A store buys 15 sweaters for $90 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of s that matches the context.

The standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x

Volume of the shipping container = Lengt * Breadth * Height

Given

Length = 4x² + 3x

Breadth = x² – 8

Height = 6x +15

Volume of the container = ( 4x² + 3x)( x² - 8)(6x+15)

( 4x² + 3x)( x² - 8)  = 4x⁴-32x²+3x³-24x

( 4x² + 3x)( x² - 8) = 4x⁴+3x³-32x²-24x

(4x⁴+3x³-32x²-24x)(6x+15) = 24x⁵+60x⁴+18x⁴+45x³-192x³-480x²-144x²-360x

Collect like terms

( 4x² + 3x)( x² - 8)(6x+15) = 24x⁵+78x⁴-147x³-624x²-360x

Hence the standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x

The angle measure of m∠O is 13°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

In ΔMNO,

[tex]\overline {OM}[/tex] ≅ [tex]\overline {ON}[/tex]

Then the angle opposite to the sides are also congruent.

m∠N = m∠O

And we have, m∠N = 13°.

So, m∠O = 13°.

Therefore, the angle measure is 13°.

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The number of unique ways to complete a quiz with 5 questions and 4 possible answers to each question is [tex]4^5[/tex], or 1024.

This can be calculated using exponential notation, which states that a number raised to the power of another number is equal to the number multiplied by itself that many times. In this case, 4 to the power of 5 is equal to 4 x 4 x 4 x 4 x 4, or 1024.

In other words, the number of unique ways to answer a quiz with 5 questions and 4 possible answers to each question is equal to 4 multiplied by itself 5 times. This can also be written using the exponential notation as [tex]4^5[/tex]. There are 1024 unique ways to complete a quiz with 5 questions and 4 possible answers to each question.

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A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.

here, we have,

a rectangle's length is 5 inches greater than its width.

if the perimeter of the rectangle is 42 inches

let, width = x

then, length = x+5

so, perimeter= 2(x+5 +x)

                      = 4x+10

ATQ, 4x+10 = 42

solving we get,

x=8

the length = 13

Hence, A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.

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Tiffany didn't deposit any more money and didn't withdraw any,

her balance is $1,413.82.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P(1 + r/n[tex])^{nt}[/tex]

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Tiffany makes some extra money selling vinyl's to teachers.

She deposited the $1,245 extra money into an account that earned 3.7% interest that was compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.7/100

r = 0.037 rate per year,

Then solve the equation for A

A = P(1 + r/n[tex])^{nt}[/tex]

A = 1,245.00(1 + 0.037[tex])^{3.5}[/tex]

A = $1,413.82

Therefore, the amount is $1,413.82.

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Answer:

Problem 1: the price of one adult ticket is $8.25 and the price of one student ticket is $30.75

Problem 2: there were 10.33 students in each van and 152.67 students in each bus.

Step-by-step explanation:

Problem 1:

Let's call the price of an adult ticket as "a" and the price of a student ticket as "s". We know that on the first day the total cost was $39 and they sold 1 adult ticket and 1 student ticket, so we have the equation:

a + s = 39

And on the second day, the school took $105 from selling 9 adult tickets and 8 student tickets, so we have the equation:

9a + 8s = 105

We can use these two equations to solve for "a" and "s".

Solving for "a":

9a + 8s = 105

a - s = -39

8a = 66

a = $8.25

So the price of one adult ticket is $8.25.

Solving for "s":

a + s = 39

a = $8.25

s = 39 - 8.25 = $30.75

So the price of one student ticket is $30.75.

Problem 2:

Let's call the number of students in each van as "v" and the number of students in each bus as "b". We know that the senior classes at High School A rented and filled 2 vans and 2 buses with 326 students, so we have the equation:

2v + 2b = 326

And High School B rented and filled 11 vans and 6 buses with 233 students, so we have the equation:

11v + 6b = 233

We can use these two equations to solve for "v" and "b".

Solving for "v":

2v + 2b = 326

11v - 6b = -233

-9v = -93

v = 10.33 students in each van

Solving for "b":

2v + 2b = 326

2(10.33) + 2b = 326

20.66 + 2b = 326

2b = 326 - 20.66 = 305.34

b = 152.67 students in each bus

So there were 10.33 students in each van and 152.67 students in each bus.

Answer:

To subtract the two mixed numbers, we need to convert both mixed numbers to improper fractions.

So,

8/9 = 72/81 (by multiplying both numerator and denominator by 9)

and

4/6 = 40/60 = 2/3 (by multiplying both numerator and denominator by 10/10)

So,

72/81 - 2/3 = (72 * 3 - 2 * 81) / (81 * 3) = (216 - 162) / 243 = 54/243.

So,

8/9 - 4/6 = 54/243.

Answer:

Step-by-step explanation:

ok so basically you want to turn 8/9 and 4/6 into decimals. When your done turning them into decimals subtract them.

you can also simplify the fractions and then subtract them!

Sorry tried my best hope this helps! :)

Answer:

x = 8, y = 1

Step-by-step explanation:

11x - 20y = 28 ...(1)
3x + 4y = 36
or 15x + 20y = 180 ...(2)
Adding (1) and (2),
26x = 208
Or x = 8
Now, 3x + 4y = 36
3(8) + 4y = 36
4y = 36 - 32 = 4
so y = 1

Bar graph. This type of graph is ideal for comparing the number of sneakers sold by brand, as it clearly displays the numerical differences between them. It is also easy to interpret and visually appealing.

A bar graph is the best choice for displaying the number of sneakers sold by brand for the month. Bar graphs are used to compare data and show the differences between them. Each brand would be represented by its own bar, and the length of each bar would be determined by the number of sneakers sold. The bars can be labeled with the brand's name, and a numerical scale would be used at the bottom of the graph to indicate the number of sneakers sold. The data can be organized by either the number of sneakers sold (descending) or by the brand name (alphabetically). The bar graph would be easy to interpret and visually appealing. It is also a great way to compare the performance of different brands in a given period.

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-x² - x( 3 + 2√x) + 12  is the simplified form of the expression

x-2√x ³ - x² - 4x+12.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given an expression that needs to be rewritten in simplified form

Equation is:

=> x-2√x ³ - x² - 4x+12

Solving the square root

=> x - 2 * x√x - x²- 4x + 12

=> -x² +  x(-3 -2√x) + 12

=> -x² - x( 3 + 2√x) + 12

therefore,  -x² - x( 3 + 2√x) + 12  is the simplified form of the expression

x-2√x ³ - x² - 4x+12.

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Answer:

1. subtract 12 to the right side and remove the 12 from the left.

You will have -4x=-16

2. divide -4x and  -16 by -14

ANSWER= 4

Step-by-step explanation:

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 3100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (3100)(0.08)(3) \implies I = 744[/tex]

The equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

Since the temperature changes linearly with time after sunset, we can represent the temperature as a linear equation:

y = mx + b

where y is the temperature in degrees Fahrenheit, x is the number of hours after sunset, m is the rate of change of temperature and b is the y-intercept.

Given that at 2 hours before sunset, the temperature is 0°F and at 2 hours after sunset, the temperature is -4°F, we can use these points to find m and b.

At x = -2: y = 0°F

At x = 2: y = -4°F

So, m = (y2 - y1) / (x2 - x1) = (-4°F - 0°F) / (2 - (-2)) = -2°F/hour

And, b = y - mx = 0°F - (-2°F/hour * -2) = 4°F

Therefore, the equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

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A line graph is the most basic method of illustrating data.

A line graph is a special type of graph that is frequently employed in statistics. In relation to another quantity, it shows how one quantity has changed. For instance, we may use this graph to illustrate how the cost of various chocolate flavors fluctuates. Typically, a two-dimensional XY plane is used to plot this variation. A graph is said to be linear if it can represent the relationship between any two measurements by a straight line. Consequently, a line graph is often known as a linear graph.

The three different types of line graphs are simple line graphs, numerous line graphs, and compound line graphs.

Option B is the proper response, thus.

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Answer:

y = 3x+9

Step-by-step explanation:

We start by finding the slope

find find this by (y_end - y_beginning)/(x_end - x_beginning)

(39-24)/(10-5)=15/5=3

now to find the intercept we y_beginning - (slope*x_beginning)

24-(5*3) = 24-15 = 9

so the equation is

y = 3x+9

The walking speed x = (L/t) - (3/65) L + (2/50) L .We can solve this problem using the concept of average speed and the time and distance relationship.

Let's assume the length of the moving sidewalk be L and the speed of the moving sidewalk be v.

When the moving sidewalk is working, the person's speed is v + w, where w is the walking speed.

And, the time taken to travel the distance L is 65s.

So, using the average speed formula, we have:

(v + w) = L/65

And, when the moving sidewalk is not working, the person's speed is w.

And, the time taken to travel the distance L is 50s.

So, using the average speed formula, we have:

w = L/50

Now, we can equate the above two equations to find the walking speed w.

v + w = L/65

w = L/50

Subtracting the second equation from the first equation, we get:

v = (L/65) - (L/50)

Since, L is common in both the numerators, we can simplify the above expression as:

v = (3/65 - 2/50) L

Thus, the speed of the moving sidewalk is (3/65 - 2/50) L.

Let's assume the walking speed be x.

So, the average speed of the person is (v + x) = (3/65 - 2/50) L + x.

And, the time taken to travel the distance L is t.

Using the average speed formula, we have:

(v + x) = L/t

Substituting the value of v, we get:

((3/65 - 2/50) L + x) = L/t

Simplifying the above equation, we get:

x = (L/t) - (3/65 - 2/50) L

Now, substituting the values of L/50 and L/65, we get:

x = (L/t) - (3/65 - 2/50) L

x = (L/t) - (3/65) L + (2/50) L

So, the walking speed x = (L/t) - (3/65) L + (2/50) L.

Therefore, the walking speed can be calculated using the above expression.

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The complete question is :

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 65 s to travel the same distance.

How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Express your answer using two significant figures.

Answer:7828

Step-by-step explanation:

The velocity of the cheetah between 5 and 15 seconds is 5 meters per seconds.

From the given distance time graph, between 5 to 15 seconds cheetah ran 50 meter.

Velocity is the measure of the amount of distance an object covers in a given amount of time. Here's a word equation that expresses the relationship between distance, velocity and time: Velocity equals distance travelled divided by the time it takes to get there.

So, velocity = 50/10

= 5 meters per seconds

Therefore, the velocity of the cheetah between 5 and 15 seconds is 5 meters per seconds.

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A point is placed 2 units left and 3 units down from the origin is (-2, -3) and a point is placed 3 units left and 2 units up from the origin is (-3, 2)

Statement 1:

Given that

A point is placed 2 units left and 3 units down from the origin.

This is represented as

(0 - 2, 0 - 3)

Evaluate

(-2, -3)

Statement 2:

A point is placed 3 units left and 2 units up from the origin.

This is represented as

(0 - 3, 0 + 2)

Evaluate

(-3, 2)

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Answer:

Step-by-step explanation:

2+2=4

250g tin of coffee: 29.99/250 = R0.12 per gram

750g tin of coffee: 69.99/750 = R0.09 per gram

750g tin of coffee is better value for money.

The length GF in the rhombus is 26.4 and the value of x in the square is 12

The given shape is a rhombus

The diagonals of a rhombus intersect at 90 degrees

This means that

GF^2 = 21^2 + 16^2

So, we have

GF^2 = 697

This gives

GF = 26.4

The given shape is a square

The vertex of a square has a measure of 90 degrees

This means that

11x - 32 = 90

So, we have

11x = 132

This gives

x = 12

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The result of [tex] \frac{x - 3}{8} [/tex] is x = 8k + 3

To solve the fraction [tex] \frac{x - 3}{8} [/tex], you need to isolate the fraction on one side of the equation. Then, multiply both the numerator and denominator by the same number to make the denominator equal to 1. Finally, simplify the fraction by dividing the numerator by the denominator. The steps are as follows:

[tex] \frac{x - 3}{8} = k[/tex], where k is a constant.

Then, [tex](x - 3) \times {8}^{ - 1 } = k[/tex].

This simplifies to x-3 = 8k.

Finally, you have x = 8k + 3. This is the solution to the fraction [tex] \frac{x - 3}{8} [/tex].

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The value of a is 12 when transversal t crosses over parallel lines p and s.

A transversal line is one that crosses two or more other lines. A transversal is frequently used in geometry to establish connections between angles created by crossing lines. When a transversal connects two parallel lines, it produces equivalent pairs of alternate interior and alternative exterior angles. These connections can be used to demonstrate the parallelism of two lines. In a broader sense, the term transversal refers to any line that meets another line, regardless of their angle connections. A transversal, for example, might be used to locate the point of intersection of two lines or to divide a form into two distinct pieces.

Here,

5a-2+10a+2=180

15a=180

a=12

The value of a for which transversal t passes through parallel lines p and s is 12.

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Cost of 15 liters of paint is, 630 Rs.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Five liters of paint cost = 210 Rs.

Hence, We get;

Cost of 1 liters of paint = 210/5

                                   = 42 Rs.

So, Cost of 15 liters of paint is,

⇒ 15 × 42

⇒ 630 Rs.

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The estimation helps us to get simpler digits to perform operations.

An approximate value close enough to the correct value is called estimation.

Given that, how can an estimate help when multiplying 5.3 x 3.9

So, here we see that, multiplication of two decimal number are getting performed,

To multiply decimal numbers, sometimes gets lengthy, so we use estimation,

Here, the two numbers are, 5.3 and 3.9,

Rounding the numbers for estimation,

The rule of rounding says, that, when the digit after decimal is less than five then we round down and if it is greater than five then we round up,

Therefore,

5.3 = 5

3.9 = 4

Now, as we get two simpler numbers, we can easily multiply them

5 x 4 = 20

That mean, the estimated value of 5.3 x 3.9 is 20

Hence, the estimation helps us to get simpler digits to perform operations.

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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A scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

The type of chart in Excel that plots a point at its Cartesian coordinates using an x-coordinate and a y-coordinate is a Scatter Plot. A scatter plot is a type of graph in which individual data points are represented by dots on a graph. Each data point has two coordinates: the x-coordinate and the y-coordinate, which are used to plot the point on the graph.

In Excel, to create a scatter plot, you need to first select your data, then go to the Insert tab and click on the Scatter chart button. You can then choose the type of scatter plot you want to create. Once the chart is created, you can add data labels to show the x-coordinate and y-coordinate of each data point.

In summary, a scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

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According to the above, to draw a 1:2 scale we must divide the figure in 2.

The scale model is a way of drawing a figure that is smaller or larger in size. In this case, the size would be smaller, 1:2 means that for each unit of measurement (cm) of the original figure, there are 2 units on the scale.

According to the above, if the circle has a 12cm radius, then the scale model would have a 6cm radius, that is, it would be smaller than the original as shown in the second image.

Note: This question is incomplete. Here is the complete information:

Draw a scale of 1:2 of the following figure:

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Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

The best tool for collecting data on which gas pump is used most frequently by customers would be a check sheet.

A check sheet is a simple tool used to collect and categorize data in a structured manner. In this case, the operator can use a check sheet to keep track of which gas pump is being used by customers by marking each time a customer uses a certain pump.

The operator can then tally the marks to determine which pump is used most frequently. This method provides an easy and efficient way to collect data and quickly see patterns and trends in the data.

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--The given question is incomplete; the complete question is

"A gas station operator is interested in determining which gas pump is used most frequently by customers. The best tool for collecting this data would be a

Run chart.

Check sheet.

Histogram.

Pareto diagram."--