Monica has $20. She needs to buy a gallon of milk that costs $2.50. She also wants to buy yogurt, which costs $1.20 a cup. What is the greatest number of cups of yogurt Monica can buy?
Use the inequality 1.20x + 2.5 ≤ 20 to solve the problem.
Greatest number of cups of yogurt Monica can buy is equals to 14cups.
What is Linear inequality?
" Linear inequality is the algebraic mathematical expression which compares two value with the sign of inequality, <, > , ≤, ≥ ."
According to the question,
Given,
Total amount with Monica = $20
Cost of a gallon on milk = $2.50
Cost of 1cup of yogurt = $1.20
Given linear inequality
1.20x + 2.5 ≤ 20
x represents the number of cups of yogurt
Solve linear inequality to get the value of x we have,
1.20x+2.5 -2.5 ≤ 20-2.5
⇒1.20x ≤ 17.5
⇒x ≤ 17.5 / 1.20
⇒x ≤ 14.58
14 ≤ 14.58 ≤ 15
Therefore, 14 of cups of yogurt Monica can buy.
Learn more about Linear inequality here
https://brainly.com/question/11897796
#SPJ2
Recall the Survivor: 21 Flags game from the page on backward induction. Assume that you are playingthe same game with the same rules EXCEPT now the team who takes the last flag loses.a) (30 points) What should each team’s strategy be?b) (5 points) What is the best move for the first team to move?c) (5 points) What is the best move for the second team to move?
Answer:
Given that there are 21 flags, NOW using backward induction we can see that;
If there is only one flag left, whosoever picks up that particular flag will lose. Therefore, 1 is loosing number.
Now if there are 2 flags left, whosoever's turn it is, can pick 1 flag and leave one for the opponent and win the game. Therefore, 2 is winning number. Similarly if there are 3 flags left then whosoever's turn it is can pick 2 flags and leave one for the opponent and can win the game. Hence 3 is winning number. Similarly when 4 flags left, 3 can be picked up and leave one for the opponent and win the game. So, 4 is also winning number.
Now, if there are 5 flags left, then no matter whichever number you choose among 1,2 or 3 you gonna leave other team with 4,3 or 2 respectively and all 3 are winning number. Therefore, 5 is loosing number.
Similarly, if you have 6,7,8 then by taking 1,2,3 respectively you can leaveyour opponent with number 5 and that is loosing number and you can win certainly. Therefore, 6,7,8 are also winning number.
Following above discussion, we see a pattern among the number that would make sure you win and with other numbers you loose.
we see after 1 if we go in positive direction on number line till 21 then every fourth number is loosing number because no matter what you choose you will leave your opponent with a winning number of flags and if your opponent knows and follows the optimal strategy can win. Therefore,
Loosing Numbers = 1,5,9,13,17 and 21
Winning Numbers = 2,3,4,6,7,8,10,11,12,14,15,16,18,19 and 20
a) STRATEGY
If you are a team that is stuck with any of loosing number that is 1,5,9,13,17 or 21 then no matter what strategy you follow you gonna loose. Therefore, there is n winning strategy in this situation given other team also knows the winning strategy
But if you have any of winning numbers at any point then you can follow the following strategy and can win
- 2 flags = pick up one flag and leave 1 for the opponent, win
- 3 flags = pick up 2 flags and leave 1 for the opponent, win
- 4 flags = pick up 3 flags and leave 1 for the opponent, win
- 6 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win
- 7 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win
- 8 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win
- 10 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win
- 11 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win
- 12 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win
- 14 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win
- 15 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win
- 16 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win
- 18 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win
- 19 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win
- 20 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win
b)
Since team moving first will have 21 flags left on ground and it is a loosing number, no matter which number it chooses to pick it is gonna loose as it will leave other team with winning number. So, they will be indifferent between choosing 1,2 or 3
c)
If first teams removes 1 flag then best strategy for second team would be to remove 3 flags and again leave first team with loosing number
similarly, If first teams removes 2 flags then best strategy for second team would be to remove 2 flags and again leave first team with loosing number
and If first teams removes 3 flags then best strategy for second team would be to remove only 1 flag and again leave first team with loosing number
The Lions won 35 out of 40 games this season. What fraction of the games did the Lions win?Write your answer in simplest form.___________________________________
Answer:
7/8
Step-by-step explanation:
Answer:
7/8
Step-by-step explanation:
Divide common factors from both the numerator and denominator. Divide 5 from both top and bottom:
(35/40)/(5/5) = 7/8
7/8 is your answer.
~
what is -66 2/3 - 24 1/8 + -78 3/4
Answer:
-169.541667
Step-by-step explanation:
Answer:
Step-by-step explanation:
i belive your asnwer would be -257/24 but what are u trying to find?
Dante’s cell phone company charges $45 per month for unlimited calls and texts,plus $0.25 per gigabyte of data.His last cell phone bill was $60.50.How many gigabytes of data did Dante use last month?
10X10 in exponent form?
Answer:
[tex] {10}^{2} [/tex]
Step-by-step explanation:
If you get this you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the garden. Good luck! If you get it correct your answer will be deleted and l will message you to continue the game.
Answer:
35
Step-by-step explanation:
34+ you = 35
After killing still people are inside room.
Suppose 7 quarters, 4 dimes, 4 nickels, and 3 pennies are in a box. One coin is selected at random. What is the expected value of the money drawn from the box?
Since the quarters have a highest percentage. You would likely draw 25 cents from the box
a gallon of paint can cover about 350 square feet of wall space. You have measured a wall to be 210 inches by 120 inches. Will one gallon of paint be enough to cover the wall?
1 foot = 12 inches.
210/12 = 17.5 feet
120/12 = 10 feet
17.5 x 10 = 175 square feet
175 is less than 350 so yes one gallon will be enough.
Answer: yes
Step-by-step explanation: because it is only 175 ft of wall
What is the degree of the polynomial
a well is being dug into the ground. the well needs to reach the depth of 120 feet. a machine can dig down in 12 minutes. what is the change in depth each minute the machine is digging
Answer:
10 feet
Step-by-step explanation:
PLEASE HELP IF YOU KNOW
Your answer is going to be A
Step-by-step explanation:
How many days equal 7344 minutes?
The answer is 5.1 days
60*24= 1440 minutes in one day
7344/1440= 5.093 or 5.1 rounded to the nearest tenth
Find the interest
earned:
$ 15,500 for 7.5 years
at 4.9% annual
compound interest
Answer:
In 7.5 years, you will have $21,665.07 - $15,000 = $6,665.07 Interest
Step-by-step explanation:
4 kitchen assistants can prepare 10kg of vegetables in 45 minutes. How long would it take 25 assistants to prepare
A scuba driver was swimming at an elevation of -8 meters. A shark was swimming at an elevation of -29 meters. Find the difference between these two elevations.
Answer:
-21
-29-(-8)=-21
OPEN ENDED QUESTION
Rewrite the following problem using
commutative property of addition: -3 + 7
Answer:
4
Step-by-step explanation:
7+-3=4
Answer:
4
Step-by-step explanation:
Step 1:
7 + ( -3)
Step 2:
7 - 3
Answer:
4
Hope This Helps :)
Help. Your backyard is 10 feet longer than it is wide. Its area is 8624 square feet. Its width is Solve in quadratic equation.
Would you say 88in by 98in is correct?
study of class attendance and grades among first-year students at a state university showed that, in general, students who missed a higher percent of their classes earned lower grades. Class attendance explained 36% of the variation in grade index among the students. What is the numerical value of the correlation between percent of classes attended and grade index?
work out the difference in minutes between 1 hour 25 minutes and 1 1/4 hours step by step please :)
[tex]\huge\boxed{\boxed{\bold{10\ \bftext{minutes}}}}[/tex]
[tex]\hrulefill[/tex]
First, let's change both of these times into just minutes. (We know that one hour is sixty minutes.)
[tex]\text{First time: } 1*60+25=60+25=85[/tex]
[tex]\text{Second time: } 1*60+\frac{1}{4}*60=60+15=75[/tex]
Now, just subtract:
[tex]85-75=\large\boxed{10}[/tex]
Is x a natural number
Answer:
no because natural numbers are positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well. not variables
factor an expression:
(x²+x+1)²+3x(x²+x+1)-18x²
Answer:
( x - 1 ) ^ 2 ( x ^ 2 + 7 x + 1 )
Step-by-step explanation:
Sorry about the spaces, thought it would make it look better!
Please help!! What is the quotient??
12 x 3 x 8 + 3 + 1 - 100 x 2323
Answer:
-232008
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
12 x 3 x 8 + 3 + 1 - 100 x 2323
Step 2: Multiply
36 x 8 + 3 + 1 - 100 x 2323
Step 3: Multiply
288 + 3 + 1 - 100 x 2323
Step 4: Multiply
288 + 3 + 1 - 232300
Step 5: Add
291 + 1 - 232300
Step 6: Add
292 - 232300
Step 7: Subtract
-232008
Answer
-232,008 is ans of this simplification
A line passes through (0, 2) and has a slope of 3. Which function's graph is parallel to this line?
A. f(x) = 2 O
B. f(x) = 3 O
C. f(x) = 2x O
D. f(x) = 3x o TUL earch
ANSWER IS B 30
Step-by-step explanation:
The function's graph is parallel to this line is 3x.
What is equation of a straight line ?The general equation of a straight line is y = mx + c, where m is the gradient or slope, and y = c is the value where the line cuts the y-axis. This number c is called as intercept.
From the question,
Parallel lines have same slope.
The slope given, m =3.
The function's graph is parallel to this line is 3x.
Hence the required answer is f(x)= 3x.
To learn more on equation of straight line click:
brainly.com/question/28951575
#SPJ2
Item 3 A snail travels 3/8 feet in 1/2 hour. How many feet does the snail travel in one hour? Express your answer in simplest form. 3/16ft 1/4ft 1/8ft 3/4ft
two groups of people need to get to the top floor of a building. the first. group had 33 people, and its elevator can carry 6 people per trip. the second group has 49 people,but its elevator can carry 7 people per trip..... group 1 is represented by the equation 6x=33. solving the equation gives x what
Step-by-step explanation:
6x = 33
or, x=33/6
x=5.5
State the domain and range in set notation
Answer:
Image result for State the domain and range in set notation
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
The last option is not complete, but since the first three options are incorrect, the last option is correct
State the horizontal asymptote of the rational function.
f(x) = quantity x plus nine divided by quantity x squared plus four x plus two
Answer:
there is no meme
Step-by-step explanation:
Can you solve (x-2)(x+3)=5 by solving x-2=5 and x+3=5? Explain
Will MARK BRAINLIEST
Answer:
Yes you can.
Step-by-step explanation:
You can because you can just subsitute x-2=5 and x+3=5 into the equation.
Answer:
x=3±/5
Step-by-step explanation:
i don't actually know how to do certain symbols sorry but i hope you know what this means