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.

Answer:

See attachment

Step-by-step explanation:

Given : Jennifer is on a hiking trip. She begins her hike at an altitude of 4,000 feet, and she is descending with an average speed of 40 feet per minute.

We have to Graph the function that represents the given situation.

Let the y - axis represents the height of Jennifer (in feet) and x axis represents the time (in minutes)

Since initially, Jennifer is at 4000 feet.

and is descending with an average speed of 40 feet per minute.

So when she begins to descend she is at 4000 feet that is y- intercept is 4000.

Then, the equation of graph is given by

y = -40x + 4000

As she is descending at the rate of 40 feet per minute so  -40x

Thus, The graph for the given equation can be drawn as shown below.

also, when x = 100

then y = -40(100) - 4000 = 0

Plot points (0, 4000) , (100,0) to obtain the graph.

Answer:

The value of g(-1) is -2

Step-by-step explanation:

[tex]g(x) = 2x^4 + 3x^3 - x^2[/tex]

Now we find g(-1)

To find g(-1) plug in -1 for x  in the given g(x) equation

Replace all x by -1

[tex]g(x) = 2x^4 + 3x^3 - x^2[/tex]

[tex]g(x) = 2(-1)^4 + 3(-1)^3 - (-1)^2[/tex]

[tex]g(x) = 2-3-1=-2[/tex]

The value of g(-1) is -2

Answer:

-2

Step-by-step explanation:

g(-1) = 2(-1)4 + 3(-1)3 - (-1)2 = 2(1) + 3(-1) - 1 = 2 - 3 - 1 = -2

The correct answer is (A) -2y - 2 for x in 3x - 2y = 10.

x + 2 = -2y

3x - 2y = 10

In order to find the second variable, we must take either x or y out of one of the equations. We can specifically exclude x by substituting the following in the expression:

From the first equation into the second, x = -2y - 2. With this change, x will no longer be present in the second equation, allowing us to determine the value of y. As a result, we must replace the phrase with:

For x in the equation, -2y - 2:

3x - 2y = 10

To acquire:

3(-2y - 2) - 2y = 10

To put it simply: -6y - 6y - 2y = 10

combining comparable phrases

-8y = 16

y = -2 after dividing both sides by -8.

Once y has been determined, we can add this result back into one of the original equations.

Therefore, the correct answer is (A) -2y - 2 for x in 3x - 2y = 10.

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m=4g+5 is the equation for money will Walter owe if he buys g gallons of gas

An expression is combination of variables, numbers and operators.

Given that Walter pays $4 for each gallon, g, of gas for his lawn mower.

Walter uses a gift card worth $5 to reduce the amount he owes for his purchase.

We need to find the money, m, will Walter owe if he buys 4 gallons of gas.

m=4g+5

Now for 4 gallons we have to find the money.

m=16+5

m=21

Now for gallon =2

m=13

Now for gallon =3

m=17

Hence, m=4g+5 is the equation for money will Walter owe if he buys g gallons of gas

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When 250 is divided by 10 the 2nd power will be 5².

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

250 is divided by 10. Then the value of the expression will be

⇒ 250 / 10

⇒ 25

Write the expression in the form of 2nd power, then we have

⇒ 25

⇒ 5 x 5

⇒ 5²

When 250 is divided by 10 the 2nd power will be 5².

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To create a scale diagram, determine the ratio between the length and width of the scale drawing and the actual object.

To create a scale diagram, we need to determine the ratio between the length and width of the scale drawing and the actual object.

In this case, the length of the scale drawing is 8 inches and the actual length of the mp3 player is 4 centimeters.

So the length ratio is 8 inches / 4 centimeters = 2 inches / centimeter.

Similarly, the width ratio can be calculated as 14 inches / 7 centimeters = 2 inches / centimeter.

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In Renee's scale drawing of the mp3 player, every 1 cm of the actual mp3 player is represented by 5 cm in the scale drawing. This is calculated by comparing the actual length to the length on the drawing, converting the units to centimeters first. The scale should be consistent for both length and width.

The question describes a situation where Renee is making a scale diagram of her mp3 player. In this case, there is a comparison between the actual size of the mp3 player and it's representation on the scale drawing. Let's use the lengths as a basis for the scale.

The length of the actual mp3 player is 4 cm and the length on the scale is 8 inches. But, to make our comparison valid, we need to make sure that both measurements are in the same unit. Now, since 1 inch is approximately 2.54 cm, our 8 inches become 8 × 2.54 = 20.32 cm.

This means Renee's scale is roughly 5 to 1 (since 20.32 divided by 4 is about 5). Therefore, every 1 cm of the actual mp3 player is represented by 5 cm in the scale drawing.

We can follow the same process for the width and verify that the scale is consistent, which it should be, but in this case, it's not necessary because we've been given that the lengths and the widths have exactly the same proportions in both the drawing and the real object.

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Without further information, we can say that the prediction of drawing a blue or purple marble in six attempts depends on the total number of marbles and the number of blue and purple marbles.
If half the marbles are blue or purple, there is a predicted average of three such draws in six attempts.

To predict how many times you could pick a purple or blue marble, we would need to first know the total number of marbles and the number of blue and purple marbles. This information isn't provided in the question. However, we can discuss this concept further. When you select a marble and put it back, the probabilities remain the same for each draw because the total number of marbles in the bag and the number of desirable marbles (blue or purple in this case) do not change.

For example, if a bag contains four blue marbles and three white marbles, and you draw one marble six times with replacement (meaning each time after drawing, you put the marble back into the bag), the probability of drawing a blue marble each time is 4/7, because there are four blue marbles and seven total marbles.

Therefore, the best prediction of the number of times you will draw a blue or purple marble in six tries depends on these individual probabilities. If we assume half the marbles are blue or purple, then on average, we would expect to draw a blue or purple marble about three times.

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The best prediction possible for the number of times you will pick a purple or a blue marble after 6 draws is 3.43 times.

To predict the number of times you will pick a purple or a blue marble, you need to determine the probability of picking a purple or a blue marble for each individual draw and then multiply that probability by the number of draws. In this case, the bag contains 4 blue marbles out of a total of 7 marbles.

Therefore, the probability of picking a blue marble on each draw is 4/7.

Since you are drawing 6 times, you can predict that you will pick a purple or a blue marble approximately (4/7) x 6 = 24/7 = 3.43 times.

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Answer:

I can ride 3.3 miles in $10.

Step-by-step explanation:

Let i can ride x miles in $10.

So for first 0.5 miles I have paid = $2.4

The for remaining ride of (x - 0.5) payment done = $[tex]\frac{0.20}{0.1}\times (x-0.5)=2(x - 0.5)[/tex]

I gave the tip = $2

Total payment I have done for the ride = $10

So equation will be

2.4 + 2(x - 0.5) + 2 = 10

4.4 + 2x - 1 = 10

3.4 + 2x = 10

2x = 10 - 3.4

2x = 6.6

x = [tex]\frac{6.6}{2}=3.3[/tex]

Therefore, i can ride 3.3 miles in $10.

Answer:

Mia switched the numerator and the denominator.

Step-by-step explanation:

The slope formula is given by:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Where we have two ordered pairs:

P1 = (x1, y1)

P2 = (x2, y2)

Given is : Mia’s work to find the slope of a trend line through the points (3, 10) and (35, 91)

Step 1: [tex]\frac{3-35}{10-91}[/tex]

If we compare the formula with Mia's step, we can see that she switched the numerator and the denominator.

Hence, the error made is : Mia switched the numerator and the denominator.

Answer:

Step-by-step explanation:

given equation,

-4 x = y + 3

y = -4 x -3........................(1)

comparing equation 1 with

 y = m x + c

m = -4 and  c = -3

now using this we can easily plot the graph where c is the y-intercept and m is the slope of line .

so, the plot is shown in the graph attached below.

Answer:

It means that you have to put the decimal point in the quotient exactly above the decimal point in the dividend.

Step-by-step explanation:

In the picture attached, the decimals chart is shown. There you can see where you have to put the decimal point in the quotient when you are dividing a decimal number by a whole number.

Answer:

The ratio would be A. 2:1

Step-by-step explanation: