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Determine if the table shows a proportional relationship.



Time (hours) 0 7 14 21 28

Pay (dollars) 0 91 182 273 364






Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.

Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.

No, it is not proportional because 91 over 7 does not equal 273 over 21.

No, it is not proportional because 273 over 21 does not equal 364 over 28.

The most appropriate choice for set will be given by -

1) Number of students who went to Nashville but not Pittsburg = 5

2) Number of children who like to use markers but not colour pencils = 2

3) Number of students who have been on TV but not in a play =2

What is a set?

Set is a well defined collection of distinct objects. The objects are called elements of the set.

Set can be empty or non empty, finite or infinite.

The number of elements in a set is known as the cardinal number of the set

Here,

1) Number of students went to Nashville = 12

Number of students went to Pittsburg = 10

Number of students went to both cities = 7

Number of students who went to Nashville but not Pittsburg = 12 - 7

                                                                                                     = 5

2) Number of children who like to use markers = 5

Number of children who like to use coloured pencils  = 10

Number of children who like to use both coloured pencils and markers          

                                                                                                           = 3

Number of children who like to use markers but not colour pencils = 5 - 3

                                                                                                                = 2

3) Number of students who like to play = 9

Number of students who like to watch TV = 7

Number of students who both like to play and watch TV = 5

Number of students who have been on TV but not in a play = 7 - 5

                                                                                                    = 2

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Answer: 12 is the answer. Hope this helps Have a good day mark me brainlist

Step-by-step explanation:

4•(5-8)

Calculate the difference

4•(-3)

The absolute value of any number is always positive is always positive.
4•3

Multiply the numbers

=12

The product of the HCF and LCM of 12 ,18,30 can be written as 1080.

The H.C.F.  can be described as the greatest factor  that can be found when expressing given two or more numbers, on the other hand the LCM can be described as the least factor that exist between a two given number.

factors of 12 are: 3, 4, 2, 6, 12.

factors of 18 are: 2, 3 , 6 9 , 18

factors of 30 are ; 2, 3, 6, 5, 10

HCF; The factor that is greatest among the factors of the numbers = 6

To calculate the LCM, we need to find to find the prime factor of the three numbers as:

Prime factor of 12 are ;  2*2*3

Prime factor of 18 are ; 2*3*3

Prime factor of 12 are ; 2*3*5

LCM is now the multiplication of the prime factors which is the highest occurrence of them in either numbers as ; 2*2*3*3*5 =180

From the given numbers we can see that the HCF = 6 and LCM = 180, then if we find the product as (6*180)=1080 which is the number of the product of the lowest common factor as well as the highest common factor.

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We can say that the graph of 4x+5y = 3/7 is a line because it can be represented by the straight line equation.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.

Given equation :   4x+5y = 3/7

The given equation can be written as

5y = -4x + 3/7

y = (-4/5)x + 3/35

This is a form of y = mx + c

It is a the equation of the straight line.

Therefore, we can say that the graph of 4x+5y = 3/7 is a line as it can be represented as the equation of the straight line.

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In the picture, there is graph with a line. The equation of the line is

2x+y-1=0.

Given that,

In the picture, there is graph with a line.

We have to find the equation of the line in the graph.

The equation of a line can be constructed using the slope of the line and a point on the line.

The equation for a line traveling through a point (x₁,y₁) and having a slope of m is given as follows: y-y₁=m(x-x₁)

Additionally, this equation can be resolved and condensed into the equation of a line in its usual form.

Here, we have points (0,1) and (1,-1).

Slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=(-1-1)/(1-0)

m=-2/1

m=-2

We got Slope of the line m=-2

Take point (0,1)

y-1=-2(x-0)

y-1=-2x

2x+y-1=0

Therefore, the equation of the line from the given graph is 2x+y-1=0.

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Answer:

8 Gallons

Step-by-step explanation:

The question is asking you how many gallons it takes to travel 184 miles given that 138 miles took 6 gallons

You first divide 138 by 6 to find the Miles Per Gallon

138 ÷ 6 = 23
This means that each gallon was 23 miles

Now you divide 184 by 23 to find how many gallons it took to drive 184 miles.

184 ÷ 23 = 8
This means that it took 8 Gallons for Josiah to travel 184 Miles

Answer:

3n/10

Step-by-step explanation:

Answer:

Yes! Water is moist.

Step-by-step explanation:

Water is moist because water is a liquid.

From the dictionary:

moisture:

"water or other liquid diffused in a small quantity as vapor, within a solid, or condensed on a surface."

moisture is a type of liquid, and water can be 'diffused in a small quantity as vapor'

So, logically, water is moist.

The bridge is 895.79 feet above the river.

The length of the section of the bridge above the arch is 179.58 feet.

The underside of the bridge is in the shape of an arc.

The height of the bridge is represented by the function,

y = - 0.000475x² + 0.851x

Now, when the height will be maximum, dy/dx = 0

Therefore,

dy/dx = (d/dx)( - 0.000475x² + 0.851x )

dy/dx = - 0.00095x + 0.851 = 0

- 0.00095x + 0.851 = 0

Subtracting 0.851 from each side,

- 0.00095x = - 0.851

Dividing each side of the equation by 0.00095

x = 895.7895 feet ≈ 895.79 feet

Therefore, the maximum height of the bridge is h = 895.79 feet.

The length of the section is represented by x,

y = - 0.000475x² + 0.851x

To obtain the x-intercept, we put y = 0:

- 0.000475x² + 0.851x = 0

x ( - 0.000475x + 0.851) = 0

Therefore,

x = 0 and,

- 0.000475x + 0.851 = 0

- 0.000475x = - 0.851

x = 1791.58 feet

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The area is 28.26 in²

If a caterer needs 21 pounds of pasta and a local store sells 8 pounds of pasta for $12, then the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta, calculated using the unitary method.

As per the question statement, a caterer needs 21 pounds of pasta to cater a wedding, while a local store sells 8 pounds of pasta for $12.

We are required to calculate the total amount which the caterer will have to pay at the store for their 21 pounds of pasta.

To solve this question, first we will need to calculate the price of 1 pound of pasta at the local store, from their rate provided in the question statement, and then multiply the cost of unit pound of pasta with the number of pounds the caterer needs, to obtain our desired answer, that is,

Using the unitary method, we get,

The local store sells 8 pounds of pasta for $12,

Or, it then sells 1 pound of pasta for $(12/8)

Or, the cost of 21 pounds of pasta at this store will $[(12/8) * 21] = $31.5

Hence,  the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta.

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Answer:

Your answer is 1649 miles.

Step-by-step explanation:

[tex]5^{4} + 4^{5} = 1649[/tex]

The solution of the inequality expression given as 12 + 4y < 32 is y < 5

An inequality expression is an expression where both sides of the expression have unequal values and they make use of any of the symbols <, >, <=, >= and !=

The inequality expression is given as

12 + 4y < 32

Subtract 12 from both sides of the inequality

So, we have the following expression

12 - 12 + 4y < 32 - 12

Evaluate the like terms in the above inequality

So, we have the following expression

4y < 20

Divide both sides of the inequality by 4

So, we have the following expression

4y/4 < 20/4

Evaluate the quotient

y < 5

Hence, the solution is y < 5

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10 is a natural number, whole number and an integer.

Natural numbers may be defined as the numbers which include all the positive integers that is non-negative integers, and the numbers will be from 1 to infinity. 10 is a natural number as it lies in the range from 1 to infinity. Whole numbers may be defined as the numbers which include all the positive integers as well as zero. So, the range of whole numbers is from zero to infinity and 10 is a whole number as it lies in this range. Integers may be defined as the collection of positive and negative numbers along with zero but no fractions. 10 lies in this range so 10 is an integer.

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Answer:

x = 10

Step-by-step explanation:

3(3x+10) = 120

Expand: 9x + 30 = 120

Cross sides: 9x = 120-30

Simplify: 9x = 90

Divide : x = 90\9

We have that the angles that are congruent with m<3=20° are the ones that we can see in the image in red

m<3=m<1=m<5=m<7=m<9=m<11=m<14=m<16=20°

Answer:

2a

Step-by-step explanation:

when you have two of the same variable you can combine them. We know that all variables that do not have a coefficient by default have the constant 1 so 1a+1a equals 2a

Answer:

(-x, y) is the correct answer. Drawing a graph may help.

Answer: no clue sonny boi but good luck

Answer:

Jos is 14 years

Step-by-step explanation:

Let Father's age be x

[tex]{ \tt{father = x}} \\ { \tt{jos = x - 33}}[/tex]

- The question says, product of their ages is 658

[tex]{ \tt{x(x - 33) = 658}}[/tex]

- Open the brackets following distributive property;

-

[tex]{ \tt{ {x}^{2} - 33x = 658 }} \\ { \tt{ {x}^{2} - 33x - 658 = 0 }}[/tex]

- Using bulldozer method;

[tex]{ \tt{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ [/tex]

- A general quadratic equation has a format ax² + bx + c = 0

[tex]{ \tt{x = \frac{ - ( - 33) \pm \sqrt{ {( - 33)}^{2} - (4 \times 1 \times - 658)} }{2 \times 1} }} \\ \\ { \tt{x = \frac{33 \pm \sqrt{3721} }{2} }} \\ \\ { \tt{x = \frac{33 \pm61}{2} }} \\ \\ { \tt{x = \frac{33 + 61}{2} \: \: or \: \: \frac{33 - 61}{2} }} \\ \\ { \tt{x = 47 \: \: \: or \: \: \: - 14}}[/tex]

- Father's age = 47 years

- Jos's age = (47 - 33) = 14 years

Answer: Jos is 14 years old

Step-by-step explanation:

Let Jos is x years old

Hence, father is (x+33) years old

[tex]x(x+33)=658\\\\x^2+33x=658\\\\x^2+33x-658=658-658\\\\x^2+33x-658=0\\\\a=1 \ \ \ \ \ b=33\ \ \ \ \ c=-658[/tex]

[tex]\displaystyle\\x=\frac{-bб\sqrt{D^} }{2a} \\\\D=b^2-4ac\\\\D=33^2-4(1)(-658)\\\\D=1089+2632\\\\D=3721\\\\\sqrt{D}=\\\\ \sqrt{3721}=\\\\61\\\\ x=\frac{-33б61}{2(1)}\\\\ x=\frac{-33-61}{2}\\\\x=-47\notin\\\\x=\frac{-33+61}{2} \\x=\frac{28}{2} \\\\x=14[/tex]

Answer:

follow these steps to find your answer

The value of k after eliminating the fraction in 3/5k -5 = 7/10k is 7.

To get the answer follow the given steps below:

3 / 5 k - 5 = 7 / 10 k

Step 1 => 3 (10 k) = 7 (5 k - 5)               by cross multiplying the numerator                  and denominator of both the sides.

Step 2 => 30 k = 35 k - 35                    multiplying 5 inside the brackets with 5k - 5

Step 3 => 35 = 5 k

Step 4 => 5 k = 35

Step 5 => k = 35 / 5                               dividing

           => k = 7

Hence the value of k after eliminating the fraction is 7.

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we have the equation

2x^2-11x=1​

2x^2-11x-1=0

where

a=2

b=-11

c=-1

substitute in the quadratic formula

the solutions are

The table can be given as for 3 hours we have 18 km and for 4 hours we have 24km, founded by using average.

So, we are given that Callan hikes at a rate of 6 km an hour.

In this way, he will hike 18 km in 3 hours.

(Refer to the graph attached below)

Hence, using averages, we know that the table can be given as for 3 hours we have 18 km and for 4 hours we have 24km.

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A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

where m is the slope and y=mx+b

You can also write y =-x+7 as y=-1x +7.

Therefore, the slope is determined by the number before x.

The slope is -1

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The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

The number of letters in DARWIN = 6

The vowels are "A" and "I"

Number of vowels = 2

Number of ways of arranging the two vowels that will be at the beginning and end = 2! = 2 x 1 = 2 ways

There are 4 remaining letters after excluding the vowels

Number of ways of arranging the 4 remaining letters = 4!

Number of ways of arranging the 4 remaining letters = 4 x 3 x 2 x 1

Number of ways of arranging the 4 remaining letters = 24 ways

Therefore, the number of arrangements of the word DARWIN beginning and ending with a vowel = 2 x 24

The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

Answer:

G(0) = 5

Step-by-step explanation:

substitute x = 0 into G(x) , then

G(0) = - 3(0) + 5 = 0 + 5 = 5