Two groups of friends went to the local movie theater. The first group bought four large buckets of
popcorn and five boxes of candy and spent $42.75. The second group spent $25.50 on two boxes of
candy and three large buckets of popcorn.
How much would one large popcorn and one box of candy cost?
Answers
One large bucket of popcorn costs $6 and one box of candy costs $3.75.
To solve this problemLet's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :
Equation 1: 4p + 5c = 42.75 (first group's purchase)
Equation 2: 3p + 2c = 25.50 (second group's purchase)
We can use any method to solve these equations, such as substitution or elimination.
Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":
8p + 10c = 85.50 (multiplying Equation 1 by 2)
-15p - 10c = -127.50 (multiplying Equation 2 by -5)
Adding the two equations, we get :
-7p = -42
p = 6
Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:
4(6) + 5c = 42.75
24 + 5c = 42.75
5c = 18.75
c = 3.75
Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.
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Related Questions
This triangle has one side that lies on an extended line segment.
Based on this triangle, what statement about x is true?
Responses
x = 33 because 180−147=33
x, = 33 because , 180 minus 147 equals 33
x = 62 because 147−85=62 and 85 + 62 = 147
x, = 62 because , 147 minus 85 equals 62, and 85 + 62 = 147
x = 95 because 180−85=95 and 85 + 95 = 180
x, = 95 because , 180 minus 85 equals 95, and 85 + 95 = 180
x = 118 because 180 − 147 + 85 = 33 + 85 = 118
Answers
In a triangle one side that lies on an extended line segment, statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct
What is a triangle?In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°
Given that,
A triangle, which has one interior angle 85° and one exterior angle 147°
Another exterior angle x = ?
It is already known that,
Sum of complementary angles are 180
So,
⇒ Y + 147 = 180
⇒ Y = 180 - 147
⇒ Y = 33
sum of all the interior angles of the triangle is 180°
X + Y + 85 = 180
X = 180 - 85 - 33
X = 62
Hence, the value of x is 62
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suppose that c→=a→−b→. under what circumstances is the length of c→ equal to the sum of the lengths a→ and b→ ?
Answers
The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.
This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.
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Sample Response/Explanation: No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.
Which of the following did you include in your response? Check all of the boxes that apply.
The formula was not simplified correctly.
The 64 should have been added.
The radicand should be 73.
There should be 2 real roots.
Answers
Answer:
answer a,b,c
Step-by-step explanation:
A bus drives for 3½ hours at an average speed of 56 mph. How far does the bus drive?
Answers
distance = speed x time
where speed is given in miles per hour (mph) and time is given in hours.
In this case, the speed of the bus is 56 mph and the time it travels is 3.5 hours. So we can calculate the distance it travels as:
distance = speed x time
distance = 56 mph x 3.5 hours
distance = 196 miles
Therefore, the bus drives a distance of 196 miles.
Answer:
196 miles
Step-by-step explanation:
To find the distance that the bus drives, we can use the formula:
distance = rate x time
where rate is the average speed and time is the duration of the trip.
In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:
3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours
Now we can plug in the values into the formula:
distance = rate x time
distance = 56 mph x 7/2 hours
We can simplify by multiplying 56 by 7 and then dividing by 2:
distance = (56 x 7) / 2 = 196 miles
(-2,-4)
(-2,4)
(2,4)
(2, 4)
Answers
Answer:
(-2,-4) is in quadrant 3
(-2,4) is in quadrant 2
(2,4) is in quadrant 1
(2,-4) is in quadrant 4
Step-by-step explanation:
Quadrant 1 is Positive, Positive
Quadrant 2 is Negative, Positive
Quadrant 3 is Negative, Negative
Quadrant 4 is Positive, Negative
Feel free to ask if you have anymore questionsHope this helped :)Step-by-step explanation:
(-2,-4) in 3rd Quadrant
(-2,4) in 2nd Quadrant
(2,4) in 1st Quadrant
(2, -4) in 4th Quadrant
-TheUnknownScientist
5(x – 2) – X – 5 = -3
Answers
Answer:
5(x-2) - x - 5 = - 3
5x - 10 - x - 5 = -3
4x - 15 = -3
4x = -3 + 15
4x = 12
x = 12/ 4
Therefore x = 3.
use absolute value notation to define the interval (or pair of intervals) on the real number line. (use the variable x.) all real numbers at least two units from 4
Answers
The point is [-13,-7] when the actual numbers are all at least two units away from 4.
Given that,
To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.
We know that,
We get,
|-4-x| = 3
-3 = -4-x = 3
7 = -x = 13
-13 = x = -7
Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.
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Which is the graph of f(x) = (x – 1)(x + 4)?
On a coordinate plane, a parabola opens down. It goes through (negative 1, 0), has a vertex at (1. 75, 6.2), and goes through (4, 0).
On a coordinate plane, a parabola opens down. It goes through (negative 4, 0), has a vertex at (negative 1. 75, 6.2), and goes through (1, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1. 75, negative 6.2), and goes through (4, 0).
Answers
Below is the graph. In other words, the last one is correct.
Answer:
D on edge
Step-by-step explanation:
put the function into desmos
What are the interest cost and the total amount due on a six-month loan of $1,500 at 13. 2 percent simple annual interest?.
Answers
The interest cost and the total amount due on a six month loan is $1500 and total amount due is $1599
SI is equal to 100. r = 10% T=6 months, or 6/12 years.
Idea employed: SI = Prt/100. Interest rate in principle.
Calculation: P = (100 100 12)/(10 6) 100
= (P 10 6)/(12 100)
P = 2000.
For instance, if your current APR is 17.99% and you currently owe $500 on your credit card over the course of the month, you can get your monthly interest rate by dividing 17.99% by 12, which is roughly 1.49%. Then multiply $500 by 0.0149 to get a monthly payment of $7.45.
annual interest = $1,599
full amount due = ($1,500 + $99).
= $1599
Hence we get the required answers.
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Which graph best represents y=-x2 + 6 x - 1?
Answers
Answer:
Assuming
\(y = -2x + 6x - 1\\y = 4x - 1\)
Step-by-step explanation:
See Graph
The marked price on a Bridget slippers is $2500. Sales tax of 8% is added. What is the cost of the item?
Answers
Answer:
Cost of item = $2500 + $200
Cost of item = $2700
Step-by-step explanation:
0_0
When twice a number is added to 5 the result is 27 + Brain
Answers
Answer:
11
Step-by-step explanation:
Let x be the unknown number
2x+5 = 27
Subtract 5 from each side
2x+5-5 = 27-5
2x = 22
Divide each side by 2
2x/2 = 22/2
x = 11
The number is 11
Answer:
11
Step-by-step explanation:
Given h(x) = 4x - 5, solve for a when h(x) = 7.
Answers
Answer: h(x) = 23
Step-by-step explanation:
Plug x in the equation
h(x) = 4(7) - 5
h(x) = 28 - 5
h(x) = 23
what is the domain of this relation (1,3) (2,5) (0,1) (-1,-1 )
Answers
Here u go
Answer:
Domain=(1,2,0,-1)
Range=(3,5,1,-1)
5 MINS LEFT! A group of students decides to sell pizzas to help raise money for their senior class trip. They sold a pepperoni pizza for $14, a sausage pizza for $11, and a cheese pizza for $10. At the end of their sales, the class sold a total of 400 pizzas and made $4560. The students sold 80 more cheese pizzas than pepperoni pizzas. How many of each type of pizza were sold?
Answers
Answer:
The number of cheese pizza sold is 200 cheese pizzas
The number of sausage pizza sold is 80 sausage pizzas
The number of pepperoni pizza sold is 120 pepperoni pizzas
Step-by-step explanation:
The price at which the pepperoni pizza was sold is $14
The price at which the sausage pizza was sold is $11
price at which the cheese pizza was sold is $10
The total number of pizzas sold = 400
The total amount made = $4560
The number of cheese pizza sold = 80 + the number of pepperoni pizzas
Let the number of cheese pizza sold = C
The number of sausage pizza sold = S
The number of pepperoni pizza sold = P
We have;
C + S + P = 400..........................(1)
C = 80 + P...................................(2)
10·C + 11·S + 14·P = $4560.......(3)
Substituting the value for C from equation (2) in equation (1), we get;
C + S + P = 400 = 80 + P + S + P = 400
2·P + S = 400 - 80 = 320
∴ S = 320 - 2·P..........................(4)
Substituting the value for C from equation (2) and the value for S from equation (4) into equation (3), we get;
10·C + 11·S + 14·P = $4560
10·(80 + P) + 11·(320 - 2·P) + 14·P = 4560
800 + 10·P + 3,520 - 22·P + 14·P = 4560
4,320 + 2·P = 4560
2·P = 4560 - 4,320 = 240
P = 240/2 = 120
P = 120
C = 80 + P = 80 + 120 = 200
C = 200
S = 320 - 2·P = 320 - 2×120 = 320 - 240 = 80
S = 80
Therefore;
The number of cheese pizza sold = C = 200
The number of sausage pizza sold = S = 80
The number of pepperoni pizza sold = P = 120.
question some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. to estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a random sample of patients who have the blood disorder. what sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3%?
Answers
The sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3% is 1067.11
In medical research, it is essential to determine the effectiveness of a drug on a certain disease or disorder. Scientists often use statistical methods to estimate the proportion of patients who would benefit from taking the drug. In this case, the scientists want to estimate the proportion of patients who would benefit from a new drug for a certain blood disorder.
To estimate the proportion of patients who would benefit from the drug, the scientists need to create a confidence interval. A confidence interval is a range of values that is likely to contain the true value of the proportion of patients who would benefit from the drug. The margin of error is the maximum amount by which the confidence interval is expected to differ from the true value of the proportion.
To determine the sample size needed to create a confidence interval with a margin of error of no more than 3%, the scientists need to use a formula. The formula is:
n = (Z² * p * q) / E²
Where:
n = sample size
Z = the Z-score for the desired confidence level (in this case, a 95% confidence interval corresponds to a Z-score of 1.96)
p = the proportion of patients who would benefit from the drug (unknown)
q = 1 - p
E = the desired margin of error (in this case, 0.03 or 3%)
The scientists know that they want a margin of error of no more than 3%, which means that E = 0.03. They also know that they want a 95% confidence interval, which corresponds to a Z-score of 1.96. The only unknown in the formula is the proportion of patients who would benefit from the drug (p).
The scientists estimate that about half of all people with the blood disorder would benefit from the drug. Therefore, they assume that p = 0.5. They plug in the values into the formula:
n = (1.96² x 0.5 x 0.5) / 0.03²
n = 1067.11
They round up to the nearest whole number and determine that they need a sample size of at least 1068 patients to create a 95% confidence interval with a margin of error of no more than 3%.
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Prior to going, Ben read that the lobster population in the area labeled NBHK is estimated to be 6, 817. What is the density of the lobster population in the area labeled NBHK?
A) 84 lobsters/mi^2
B) 756 lobsters/mi^2
C) 9.02 lobsters/mi^2
D) 81.15 lobsters/mi^2
Answers
The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.
How to calculate the densityPopulation density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.
To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.
The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².
Lobster population will be:
= 6817 / 756
= 9
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find the first four terms of the taylor series for the function 2x about the point a=1. (your answers should include the variable x when appropriate.)
Answers
The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).
What are the initial terms of the Taylor series expansion for (2x) centered at (a=1)?To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:
\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)
Let's calculate the first four terms:
Starting with the first term, we substitute
\(\(f(a) = f(1) = 2(1) = 2x\)\)
For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).
\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)
\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)
Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)
Since the second derivative is zero, the third term is zero.
Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)
Similarly, the fourth term is also zero.
Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:
(2x + 2x - 2)
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ANSWER PLEASE!!!!!!!!!!
if 5 hamburgers cost $12.50 how much would 12 hamburgers costs?
Answers
Answer:
$30
Step-by-step explanation:
12.50/5=2.50
2.50*12=30
In how many ways can one select two professors among 12 CS professors, 6 Math professors and 5 Statistics professors, so that each professor is from a different field
Answers
The number of ways to select two professors from different fields is 360.
We have,
To select two professors, one from each field (CS, Math, and Statistics), we need to multiply the number of choices in each field.
Number of ways to select one CS professor from 12: 12
Number of ways to select one Math professor from 6: 6
Number of ways to select one Statistics professor from 5: 5
By the multiplication principle, the total number of ways to select two professors, one from each field, is:
12 x 6 x 5 = 360 ways
Thus,
The number of ways to select two professors from different fields is 360.
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Indicate whether (1, 5) is a solution of the given system.
Answers
Answer:
To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.
For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.
Substituting these values into the first equation, we get:
5 = 2(1) + 1
5 = 2 + 1
5 = 3
This statement is not true, so (1, 5) is not a solution of this system.
On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.
I hope this helps! Let me know if you have any more questions.
Step-by-step explanation:
Please help 20 points question
Answers
Answer:
y>-2x-1 answer is b
-4x+y> 1 is c I believe
Step-by-step explanation:
Solve for v.-3v + 16 > -7V - 8Write your answer with v first, followed by an inequality symbol.>
Answers
Simplify the inequality for v.
\(\begin{gathered} -3v+16>-7v-8 \\ -3v+7v+16>-7v-8+7v \\ 4v+16-16>-8-16 \\ 4v>-24 \\ \frac{4v}{4}>-\frac{24}{4} \\ v>-6 \end{gathered}\)So answer is,
\(v>-6\)1. Ralin and Michael each opened a savings account with a deposit of $15,950.
· Ralin earn 5.5% simple interest per year.
· Michael earned 3% simple interest per year.
· Neither of them made additional deposits or withdrawals.
How much more did Ralin receive in interest than Michael after 18 months?
2. Mr. Smith borrowed $3000 to buy a used car. The simple interest rate is 12% per year. Mr. Smith paid off the loan in 48 months. How much did he pay for his car?
3. Athena and Jeremiah each opened a savings account with a deposit of $7,050.
· Athena earn 5.5% simple interest per year.
· Jeremiah earned 6% simple interest per year.
· Neither of them made additional deposits or withdrawals.
How much more did Jeremiah receive in interest than Athena after 8 years?
4.Ms. Brennan opened a savings account with a deposit of $950.
· She earned 3.65% simple interest per year.
· There was no additional deposits or withdrawals.
How much money does she have after 12 years?
Answers
Answer:
Simple interest formula
I = Prt, I- amount of interest, P- principal, r- interest rate, t - timeA = P(1 + rt), A - final amount, the rest as above#1
18 months = 1.5 years
The difference in the amount of interest:
$15950*1.5*(5.5-3)/100 = $598.13#2
$3000*(1 + 4*12/100) = $4440#3
$7050*8*(6 - 5.5)/100 = $282#4
$950*(1 + 12*3.65/100) = $1366.109.2 HW Central Angles, Arc Measures, & Arc Length
Answers
Answer:
I can help you with this, i just need the actual questions.
Step-by-step explanation:
Guys, Please Help me Fast
Answers
I will help u so fast, first
you help me
can u answer this
some fanicial and environmental damages that have been made by cars.
please help me
this is exam
teacher giving us 10 minutes to discuss about and I am in washroom of school writing this
Step-by-Step Explanation:
1/7 = 1 x 2/7 x 2 = 2/14
3/14 = 3/14
Therefore,
1/7 + 3/14
= 2/14 + 3/14
= 5/14
Select the correct answer from each drop-down menu. the four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4. the four angles of the quadrilateral are °, °, °, and °.
Answers
The four angles of a quadrilateral are 30°, 60°, 150°, and 120° if the four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We have the four vertices of an inscribed quadrilateral divide a circle in the ratio:
1:2:5:4
Let the sides of the quadrilateral be x, 2x, 5x, 4x.
We know the sum of all angles of quadrilateral = 360°
x+2x+5x+4x=360
12x = 360
First angle, x = 30°
Seconds angle, 2x = 2×30 ⇒ 60°
Third angle, 5x = 5×30 ⇒ 150°
Fourth angle, 4x = 4×30 ⇒ 120°
Thus, the four angles of a quadrilateral are 30°, 60°, 150°, and 120°
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The four angles of a quadrilateral are 30°, 60°, 150°, and 120°
Step-by-step explanation:
A scatterplot shows a set of data points that fit very loosely around a line that slopes down to the right. Which of the following values would be closet to the correlation for these data?
A.) 0.75
B.) 0.35
C.) -0.75
D.) -0.35
Answers
The value closest to the correlation for the given scatterplot would be C.) -0.75.
Which option is the closest value to the correlation for the loosely scattered data points with a downward sloping line?In a scatterplot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. A value of -0.75 indicates a strong negative correlation. Since the data points fit loosely around a line that slopes down to the right, it suggests a negative correlation. The closer the correlation coefficient is to -1, the stronger the negative correlation. Option C.) -0.75 is the value closest to -1 and represents a stronger negative correlation compared to the other options.
To determine the precise correlation coefficient, statistical calculations or software can be used. These calculations involve measuring the covariance and standard deviations of the variables. However, based on the given description, it is apparent that the data points exhibit a loose fit around a downward-sloping line, indicating a strong negative correlation.
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Classify the following into odd and even numbers
I) 47. II) 458 II) 15280
Iv)
Answers
47 is an odd number and 458, 15280, 1600 are even numbers.
We know,
An even number is a number that can be divided by 2 without a remainder, while an odd number cannot be divided evenly by 2.
I) 47 is an odd number because it can't be divisible evenly by 2. 47 is only divisible by 1 and itself, and when divided by 2, the quotient is not a whole number.
So, 47 is an odd number.
II) 458 is an even number because it can be divided evenly by 2. When divided by 2, the quotient is a whole number which means it is an even number.
III) 15280 is an even number because it can be divided evenly by 2. When divided by 2, the quotient is a whole number, which means it is an even number.
IV) 1600 is an even number because it can be divided evenly by 2. When divided by 2, the quotient is a whole number, which means it is an even number.
So, 47 is an odd number and 458, 15280, 1600 are even numbers.
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Correct question is "Classify the following into odd and even numbers
I) 47. II) 458 II) 15280 Iv) 100"
helppp plsssssssssssss
Answers
Answer:
C. 40%
Step-by-step explanation:
8 - black
12 - red
total: 20
8/20 = 40%