5. Max wants to start his own lemonade stand. It cost him $3 to make each cup of lemonade plus he has
to pay a $35 renters fee for his stand. He sells the lemonade for $5 per cup.
a. Write a system of linear equations for his cost and his revenue.

The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.

Given that:

The probability of pulling a red marble at random is 1/10

Probability of not pulling red marble is = 1-(1/10)= 9/10

The odds of pulling red marble is (1/10)/(9/10)

The probability of odds of pulling red marble is 1/9.

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Answer:

Step-by-step explanation: Here's your answer 50√3 m.

By using the concept of mode, it can be calculated that-

Mode number of hours spent on the computer is 11 hours.

What is mode?

Mode of a data set is that value which occurs most number of times in the data set. In other words, the value whose frequency is the largest is the mode of the data set.

The number of hours that 9 students spend on the computer on a typical day: 2 5 5 7 11 11 11 14 15

Here 11 occurs most number of times (3 times)

Mode number of hours spent on the computer is 11 hours.

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The rate of change of the graphs are as follows:

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Therefore,

rate of change = change in y / change in x

Hence,

rate of change = y₂ - y₁ / x₂ - x₁

let's find the rate of change of the graphs.

a.

using (-5, -1) and (5, 7)

rate of change = 7 + 1 / 5 + 5

rate of change = 8 / 10

rate of change = 4 / 5

b.

using (0, 3)(-4, 0)

rate of change = 0 - 3 / -4 - 0

rate of change = - 3 / - 4

rate of change = 3 / 4

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Answer:

48°

Step-by-step explanation:

this is because no if you take any two points in along line AB and CB it will always be 48°.

The function that represent the company's profit is (2.52x - 700).

As per the known formula, Profit = Revenue - Cost

Now keeping the functions of revenue and cost to find the function of profit.

Profit = 2.9x - (0.38x + 700)

Performing subtraction on Right Hand Side of the equation to find the profit of company

Profit = 2.9x - 0.38x - 700

Performing subtraction on Right Hand Side of the equation to find the profit of company

Profit = 2.52x - 700

Thus, the the profit of company will be represented by the function 2.52x - 700.

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The complete question is -

The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x. Find the function that represent the company's profit.

The value of x for the given right-angle triangle using the trigonometric function will be 1.0.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

As per the given right angle triangle,

sin 16° = x/3.5

x = 1.0

Hence "Using the trigonometric function, the value of x for the given right-angle triangle will be 1.0.".

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By using some exponent properties, we will see that the equivalent expression to √(x⁵*y⁶) is:

x²*y³*√x

So the correct option is the first one.

Here we need to remember 3 properties about exponents that we will need to use.

These are:

√x = x¹´²

Also remember that:

(xⁿ)ᵃ = xⁿ*ᵃ

And that:

√(a*b) = √a*√b

Well, our expression is:

√(x⁵*y⁶)

We can rewrite this as:

√x⁵*√y⁶

And using the first and second properties we can rewrite.

√x⁵ = x⁵´² = x⁴´²*x¹´² = x²*√x

√y⁶ = y⁶´² = y³

Replacing all that we get:

√(x⁵*y⁶) =  x²*y³*√x

Thus, the correct option is the first one.

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A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

2x² + 7x - 15.

Step-by-step explanation:

The product when x- 5 is multiplied by 2x + 3 is 2x² +7x - 15. To find the product, we need to use the distributive property. This states that for any two expressions, a and b, and a constant, c, we have the following:

c * (a + b) = c * a + c * b

We can use this property to expand the expression (x - 5)(2x + 3) as follows:

(x - 5)(2x + 3) = (x * 2x) + (x * 3) + (-5 * 2x) + (-5 * 3)

               = 2x^2 + 3x + (-10x) + (-15)

               = 2x^2 + 7x - 15

Therefore, the product of the expression (x - 5)(2x + 3) is 2x^2 + 7x - 15, which matches the answer choice 2x² + 7x - 15.

The solution is

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The angles 5 , 6 , 7 and 8 are all on the straight line t

The angles 1 , 2 , 3 and 4 are all on the straight line n

The line m is the transversal line

Now ,

From the theorem of angles on a parallel lines , we get

Alternate angles are equal

So , 2 = 8 and 3 = 5

Now ,

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

Corresponding angles are equal

So , 1 = 5 and 2 = 6

Now ,

Angle 1 and Angle 5 = Corresponding Angles

Co-Interior angles are supplementary

So , 1 + 8 = 180°

Now , Angle 1 and Angle 8 = Co-Interior Angles

Hence ,

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

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The equation of the line is y = 0.4x - 793.65 and the minimum wage is $18.35

The equation of a line can be formed with the help of the slope of the line and a point on the line. Let us understand more about the slope of the line and the needed point on the line, to better understand the formation of the equation of a line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

a)

Taking two points from the table;

Using 1996 and 1997

The data are; (1996, 4.75), (1997, 5.15)

m = y₂ - y₁ / x₂ - x₁

m = 5.15 - 4.75 / 1997 - 1996

m = 0.4

The slope of the line is 0.4

Using the line equation;

y = mx + c

Taking one point, we can find y-intercept here

5.15 = 0.4(1997) + c

5.15 = 798.8 + c

c = 5.15 - 798.8

c = -793.65

The equation of the line is y = 0.4x - 793.65

b) The minimum wage in 2030

y = 0.4x - 793.65

y = 0.4(2030) - 793.65

y = 18.35

The minimum wage is $18.35

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Answer:

A. Here are three more equations that are true based on the information you provided:

1. 3w + 2 = 2w + 6

2. 5w - 6 = 4w - 8

3. 7w - 5 = 6w - 7

B. To find the value of 2w, we need to first solve for w in the original equation 7w + 4 = 5w + 12. We can do this by subtracting 5w from both sides of the equation, which gives us 2w + 4 = 12. Then we can subtract 4 from both sides to get 2w = 8. Therefore, the value of 2w is 8.

C. To find the value of w, we can divide both sides of the equation 2w = 8 by 2, which gives us w = 4. Therefore, the value of w is 4.

The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.

In the question ,

it is given that ,

the system of 2 linear equations in 2 variables .

we know that the linear equations represent a line .

(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .

(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .

(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .

Therefore , the number of solutions of linear equation is explained above .

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Answer:

3 : 7

Step-by-step explanation:

Ratios are Proportinalised Numbers that we can use to compare number of units relative to the other value.

Eg. 3 : 15 = 1 : 5

Given Information from the Question:

15 Child Tickets : 35 Adult Tickets

Now we reduce them to simplest form.

(15 ÷ 5) : (35 ÷ 5) = 3 : 7.

Therefore the ratio of Child Tickets to Adult Tickets is 3 : 7.

The values that would be excluded from the domain of the function are those that create vertical asymptotes in the graph.

Vertical asymptotes can be found by setting the expression in the denominator equal to 0 (zero) and solving for x. The resulting values of x are the values that are excluded from the domain of the function.

Expression in the denominator = x^2 - 5x + 6

x^2 - 5x + 6 = 0

(Factor to solve)

(x - 3)(x - 2) = 0

x - 3 = 0 || x = 3

x - 2 = 0 || x = 2

The values that are excluded from the domain of the function are 3 and 2.

Hope this helps!

Answer:

the answer is

-3/2

I hope that helps

Answer: 30 combinations

Step-by-step explanation:

Multiply 3x2x5 to get 30.  

The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5

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

0.5 ( x +3)

Write the expression properly

So, we have the following representation

0.5 (x + 3)

Express the brackets as products

So, we have the following representation

0.5 (x + 3) = 0.5 * (x + 3)

Open the brackets using products i.e. distributive property

So, we have the following representation

0.5 (x + 3) = 0.5 * x + 0.5 * 3

Evaluate the products

So, we have the following representation

0.5 (x + 3) = 0.5x + 1.5

Hence, the expression as a sum is 0.5x + 1.5

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Answer:

1. 0.5x + 1.5

2. are not

The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".

What is Principle of specificity ?

According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.

if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.

This an example of  "Principle of specificity or specific adaption to imposed demands (SAID Principle) "

Tenet according to which the body will adjust to the unique demands imposed upon it.

Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.

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The length of the shadow of man is 0.8 m/s.

How to solve word problems?

Here are some actions to take:

1. Recognize the issue.

Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.

2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.

3. Put the strategy into action and find a solution.

dx/dt  =1.2 m/s

4.5 / x+ y = 1.8 / y

1.8x + 1.8y = 4.5y

1.8x = 2.7y

2x = 3y

3 dy/dt = 2dx/ dt = dy/dt = 2/3

​ =0.8

Hence, The length of the shadow of man is 0.8 m/s

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The empirical probability that George will get back on his feet the next time Angie knocks him down is 5/114.

Event probabilities are closely related to empirical probabilities, also called empirical probabilities.

Empirical probability is an estimate of the probability of a particular outcome occurring again, based on the number of instances of that outcome in the sample set.

In the given question.

Also includes George the Turtle, who flipped Angie the Tortoise 114 times.

Three times George got back on his feet with help. Empirical probabilities are exactly what we are looking for.

Based on our observations, we will now empirically calculate whether George will be able to stand again.

Therefore,

The Empirical probability = 5/114

So, the next time Angie knocks George down, the empirical probability that George will be able to get back up on his own will be his 5/114.

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The probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

Given, a and b are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

we have to find the probability that a will have more heads than b.

Now, p1  = "probability that A obtains more heads than B.".

p2 = "probability that B obtains more heads than A.".

p3 = "probability that A obtains as many heads as B.".

Such that p1 + p2 + p3 = 1.

Since, both flips n coins, A wins with the same probability as B.

p1 = p2

Now, A flips and extra coin.

½ of the time it gives tails and doesn't contribute, but ½ of the time is gives heads meaning that A now wins if they before had equal number of heads.

p1+1/2(1 − p1 − p2)=1/2.

Hence, the probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

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Answer: 4

Step-by-step explanation:

10/14 = 5/7

True, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line.

As given in the question,

Given statement is: Parabola consist of set of all the points which are equidistant from fixed point and fixed line.

Therefore, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line is a true statement.

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There are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

What is a combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we

Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:

x BR x BR x BR x BR x BR x BR x BR x B x

Note that this is the same even if our arrangement is

x B x RB x  RB x RB x RB x RB x RB x RB x

There is a total of 13 places to arrange 8 blue marbles among 12 red marbles.

8 marbles can be placed in ¹³C₈ ways

Total possible arrangements = ¹³C₈ = 1287

Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

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Answer:

2 gallons

Step-by-step explanation:

1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4

Then:

5/4 gallons ⇒ 5/8 fence

x  gallons ⇒ 8/8 fence

x = (5/4)(8/8) / (5/8)

x = ((5*8)/(4*8)) / (5/8)

x = (5/4) / (5/8)

x = (5*8)/(4*5)

x = 40/20

x = 2

The lines with the equations 10x+5y =-5 and y=-2x+6 are parallel

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

10x+5y =-5 and y=-2x+6

Make y the subject in both equations

So, we have the following representation

y = -2x - 1 and y = -2x + 6

As a general rule of linear equations

Parallel lines have equal slope

A linear equation is represented as

y = mx + c

Where

slope = m

Using the above as a guide, we have the following:

The slope of y = -2x - 1 and y = -2x + 6 is -2

Hence, the lines are parallel

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Answer:

The inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality can be derived by first calculating the total cost of renting the car for 2 days at $39.90 per day and $0.20 per mile. This gives us a total cost of $79.80 for the rental plus $0.20 per mile for the number of miles Henry drives. Since Henry has $150.00 to spend, we can set up the following inequality to represent the maximum number of miles he can drive:

150.00 >= 79.80 + 0.20m

We can then solve for m by subtracting 79.80 from both sides of the inequality and dividing both sides by 0.20, which gives us:

m <= 550.5

Therefore, the inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality states that Henry can drive the car for a maximum of 550.5 miles.

Step-by-step explanation:

Answer:

It is a function

Step-by-step explanation:

for a relation to be a function, every X must have one and only one y. That is true for the given values