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David and Ryan go to the movie theater and purchase refreshments for their friends. David spends a total of $24.75 on 3 bags of popcorn and 5 drinks. Ryan spends a total of $33.00 on 9 bags of popcorn and 4 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Final answer:
To find the price of one drink, we create a system of equations based on the purchases at the movie theater and solve it using the elimination method. The calculated price of one drink is $3.75, to the nearest cent.
Explanation:
David and Ryan's purchases at the movie theater can be represented by the following system of equations to find the price of one bag of popcorn (p) and one drink (d):
3p + 5d = 24.75
9p + 4d = 33.00
We'll solve this system using the substitution or elimination method. For this example, we will use the elimination method.
Multiply the first equation by 9 and the second by 3 to equalize the coefficients for p:
(3p + 5d) × 9 → 27p + 45d = 222.75
(9p + 4d) × 3 → 27p + 12d = 99.00
Subtract the second equation from the first:
27p + 45d - (27p + 12d) = 222.75 - 99.00
33d = 123.75
Divide by 33 to find the price of one drink:
d = 123.75 / 33
d = 3.75
So, the price of one drink is $3.75, to the nearest cent.
Simplify the expression 53 + 3(5 − 3). 137 131 27 21
Answer:
Its 131, I did the test, and got it right.
Explanation:
Socks cost $5 per pair. The expression 5p represents the cost in dollars of p pairs of socks. Why must p be a whole number?
Answer:
Step-by-step explanation:
p must be a whole number because $5 which is the cost of socks per pair is a perfect divisor of the expression 5p.
i.e 5p/5 = p
And in the expression p represent number of pairs
What’s the surface area
the sales tax on a $350 computer is $22.75 find the sales tax
55% of 387 is what number
A car maintains a speed of 23 mi/h for 5 seconds. It then accelerates to a speed of 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds. Which graph shows the car’s speed over time?
(80 points)
A car maintains a speed of 23 mi/h for 5 seconds. It then accelerates to a speed of 46 mi/h in 5 seconds. It maintains that speed for the next 5 seconds. Which graph shows the car’s speed over time?
Solution:
The graph is Time versus Speed.
In figure (a), the graph has a speed or y-axis=23mi/h for time or x-axis=5seconds.
The car maintains a speed of 23mi/h for 5 seconds.
For next 5 seconds, in figure a the graph increases linearly or we have a acceleration and reaches to 46mi/h.
It accelerates to a speed of 46 mi/h in 5 seconds.
It maintains that speed for the next 5 seconds. In figure (a), after we reach speed=46mi/h, there is a straight line for 5 seconds at speed=46mi/h.
So, Answer Graph a
Convert. Into degrees
why is one half of the Box wider than the other half of the box
Jeremy has saved $440 from his summer job. He plans to set aside $55 each week for his expenses. Several weeks later he has $110 left.How many weeks have passed?
To find out how many weeks have passed, we subtract the remaining amount from the initial amount, and then divide by the amount saved each week. In this case, 6 weeks have passed.
Explanation:To find out how many weeks have passed, we need to subtract the remaining amount from the initial amount, and then divide by the amount saved each week.
Initial amount saved = $440
Amount saved each week = $55
Remaining amount = $110
Weeks passed = (Initial amount saved - Remaining amount) / Amount saved each week
= ($440 - $110) / $55
= $330 / $55
= 6 weeks
Therefore, 6 weeks have passed.
Jim has a quarter and Jane has a number cube. In two or more complete sentences, explain why Jim is just as likely to get a head as Jane is to get an even number.
Jim is just as likely to get a head as Jane is to get an even number since the chance or probability of getting a head for Jim and getting a even number for Jane are equal i.e. 1/2=0.5
Step-by-step explanation:In a quarter there are just two outcomes-- Head and Tail
The probability of getting a head is: 1/2
Similarly in a number cube that has six possible outcomes i.e. {1,2,3,4,5,6}
The number of outcomes that represents a even number are: 3
(Since outcomes are: 2,4 and 6)
Hence, the probability of getting a even number is: 3/6=1/2
Hence, we see that the probability of getting a head and a even number is same.
PLZ HELP Harry baked a cake in the shape of a right rectangular prism and cut it in half parallel to the base of the cake. The base is 6 inches long and
4 inches wide, and the cake is 5 inches tall. Harry puts icing on the surface of each half of the cake. What is the shape of the cross section? What is the total area that is iced?
The cake’s cross section is a . The total area that is iced is square inches.
1/a.rectangle.b.square.c.kite.d.trapezoid
2/a.40.b.48.c.60.d.84
The answer is B, a square. I don't know about the area though.
Quadrilateral ABCD is inscribed in a circle. What’s the measure of angle B
Kasimir rode his bike 34,478 centimeters. He converts the distance to kilometers. His work is shown below.
A.Kasimir should have divided by 10,000.
B.Kasimir should have multiplied by 100.
C.Kasimir should have divided by 100,000.
D.Kasimir should have multiplied by 0.001.
Answer:
c) Kasimir should have divided by 100,000.
Step-by-step explanation:
Given that Kasimir rode his bike 34,478 centimeters.
We have the table
10 mm=1 cm
10 cm =1dm
10dm = 1 m
...
Hence we have 100 cm = 1 m
100x1000 cm = 1 km
1 km = 34478/100000 = 0.34478
Hence C) is right
Kasimir should have divided by 100,000.
Chang and Cal both collect pearls. Chang has three more pearls in her collection than Cal. Write an expression to represent the total number of pearls in both collections.
Look at the following math problems. 10 + 2 = 12 12 − 2 = 10 What are these operations called?
They are called inverse operations:
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
10+2.5X_<40
Which best describes the number of bags of balloons she can buy?
A.She can buy from 0 to 12 bags, but no more.
B.She can buy from 0 to 20 bags, but no more.
C.She must buy 12 or more bags.
D.She must buy 20 or more bags.
Answer:
Option A is the correct choice.
Step-by-step explanation:
We have been given that Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50.
The inequality [tex]10+2.5x\leq 40[/tex] represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
Let us solve for x by subtracting 10 from both sides of our inequality.
[tex]10-10+2.5x\leq 40-10[/tex]
[tex]2.5x\leq 30[/tex]
Now we will divide both sides of our inequality by 2.5.
[tex]\frac{2.5x}{2.5}\leq \frac{30}{2.5}[/tex]
[tex]x\leq 12[/tex]
Therefore, Ling can buy from 0 to 12 bags, but no more and option A is the correct choice.
Please help me on this
The expression 3/4×1/2 represents a fraction of a circle that is shaded. Which diagram shows the correct shading?
Circles with centers (2,1) and (8,9) have radii 1 and 9, respectively. The equation of a common external tangent to the circles can be written in the form y=mx+b with m < 0. What is b?
PLEASE HELP ASAP!!! ON TIME LIMIT!!!
The figure below shows a shaded rectangle inside a large rectangle:
https://learn.flvs.net/webdav/assessment_images/educator_mjmath2_v14/06_14_p1_27.jpg
If you choose a point inside the large rectangle, what is the probability that it is not inside the shaded rectangle?
24%
27%
46%
54%
5.65 times 3.4 estimate
What is it defining?
Define oblique prism.
An oblique prism can be thought of as a leaning prism where the altitude or height of the prism is not the same as the lateral edge of the prims.
in the right triangle what is the value of pq
In this Pythagorean theorem question, The value of pq in the right triangle is 8 cm. Therefore, the correct answer is option C.
The given triangle is a right triangle, with two sides measuring 17 cm and 15 cm. The side opposite the right angle (perpendicular) is represented by the variable pq.
To find the value of pq, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. So, applying the Pythagorean theorem:
a2 + b2 = c2
(15 cm)2 + pq2 = (17 cm)2
225 cm2 + pq2 = 289 cm2
pq2 = 289 cm2 - 225 cm2
pq2 = 64
pq = √64
pq = 8 cm
Learn more about Pythagorean theorem here:
https://brainly.com/question/28361847
#SPJ6
in circle P, chord AB is 3 inches from the center and chord CD is 5 inches from the center. Chord CD is ____ than chord AB.
A. longer
B. congruent
C.shorter
D. proportional
It took Jen, who biked at a speed of 12 mph, 20 minutes to get home. What is Jim’s speed, if it took him only 15 minutes to bike that distance?
Answer:
16 mph
Step-by-step explanation:
Explain when you know you need to rename a mixed number to subtract.
Jesse has a storage container in the shape of a right rectangular prism. The volume of the container is 43.875 cubic meters, the length is 5 meters and the width is 3.9 meters.
What is the height of Jesse's storage container?
I NEED HELP!!!!!!!!!!!!!!!!!!!!!!! :(
Answer:
2.25 meters
Step-by-step explanation:
all you have to do is divide the volume of the container (43.875) by 5 (length) and 3.9 (width) because the formula for the volume of a rectangular prism is V=lwh. So the answer/height of the storage container is 2.25 meters.