1.2)to the x models a population of mice after x years. What will the population be in 7 years?

about 1,400 (b)

Which of the following sampling methods would bias the set of response? Select all that apply.

asking people to return a mail in card, toasting a chipped number cube, and calling people between 3-4pm; (a,b and c)

simplify (a to the 4th times b to the negative 8) to the -3/4

b to the 6th over a to the 3rd

For the survey question below, is the variable quanitative or categorical? " What is your eye color? "

categorical

What is the cosθ if the sinθ= -8/10 and θ is in quatrant IV?

cosθ= 6/10 (b)

Which of the following is a decreasing function?

f(x)= 2 - rootx (c)

Which of the following functions has a smaller average rate of change on the interval (-1,1) than the function shown in the graph?`

f(x)=10(2)to the x (d)

A store increases all its prices by 20% and then offers a $50 discount on all purchase prices. Let x represent the price in dollars. Let f(x)=1.20x present the increase and g(x)= x-50 represent the discount. Which function can the store manager use to find the final purchase prices?

g(f(x)) (c)

which function g represents the exponential function f(x)= 3∧x after a horizontal stretch of 4 and a reflection across the y-axis?

g(x)=(3) to the -x/4 (a)

Which type of conic section does the equation 5x²-9y+3=0 represent?

hyperbola

If f(x)= 1-√x, which of the following are true? select all that apply

inverse f = (x-1)² (b) and (inverse f(f(x))=x (d)

If a(x)= 1/x-1, what is an equation for inverse a(x)?

inverse of a = x+1/x (b)

What is the inverse of f(x)=2x²-9

inverse= √x+9/2 (c)

Malia found the margin of error for the percent of lengths of 100 willow leaves greater than 5cm. If she increases her sample of 400, how will this affect her margin of error?

it will reduce the margin of error by 1/2 (c)

xlog2-log1/3

log2tothex/1/3

solve (√x-2) -1 =-4

no solution

10m² = 4/3πr³

r=1.3

Which transformation in the coordinate plane is represented by the matrix (-1, 0, 0, 1)?

reflection over the y-axis (b)

From a population of 1,600 cars, a sample of 25 is chosen. The dealer calculated the mean weight of those 25 cars. Tell whether this mean weight is an example of a statistic or a parameter.

statistic

The function d(t)=4.9t² models the distance in meters an object falls after t seconds where t≥0. Which function t(d) best models in seconds that it will take an object to fall d meters?

t(d)= 0.45√d (b)

When the sun shrines at a 60° angle to the ground, Noemi's shadow is 39 in long. To the nearest inch, how tall is Neomi?

tan60=x/39 so she is 67 inches

Nicholas is observing a piece of cargo being hoisted up the side of a ship. Nicholas is standing on a dock about 150 feet away. Which function models the height of h in feet of the cargo as a function of the angle of inclination θ from Nicholas's position from the dock?

tanθ= h/150

A student wants to study the effect of meditation on the time a person is able to balance on one leg. She finds 40 volunteers who have never meditated, and records their balance times. She selects 20 of them at random, and instructs them to practice meditation daily for two weeks. In two weeks, she records the balance times for all forty volunteers again. What is the group of volunteers who were asked to mediate called?

the experimental group (b)

Which statement is true for the hyperbola represented by y²/81-x²/40=1

the foci are (0, ±11) (b)

Which of the statements about the parabola represented by x=1/20(y-1)² +3 are true?

the focus is (8,1) & the vertex is (3,1); (a and b)

Which of the following is an example of a quantitative variable?

the number of hours the veterinarian works in one week (d)

Which of the following is likely to be an example of normal distribution?

the scores on a nationwide math test (c)

Which of the following are conditions for a binomial experiment? Select all that apply

there is a fixed # of trials, each trial has 2 possible outcomes, the trials are independent, and the probability is constant throughout the trials (a,b,d,e)

A veterinarian polled her clients who own dogs as to whether or not they used dry food only for their dogs. Which of the following describes the population on this survey?

this veterinarian's dog-owing clients (d)

simplify (x to the 3/4 over y to the -1/4) to the 12

x to the 0 y to the 0

simplify root x to the fourth times y

x to the 2 times y to the 0

What is the solution to the equation 2 to the x=5?

x= log5/log2 (a)

What is the equation for the parabola with vertex (0,0) and directrix x=4

x=-1/16y² (d)

solve (√x-3)+5=x

x=7,4 (4 is extraneous)

What is the equation for the circle with radius 4 and center (0,0)?

x²+y²=16 (d)

simplify 4 root y times 2 root y

y to the 7/12

What function is the inverse of the exponential function y=(1/3) to the x?

y= log1/3 to the x (c)

The graph of y= 2+ √x has been translated to the left 2 units and up 1 unit. What is the equation of the translated graph?

y=3+ √x+2 (a)

What are the asymptotes of the hyperbola w/ vertices (±3,0) and foci (±6,0)?

y=±√3x (c)

Which of the following are real numbers? Select all that apply.

√0 and 3√ -√16 (b and c)

Which of the following is equivalent to m-1/√m -1?

√m+1 (c)