Homework 2&8 Consider the following equation. 8 y +7 x =-11 Solve the equation for y . (Do not use mixed numbers in your answer.) y = Solve the equation. (Enter solutions from smallest to largest. If...

Homework 2&8
Consider the following equation.
8y+7x=-11

1. Solve the equation fory. (Do not use mixed numbers in your answer.)
   
   y=

Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.)

x
²- 5x+ 5 = 0

x=

x=
Factor the expression by using areas.


=
Choose the solution set. Pick the right answers.
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Solve the inequality. (Enter INFINITY forand -INFINITY for -as needed.)


,


Solve the inequality. (Enter INFINITY forand -INFINITY for -as needed.)
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,


If a number is less than five minus twice its opposite, what are the possible numbers?


Choose a formula to express the given relation.
(a)The areaAof a parallelogram is the product of the baseband the heighth.


(b)The areaAof a trapezoid is the product of one-half the heighthand the sum of the basesaandb.


(c)The volumeVof a cone is one-third the product of pi, the square of the radiusr, and the heighth.


(d)The volumeVof a sphere is the product of four-thirds pi and the cube of the radiusr.




Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 70-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
sec


One-fifth of a hive of bees flew to the Kadamba flower; one-third flew to the Silandhara; three times the difference of these two numbers flew to an arbor, and one bee continued flying about, attracted on each side by the fragrant Keteki and the Malati. Find the number of bees.
bees


If you drive 253 miles on 11 1/2 gallons of gas, what is the simplified ratio of miles to gallons?
to 1
Solve the proportion.



H=
Thepitchof a roof is the ratio of the rise to the half-span. If a roof has a rise of6feet and a span of30feet, what is the pitch?




If you were charged$522in taxes on a$1,160purchase, what percent tax were you charged?
%


The combined area of New York and California is 204,192 square miles. The area of California is 108,530 square miles more than that of New York. Find the land area of each state.

CA,	mi2
NY,	mi2

Assume that the pointer can never lie on a border line. Find the following probabilities. (Enter each answer as a fraction.)

P(A)	=
P(B)	=
P(C)	=
P(D)	=
P(E)	=
P(F)	=
P(G)	=
P(H)	=
P(I)	=

Suppose that you toss a coin and roll a die. What is the probability of obtaining each of the following combinations? (Enter your answers as fractions.)

P(tailsand6)	=
P(headsor6)	=
P(tailsandanoddnumber)	=

A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities. (Enter the answers either as fractions or as decimals rounded to three places.)

P(five of clubs)	=
P(five)	=
P(club)	=
P(jack)	=
P(spade)	=
P(jack of spades)	=
P(five and a jack)	=
P(five or a jack)	=
P(heart and a jack)	=
P(heart or a jack)	=

Consider a die with eight sides, marked one, two, three, and so on. Assuming equally likely outcomes, find the probability that the sum of two dice is the given number. (Enter the answer either as a fraction or as a decimal rounded to three places.)
(a)P(3) =
(b)P(5) =
(c)P(7) =
(d)P(10) =
(e)P(13) =
(f)P(14) =


The campus vets club is having a raffle and is selling1,600tickets. If the people on your floor of the dorm bought368of those tickets, what is the probability that someone on your floor will hold the winning ticket? (Enter your answer as a decimal.)


Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probabilities. (Use a calculator and give the answer to five decimal places.)


(a) What are the chances of being dealta flushora straight (but not royal) flush?
(b) What are the chances of being dealtone pairor better?
(c) What are the chances of being dealt a hand that will lose tothree of a kind?
Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. In a certain game, if atwoornineoccurs on the first roll, the player wins. What is the probability of winning on the first roll?


Suppose you and an opponent each pick one of the spinners shown in the following figure. A "win" means spinning a higher number. Construct a sample space and determine which of the two spinners is more likely to win in the following cases.


IfCplaysBis more likely to win.
IfEplaysDis more likely to win.
IfFplaysEis more likely to win.


Find the requested probabilities.



P(A) =



P(B) =



P(C) =



P(D) =


Suppose the following.


Find the following probability.

=

List the outcomes considered a failure, as well as the probability of failure, for the experiment.

Experiment	Success	P(success)
Card game	drawing a heart	0.28

drawing a spade 0.72drawing a spade, club, or diamond 0.72drawing a spade 0.62drawing a spade, club, or diamond 0.73
What is the probability of obtaining a sum of at least6when rolling a pair of dice?


Choose a natural number between 1 and26, inclusive. What is the probability that the number is a multiple of 3?


A history teacher gives a28question T-F exam. In how many different ways can the test be answered if the possible answers are T or F, or possibly to leave the answer blank?
What is the probability of getting a license plate that has a repeated letter or digit if you live in a state that hasfour lettersfollowed bythree numeralsfollowed bytwo letters? (Round to the nearest whole percent.)
%
Find the odds in favor of the event whose probability is given in the problem.


to


Find the probability whose odds against are given in the problem.
Odds against are4to1.
Find the probability which odds in favor are given in problem.
Odds in favor are9to2.
What are the odds in favor of drawinga card higher than a 9from an ordinary deck of cards?
to
What is the probability of obtaining exactlyfourheads infiveflips of a coin, given that at least one is a head?
A single card is drawn from a standard deck of cards. Find the following probabilities. A face card is a jack, queen, or king.

P(jack|red) =

P(face card|queen) =
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the following probabilities of the second card.

P(queen|queen) =

P(red|red) =
If your expected value when playing a $1 game of chance is$0.01. How much should you have netted after playing the game70times?
about$0.70about $0.00about-$0.70about$69.30about-$69.30
What are the expectations for the following $1 bets on a U.S. roulette wheel? (Round each answer to the nearest cent.)


Even
$
Single-number bet
$
Five-number bet
$
0 & 00 split
$
An oil-drilling company knows that it costs $28,000 to sink a test well. If oil is hit, the income for the drilling company will be $445,000. If only natural gas is hit, the income will be $145,000. If nothing is hit, there will be no income. If the probability of hitting oil isand if the probability of hitting gas is, what is the expectation for the drilling company?
$
Should the company sink the test well?
YesNo
Determine whether the following figure represents a fair game. Assume that the cost to spin the wheel once is $5.00 and that you will receive the amount shown on the spinner after it stops.



E= $
Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed on the board. How much should you be willing to pay for the opportunity to play this game? (Give your answer to the nearest cent.)

$64	-$13
$32	$8	$4
$16

$
Calculate the expectation (to the nearest cent) for theReader's Digestsweepstakes described below. Assume there are 197,000,000 entries.


$