Antonio's dad bought gas for their family's ATV two weeks in a row. Last week, he bought 12 gallons for $35.40. This week, he bought 9 gallons for $25.83. How much more did Antonio's dad pay per gallon last week?
$
per gallon

The domain of the given function is {2, 29, 44, 54} and the range is {-7, 2, 4}.

The domain of a function represents the set of input values to the function and the range of a function represents the set of output values for the domain of the function.

Domain - {x coordinates of the points in a function}

Range - {y coordinates of the point in a function}

The given function is

f = {(2, 4), (29, -7), (44, 4), (54, 2)}

So, the x coordinates of the function are formulated in a set as {2, 29, 44, 54} and the y coordinates are {-7, 2, 4}

Where output 4 is repeated.

Then, the domain of the function is given by the set {2, 29, 44, 54} and the range of the function is given by the set {-7, 2, 4}.

The mapping of the given function is shown in the figure below.

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Therefore, the perimeter of the irregular shape is 34cm .

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. The outermost border of an ellipse or circle is its circumference.

Here,

The perimeter of the irregular shape is

Given:

9 cm is the length of the below line and 4cm , 3cm and x is the length of the above line .

So x value is => 9 = 4 + 3+x

=> 9-7 = x

=>x= 2cm

and

thus we get all the length of the irregular shape

so adding =>

=> 4+2+3+2+3+6+5+9=  34 cm

Therefore, the perimeter of the irregular shape is 34cm .

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The number of elements of set (XUY) = 8

A set is simply an organized collection of distinct objects forming a group and can be expressed in set-builder form or roaster form.

Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). .

Means write all the elements in X and Y, then

X = {x|x is a whole number less than 10}

Means write the common elements in X and Y

Y= {-3, -2, 1, 3, 5, 7, 20).

Since there are no common elements in X and Y, then

(XUY) is null set.

The number of elements in (XUY)  is 4 + 4 = 8 elements

Then (XUY) = 8

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Answer: 0.159

Step-by-step explanation:

0.159

The value of a percentage between 11% and 17% is,

⇒ 0.14

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

To find value of a percentage between 11% and 17%.

Now, We can formulate;

The value of a percentage between 11% and 17% is,

⇒ (11% + 17%) /2

⇒ 28% / 2

⇒ 14%

⇒ 0.14

Thus, The value of a percentage between 11% and 17% is,

⇒ 0.14

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Answer:

Step-by-step explanation:

E(x) = 791*0.97 - 23600*0.03 = 59.27. The answer is positive so they will make a profit of $59.27 for each policy sold.

However the correct answer is $83. By trial and error.

Answer: 7,176 inches

Step-by-step explanation:

Areas equation is Length times width so applying that we have 78 times 92 giving you the answer of 7,176

The area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in²,  16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given

A company makes different-sized shoeboxes in the shape of rectangular prisms.

We have to match the area of the material needed to make each box to the box’s dimensions.

S₁ = 12in× 5in× 6in

S₁ = (12×5+12×6+6×6)×2

S₁ = 162×2

S₁ = 324in²

S₂ = 10in× 6in ×6in

S₂ = (10×6+10×6+6×6)×2

S₂ = 156×2

S₂ = 312in²

S₃ = 16in× 6in× 4in

S₃  = (16×6+16×4+6×4)×2

S₃  = 184×2

S₃  = 368in²

S₄ = 14in× 5in× 5in

S₄ = (14×5×2+5×5)×2

S₄ = 165×2

S₄ = 330in²

Hence, the area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in²,  16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².

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Answer:

x=45

Step-by-step explanation:

89+112+114+x=360(Sum of angles of a quadrilateral)

315+x=360

x=360-315

x=45

Hope this helps u

When the rule reads, "Add 12, Subtract 3," and the pattern begins at 41, the sixth number in the pattern is 71.

A pattern is defined in mathematics as a sequence of repeated objects, forms, or numbers. A pattern can be associated with any form of event or object. A pattern has a rule that informs us which items belong to the pattern and which objects do not. Patterns are items that repeat logically, such as vertical stripes on a shirt. They can take the form of numbers, pictures, or forms. A pattern constructed of plastic animals, for example, can alternate between two and four legged creatures, or animals that swim and animals that fly.

Here,

pattern begin at 41,

=41+12

=53

=53-3

=50

=50+12

=62

=62-3

=59

=59+12

=71

The 6th number in the pattern is 71 when the rule says, "Add 12, Subtract 3." and pattern start at 41.

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How to solve a system of equations by elimination.

How to solve a system of equations by Substitution.

Let us take an example :

y = 3x - 4

2y = -x + 6

Order of Operations: BPEMDAS

Step 1: Define Systems

y = 3x - 4

2y = -x + 6

Step 2: Solve for x

Substitution

Step 3: Solve for y

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Answer:

Step-by-step explanation:

f x = (4x/9)

so it will be x into 4x = 9/f

so 4x square = 9/f

a) The graph is drawn and attached below by using graphing calculator:

b) The equation of the curve of best fit is y=0.75x

c) The horizontal distance of the ball travelled with this hit is 58.33

d)  It does not touch the hall land on the green.

A relation is shown graphically in a function graph. In set theory and modern mathematics, a function is truly equivalent to its graph. For instance, a codomain should be considered while determining whether or not a function is onto (surjective). A function's graph by itself does not show the codomain.

a) The graph is drawn and attached below by using graphing calculator:

b) The equation of the line of best fit is:

Consider any points from the table,

(0,0) and(30,22.5)

y=mx+c

(0,0)  -----> 0=0+c

c=0

(30, 22.5)

m=0.75

y= (0.75)x

c) The horizontal distance of the ball travelled with this hit is 58.33

d) For 10m ------>5.8m

For 20m ------->x

x=11.6m

For 120m it will be near to the ground,

16.7-11.6

=5.1m

It does not touch the hall land on the green.

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After solving the equation the required solution is ∠DHG = ∠EHG

What is angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given, ∠1 = ∠3

now,

       ∠DHF = ∠1 + ∠2

and, ∠EHG = ∠3 + ∠2

         ∠EHG = ∠1 + ∠2 (As ∠1 = ∠3)

Hence, ∠DHG = ∠EHG

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Answer:

f (-4) = -5

Step-by-step explanation:

Look at the graph and see the y coordinates when x = -4.

Here, when x = -4, y = -5.

C have dimension of [tex]\frac{L}{T^2}[/tex] in the given equation.

The term "dimension" refers to the power to which the fundamental quantities are magnified in order to express a physical quantity. The letters [M], [L], and [T] stand for mass, length, and time, respectively.

given the equation is:

x = [tex]\frac{1}{2}Ct^2[/tex]

and given that x represents distance and t represents time

as we know Dimension of x id L and dimension of time is T

and according to dimensional analysis dimesion of Left side must be equal to dimension to Right side.

let [x] denote dimension of x

so [x] = [C] [[tex]t^2[/tex]]

as [x] = L and [[tex]t^2[/tex]] = [tex]T^2[/tex]

L = [C] *  [tex]T^2[/tex]

so [C]  = [tex]\frac{L}{T^2}[/tex]

so dimenstion of C is  [tex]\frac{L}{T^2}[/tex]

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18 inches is not a possible length for the thrid side of a triangle.

A triangle is a polygon with the 3edges and 3 vertices. It  is 1 of the basic shaped on geometry. A triangle with vertices A, B, and C is denoted ∆ ABC. In Euclidean geometry, any 3 points, when non-colli early, determined a uniquely ∆ and simultaneously, to unique plane.

As we know in a ∆ if the measurement of two sides are given than the sum of these 2 sides.

Otherwise buliding of a triangle is never possible.

Here two side are 10 and 8 inches.

So, 3rd side of the triangle should be less than

10+8 = 18

Third sides=

2<x<18

Now we have to calculate the range of 3rd sides

2<x<18

Thus,3rd side of the measurement with 18 inches is not possible.

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Answer:

it will be 37.8 cm tall

If John has 4266 cars, then Noah will have 79 cars

We can solve this question in the following way,

We have been given the condition that John owns 54 times more cars than Noah.

That means,

If Noah owns 1 car, John will own 1*54 = 54 cars

Similarly, if Noah owns 2 cars, John will own 2*54 = 108 cars

This will follow the pattern,

when Noah owns n cars, John will own n*54= 54n cars

In the question, we know that John owns 4266 cars,

That means we know that

54 * n= 4266

We have to calculate how many cars Noah owns, which is n

therefore the value of n will be

n= [tex]\frac{4266}{54}[/tex]

n= 79 cars

Therefore Noah will own 79 cars while John will have 4266 cars.

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Answer: y=7

Step-by-step explanation:

Slope intercept form

y=mx+b

m=slope

b= y-intercept

find the slope with the slope formula

y2-y1/x2-x1

7-7/6-(-1)

0/7

the slope is 0, meaning this is a horizontal line.

Find the y-intercept

7=0(-1)+b

b=7

y=7

The percentile rank of a score of 71 on this test will be 33.33% and the score of the 60th percentile will be 84.

Percentile is the amount to measure the rank of a student in respect to the other students.

For example, the 90 percentile score means that there is 10 percent of members higher than you.

As per the given test scores,

The score of 71 from left to is at the 5th number.

Percentile = 5/15 x 100 = 33.33%

If the percentile is 60%.

x/15 = 60/100

x = 9

The 9th from left to is 84

Hence "On this test, a score of 71 will yield a percentile rank of 33.33%, while an outcome of 84 will represent the 60th percentile.".

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Answer:

A.

Step-by-step explanation:

since we are using the absolute value this means the result to be between 0 and 3.

the difference to C. is that the endpoints are not included (empty dots). that is correct, because the inequality uses the "<" sign. being equal to 3 is not valid.

but any real number higher than 2 and lower than 8 will provide a valid solution.

the higher or lower numbers used in B. and D. will not create anything between 0 and 3.

Answer:

A

Step-by-step explanation:

According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

The standard deviation and the mean of the provided data must first be determined.

Below are the standard deviation and mean

Mean = (50 + 46 + 54 + 51 + 29 + 52+ 48 + 54 + 47 + 48)/10

Mean x = 47.9

Standard deviation: √∑(x - x')²/(n - 1)

s = √(50 -  47.9)² + (46 -  47.9)² + (51 -  47.9)² + .....+ (48 -  47.9)²)/(9)

s = 7.20

We possess:

x' ± s = (47.9 ± 7.2)

x' ± s = (40.7, 55.1)

The proportion of values that are within 1 standard deviation of that mean is thus:

9/10 * 100 = 90%.

According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

As a result, the percentage of values seen to be within 1 standard deviation of a mean is significantly larger than the percentage a normal distribution would predict.

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Answer:

c. 3 [tex]\leq[/tex] y [tex]\leq[/tex] 5

Step-by-step explanation:

Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.

Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.  

So, the range of this relation is 3 ≤ y ≤ 5.

Answer:

c

Step-by-step explanation:

the maximum of y is 5 the minimum of y is 3

Answer: y=-5x+6

Step-by-step explanation:

Answer:

[tex]C[/tex]

Step-by-step explanation:

[tex]|2x+2|=10\\\\2x+2=10,2x+2=-10\\\\2x=8,2x+2=-10\\\\x=4,2x=-12\\\\x=4,x=-6[/tex]

Answer:

0.2025 or 20.25%

Step-by-step explanation:

The problem says the probability of ONE person having a Dog is 45%

This is 0.45 in decimal form

But what are the chances TWO random people BOTH have Dogs. The chances would decrease!

To find the probability, you need to multiply the probability of one person by the probability of another person. They both have the same probability of having a Dog.

This looks like:

0.45 (person 1)  × 0.45 (person 2) = 0.2025

The number of times 0.45 is in the equation above is the same number as the people in the problem!

If the ratio of the number of students and adults in the book fair is 4:3, the new ratio when 169 students left the fair is 4:5, then the number of adults in the book fair is 318

Let the number of students be 4x

Let the number of adults be 3x

When 169 students left the fair, number of students left = 4x - 169

According to question,

(4x-169)/3x = 4/5

⇒ 5(4x-169) = 4×3x

⇒ 20x - 845 = 12x

⇒ 20x - 12x = 845

⇒ 8x = 845

⇒ x = 845/8

⇒ x = 105.625

⇒ x = 106

Number of adults = 3x = 3×106 = 318

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Answer:

y = 12.50x + 50

Step-by-step explanation:

The linear equation is y=mx + b

b in this one is 50

And the x  or the slope is 12.50

The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A jumper is at a height of - 18 feet comparative with ocean level. The jumper plunges to an undersea cavern that is 4 times as distant from the surface

The elevation of the cave is given as,

Elevation = - 18 x 4

Elevation = - 72 feet

The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.

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The statistical measures for the data-set are given as follows:

From the stem plot, the observations of the data-set are given as follows:

45, 46, 48, 74, 74, 75, 76, 93, 95.

The mean is given by the sum of all observations divided by the number of observations, hence:

Mean = (45 + 46 + 48 + 74 + 74 + 75 + 76 + 93 + 95)/9 = 69.6

The median is the middle element of the data-set. The data-set has 9 elements, hence the median is the 5th element, which is of 74.

The mode is the element that appears the most times in the data-set, which is also 74.

The first quartile is the median of the first half of the distribution, which is  the median of the first four elements, hence:

Q1 = (46 + 48)/2 = 47.

The third quartile is the median of the last four elements, hence:

Q3 = (76 + 93)/2 = 84.5.

Then the midrange is given as the difference of the quartiles, as follows:

IQR = Q3 - Q1 = 84.5 - 47 = 37.5.

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