Madelyn and her children went into a movie theater and she bought $39 worth of bags of popcorn and pretzels. Each bag of popcorn costs $6.50 and each pretzel costs $3.25. She bought 4 times as many pretzels as bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Madelyn bought.
***(just need equations)***
Answers
Answer:
Madelyn bought 2 bags of popcorn and 8 pretzels.
Step-by-step explanation:
Madelyn and her children went into a movie theater and she bought $39 worth of bags of popcorn and pretzels. Each bag of popcorn costs $6.50 and each pretzel costs $3.25. She bought 4 times as many pretzels as bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Madelyn bought.
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of bags of popcorn}
the number of bags of popcorn
y=
y=
\,\,\text{the number of pretzels}
the number of pretzels
One bag of popcorn costs $6.50, so xx bags of popcorn cost 6.50x.6.50x. One pretzel costs $3.25, so yy pretzels cost 3.25y.3.25y. The total 6.50x+3.25y6.50x+3.25y equals \$39:$39:
6.50x+3.25y=39
6.50x+3.25y=39
Since Madelyn bought 4 times as many pretzels as bags of popcorn, there are more pretzels, so if we multiply 4 by the number of bags of popcorn, we will get the number of pretzels, meaning yy equals 4x.4x.
y=4x
y=4x
\underline{\text{Write System of Equations:}}
Write System of Equations:
6.50x+3.25y=
6.50x+3.25y=
\,\,39
39
y=
y=
\,\,4x
4x
\underline{\text{Solve for }y\text{ in each equation:}}
Solve for y in each equation:
6.50x+3.25y=39
3.25y=−6.50x+39
3.25
3.25y
=
3.25
−6.50x+39
y=−2x+12
y=4x
0
the number of bags of popcorn
the number of pretzels
x
y
(2, 8)
0
the number of bags of popcorn
the number of pretzels
The xx variable represents the number of bags of popcorn and the yy variable represents the number of pretzels. Since the lines intersect at the point \left(2, 8\right)(2,8) we can say:
Madelyn bought 2 bags of popcorn and 8 pretzels.
Related Questions
suppose that a fair coin is tossed repeatedly until exactly k heads have been obtained. determine the expected number of tosses that will be required.
Answers
The expected number of tosses required to obtain exactly k heads is k/2.
Let X be the random variable representing the number of tosses required to obtain exactly k heads. We can express X as a sum of indicator variables, where Xᵢ = 1 if the i-th toss is a head, and Xᵢ = 0 otherwise. Then, we have:
X = X₁ + X₂ + ... + Xₖ
The expected value of X is given by the linearity of expectation:
E(X) = E(X₁ + X₂ + ... + Xₖ) = E(X₁) + E(X₂) + ... + E(Xₖ)
Since the coin is fair, each toss has a probability of 1/2 of being a head. Therefore, the expected value of each indicator variable is:
E(Xᵢ) = P(Xᵢ = 1) * 1 + P(Xᵢ = 0) * 0 = 1/2
Using this, we can find the expected value of X:
E(X) = E(X₁ + X₂ + ... + Xₖ) = E(X₁) + E(X₂) + ... + E(Xₖ) = k * 1/2
Therefore, the expected number of tosses required to obtain exactly k heads is k/2. This result makes sense, since on average, we would expect to obtain one head for every two tosses of a fair coin.
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The Select] of a system of linear inequalities is the graph of all ordered pairs that simultaneously satisfy all the inequalities in the system.
Answers
The solution set of a system of linear inequalities represents the region on a graph where all the inequalities in the system are true simultaneously.
Each inequality in the system represents a boundary or constraint, and the solution set is the intersection of these boundaries. For example, consider a system of two linear inequalities:
y ≤ 2x + 3
y ≥ -x + 1
To find the solution set, we graph the individual inequalities and identify the overlapping region. In this case, the solution set would be the area where the shaded regions of both inequalities overlap. This region represents the ordered pairs that satisfy both inequalities simultaneously.
The solution set can be empty if the inequalities do not intersect, or it can be a bounded or unbounded region depending on the nature of the inequalities.
Overall, the solution set of a system of linear inequalities provides a visual representation of the feasible region or the set of all possible solutions that satisfy all the given inequalities in the system.
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A soccer dome shaped like a hemisphere has a volume of 450,000 cubic meters. What is the area of its floor? Use 3.14 for π in your calculations and round your answer to the nearest square meters
Answers
Answer:
3282 m^2
Step-by-step explanation:
volume of a hemisphere = (2/3) x (n) x (r^3)
n = 22/7
r = radius
r = (450,000 x (3/2) x(1/3.14)) ^1/3
r = 45.72
Area of a semicircle = 1/2 x n x r^2
1/2 x 45.72^2 x 3.14 = 3282 m^2
*URGENT*
PLEASE HELP ILL GIVE BRAINLIEST !!!!!!
Answers
More info a. Theoretical capacity-based on three shifts, completion of five motorcycles per shift, and a 360 -day year-3 −3×360=5,400. b. Practical capacity-theoretical capacity adjusted for unavoidable interruptions, breakdowns, and so forth-3 −4×320=3,840. c. Normal capacity utilization-estimated at 3,240 units. d. Master-budget capacity utilization-the strengthening stock market and the growing popularity of motorcycles have prompted the marketing department to issue an estimate for 2020 of 3,600 units. Requirement 2. What are the benefits to Zippy, Inc., of using either theoretical capacity or practical capacity? to managers. As a general rule, however, it is important on the production-volume variance as a measure of the economic costs of unused capacity. Requirement 3. Under a cost-based pricing system, what are the negative aspects of a master-budget denominator level? What are the positive aspects? What are the negative aspects of a master-budget denominator level? referred to as the demand spiral. What are the positive aspects? The positive aspects of the master-budget denominator level are that is based on for the product and indicates the price at which would be recovered to enable the company to make a profit.
Answers
The benefits of using the theoretical capacity for Zippy, Inc. include providing a maximum production potential based on ideal conditions, aiding in long-term planning, and setting performance benchmarks. Practical capacity considers unavoidable interruptions and breakdowns, providing a more realistic estimate. The negative aspect of a master-budget denominator level is the potential for unused capacity costs, while the positive aspect is using a predetermined cost base for pricing decisions.
Theoretical capacity, based on three shifts and completion of five motorcycles per shift, gives Zippy, Inc. a maximum production potential of 5,400 units per year. This capacity measure helps in long-term planning, resource allocation, and setting performance benchmarks. On the other hand, practical capacity takes into account unavoidable interruptions, breakdowns, and other factors that can impact production. It provides a more realistic estimate of 3,840 units.
Regarding cost-based pricing, the negative aspect of a master-budget denominator level is that it may lead to unused capacity costs. If the estimated demand falls below the master-budget level, there could be underutilized resources, resulting in economic costs for the company. However, the positive aspect of using a master-budget denominator level is that it provides a predetermined cost base for pricing decisions. It helps in setting prices that ensure the company's costs are covered and profitability is achieved.
In summary, theoretical capacity aids in long-term planning and setting benchmarks, while practical capacity considers interruptions. The negative aspect of a master-budget denominator level is unused capacity costs, but it provides a predetermined cost base for pricing decisions, ensuring cost recovery and profitability.
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I have trouble understanding the strategy used to solve this type of equation....
Answers
Answer:
Step-by-step explanation:
-3x + 18y = -12
3x - 18y = 4
0 ≠ -8
no solution
How do you round 0.682 to the nearest tenth
Answers
Answer:
0.70 is nearest tenth
Step-by-step explanation:
what will the median of a sample always equal? (smallest value largest value)/2 50th percentile (q1 q3)/2 square root of the variance
Answers
The median of a sample will always equal the 50th percentile.
What is the median of a sample?The median of sample data is the middle value when the data is arranged in order from lowest to highest. In other words, it is the value that separates the lower 50% of the data from the upper 50%.
The median is often used as a measure of central tendency in a dataset because it is not affected by extreme values or outliers in the way that the mean is. If the sample size is odd, the median is simply the middle value, If the sample size is even, the median is the average of the two middle values.
The median is also known as the second quartile and the 50th percentile. As a result, the median of a sample will always equal the 50th percentile.
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I need help please it would really help
Answers
Answer:
B
Step-by-step explanation:
V = 4/3 * radius^3 * pi = 4/3 * 4^3 * pi = 256 /3 * pi
If f(x) = -2x + 3 and g(x) = 4x - 3, which is greater, f(5) or g(-2)?
Answers
Need help with the following Questions
How would you calculate the distance in miles between two people on the same line of latitude? First, sum to the total distance between the points in degrees, then multiply that sum by the statute miles per degree for the shared line of latitude. (Hint: Sometimes it is easier to visualize this by plotting it on a graph).
A. How many miles are between the following two locations: 60°N, 30°W & 60°N 50°E
B. How many miles are between the following two locations: 30°S, 60°W & 30°S 90°E
Answers
The distance between two locations on the same line of latitude can be calculated by summing the total distance between the points in degrees and multiplying it by the statute miles per degree for the shared line of latitude.
To calculate the distance in miles between two locations on the same line of latitude, we first need to find the total distance between the points in degrees. In the case of location A, which is 60°N, 30°W, and location B, which is 60°N, 50°E, the total distance between the two points is 80 degrees (50°E - 30°W).
Next, we need to multiply the sum of the degrees by the statute miles per degree for the shared line of latitude. Since the line of latitude is 60°N, we need to determine the statute miles per degree at that latitude.
The Earth's circumference at the equator is approximately 24,901 miles, and since a circle is divided into 360 degrees, the distance per degree at the equator is approximately 69.17 miles (24,901 miles / 360 degrees).
Multiplying the total distance in degrees (80 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 5,533.6 miles.
Similarly, for location C, which is 30°S, 60°W, and location D, which is 30°S, 90°E, the total distance between the points is 150 degrees (90°E - 60°W). Since the line of latitude is 30°S, we use the same statute miles per degree value (69.17 miles).
Multiplying the total distance in degrees (150 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 10,375.5 miles.
Therefore, the distance between locations A and B is approximately 5,533.6 miles, and the distance between locations C and D is approximately 10,375.5 miles, when calculated using the given method.
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what is the probability of five people with different ages sitting in ascending or descending order at a round table?
Answers
The probability of five people with different ages sitting in ascending or descending order at a round table can be calculated as the ratio of favorable outcomes to total outcomes.
In this case, the favorable outcomes are the arrangements where the five people are seated in ascending or descending order, and the total outcomes are all possible seating arrangements of the five people. To determine the favorable outcomes, we can consider the two cases separately: ascending order and descending order.
For the ascending order case, we fix one person at a position and arrange the remaining four people in ascending order around the table. There are 4! (4 factorial) ways to arrange the remaining four people. Similarly, for the descending order case, there are also 4! ways to arrange the remaining four people.
Since we have two cases (ascending and descending), the total number of favorable outcomes is 2 * 4! = 48. To calculate the total outcomes, we need to consider that the five people can be arranged in 5! ways around the table. Therefore, the probability of five people with different ages sitting in ascending or descending order at a round table is 48 / 5!.
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A uniform continuous distribution has a maximum of 14 and a minimum of 2. Samples of size 36 are drawn from the distribution. What is the variance of the sample means?.
Answers
The sample mean variance of the continuous distribution will be 0.3428.
The population variance is equal to the sample size divided by the variance of the sampling distribution of the mean.
14 is the greatest and 1 is the smallest value in a uniform continuous distribution.
36-size samples are taken from the distribution.
Now,
Variance among the population = 14 – 2 = 12
The sample size is 36.
Given that the sample means' variance is defined as;
= Variation in the population / Sample Size
If you replace all the values, you get;
= 12 / 35
= 0.3428
As a result, the sample mean variance will be 0.3428.
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A cut in an undirected graph is a separation of the vertices V into two disjoint subsets S and T. The size of a cut is the number of edges that have one endpoint in S and the other in T. Let MAX-CUT = {(G, k)| G has a cut of size k or more}. Show that MAX-CUT is NP-complete. You may assume the result of Prob- lem 7.26. (Hint: Show that #SAT
Answers
The cut separates the variables from their negations, each clause will have at least one true literal, satisfying the 3SAT instance.
To show that MAX-CUT is NP-complete, we need to demonstrate two things: First, that MAX-CUT is in the NP complexity class, meaning that a proposed solution can be verified in polynomial time. Second, we need to reduce a known NP-complete problem to MAX-CUT, showing that MAX-CUT is at least as hard as the known NP-complete problem.
MAX-CUT is in NP:
To verify a proposed solution for MAX-CUT, we can simply check if the cut separates the vertices into two disjoint subsets S and T, and count the number of edges that cross the cut. If the number of crossing edges is equal to or larger than k, we can accept the solution. This verification process can be done in polynomial time, making MAX-CUT a member of the NP complexity class.
Reduction from a known NP-complete problem:
We will reduce the known NP-complete problem, 3SAT, to MAX-CUT. The 3SAT problem involves determining if a given Boolean formula in conjunctive normal form (CNF) is satisfiable, where each clause contains exactly three literals.
Given an instance of 3SAT with n variables and m clauses, we construct a graph G for MAX-CUT as follows:
Create a vertex for each variable and its negation, resulting in 2n vertices.
For each clause (a ∨ b ∨ c), introduce three additional vertices and connect them in a triangle. Label one vertex as a, another as b, and the third as c.
Connect the variable vertices with the corresponding clause vertices. For example, if the variable is x and it appears in the clause (a ∨ b ∨ c), create edges between x and a, x (negation of x) and b, and x and c.
Now, we claim that there exists a cut in G of size k or more if and only if the 3SAT instance is satisfiable.
If the 3SAT instance is satisfiable, we can assign truth values to the variables such that each clause evaluates to true. We can then define the cut by placing all true variables and their negations in one subset S, and the remaining variables and their negations in the other subset T. The number of crossing edges in the cut will be at least k, as each clause triangle will have at least one edge crossing the cut.
If there exists a cut in G of size k or more, we can use it to derive a satisfying assignment for the 3SAT instance. Assign true to all variables in subset S and false to those in subset T.
Therefore, we have successfully reduced 3SAT to MAX-CUT, showing that MAX-CUT is NP-complete. This conclusion is based on the assumption that 3SAT is already a known NP-complete problem, as stated in Problem 7.26.
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8/7 + 7/7 = ? Help please ?
Answers
Answer:
15/7
Step-by-step explanation:
8/7 + 7/7 = 8+7 = 15
Therefore, the sum of 8/7 + 7/7 is equals to 15/7
Answer:
To add fractions, find the LCD and then combine.
Exact Form:
1 5/7
Decimal Form:
2.142857
Mixed Number Form:
2 1/7
The circumference of the great circle of a hemisphere is 19π inches. Which statements about the hemisphere are true? Check all that apply. (Use 3.14 for π and round answers to the nearest tenth, if necessary. Recall that the formula for the surface area of a hemisphere is S = 3πr2 and the formula for the circumference of the great circle is C = πd.)
Answers
The radius of the hemisphere is 9.5 inches.
The diameter of the hemisphere is 19 inches.
The surface area of the hemisphere is 850.2 inches²
How to find the surface area of an hemisphere?circumference of a circle = 2πr
where
r = radiusTherefore,
19π = 2πr
2r = 19
r = 19 / 2
r = 9.5 inches
diameter = 9.5 × 2 = 19 inches
Therefore,
surface area of an hemisphere = 3πr²
surface area of an hemisphere = 3 × 3.14 × 9.5²
surface area of an hemisphere = 850.155 inches²
surface area of an hemisphere = 850.2 inches²
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inagameofpoker,fiveplayersareeachdealt5cardsfroma52-carddeck.how many ways are there to deal the cards?
Answers
There are a total of 2,598,960 ways to deal 5 cards to each of the five players in a game of poker.
To calculate the number of ways to deal the cards, we can use the concept of combinations. In this case, we need to determine the number of combinations of 5 cards from a deck of 52 cards.
The number of combinations can be calculated using the formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen.
In this scenario, there are 52 cards in the deck, and each player is dealt 5 cards. So, we need to calculate C(52, 5) for each player. Since there are five players, we multiply the result by 5.
Therefore, the total number of ways to deal 5 cards to each of the five players is C(52, 5) = (52! / (5! * (52 - 5)!)) = 2,598,960.Hence, there are 2,598,960 ways to deal the cards in a game of poker when each of the five players is dealt 5 cards from a 52-card deck.
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What is the name for the marked angel ?
Answers
Answer:
A
Step-by-step explanation:
Answer:
The answer is <ead
please mark me brainliest
Find the value of g(25) for the function below.
g(x) = 24(x − 39)
Answers
Answer:
-336
Step-by-step explanation:
g(x) = 24(x − 39)
Let x = 25
g(x) = 24(25 − 39)
= 24 (-14)
= -336
Use the distributive property to rewrite the expression -3 + 9(-4x + 4)
Answers
Answer:
-3(-11+12x)
Step-by-step explanation:
that should be the answer
What is the Coefficient in the following expression:
10+4a−3
Answers
Answer:
4
Step-by-step explanation:
Coefficient is the number next to the variable, making it 4.
A fast food restaurant was selling 7 boxes of chicken nuggets for $25.90 ANd a competing restaurant was selling 3 boxes of chicken fingers for $11.07. Which food has a higher unit price?
Answers
Answer:
The fats food restraunt that was selling 7 boxes of chicken nuggets for $25.90 is the one with the highest price.
Step-by-step explanation:
You can find the unit rate of Both restaurants
25.9/7= $3.70
11.07/3= $3.69
Theres a 1 cent difference
So the reastraunt witht he greater cost woul be the one seeking 7 boxes for 25.90
Slope of line that passes through the points (19,-16) (-7,-15)
Answers
Answer:
m= -1/26
Step-by-step explanation:
plug into the formula and solve
normal approximation for binomial distribution
when n is large we can use this to determine probabilities for binomial settings
Answers
In mathematical terms, if X is the sum of successes in n different Bernoulli trials, and p is the likelihood of success in each trial, then X may be represented as a normal distribution with mean increasing as n rises.
μ = np
variance σ^2 = np(1-p)
What is binomial distribution?The binomial distribution is a discrete probability distribution that produces just two outcomes in an experiment: success or failure. In a binomial distribution, the chance of success must remain constant during the trials under consideration. For example, because there are only two possible outcomes when tossing a coin, the chance of flipping a coin is 1/2 or 0.5 for each experiment we do.
Here,
When the sample size (n) is high, the distribution of the total of successes (k) in n separate Bernoulli trials approaches a normal distribution, according to the normal approximation for the binomial distribution.
In mathematical terms, if X is the total of successes in n separate Bernoulli trials, with p being the chance of success in each trial, then X may be represented by a normal distribution with mean as n increases.
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how are binary categorical variables included in multiple linear regression?
Answers
Binary categorical variables are typically included in multiple linear regression models using a technique called "dummy coding" or "indicator coding".
These dummy variables are then included in the multiple linear regression model as additional predictor variables, along with the continuous predictor variables. The coefficient estimates for the dummy variables represent the differences in the intercept or slope between the two categories of the binary categorical variable.
It is important to note that when using dummy coding, one of the categories of the binary categorical variable must be chosen as the reference category, and the coefficient estimates for the other categories are interpreted relative to the reference category. The choice of reference category can affect the interpretation of the coefficient estimates and should be chosen based on the research question and the goals of the analysis.
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WILL GIVE 30 POINTS
It costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expression 100 + 4n. The cost for 15 people equals $ ___.
Answers
Answer:
Step-by-step explanation:
Cost of renting bowling alley = $ 100
Additional cost of renting bowling alley per person = $ 4
⇒ Total Cost for n no. of people = 100 + 4 × n
So, Cost for 15 people = Fix $100 for bowling alley
+ $4 for each 15 people
= 100 + 4 × 15
= 100 + 60
= 160
Therefore, The cost for 15 people equals to $ 160.
I’m confused on what number 4 means. Can someone please help?
Answers
Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on
Step-by-step explanation:
i’m so confused lol need help
Answers
-10 and -1
Step-by-step explanation:
Answer:
-10, and -1
Step-by-step explanation:
9(x+2) - 4x+2)
Solve equation
Answers
Answer:
Step-by-step explanation:
Ok:I'm preassuming that the second equation is 4(x+2)
1.So first multiply within the parentheses.
9x+18-4x-8
2. Then add the x's and numbers
9x-4x+18-8
3. Add and Subtract
5x+10 as answer
Answer:
x=-2
Step-by-step explanation:
a parabola had a vertex of (-5,0) and passes through the point (-3,1)
Answers
Answer:
Step-by-step explanation:
let the parabola be y=a(x+5)²+0
or y=a(x+5)²
∵ it passes through (-3,1)
1=a(-3+5)²
4a=1
a=1/4
so parabola is y=1/4(x+5)²