Samuel and Christopher go to the movie theater and purchase refreshments for their friends.

Samuel spends a total of $34.00 on 6 bags of popcorn and 4 drinks.

Christopher spends a total of $66.25 on 12 bags of popcorn and 7 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.

Answers

Answer 1

Answer:

Drink=5.75

Popcorn=1.83

Percentage for drink=75.9%

Step-by-step explanation

Let the popcorn be p

the drinks be d

6p+4d=34....(1)

12p+7d=66.25...(2)

Multiply (1) by 2

12p+8d=72....(3)

Substrate (2) from (3)

d=5.75

Substitute the value for d into (1)

6p+4(5.75)=34

6p+23=34

Substrate 23 from both sides

6p=11

Divide both sides by 6

p=1.83

So for one drink=$5.75

For one popcorn=$1.83

To determine the% for drink

5.75+1.83=7.58

5.75/7.58 ×100

575/7.58

75.858~75.9%

The percentage for drink is 75.9%


Related Questions

a coin is flipped and a number cube is rolled what is the sample space for this experiment​

Answers

Answer:

h1,h2,h3,h4,h5,h6,t1,t2,t3,t4,t5,t6

Step-by-step explanation:

h or t is the coin, the number is the die

Final answer:

The sample space for flipping a coin and rolling a number cube consists of 12 possible outcomes. The probability of event A occurring is 1/6. Events A and B are mutually exclusive as they cannot occur at the same time.

Explanation:

A coin is flipped and a number cube is rolled; the sample space for this experiment can be listed by combining each possible outcome of the coin flip with each possible outcome of the number cube roll. The coin can either be heads (H) or tails (T), and the number cube, which is a six-sided die, can land on any number from 1 to 6.

H1

H2

H3

H4

H5

H6

T1

T2

T3

T4

T5

T6

Therefore, the sample space consists of 12 possible outcomes.

For part b, event A is "either a three or a four is rolled first, followed by landing a head on the coin toss." The favorable outcomes for event A are H3 and H4. Since there are 12 possible outcomes, and 2 of them are favorable, the probability P(A) is 2/12, which simplifies to 1/6.

For part c, event B is "the first and second tosses land on heads," which is not possible since the first "toss" is actually a roll of a die. Therefore, events A and B are mutually exclusive, as they cannot occur simultaneously. The occurrence of event A does not involve a second toss of the coin and event B is not possible within the context of this experiment.

The perimeter of a rectangular shop in the mall is 34 m the area is 70 m² what are the dimensions of the shop

Answers

Answer:7 x 10

1) Can be done by trail and error

Or

2) setting and slowing two equations

Step-by-step explanation:

If a and b are sides of rectangle

(1). 2a + 2b = 34

(2). ab = 70

From 1

a= 17-b

Substitute above a to (2)

(17-b)b = 70

17b - b^2 = 70

-b^2 + 17b -70 = 0

Multiple above by -1

b^2 - 17b + 70 = 0

Solving quadratic equation by factorising

(b-7)(b-10)=0

b=7 or b=10

If b= 7. a =10

If b=10. a=7

Final answer:

The dimensions of the rectangular shop that satisfies the given condition of having a perimeter of 34 m and an area of 70 m² are length=20 m and width=7 m.

Explanation:

The question is about finding the dimensions of a rectangular shop, given its perimeter and area. The perimeter and area of a rectangle can be expressed using the formulas Perimeter = 2*(length + width) and Area = length * width. In the problem, we are given that the perimeter is 34 m and the area is 70 m².

Let's denote the length as 'l', and the width as 'w'. To solve this, we can setup and solve a system of equations based on our formulas:

2*(l + w) = 34

l * w = 70

From these equations we can find that the dimensions of the rectangular shop that fit the conditions are length=20 m and width=7 m.

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MATH EASY POINTS: the volume of water y (in cubic meters) that flows over niagara falls during peak daytime tourist hours in x minutes can be approximated by the equation y=168,000x. Approximately how many cubic meters of water flow over the falls in one hour

Answers

Answer:

10,080,000 cubic meters is the answer.

Step-by-step explanation:

For every minute (x), 168,000 cubic meters (y) of water are added. 1 hour has 60 minutes, so 60 x 168,000. That gives 10,080,000.

Please Help me !! Really I don’t know

Answers

Your answer is b) 18.3.

To find the area of the shaded region, we need to find both the area of the isosceles triangle and the area of the whole shape, so we can subtract the triangle from the whole shape.

To find the area of the triangle you can use the equation A = (b × h)/2 which gives you 64/2 = 32 in².

To find the area of the whole shape, you need to find the area of the circle that it would be in, and divide it by 4. This is because the shape is a quarter circle, so by finding the whole circle and dividing by 4 we get just the quarter.
The area of a circle is πr², so:
A = 1/4(64π)
A = 16π
A = 50.3

So now we can do 50.3 - 32 = 18.3

I hope this helps! Let me know if you have any questions :)

Based on your results in Question 1, how is the volume of the cone related to the volume of the cylinder, given that their bases and heights are the same? (Keep in mind that the volumes you recorded were rounded, not exact values.)

Answers

Answer:

in a similar way,the volume of a cone and a cylinder that have identical bases and height  are proportional. if a cone and a cylinder have bases (shown in color) with equal areas and both have identical heights, the the volume of a cone is one-third that volume of a cylinder is V=πr2h

Step-by-step explanation:

Answer:

If the base dimensions and the heights are the same, the volume of the pyramid is approximately 1/3 the volume of the cube.

Step-by-step explanation:

awnser for plato math

Amanda surveyed 13 students in her class about their heights in inches. Her data are listed below.
52, 53, 55, 55, 56, 57, 58, 58, 59, 59, 59, 62, 65 Which box plot correctly displays her data?

Answers

Answer: The answer is A

Step-by-step explanation:

because you have to take your lowest number 52 and put a line the your highest number 65 and put a line then 55, 58 and 59 are being repeated so therefor you do a like box thing to get your answer dont really know how to explain hope this helps

Express this equation in logarithmic form.
4^0.5=2

Answers

Answer:

Log₄2=0.5

Step-by-step explanation:

Answer:

[tex]log_{4}[/tex] 2 = 0.5

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]4^{0.5}[/tex] = 2 ← with x = 2, b= 4 and n = 0.5, then

[tex]log_{4}[/tex] 2 = 0.5

If x varies directly as y and x= 18 when y =3 find x when y=7

Answers

Answer:

42

Step-by-step explanation:

x = Ky

18 = K(3)

K = 18/3 = 6

x = 6y

x = 6(7) = 42

What is
The lines graphed below are parallel. The slope of the red line is
the slope of the green line?

Answers

Answer:

2/5

Step-by-step explanation:

The lines are parallel, so they have the same slope.

The red lines has a slope of 2/5

The green line has a slope of 2/5

Answer: 2/5

Step-by-step explanation:

if they did not have the same slope, they would not be parallel

3 children share 6 crayons equally
How many pencils will each child get?

Answers

Answer:

2

Step-by-step explanation:

=6/3

=2

Answer: 2crayons

Step-by-step explanation:

3 children share 6crayons equally

Looking at this

We have 3 children

We have 6crayons

How many does each one of them get

Let the each child's crayon represent p

I child to p crayon

3children to 6crayon

Cross multiply

1 ----- p

3 -----6

So we have

6×1=3×p

6=3p

P=6/3

P=2

So 1 child is entitle to 2crayons

Therefore, each child has 2crayons to themselves.

Part A picture above
Part B. What are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin?
A. D’(0,2)
B. D’(0,5)
C. D’(0,10)
D. D’(10,0)

Answers

Answer:

Part A C = (10,5)  Part B C. D'(0,10)

Step-by-step explanation:

Part A

Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5

(2,1) * 5 = (10,5)

The new point C is going to be (10,5)

Part B

If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from the origin by 5.

In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)

Pumpkins are being sold for $1.30 at the local farmers market. How much would a pumpkin be weighing 6lb 9oz

Answers

Answer:

$8.53

Step-by-step explanation:

The first thing you do is convert the oz into pounds. There is 16 oz in a pound so our fraction is 9/16 which is 0.5625 . Then adding to the pounds it becomes 6.5625 pounds. Then multiply by 1.3.

Which graph represents the function given by the table of values? A) A B) B C) C D) D

Answers

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You are measuring the height of a lamppost. You stand 40 inches from the base
of the lamppost. You measure the angle of elevation from the ground to the top!
of the lamppost to be 70°. Find the height h of the lamppost to the nearest inch.

Answers

Answer:

110in

Step-by-step explanation:

The horizontal distance from where you stand to the lamp post is 40 inches.

Let the height of the lamp post be y inches.

The angle of elevation from the ground to the top!

of the lamppost to be 70°.

The height , y and the horizontal distance, form the legs of a right triangle .

We can use the tangent ratio, to calculate the height of the lamp post .

[tex] \tan(70 \degree) = \frac{y}{40} [/tex]

[tex]y = 40 \tan(70) [/tex]

[tex]y = 109.9[/tex]

To the nearest inch, the height is 110 inches

The height of the lamppost is approximately 110 inches, calculated using the tangent of a 70° angle with a base distance of 40 inches.

To find the height ( h ) of the lamppost, we can use trigonometric relationships. Given that we stand 40 inches from the base of the lamppost and measure the angle of elevation to be 70°, we can use the tangent function:

[tex]\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\][/tex]

In this scenario:

- The angle [tex]\(\theta = 70^\circ\)[/tex]

- The adjacent side (distance from the base) is 40 inches

- The opposite side is the height \( h \) of the lamppost

Using the tangent function, we have:

[tex]\[\tan(70^\circ) = \frac{h}{40}\][/tex]

To solve for ( h ), we rearrange the equation:

[tex]\[h = 40 \cdot \tan(70^\circ)\][/tex]

Now we need to calculate [tex]\( \tan(70^\circ) \):[/tex]

[tex]\[\tan(70^\circ) \approx 2.747\][/tex]

Multiplying this by 40 inches:

[tex]\[h = 40 \cdot 2.747 \approx 109.88\][/tex]

Rounding to the nearest inch:

[tex]\[h \approx 110 \text{ inches}\][/tex]

Therefore, the height of the lamppost is approximately  110  inches.

Please help asap please i will mark branlist

Answers

Answer:

B. (-3,3)

Step-by-step explanation:

We want to know the solution to the equations, which just means where the two lines intersect.

If we just count the spaces, we can see that they touch at (-3,3). Remember that coordinates are (x,y), so we go left 3 (-3,3) and up 3 (-3,3).

Answer: the answer to this question is B

Step-by-step explanation:

The table represents the function f(x) and g(x).
Which input value produces the same output value for the two functions.
A. x = -3
B.x = -1
C. x = 0
D. x =1

Answers

D. x =1 input value produces the same output value for the two functions.

What is F x and G x?

Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”. The function g (x) is called an inner function and the function f (x) is called an outer function.

What is the sum of G x and f x?

Suppose we have two functions, f(x) and g(x). We can define the sum of these two functions by, (f + g)(x) = f(x) + g(x), where x is in the domain of both f and g.

How do you find the intersection of FX and GX?

When the graphs of y = f(x) and y = g(x) intersect , both graphs have exactly the same x and y values. So we can find the point or points of intersection by solving the equation f(x) = g(x). The solution of this equation will give us the x value(s) of the point(s) of intersection.

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2/5 divided by 4 ..........................................











































Answers

Step-by-step explanation:

When 2/5 is divided by 4 we get or we can do the reciprocal

Here we Get

2/5 * 1/4

= 1 / 10

Answer:

2/20 = 1/10

Step-by-step explanation:

When a number is increased by 48%, the result is 92. What is the original number to the nearest tenth?

Answers

Answer:

So you are trying to find 48% of 92, correct?

Step-by-step explanation:

Answer:

44.2

Step-by-step explanation:

Take 92 and multiply it by .48

Maia mixed a batch of punch for the class party. Her recipe called for 3½ cups of orange juice, 2½ cups lemonade, and 2 quarts of ginger ale. How many 1-cup servings does the recipe make?

Answers

Answer:

10

Step-by-step explanation:

3 1/2 cups of orange juice

2 1/2 cups of lemonade

1 quart = 4 cups

4 cups of ginger ale

add them all together...

so there should be:

10 1-cup servings!

i hope this helped you!!

:)

f(x)=x^2 what is g(x)

Answers

Answer:

Step-by-step explanation:

when x=2,g(x)=1

from B when x=2

g(x)=1/4×2²=1

which is true .

so B

If the center of the circle were moved from the origin to the
point (h, k) and point P at (x, y) remains on the edge of the
circle, which could represent the equation of the new
circle?
O (h + x)2 + (k + y)2 = 22
0 (x – n)2 + (y – k)2 = p2
O (k + x)2 + (h + y)2 = 22
0 (x – k)2 + (y – 5)2 = 12

Answers

Answer:(x-h)^2+(y-k)^2=r^2

Step-by-step explanation:

I just answered it and it’s correct

The equation of the new circle will be,

⇒ (x - h)² + (y - k)² = r².

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle.

Then, Equation of the new circle,

(x - h)² + (y - k)² = r²

Where center = (h, k)

radius = r

Hence, the equation of the new circle will be,

⇒ (x - h)² + (y - k)² = r².

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Select the correct answer.
What is the justification for step 3 in the solution process?

10d − 5 = 4d − 15 − 3d
Step 1: 10d − 5 = d − 15
Step 2: 9d − 5 = -15
Step 3: 9d = -10

Answers

Answer: subtraction property of equality

Step-by-step explanation:

subtracting d from both sides is the subtraction property of equality

Answer:

subtraction property of equality

Step-by-step explanation:

Which table represents a linear function? Explain how you know.

Answers

Answer:

Table A represents a linear function. I know because the rate of change between the x and y values is always 1. If you look at the table diagonally, you can see that you can add one to all of your x values to get your y.

Step-by-step explanation:

100 points!!!!!!!!!!!!!!!!!!!!What should the numerator of the second fraction be so that the fractions are equivalent?

[tex]\frac{2}{3} =\frac{?}{14}[/tex] =

Answers

Answer:

28/3 or 9⅓

Step-by-step explanation:

2/3 = x/14

x = 2×14/3

x = 28/3

Answer:

28/3 =x

Step-by-step explanation:

2/3 = x/14

We can solve using cross products

2*14 = 3x

28 = 3x

Divide each side by 3

28/3 = 3x/3

28/3 =x

A. 18 is 20 percent of what number? B. 15 is 25 percent of what number? C. 12 is 30 percent of what number? D. 24 is 40 percent of what number? E. 39 is 60 percent of what number? F. 78 is 30 percent of what number? Question: Represent each as an equation with x as the unknown number, and solve.

Answers

A. 18 is 20% of 90

B. 15 is 25% of 60

C. 12 is 30% of 40

D.  24 is 40% of 60

E. 39 is 60% of 65

F. 78 is 30% of 234

(Sorry I have to go, but hopefully I helped you)

Angles A and B are two acute angles in a triangle. If sin A equals cosine B, what can you conclude about the triangle?

Answers

Answer:

It's a right angle triangle with 90° at C

Step-by-step explanation:

sin A = cosB when

A + B = 90

Final answer:

The condition that sin A equals cosine B, with A and B being acute angles, indicates that both angles are complementary and add up to 90 degrees, suggesting a right-angled triangle.

Explanation:

When given the condition that sin A equals cosine B in a triangle, and both angles A and B are acute, we can determine that triangle A and B are complementary, which means they add up to 90 degrees.

This is due to the co-function identity, where sin(90° - θ) = cos(θ) and cos(90° - θ) = sin(θ) for acute angles in right-angled triangles.

If A and B are in the same triangle, and given it is a right triangle (since they are acute and the sine of one equals the cosine of the other), we can conclude that A + B = 90°, and thus, the third angle will also be 90 degrees, making the triangle a right-angled one.

Please help me solve this ASAP

Answers

Answer:

x = (164 - y)/5

y = 165 - 5x

Step-by-step explanation:

A whole rotation is 360° (All the angles together = 360°)

148 + 2x + 47 + y + 3x = 360

195 + 5x + y  = 360

165 = 5x + y

y = 165 - 5x

5x = 165 - y

x = (164 - y)/5

Choose all of the problems that result in an answer of 8.5.

A) 0.85 × 101
B) 85 × 101
C) 85 ÷ 101
D) 0.85 ÷ 102
E) 0.085 × 102

Answers

Answer:E

Step-by-step explanation:

Type it all into a calculator

It’s E ur welcome :)

1. - 4 = 7(1-n) =

2. -5x + 3(6 + 7x)

3.- 2b - (9 - 105) =

4. 10+ 5(9x - 9) =

5.-9(6x - 3) + 6(1 +4x) =

6.-10(2 - 9x) + 6(x - 10) =

7. 5(-2n+4) + 2(n + 3) =

8. - 7(n+3) - 8(3 +8n) =

Answers

Hope this will help u...

the discriminant of x2 + 6x + 9 = 0

Answers

Answer:

D = 0

Step-by-step explanation:

D = b^2 - 4ac =

= 6^2 - (4*1*9) =

= 36 - 36 = 0

Final answer:

The discriminant of the quadratic equation x² + 6x + 9 = 0 is 0, which means there is one real root, and the graph of the equation is tangent to the x-axis at one point.

Explanation:

The discriminant of a quadratic equation is the part of the formula b² - 4ac that determines the nature of the roots of the equation. For the quadratic equation x² + 6x + 9 = 0, we can identify a = 1, b = 6, and c = 9. Using the discriminant formula, we get:

• Discriminant, D = b² - 4ac
• D = (6)² - 4(1)(9)
• D = 36 - 36
• D = 0

Since the discriminant is zero, it indicates that the quadratic equation has one real root, and the graph of the equation touches the x-axis at one point (the vertex of the parabola).

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Sunland Company acquires land for $77000 cash. Additional costs are as follows. Removal of shed $500 Filling and grading 1600 Salvage value of lumber of shed 170 Broker commission 1150 Paving of parking lot 11000 Closing costs 500 Sunland Company will record the acquisition cost of the land as: Which sequence represents an arithmetic sequence?A 5, 7, 10, 14, 19, B 1.5, 1.5, 1.5, 1.5, C 4.1, 5.1, 6.2, 7.2, D 1.5, 1, 0.5, 0, Where would you go to mail a letter in spainsh In this assignment you will write a function that will calculate parallel resistance for up to 10 parallel resistors. Call the function by ParallelR(Number), where Number is an integer between 1 and 10 which will be input from a command window prompt. Use a for loop Number times to find the Numerator and Denominator for parallel resistance. After the for loop you should find Solution as Num/Den. the number Solution will be returned by the function. What is the greatest common factor of 72and 18? what is the basic definition of realistic art What did Irene do this morning?Compr fruta.No compr fruta.Desayun.Comi fruta. Fractions is equipment to 3/8 Identify the spectator ions in this reaction:H+ + Br + K+ + OH --> K+ + Br + H2O H+ and K+Br and OHK+ and Br 8. What are the key elements influencing the sound of Whitman's poem? Wayne, a young adolescent male, has a history of sexual abuse from his childhood. How significant could we expect his signs and symptoms of trauma that characterize the majority of individuals with child abuse histories? Hey, I need help! 2+2+=? Residential patterns are interrelated with the authority structure and method of tracing descent in families. __________ residence refers to the custom of a married couple living in the same household (or community) as the husbands family. PL(05.02)Find the measure of angle x in the figure below: (5 points) When a newspaper decides to put a news story about a senatorial race on the front page while putting an article about a local firefighter on page seven of the paper, it is engaging in the ________ function of the news. (answer is not investigating)(A) informing(B) inducting(C) inciting (D) investigating(E) interpreting 3. Find the mean and the median of this data set: 9,6,5, 3, 28, 6, 4, 7. Describe the contributions of Mohandas K. Gandhi and Muhammad Ali Jinnah to the Indian independence movement. Which is the graph of a logarithmic function?On a coordinate plane, a parabola is shown.On a coordinate plane, a function is shown. It approaches the x-axis in quadrant 2 and then increases into quadrant 1. It goes through (0, 1) and (1, 2).On a coordinate plane, a function is shown. It approaches the y-axis in quadrant 4 and approaches y = 2 in quadrant 1. It goes through (1, 0) and (3, 1).On a coordinate plane, a hyperbola is shown. Which of these BEST describes plebeians in the Roman Empire?A)They were people banned from holding office.B)They were powerful, "aristocratic" families.C)They were the "middle class" of society.D)They were the soldiers in the military. A sample of 90 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.284 and the equation of the regression line is ModifyingAbove y with caret equals 18.4 plus 0.930 x, where x represents height. The mean of the 90 heights is 63.4 in and the mean of the 90 pulse rates is 77.9 beats per minute. Find the best predicted pulse rate of a woman who is 66 in tall. Use a significance level of alpha equals 0.01.