At 10:00 am, two boys start out on their bikes to meet each other from towns located 68 miles apart. They meet at 1 pm. If one boy travels 3 miles per hour faster than the other, what was the speed of each boy?

Given that 10 bottles were bought for a total amount of $12, the price per bottle of sport drink is $1.20.

$12 divided by ten bottles equals $1.20.

By dividing the total amount paid ($12) by the quantity of bottles bought, the price per bottle of sport drink was determined (10). As a result, each bottle cost $1.20. According to the computation, the price of 10 bottles of sport drink came to a total of $12. The cost of individual goods or greater quantities of bottles can then be determined using this cost per bottle. The price per bottle can be used to compare the costs of various sport drink brands or sizes. Customers can choose and buy sport drinks with more knowledge if they are aware of the price per bottle.

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The approximate surface area of the can is 180.55 sq.inches

A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth. A group of circular discs placed on top of one another might be thought of as a cylinder. The cylinder has both surface area and volume since it is a solid with a three-dimensional geometry.

The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.

The Surface Area of Cylinder = Curved Surface + Area of Circular bases

S.A. (in terms of π) = 2πr (h + r) sq.unit

Where, π (Pi) = 3.142 or = 22/7

r  = Radius of the cylinder

h  = Height of the cylinder

cylindrical can has a radius of 2.5 inches and a height of 9 inches

surface area =2πr (h + r) sq.unit

= 2π*2.5(9+2.5)

=180.55 sq.inches

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Answer:

              The greatest possible five-digit number you can create with the numbers 6, 0, 3, 2, and 4 is 64,320.

Step-by-step explanation:

               When it comes to creating the biggest number with a given set of digits, the one and only rule is to organize the digits from greatest to least, this way it ensures that you have the maximum possible values that aren't mitigated by having a small number before a larger one. Based on this, we can organize 6, 0, 3, 2, and 4 from greatest to least, which will be 64,320. Hence, the greatest possible five-digit number you can create with those given numbers is 64,320.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

x=3

Step-by-step explanation:

x=3

4-2x=-2

-2x=-6

x=3

Answer:

Positive

Step-by-step explanation:

She incorrectly solved it because 4-2x = 2 ( Positive )

Part 1: If Mary doubles the area of her original square garden, the expression that represents the area of Mary's new garden is 2x^2.

Part 2: If the side length of Mary's original garden is 9 feet, the area of Mary's new garden is 162 square feet.

Part 1: If Mary doubles the area of her original square garden, the new area of her garden will be 2 times the area of her original garden.

If the area of her original garden is x^2, then the area of her new garden will be:

2(x^2) = 2x^2

So, the expression that represents the area of Mary's new garden is 2x^2.

Part 2: If the side length of Mary's original garden is 9 feet, then the area of her original garden is:

x^2 = (9 feet)^2 = 81 square feet

To find the area of Mary's new garden, we can substitute 81 for x^2 in the expression we found in Part 1:

2x^2 = 2(81 square feet) = 162 square feet

So, the area of Mary's new garden is 162 square feet.

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The point equidistant from the three sides of a triangle is (c) Incenter .

The Circumcenter of a triangle is defined as a point where perpendicular bisectors of  sides of triangle intersect. It is also equidistant from  3 vertices of triangle .

The Centroid is defined as a point where 3 medians of the triangle intersect.

The Incenter is defined as a point where  angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle, and is the center of the inscribed circle of the triangle .

The Orthocenter is defined as a point where the 3 altitudes of the triangle intersect.

So , by the definition of the Incenter , the correct option is (c) Incenter .

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The given question is incomplete , the complete question is

The point equidistant from the three sides of a triangle is

(a) Circumcenter

(b) Centroid

(c) Incenter

(d) Orthocenter

Answer:

slope (m) is 4, y-intercept (m) is -3

Step-by-step explanation:

y=4x-3

use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables.

Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

From the given options, the system of equations

2x + 6y = 18 and x + 5y = 13  

4x + 7y = 10 and -3x + y = -1    

Can be solved using the Elimination method  

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

From the given options, the system of equations  

y = x + 8 and y = 4x + 2

y = 3x + 3 and y = x + 7

Can be solved by using the Substitution method

Therefore,

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

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Answer:

FG = 18

Explanation:

There is a simpler solution:

It has to do with the interior angle bisector theorem. (the illustration with the angle marks and the line show that it is being bisected)

Which will divide the opposite side into segments whose lengths have the same ratio as the adjacent sides of the bisected angle.

x / 24 = x + 10 / 54 →

54x = 24(x + 10) →

54x = 24x + 240 →

30x = 240 →

x = 8.

Since the expression x + 10 represents the length of FG, it's length must be 18.

The value of x for the similar triangles is given as follows:

x = 40.5.

Similar triangles share these two features:

A bisection divides a triangle into two similar triangles, hence the proportional relationship for the side lengths is given as follows:

x/45 = 18/20

18/20 = 0.9, hence:

x/45 = 0.9

x = 45 x 0.9

x = 40.5.

Meaning that the fourth option is the correct option.

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Answer:

Step-by-step explanation:

So first what you got to do is add and mulytplie

The constant of proportionality is 180.

Answer:

60 sopomores

Step-by-step explanation:

Let X denote the event prefer amusement park on a field trip

The probability that a sophomore will opt for a class trip to an amusement park would be 8/20 = 2/5 based on survey results

P(X) = 2/5

Based on this probability, if the number of sophomores is 150 then expected number of sophomores who prefer the amusement park trip

E(X) - P(X) x N where N is the total number of sophomores

E(X) = 2/5 x 150 = 60

Answer:

x = 28

m∠A = 76°

m∠B = 104°

Step-by-step explanation:

Given the figure we can see that the two angles which measure

2x + 20 and 4x - 8 are adjacent linear angles and therefore they are supplementary angles which further means they add up to 180°

So

2x + 20 + 4x - 8 = 180

2x + 4x + 20 - 8 = 180\

6x + 12 = 180

6x = 180 - 12

6x = 168

x = 168/6

x = 28

We also have the property that angles that are vertically opposite each other at the vertex of the intersection of two lines are equal

So the angle represented by 2x + 20 = 2(28) + 20 = 56 + 20 = 76°

∠A is a vertically opposite angle to this angle and therefore the magnitude of ∠A denoted by m∠A = 76°

The angle represented by 4x - 8 = 4(28) - 8 = 112 - 8 = 104°

Since ∠B is a vertically opposite angle to this angle we have

m∠B = 104°

The solution is, point (5,4) will correspond to (5,8).

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

1) To find that the corresponding points, let'-s plug it into that formula:

(5,4)

If we plug 5 and we have output the number 4,

then f(x) is y=x-1

now,

2f(x-3)+4  is the function f(x) with a horizontal shift of 3 units to right, a vertical stretch 4, a reflection.

2) y=2(5-3)+4 then y=2(2)+4

y=8

So point (5,4) will correspond to (5,8)

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There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

We can write the first inequality as x + y <= 12

This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.

The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:

15x + 10y >= 140

To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.

The solution to the system of inequalities will be the values of x and y that lie in the shaded region.

One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.

Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

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Answer:

Step-by-step explanation:

You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.

The required relations can be written ...

  x + y ≤ 12 . . . . . . . total hours

  15x +10y ≥ 140 . . . . total earnings

The inequalities need to be solved for y to match the answer format requirements.

  inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x

  inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x

The attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...

  (4, 8), (12, 0), and (9 1/3, 0)

Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).

She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).

One possible solution is 4 hours lifeguarding and 8 hours landscaping.

Answer:

y= 2200 (3/4)x

Step-by-step explanation:

You can model a real-world situation involving an initial value and a constant growth or decay factor with an exponential equation in the form y=a(b)x, where b>0 and b≠1.

The constant a represents the initial value. It is the y-value of the equation when x=0.

The constant b represents the growth or decay factor.

When the equation models exponential growth, b>1.

When the equation models exponential decay, 0<b<1.

An exponential equation in the form y=a(b)x can model the value of the machine, y, x years after purchase. To write the equation, first look for phrases in the problem that tell you about the initial value, a, and the growth or decay factor, b.

Tessa is opening Tessa's Terrific Tees, her own custom T-shirt business. She bought a T-shirt printing machine that is currently valued at $2,200. The machine loses  1/4 of its value every year.

The constant a is the initial value. The initial value of the machine is $2,200. So, a=2,200.

The constant b is the decay factor, since the value of the machine is decreasing. The machine loses 1/4 of its value each year. In other words, the value of the machine each year will be 1–1/4= 3/4

times the value the year before. So, b= 3/4.

The exponential equation y= 2200 (3/4)x models the value of the machine.

An exponential equation in the form y=a(b)x that can model the value of the machine, y, x years after purchase is y= 2200*14*x

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.

Given that;

The cost of tshirt printing machine= $2200.

The lose of machine= 14

Now,

Substituting all the values in equation y=a(b)x

a=2200

b=14

y=2200*14*x

Therefore, the linear equation of the question will be y=2200*14*x

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Answer: 4

Step-by-step explanation:

Answer:

a recipe uses y cups of flour and x cups of sugar the amount of flour is 4 times  the amount of sugar

my proof I took the quiz

Student 2 has lower percentage of likes as compare to student 1 ,it is equal to 71.5%.

Number of likes of student 1 is equal to 147

Number of likes of student 2 is equal to 42

147 > 42

⇒Number of likes of student 1 is greater than student 2

Difference between number of likes

= 147 - 42

= 105

Percentage difference = ( 105 / 147 ) × 100

                                     = 71.5%

Student 2 has 71.5% lower percentage of likes than student 1

Therefore, student 2 has lower percentage of likes than student 1 which is equal to 71.5%.

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Step-by-step explanation:

don't forget to smile today

and make brainalist

Answer:

the answer is 4

Step-by-step explanation:

hope this helps

Answer:

The average rate of change of a function over an interval is a measure of how the function's value changes over that interval, given by the ratio of the change in the function's value to the change in the independent variable. To find the average rate of change of a function over an interval, we need to know the function's values at two points in the interval.

In the case of the function f(x) = x^2, the interval is -4 ≤ x ≤ 0. To find the average rate of change, we need to find the difference in the function's value between two points in this interval, and divide that by the difference in the x-values.

For example, if we compare the values of the function at x = -4 and x = 0, we have:

f(-4) = (-4)^2 = 16

f(0) = 0^2 = 0

The difference in the function's value is f(0) - f(-4) = 0 - 16 = -16.

The difference in the x-values is x2 - x1 = 0 - (-4) = 4.

So the average rate of change over this interval is the difference in the function's value divided by the difference in the x-values, or -16 / 4 = -4.

In other words, the average rate of change of the function f(x) = x^2 over the interval -4 ≤ x ≤ 0 is -4, meaning that for every 4 units of change in x, the function value decreases by 16 units.

Step-by-step explanation:

Answer:

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2x-y=3 2x+7y)=3,

2x-y=3 2x+7y)=3,

2x-y=3 2x+7y)=3,

2x-y=3

The taste of the tomato in today's soup compared to the usual recipe is same .

We find the tomato to soup ratio for each day to compare the taste of tomato in today's soup with the usual recipe,

For the usual recipe, the soup shack uses 9 tomatoes for every 12 bowls of soup, which can be simplified to a ratio of 9:12 ⇒ 3:4 .

This means that for every 3 parts of tomato, there are 4 parts of soup.

For today's soup, the soup shack used 6 tomatoes to make 8 bowls of soup, which can be simplified to a ratio of 6:8 ⇒ 3:4.

This means that for every 3 parts of tomato, there are 4 parts of soup, which is the same as the usual recipe.

Therefore, based on the tomato to soup ratio, the taste of tomato in today's soup is same as the usual recipe.

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The given question is incomplete , the complete question is

The soup shack usually makes tomato soup with 9 tomatoes for every 12 bowls of soup. today, they used 6 tomatoes to make 8 bowls of soup.

How does the tomato taste in today's soup compared to the usual recipe ?

The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.

The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.

Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,

there are 2^3 or 8 possible combinations of heads and tails.

Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).

So, the probability of obtaining the same number of heads is 3/8 or 0.375.

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Answer:

24 cars are green

Step-by-step explanation:

We know

Amir notices that 3 out of every 50 cars that pass by his window are green.

So, the ratio is 3:47

To get from 50 to 400, we time 8.

If he observes 400 cars, what is the best estimate of how many will be green?

We take

3 x 8 = 24 cars are green

So, there will be 24 cars that are green.