Which decimal is equivalent to \
{31}{9}
9
31
​
start fraction, 31, divided by, 9, end fraction?

The equation of the trend line in the scatter plot is y = - 4x + 24

What is the slope-intercept form?

Writing the equation of a line in the slope-intercept form simply makes the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) obvious.

Here, we have

The yellow points are located at points (6, 0) and (4, 8)

For a linear equation that passes through the points (x₁, y₁) and (x₂, y₂), the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

Then, for the equation, the slope is

s = (8-0)/(4-6) = -4

Then the linear equation become

y = -4x + b

where b is the y-axis intercept.

To find b, we use that when x = 6, y = 0

0 = 6×(-4) + b

b = 24

Then equation become y = - 4x + 24

Hence, the equation of the trend line in the scatter plot is y = - 4x + 24

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Let's solve your system by substitution.

4x−4y=8 and 5x−3y=18

Step: Solve 4x−4y=8 for x:

4x − 4y = 8

4x − 4y + 4y = 8 + 4y (Add 4y to both sides)

4x = 4y + 8

[tex]\frac{4x}{4} = \frac{4y + 8}{4}[/tex]

x = y + 2

Step: Substitute y + 2 for x in 5x − 3y = 18:

5x − 3y = 18

5(y+2) − 3y = 18

2y + 10 = 18  (Simplify both sides of the equation)

2y + 10 + (−10) = 18 + (−10)  (Add -10 to both sides)

2y = 8

y = 4

Step: Substitute 4 for y in x = y + 2:

x = y + 2

x=4+2

x=6  (Simplify both sides of the equation)

Answer:

x = 6 and y =4

Answer: based on the information that you gave me, I think the answer is :

A. sex is an explanatory variable; starting salary is the response variable ;area of specialization is a possible confounding variable

hope this helps

Step-by-step explanation:

The probability that their next (third) child will have extra digits is 0.5

Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition. Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition.

A trait is a distinguishing characteristic that a person possesses. Dominant traits are defined as having only one copy of a gene on a chromosome that expresses a specific trait.

Individuals exhibit the dominant traits most prominently. Polydactyly is the dominant condition in this case.

The father has six fingers and six toes, while the mother is in normal condition. In this particular condition, polydactyly is a dominant trait. Twelve percent of the couple's children are expected to have extra digits.

Because the father has the dominant trait and the mother is in normal condition, there is a 50% chance that this deformity will be passed down to children.

The probability that their next child will have extra digits is 0.5

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Answer:yes

Step-by-step explanation:

yes

Answer:

Absolutely correct. you got the answer

The volume in liters a person uses daily is about 90 liters which is equivalent to 23.48 gallons

Information given in the question

everyday a person uses about 90 liters of water at home

6 gallons is about 23 liters

how many liters of water does a person use at home daily = ?

Volume is a three dimensional calculation, the formula depends on the object. how ever the calculation is usually done by area * height or thickness

the unit for volume can liters, gallons, cubic meters, and so on

The question have it that a person uses about 90 liters of water daily converting this quantity in gallon is done by

= 90 liters * 6 gallons / 23 liters

= 90 * 6 / 23

= 23.48 gallons

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The angles of the triangle will be 50°, 70°, 60° .

let the 3 angles of a triangle be A, B and C

The first acute angle A is given by = x + 20

The second acute angle B is given by = 2x + 10

The third acute angle C is given by = 4x - 60

Now we know that the sum of the angles of a triangle is 180°

So ,

A + B + C + = 180°

x + 20 + 2x + 10 +  4x - 60 = 180°

7x - 30 = 180°

7x = 210°

x = 30°

So, from the value of x , we can calculate the value of each angle

Therefore, the required angles are :

angle A = (x + 20)° = 30° + 20° = 50°

angle B = (2x + 10)° = 60° + 10° = 70°

angle C = (4x - 60)° = 120° - 60° = 60°

verification : sum of the angles = 50°  + 70° + 60°  = 180°

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Since the first child is a boy, this means we need to find the probability of another boy. This is 1/2 since we assume each gender has the same chance of happening.

the 4.3 represents The number of apples in 1 pound

The 4.3 in the equation represents the number of apples in 1 pound

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We are given equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds of apples.

Here we can see that y = 4.3x

4.3 = y/x

then we can say that 4.3 is slope of striaght line in term os linear equation.

4.3 in the equation represents the number of apples y, in dollars, of x pounds.

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Answer: 4,375 rs

Step-by-step explanation:

25% × 17,500 = 4,375

Answer:

$4375

Step-by-step explanation:

25 percent *17500 =

(25:100)*17500 =

(25*17500):100 =

437500:100 = 4375

Now we have: 25 percent of 17500 = 4375

Answer:

9(x+4)= 6

Step-by-step explanation:

I could be wrong but im not sure

The sales tax is $2 and the total cost of the item is $42.

Given:

selling price = $40

rate of sales tax = 5%

sales tax = 40*5%

= 40*5 / 100

= 200/100

= $2

Total cost = 40+2

= $42.

Therefore the sales tax is $2 and the total cost of the item is $42.

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Answer:

it is basic and .........

Using the Law of Cosines, the value of x is 40.9°.

Cosine formula, cos A [tex]=\frac{b^{2}+c^{2}-a^{2} }{2bc}[/tex].

Here, A = x

          a = 16

          b = 15

          c = 24

cos x [tex]=\frac{15^{2}+24^{2}-16^{2}}{2*15*24}[/tex]

         [tex]=\frac{225+576-256}{720}[/tex]

         [tex]=\frac{801-256}{720}[/tex]

         [tex]=\frac{545}{720}[/tex]

         = 0.756

x [tex]= cos^{-1}0.756[/tex]

 = 40.9

Hence, value of x is 40.9°.

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The  GCF of 140 and 180 in the question can be expressed as 20.

The concept that will be used in the calculation is the concept of the Prime factorization.

Prime factorization  can be described as the way that can be used to find the prime factors of a number , making sure that the  original number is evenly divisible by these factors.

Prime factorization of 140 and 180 are:

40: (2 × 2 × 5 × 7)

180: (2 × 2 × 3 × 3 × 5)

Then the  common prime factors which are common  that can be associated with 140 and 180 which is the GCF of 140 and 180 is ( 2 × 2 × 5 )= 20.

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a. Constant of proportionality is equal to 5.

b. Point (12, 60) represents that 12 pounds of sugar required to make 60 cups of coffee.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that varies over time is represented with a line graph.

Given:

We have the relation between total number of cups of coffee and the total amount of sugar:

Let y represents the number of cups of coffee

and, x represents the amount of sugar

y ∝ x

y = kx

a. 'k' is the constant of proportionality

When  y = 20 , x = 4

20 = k × 4

k = 20/ 4

k = 5

b. From the graph point (12, 60) represents 12 is on the x-axis and y is on the y-axis.

12 represents amount of sugar and 60 represents the number of cups of coffee.

Hence, the Constant of proportionality is equal to 5.

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Asymptote indicates that as time increases, the number of bacteria approaches 0.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.

There were about 15,000 bacteria prior to the treatment.

The line y = 0 is an asymptote of the graph.

The y-intercept is 15,000.

The y-intercept represents the number of bacteria when treatment began.

The asymptote indicates that as time increases, the number of bacteria approaches 0.

Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.

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Answer:

Step-by-step explanation:

Total number of candidates is:

Probability of a girl to be chosen as prefect:

Answer:

Probability = 15/23

Step-by-step explanation:

Now we have to,

→ find probability that prefect is a girl.

The total members are,

→ 15 girls + 8 boys

→ s = 15 + 8

→ [ s = 23 ]

Then the probability will be,

→ P = 15/s

→ [ P = 15/23 ]

Hence, the answer is 15/23.

From the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :

y = x + 5.5

With the constraints x and y where,

 x is any real number ≥ 0,

 y is any real number ≥ 5.5

As given in the question,

Number of cups of wheat flour used by Otto  = 5.5.cups

Number of cups of white flour used by Otto = x cups

Let y represent the total amount of flour used by Otto in the recipe

Required equation  to represent the total amount of flour used by Otto in the recipe is given by :

y = x + 5.5

Where x is any real number which is greater than or equal to 0.

As cups of flour can be in fractions.

And y is any real number which is greater than or equal to 5.5.

As y = x + 5.5, and x ≥0 and cups of flour can be in fractions.

Therefore, from the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :

y = x + 5.5

With the constraints x and y where,

 x is any real number ≥ 0,

 y is any real number ≥ 5.5

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The common difference of the arithmetic sequence -13, -22, -31, is -9.

An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.

To find a specific term in an arithmetic sequence, we use the nth term formula. Step 1: An = a + (n - 1)d gives the nth term of an arithmetic sequence.

Some arithmetic sequence examples using this expression are:

1, 5, 9, 13, 17, 21, 25, 29, 33, ...

2, 4, 6, 8, 10, 12, 14, 16, 18,...

In this case, the difference will be:

= 2nd term - 1st term

= -22 - (-13)

= -22 + 13

= -9

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Student 1 expression is correct 1/4(10 x+8) = -(1/2 x +13)+3(x +5)

Algebra is defined as a generalization of arithmetic in which numbers are represented by letters that are combined according to arithmetic rules. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are some of the sub-branches.

Given that 1/4(10 x+8) and -(1/2 x +13)+3(x +5)

Student 1: 1/4(10 x+8) = -(1/2 x +13)+3(x +5)

Student 2: 1/4(10 x+8) > -(1/2 x +13)+3(x +5)

Student 3: 1/4(10 x+8) < -(1/2 x +13)+3(x +5)

We have to find which student is correct for all values of x

Let us take x =1

Now substitute the x vale in student 1 expression

1/4(10 x+8) = -(1/2 x +13)+3(x +5)

1/4(10 (1)+8) = -(1/2 (1)+13)+3(1 +5)

1/4(18) = (-1/2 -13)+3(6)

18/4 = -1/2 -13 + 18

9/2 = -1/2 + 5

9/2 = (-1+10)/2

9/2 =9/2

So Student 1 expression satisfies

If student 1 expression is correct two are wrong

Therefore Student 1 expression is correct

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The Submarine is 7.74 Km away from its base .

In the question ,

it is given that ,

the distance travelled by Submarine from base in East direction = 4.2 Km

let the distance from base to east direction be denoted by AB ,

that means AB = 4.2 Km

the distance travelled by Submarine from East to North direction = 6.5 Km

let the distance from east to north direction be denoted by BC .

that means BC = 6.5 Km

the given situation form a right triangle ,

So , the distance from submarine to its base is the hypotnuse of the right triangle , that is AC .

So By Pythagoras Theorem ,

AC² = AB² + BC²

Substituting the values , we get

AC² = 4.2² + 6.5²

AC² = 17.64 + 42.25

AC² = 59.89

AC = √59.89

AC = 7.7388

AC = 7.74

Therefore ,  The Submarine is 7.74 Km away from its base .

The given question is incomplete , the complete question is

A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?

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Answer:2

Step-by-step explanation:i did it

Answer:

3.7miles

Step-by-step explanation:

divide the length value by 1.6

Answer:

25%

Step-by-step explanation: