At a movie theater, one group of people spent $54 on 3 large popcorns and 6 sodas.
Another group spent on $77 on 4 large popcorns and 9 sodas. Determine the cost of a
large popcorn and the cost of a soda

Answer:

3 =x

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x*x

Divide each side by x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x from each side

3x-3x +3 = 4x-3x

3 =x

Answer:

First answer is infinitely many.  It doesn't matter what x is.

Second answer is x = -5.

Step-by-step explanation:

8 + x = 3

x = - 5

Answer:

\(6,10\)

Step-by-step explanation:

Method 1:

\(\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 1:

\(\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 2:

\(\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Answer:

\({ \tt{ = \frac{(x + y)}{ {x}^{2}y } - \frac{(x - 2y)}{ {xy}^{2} } }} \)

Find the LCM of denominators: x²y²

\({ \tt{ = \frac{y(x + y) - x(x - 2y)}{ {x}^{2} {y}^{2} } }} \\ \\ = { \tt{ \frac{xy + {y}^{2} - {x}^{2} +2xy }{ {x}^{2} {y}^{2} } }}\)

Simplify further:

\( = { \tt{ \frac{(y - x)(y + x) +3xy}{ {(xy)}^{2} } }} \\ \\ = { \tt{ \frac{(y - x)(y + x)}{ {(xy)}^{2} } - \frac{3}{xy} }}\)

Answer:

3/2

Step-by-step explanation:

make into a improper fraction

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

Learn more about perpendicular lines at

https://brainly.com/question/1202004

#SPJ1

Complete Question

A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26

Answer:

The mean of sampling distribution of the sample mean ( \(\= x\)) is \(\mu_{\= x } = 77\)

The standard deviation of sampling distribution of the sample mean ( \(\= x\)) is  

    \(\sigma _{\= x} = 2.746\)

Step-by-step explanation:

From the question we are told that

    The population mean is  \(\mu = 77\)

     The  standard deviation is  \(\sigma = 14\)

     The sample size is  \(n = 26\)

Generally the standard deviation of sampling distribution of the sample mean ( \(\= x\)) is  mathematically represented as

           \(\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }\)

substituting values  

          \(\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }\)

          \(\sigma _{\= x} = 2.746\)

Generally the mean of sampling distribution of the sample mean ( \(\= x\)) is  equivalent to the population mean i.e  

      \(\mu_{\= x } = \mu\)

      \(\mu_{\= x } = 77\)

The standard form of the equation of the parabola is  \(y=-(\frac{x^2-12x+36}{24})\)

The general form of a parabola is  (x-h)=4p(y-k)

Where, (h,k) is vertex, (h,k+p) is the focus, and y=k-p is directrix.

The focus of the parabola is (6,6).

comparing the values with (h,k+p)=(6,6)

h=6

k+p=-6.... (1)

Directrix of the parabola is

k-p=-6.... (2)

On adding (1) and (2) we get

2k=0

k=0

Put this value in equation (1).

0+p=-6

The value of p= -6.

Substituent h=6,k=0, and p=-6 in the general form of a parabola, we get

(x-h)^2=4p(y-k)

(x-6)^2=4(-6)(y-0)

x^2-12x+36=-24y

Divide both sides by 24.

y=(x^2-12x+36/24)

Therefore the standard form of the equation of the parabola is

y=-(x^2-12x+36/24)

To know more about the standard form of a parabola:

https://brainly.com/question/12522945

#SPJ4

sum of observations

no. of observations

50+55+58+90+58+92+99 502

7 7

awnser is 71.7

The correct option is (b) i.e. The cosecant of an angle is defined as the length of the hypotenuse over the length of the side opposite.

What is Trigonometric ratio?

Trigonometric ratios are mathematical functions used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles. The three main trigonometric ratios are sine, cosine, and tangent

All statements contain some sort of mistake except the statement (b).

The statements should be corrected as given below:

A). The cosine of an angle is defined as the length of the side adjacent over the length of the hypotenuse.

C). The cotangent function is defined as the length of the side adjacent over the length of the side opposite.

D). The sine function is defined as the length of the side opposite over the length of the hypotenuse.

To learn more about Trigonometric ratio, visit the link:

https://brainly.com/question/25618616

#SPJ1

Answer:

the number will get 1000 times larger than its original number or 3 zeroes will be added in the last place of the number

Step-by-step explanation:

let's say x=5,

if we multiply 5 by 1000 it becomes 5000 (it is 1000 times more or larger than its orignal number and 3 zeroes are added in 5000).

The error that Martell made in determining the scale factor was using point K and point A when they weren't similar points.

The process that Martell used to find the scale factor was correct, however, he should not have used points A and K because they are not similar sides in the triangles.

Point A is similar to point H while point D is similar to point K.

Using the similar points of A (4, 2 ) and H ( 6, 3 ), we find the scale factor to be:

= 6 / 4

= 1. 5

Find out more on scale factor at https://brainly.com/question/29013176

#SPJ1

Answer:

Step-by-step explanation:

15

5x0.6 is 3 and 2.4 times 5 is 12. 12 +3 is 15

Answer:

The answer is 18tt

Step-by-step explanation:

I took the exam and I got the question right for FLVS

A graph of all points with integer x- and y-values that are exactly 5 units away from point P is shown in the image attached below.

In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

By translating the coordinates of point P five units to the right and vertically upward by 5 units, the coordinates of the image of point P' include the following:

(x, y)                               →                          (x + 5, y + 5)

Coordinate of point P = (-1, 3)   →    Coordinate of point P'= (4, 8)

Read more on translation here: brainly.com/question/16486008

#SPJ1

Answer:

180 degrees

Step-by-step explanation:

Supplementary means the 2 angles sum equals 180 degrees.

Answer:

B. 40°

Step-by-step explanation:

I calculated it logically

Answer:

the answer is 2

Step-by-step explanation:

52÷2=26

26÷2=13

Answer: 0.6

Step-by-step explanation:

Answer: I believe its 6%

Step-by-step explanation:

so sorry if i'm wrong

The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

For more questions on Probability .

https://brainly.com/question/24756209

#SPJ8

The percent of the bags of chips weigh less than 176 grams is b 16%

From the question, we have the following parameters that can be used in our computation:

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

Read mroe about z-scores at

brainly.com/question/25638875

#SPJ1

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

Step-by-step explanation:

take 71.28-21.39

Answer:

If the drum set is 30% off, this means that Susan only needs to pay 70% of the original price. We can calculate this using the following formula:

Total price = Original price x (1 - Discount rate)

where the discount rate is the percentage discount expressed as a decimal. In this case, the discount rate is 30% or 0.3. Substituting in the given values, we get:

Total price = $71.28 x (1 - 0.3)

Total price = $71.28 x 0.7

Simplifying, we get:

Total price = $49.896

However, we also know that Susan got a discount of $21.39. This means that she only needs to pay:

Total price - Discount = $49.896 - $21.39

Total price - Discount = $28.506

Therefore, Susan has to pay $28.506 in total.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer:

1 C

2 D

3 C

4 B

5 A

6 C

Step-by-step explanation:

Answer: 1 C

2 D

3 C

4 B

5 A

6 C

Step-by-step explanation:

Molina jumped the greatest distance at a long jump competition which is 9.601 feet

Decimal: A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Given in the question that, the distance each of four students jumped a long jump competition

Student Distance

Aleena  9.46 feet

Susan    9.068 feet

Molina   9.601 feet

Anna      9.04 feet

let us compare the feet jumped by the  students

write them in ascending order to get the highest feet based on decimal values

9.04, 9.068, 9.46, 9.601

by checking the order we can confirm that 9.601 feet is the highest

9.601 feet long jump was done by Molina

so we can conclude that Molina jumped the greatest distance

To learn more about Decimal visit:

brainly.com/question/548650

#SPJ1

Possible Answer 1:

Positive values represent elevations above sea level, while negative values are elevations below sea level. For example, a building may be +100 or simply 100 feet high. Another example: going scuba diving could lead the diver to reach a elevation of -10 meters. The value 0 is the exact location of sea level itself. In other words, if your elevation is 0, then you are at the surface of the water.

==========================================================

Possible Answer 2:

Often in money, loans and borrowing happens. If so, then we use negative numbers to indicate debt. If someone has a bank balance of say -10 dollars, then they owe the bank $10. Positive values mean that they don't owe the money and it's entirely theirs to spend however they want. A balance of 0 means they neither have money, nor do they owe anyone.

==========================================================

Possible Answer 3:

Let's say we define negative distance to mean that you walk some amount to the left (to match up with the fact the negative x values point left). So for instance, we could say the number -14 indicates you walked 14 feet to the left. Positive values on the other hand will mean you walk some amount to the right. Drawing an x axis number line is very recommended. The value 0 indicates that no walking has occurred at all.

==========================================================

Of course, when you write your answer, it should be in your words only. Those answers posted above are just a springboard to get you started.

Answer: C

Step-by-step explanation: