Part A


The graph shows the distance in miles, , a car travels in hours.

​

​

Explain why the graph does or does not represent a proportional relationship between the variables and .

​Enter your explanation in the box provided.

​

​Part B

​Two cars leave from the same city at the same time and drive in the same direction. The table shows the distances traveled by each car.

​


• Determine whether the relationship between the number of hours traveled and the number of miles traveled is proportional for each car.

​• Use the table to explain how you determined your answers.

​• Describe how the graph of the distance traveled by each car would support your answers.

​

Enter your answers and your explanations in the box provided.

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Using probability concepts, we calculated that the likelihood that the person plays the clarinet but not the flute is 0.2743.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.

Here,

Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.

There are 47 people who can play both the clarinet and the flute.

As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.

Probability(P),

P=( 125 / 350)

P=0.2743.

Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.

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The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.

A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be  L(x) = 2x. Using this information the perimeter of the triangle comes out to be,

P(x) = h(x) + L(x).

P(x) =  x√2 + 2x

Hence the perimeter of the triangle comes out to be P(x) =  x√2 + 2x

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The value of 3 in 5.53 is 3 hundredths.

It is important to note that place values can be defined as the value that's represented by a digit based on the position that it takes. In mathematics, place value refers to the position or location of a digit in a number.

Each digit has a specific place in a number. The position of each digit will be expanded when we represent the number in general form. Those positions begin with a unit place, also known as one's position.

In this case, we want to know the value of 3 in 5.53. It should be noted that the first 5 is 5 ones, the second 5 is 5 tenths and the 3 is 3 hundredths.

Therefore, it's 3 hundredths.

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Complete question

What is the value of 3 in 5.53?

Answer:

Part A. (4,5)

Part B. (9,7)

Step-by-step explanation:

Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

acc to our question-,

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Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.

The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.

Hence, when  i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and  then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then  the independent variable in this experiment is the book given by me.

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By using the concept of translation, it can be inferred that

The graph of the equation is translated 3 units to the left and 4 units down

What is translation?

Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.

The given equation is

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

This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.

So the first option is correct.

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In 120 different variations of this model car are possible.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.

Given,

There are five different ways to choose a car's color.

3 different car transmission selection options are available.

There are four different interior automobile selection options.

There are two different ways to pick a car's engine.

The potential number of car variations is thus:

Multiplying:

5 × 3 × 4× 2

120

In 120 different variations of this model car are possible.

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The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.

It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).

Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;

f(x) = (x - 2) (x - 3) (x - 5)

Therefore, by simplification; we have;

f(x) = (x² - 5x + 6) (x - 5)

f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.

f(x) = x³ - 10x² + 31x - 30.

Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.

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The percentage that Richard get is 8%

The statement can be interpreted as:

He answered 52 correctly from a total of 65 questions

From the above statement, we have the following parameters

Dividend = 52

Divisor  = 65

The percentage is then calculated as

Percentage = Dividend/Divisor  x 100%

Substitute the known values in the above equation

So, we have

Percentage = 52/65 x 100%

Evaluate the quotient

Percentage = 0.8x 100%

Evaluate the product

Percentage = 8%

Hence, the percentage is 8%

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Answer:

x-variable    y-variable    Inequalities

calculus       physics        7≤x≤14

                                        8≤y≤12

                                        x+y≤23

Step-by-step explanation:

An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

In this question we have been given an expression -4.5n + 3

We need to identify an expression which is factored form of given expression.

If we simplify the factored form then it must be a give expression.

consider ,A. −3(1.5n−1)

= -4.5n + 3

consider an expression B. −1.5(3n+2)

= -4.5n - 3

consider C. −1.5(−3n+2)

= 4.5n - 3

consider D. −3(1.5n+1)

= -4.5n - 3

Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

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Answer:

144 cm²

Step-by-step explanation:

1.) Find the area of all of the faces

10*4=40 (Top Face)

4*8=32 (Bottom Face)

6*8*0.5=24 (One Triangle)

6*8*.5=24 (Other Triangle)

6*4=24 (Back Face)

2.) Add them all together to get the surface area

40+32+24+24+24= 144

***Don't forget the cm². Some teachers are really annoying about this

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

The values are not equivalent to 2.2 include

2.6 - 0.6

1.8 + 2.5

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, 2.6 - 0.6 will be:

= 2.6 - 0.6

= 2.0

Also, 1.8 + 2.5 will be:

= 1.8 + 2.5

= 4.3

Therefore, they're not equivalent to 2.2

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Complete question

During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2

1.2 + 1.0

2.6 - 0.6

0.9 + 1.3

1.8 + 2.5

The probability of more than $225 is 0.35197.

Here we need to find the probability of more than $225.

We need to calculate the z-score associated with x = $225

Z(score) = 225 - 204 / 55

= 0.381818

z(score) = 0.38

For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.

Here we have to find the values greater than this value:

P(z > 0.38) = 1 - P (z < 0.38)

P( z > 0.38) = 0.35197

So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.

Therefore the probability is 0.35197.

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It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.

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a. Angle 4 is an alternate exterior angles to angle 8.

b. Angle 3 is same-side interior angle to angle 2.

c. Angle 1 is corresponding angles to angle 3.

Corresponding angles are located on the same corner and on the same side of a transversal.

For example, in the given image below, angles 1 and 3 are corresponding angles.

Alternate exterior angles are any two exterior angles that lie on two different parallel lines but on alternate sides of the transversal that crosses the two parallel lines.

For example, in the image given, angles 8 and 4 are alternate exterior angles.

Same-side interior angles are interior angles that are located on the same side of the transversal but on different parallel lines that the transversal cuts across.

For example, angles 2 and 3 are same-side interior angles as seen in the given image.

Corresponding angles are located on the same corner and on the same side of a transversal.

For example, in the given image below, angles 1 and 3 are corresponding angles.

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Analyzers should use the Alpha aesthetic.

Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.

What is a scatterplot?

A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.

A scatter plot  plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.

Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.

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The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The given system of equations is

x + y = -1          ......(1)

3x - y = 21       ......(2)

Rewrite equation (1)

y = - x - 1        ......(3)

Put equation (4) in equation (3)

3x -(-x -1) = 21

3x + x + 1 = 21

4x = 20

x = 20/4

x = 5

Put x= 5 in equation (3)

y = - 5 - 1

y = - 6

So, both the options are correct, (5, -6) is the solution of both equations.

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The equation of the linear function represented by the table would be y = 4x - 1.

What is the slope-intercept form of the line?

When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula

                               y = mx + c.

The y value of the y-intercept point is represented by c in the formula.

By using the given table,

for x = 0 , y = -1

so by using the slope-intercept form of the line, we can write

              y = mx + c

              -1 = m(0) + c

               c = -1 ----------(I)

Then for x = 1, y = 3

again by using the slope-intercept form of the line, we can write

                  y = mx + c

                 3 = m(1) + (-1)  -----from (I)

                  3 = m - 1

             ⇒ m = 3 + 1

             ⇒ m = 4 -----------(II)

Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line

                     y = 4x - 1

Hence, the equation of the linear function represented by the table would be y = 4x - 1.

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The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.

It follows from the task content that the direct variation of equation of the two points given be determined.

On this note, since the relation is said to be a direct variation.

It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;

10/-5 = 4/-2 = k = -2.

Therefore, the required direct variation equation is written as;

y = -2x.

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The equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49

The equation of the parallel line is given

6x + y = -8

y = -8 -6x

y = -6x - 8

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Comparing the equation

Slope of the line m = -6

The slope of the all the parallel lines will be equal

Then line is passing through the point (7, 7)

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values in the equation

y-7 = -6(x-7)

y - 7 = -6x + 42

y = -6x +42 +7

y = -6x + 49

Hence, the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49

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If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.

∠RTU = ∠RTG + ∠GTU

∠RTU = 5.8° + 113.6°

∠RTU = 119.4°

The measure of the angle ∠RTU will be 119.4°.

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Answer: 12⋅|x3|−512√⋅|3|

PLEASR GIVE BRAINLIEST THANK YOU VERY MUCH!!!

The points (2, 3)  (6, 3), and  (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle

The distance between the points is calculated and Pythagoras theorem is used to determine if the triple  forms a right angle

let the points be

A (2, 3)  B (6, 3), and  C (2, 7)

using the equation

d = √{(x₁ - x₂)² + (y₁ - y₂)²}

AB = √{(2 - 6)² + (3 - 3)²} = 4

BC = √{(6 - 2)² + (3 - 7)²} = 5

CA = √{(2 - 2)² + (3 - 7)²} = 4

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The probability that exactly two will be replaced under warrant is 0.1937.

The possibility of an event occurring is determined by the probability formula. The ratio of positive outcomes to the total number of outcomes serves as the basis for calculating an event's probability. The probabilities are always between 0 and 1. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given,

W = Warranty

V = Replaced

P(W) = 20/100

P(W) = 0.20

P(U/W) = 0.40

P(W ∩ U)

= P(U/W) × P(W)

= 0.40 × 0.20

0.-08

P( exactly two will be replaced under warranty)

Using binomial distribution:

= P(X = 2)

= 10/2 (0.0.8)² (0.9)⁸

= 0.1937

The probability that exactly two will be replaced under warrant is 0.1937.

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