Sarah and her children went into a movie theater where they sell bags of popcorn for $7.50 each and drinks for $4.50 each. Sarah has $90 to spend and must buy a minimum of 16 bags of popcorn and drinks altogether. If xx represents the number of bags of popcorn purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer:
A possible solution is she should by 6 bags of popcorn and 10 drinks
Step-by-step explanation:
The price of each bag of popcorn = $7.50
The price of each drink = $4.50
The amount Sarah has to spend = $90
The number of bags of popcorn and drinks Sarah must buy = 16 bags of popcorn and drinks
Let the number of bags of popcorn purchased be represented by x and the number of drinks purchased be represented by y
Therefore, we have;
x + y ≥ 16.....(1)
x × 7.5 + y × 4.5 ≤ 90
Which gives;
7.5·x + 4.5·y ≤ 90....(2)
Rewriting the inequalities as a function of y, gives;
From inequality (1), x + y ≥ 16, we have;
y = ≥ 16 - x
From inequality (2), 7.5·x + 4.5·y ≤ 90, we have;
7.5·x + 4.5·y ≤ 90
4.5·y ≤ 90 - 7.5·x
y ≤ 90/4.5 - 7.5/4.5·x
y ≤ 20 - 5/3·x
Please find attached, the plot of the inequalities
A possible solution is given as the value of x = 6, where y = 10
Therefore, she should by 6 bags of popcorn and 10 drinks.
Related Questions
Is this a function or no
Answers
A one year membership at the club costs $10. You pay an additional $1.25 each day you go.
Last year you spent a total of $45. How many days did you go?
Answers
Subtract 10 from 45
And then divide 35 by 1.25
Answer:36
Step-by-step explanation:
Marge's plan costs .14 cents per minute plus a monthly fee of $24. Dan's plan costs .12 cents per minute plus a monthly fee of $28. How many minutes (m) are required for both plans to cost the same for the month?
Answers
Answer:
6 min for Marge's and 7 for Dan's plan
Step-by-step explanation:
0.14x6=0.84
0.12x7=0.84
Determine the measure of ∠Q, rounded to the nearest tenth of a degree.
images attached.
Answers
Answer:
D
Step-by-step explanation:
Using the Sine rule in Δ QRS , that is
[tex]\frac{q}{sinQ}[/tex] = [tex]\frac{r}{sinR}[/tex] , that is
[tex]\frac{15}{sinQ}[/tex] = [tex]\frac{12}{sin50.1}[/tex] ( cross- multiply )
12× sinQ = 15 × sin50.1° ( divide both sides by 12 )
sinQ = [tex]\frac{15sin50.1}{12}[/tex] , thus
Q = [tex]sin^{-1}[/tex] ( [tex]\frac{15sin50.1}{12}[/tex] ) ≈ 73.5° ( to the nearest tenth )
Let $f(x) = 2x - 3$ and $g(x) = x + 1$. What is the value of $f(1 + g(2))$?
Answers
Answer:
The value of f(1 + g(2)) is 5
Step-by-step explanation:
Let us solve the question
∵ f(x) = 2x - 3
∵ g(x) = x + 1
We need to find the value of f(1 + g(2))
That means we will replace x in f(x) by 1 + g(2)
→ g(2) means substitute x in g by 2
∵ g(x) = x + 1
∵ x = 2
∴ g(2) = 2 + 1
∴ g(2) = 3
∵ x of f = 1 + g(2)
∵ g(2) = 3
∴ x of f = 1 + 3
∵ x of f = 4
→ To find f(1 + g(2)) substitute 1 + g(2) by 4
∵ f(x) = 2x - 3
∵ x = 4
∴ f(4) = 2(4) - 3
∴ f(4) = 8 - 3
∴ f(4) = 5
∴ f(1 + g(2)) = 5
Miguel completed the division problem below. What is Miguel's error? A.He included a 5 in the quotient, which does not belong. B.He multiplied the divisor by 10 and the dividend by 100. C.He subtracted 208 from 234 incorrectly. D.He multiplied the divisor by 100 and the dividend by 10. 754 divided by 0.52. 52 StartLongDivisionSymbol 7540 EndLongDivisionSymbol minus 52 = 234. 234 minus 208 = 260. 260 minus 260 = a remainder of 0 and a quotient of 145.
Answers
Answer:
D. He multiplied the divisor by 100 and the dividend by 10.
Step-by-step explanation:
From the question: The following steps are given:
754 divided by 0.52.
754 = Dividend
0.52 = Divisor
Step 1
7540 ÷ 52
This is where he made his error,
He multiplied the divisor by 100 and the dividend by 10.
The correct step would be
To Multiply both the Divisor and the Dividend by 100
= 75400 ÷ 52
Option D is the correct option
Answer:
The answer is D
Step-by-step explanation:
Hope this helped! :)
The concentrates were pooled from the blood of about 1000 donors per lot. If the prevalence of HIV in donor blood in the early 1980s was 1 in 3,000, what was the probability that a hemophiliac would contract HIV from a single infusion of clotting factors?
Answers
Answer:
The required probability is "0.0003".
Step-by-step explanation:
Throughout the early 1980s, reconstructed coagulation factors concentrate extracted from individual blood was collected by hemophiliacs. The concentrate was obtained from either the blood of approximately 1000 donors every lot. The occurrence of hepatitis C throughout donated blood reached 1 in 3000 throughout the early 1980s.Therefore, the risk though from a single injection of clotting factors, a hemophiliac would contracted hepatitis C seems to be:
= [tex]\frac{1}{3000}[/tex]
= [tex]0.0003[/tex]
Complete the sentence about the relation. There is x and y columns. The x column contains two, eight, thirty, and forty six values. The y column contains minus one, nine, and sixteen values. The first arrow starting from value two of column x and ended at the value minus one in column y. The second arrow started from value eight of column x and ended at sixteen in column y. The third arrow starting from value thirty of column x and ended at value nine in column y. The forth arrow starting from point forty six and ended at value sixteen in column y. The domain of the relation is Choose... and the range is Choose... .
Answers
Answer:
Domain is [tex]\{2,8,30,46\}[/tex]
Range is [tex]\{-1,9,16\}[/tex]
Step-by-step explanation:
The relation refers to the collection of ordered pairs, which contains an element from one set to another set.
Domain of a relation [tex]y=f(x)[/tex] is all the values [tex]x[/tex] that go into a function, and the range is a set of all the values [tex]f(x)[/tex] that are obtained for the given domain.
The given relation is [tex]\{(2,-1),(8,16),(30,9),(46,16)\}[/tex]
Here, domain is [tex]\{2,8,30,46\}[/tex]
Range is [tex]\{-1,9,16\}[/tex]
solve for x
-30=5(x+1)
Answers
Answer:
-7
Step-by-step explanation:
im failing pls help !!!!!
Answers
Answer:
ill suck ya wang
Step-by-step explanation:5$ and ill suck yo wang to do your homework
Answer:
It is C.
Step-by-step explanation:
If you multiply 2 times 2 you get 4. Then multiply 4 by 5 and you get 20.
Therefore, it is C.
PLEASE ANSWER ASAP WILL MARK BRAINLEST
Paul and Dana both want to find the change from the 6 AM temperature to the new 12 PM temperature.
Paul says that you can use a number line and add the distance from 0 to the 6 AM temperature and from 0 to the new 12 PM temperature. Dana says that you can subtract -1.4 from the new 12 PM temperature.
Is either Paul or Dana correct> Explain your reasoning and find the change in temperature.
Answers
Answer:
Paul is correct
Step-by-step explanation:
You can add the distance of 0 to 6 AM and 0 to 12 PM, and doing so on a number line. On a number line you would add them and lets say 6 AM is 6 degrees and 12 PM is 12 degrees, you would add 6 and 12 to get 18. While doing so you would got 1 2 3 4 5 6 7 8 9 and so on. Thus, finding the difference.
I know I'm late but can I still get that brainliest
12. The table shows the height in feet of a stack of medium sized moving boxes. What is the height of a stack of 14 boxes
Answers
height = 2.25 * box.
So, 14 boxes = 2.25 * 14 = 31.5.
Steve is turning half of his backyard into a chicken pen. His backyard is a 242424 meter by 454545 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?
Answers
Answer:
51 meters
Step-by-step explanation:
The shape of the backyard is rectangular having a length, l=45 meters, and a width, w=24 meters as shown in the figure.
As wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. So,
The length of fencing = The length of the diagonal AC or BD
As the length of both the diagonals of a rectangle are equals, AC=BD.
The length of fencing [tex]=\sqrt{l^2+w^2}[/tex] [length of the diagonal]
[tex]=\sqrt{45^2+24^2}=51[/tex] meters
Hence, Steve needs 51 meters of fencing.
- You study 4 hours per day and are in class 6 hours
per day. Find the ratio of the number of study hours to
class hours.
Answers
Answer:
2/3
Step-by-step explanation:
Initially it would be 4/6 which you can simplify as 2/3
help pls . .. a a z z z z . zz
Answers
Answer:
the lines are perpendicular
So sorry if it’s wrong
What is faster? 15 meters per minute or 15 kilometers per hour?
Answers
Answer:
15 kilometers
Step-by-step explanation:
15 kilometers is in conversion with miles
Approximate the value of the positive square root of 110 to the nearest hundredth
Answers
12 divided by 18/25 is?!?!
Answers
Answer:
16.6
Step-by-step explanation:
12 divided by 18/25 is 16.66.
Given:
12 divided by 18/25
12÷18/25
12÷0.72
=16.66
What is division?Division is one of the four basic operations of arithmetic, the ways in which numbers are combined to form new numbers. To divide rational expressions, multiply the first fraction by the reciprocal of the second. If we rewrite division as the product of the first expression by the inverse of the second, we add them all and look for common factors.
The way something is shared is called a sharing method. There are three types of distribution methods according to the degree of difficulty. They are division method or division by repeated subtraction, short division method or bus stop method and long division method.
To learn more about division, refer;
https://brainly.com/question/21416852
#SPJ2
WILL GIVE BRAINLST FOR WHOEVER ANSWERS FIRST Which of the following equations is equivalent to 6(3p – 2) = 20?
Group of answer choices
9p – 4 = 20
9p – 8 = 20
18p – 12 = 20
18p – 2 = 20
Answers
a.What is the length of A’A?
b.What is the length of B’B
Both in units
Answers
Answer:
A'A = 18 units, B'B = 9 units
Step-by-step explanation:
Δ ACB and Δ A'CB' are similar triangles, thus the ratios of corresponding sides are equal, that is
[tex]\frac{AC}{A'C}[/tex] = [tex]\frac{AB}{A'B'}[/tex] , substitute values
[tex]\frac{AC}{12}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )
8AC = 240 ( divide both sides by 8 )
AC = 30
Thus A'A = AC - A'C = 30 - 12 = 18 units
--------------------------------------------------------------------
and
[tex]\frac{CB}{CB'}[/tex] = [tex]\frac{AB}{A'B'}[/tex] , that is
[tex]\frac{CB}{6}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )
8CB = 120 ( divide both sides by 8 )
CB = 15
Thus
B'B = CB - CB' = 15 - 6 = 9 units
GIVING BRAINLIEST!!! A student observes a beaker of room temperature water resting on a table. She states that the beaker of water does not have any energy. Which statement below is accurate regarding her observation?
a. She is correct because the beaker of water is not moving.
b. She is incorrect because the beaker of water has thermal energy.
c. She is incorrect because all water contains hydrogen and oxygen.
d. She is correct because the beaker of water is at room temperature.
Answers
Answer:
b
Step-by-step explanation:
Write the proportional equation that represents the table below.
Answers
HELP ASAP PLS, matching sequence to its recursive formula
Answers
What is 13 / 143 as a unit fraction
Answers
Answer:1/11
Just got it using some brain cells >:)
Answer:
1/11
Step-by-step explanation:
13/143=1/11
A half of a number added to 7 gives 19. What is the number? *
Answers
Answer:
24
Step-by-step explanation:
---------------
24÷2=12
12+7=19
---------------
I need helps please and ty
Answers
Answer:
y=7x+4
Step-by-step explanation:
Values of x and y satisfy the equation y=7x+4
Candace is a salesperson at the local boat store. She receives a 14% commission on every sale that she makes. How much commission does Candace
make on a boat that sells for $1,995?
Answers
Answer: 00000
Step-by-step explanation:
-3 = 1 3/5 + m .
what is m
Answers
Answer:
m = -4 3/5 or -4.6
Step-by-step explanation:
First, we need to isolate the variable, m. We subtract 1 3/5 on both sides of the equation, and then we should get -4 3/5 = m.
hope this helped !! :D
Guys pls answer this for me in a minute it is really hard
Answers
Check all fractions equivalent to 2⁄8.
Check all that are true.
1⁄2
1⁄6
4⁄16
1⁄4
4⁄12