Find the slope of the following graph

There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30

It is given that,

Total number of students = 10

Number of boys = 6

Number of girls = 4

Total number of ways to select 3 students from 10 students.

10C3= 10!/ 3!7!= 120

Total number of ways to select 3 students from 4 girls

4C3 = 4!/ 3!=4

The probability that everyone in the group is a girls is

P = 4/120

  = 1/30

Hence ,  the probability that everyone in the group is a girl is 1/30

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Answer:

Each pineapple costs £0.70.

Step-by-step explanation:

Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.

Helen's total cost would be:  P*C = total cost.

The total cost is the difference between £5 and £3.60, which is  £1.40.

We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:

P*C = total cost

2*C = £1.40

C = £0.70

The percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

For the given question.

The statement defining the percentage is ;

28 is 35% of 80.

This can be written as;

35% of 80 = 28

Solve percentage.

35×80/100 = 28

35/100 = 28/80

Or,

28/80 = 35/100

This is the form

a/b = p/100

a = 28

b = 80

p = 35

Thus, the percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

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A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

We need to identify the properties of the given figure in order to answer why one figure can not be the other one:

A rhombus has all sides equal as well as parallel but all angles might not be right angles.

A square has all four sides equal and has 4 right angles.

A rectangle has equal opposite sides and 4 right angles.

A parallelogram has opposite parallel sides.

Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

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Answer:

On the attached graph

Step-by-step explanation:

See attached graph

The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

2x + 8y = -3

3x + 6y = -4

We can multiply the top by 3 and the bottom by -2 which will result in:

6x + 24y = -9

-6x - 12y = 8

They are then added to each other to give:

6x - 6x + 24y - 12y = -9+8

12y = -1

y = -1/12

From this we can notice that the variable x was eliminated which is why option B is the correct choice.

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1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD

1b) The additional information required using ASA Congruency postulate  is BC ≅ QR

2a) The symbolic form of the congruent triangles is written as;

ΔABC ≅ ΔADC

2b) The congruence Postulate that is used is SAS Congruency postulate.

1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;

∠AOB ≅ ∠BOD

1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;

∠Q = ∠B

∠R = ∠C.

Therefore, the additional information is BC ≅ QR

2a) The symbolic form of the given congruent triangles is expressed as;

ΔABC ≅ ΔADC

2b) The congruence postulate that was used here is SAS Congruency postulate.

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Answer:

pick any two points

im going to chose (1,3) and (3,7)

so the equation y2-y1/x2-x1

1 = x1

3=y1

3=x2

7=y2

so 7-3/3-1 is 4/2

which is 2

The graph of the function [tex]y+3=\frac{5}{2}(x - 5)[/tex] is attached below.

What is graph of the function?

In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Consider the given function, [tex]y+3=\frac{5}{2}(x - 5)[/tex]

It is in the form [tex]y-y_1=m(x-x_1)[/tex]

Where,  [tex](x_1, y_1)[/tex]is the point and m is the slope.

Graph passes through the point [tex](x_1, y_1)[/tex] and having slope m.

Here, [tex](x_1, y_1) = (5, -3), m = \frac{5}{2}[/tex]

Therefore, graph passes through the point (5, -3) and having slope 5/2.

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Probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.

As given in the question,

From the given table we have,

Total number of girls and boys in the class = 30

Total number of boys in class = 12

Total number of girls in class = 18

As per given Hint: P(A/B) = P(A and B) / P(B)

A is the Junior

B is the girl

Probability as per given condition is:

P(Junior / Girl) = P(Junior and girl) / P(girl)

                       = (3/30) / (18/30)

                       = 3/18

                       = 1/6 ( lowest term of fraction)

Therefore, probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to  1/6.

The complete question is:

Find P(Junior / Girl)         Hint: P(A/B) = P(A and B) / P(B) .

Classroom of Students

                            Boys     Girls

Freshman              4            4         8

Sophomore           5             7         12

Junior                    2             3           5  

Senior                    1            4           5            

                             12           18

Reduce your fraction to lowest terms.

Enter the number that belongs in the green box.

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The values of x and y if the mean and median are equal are:

x = 7

y = 8.

The mean is the total sum of the values in a data set divided by the number of values of the data set.

The median of a data set is the center value when the data distribution is ordered.

Given the ordered data set as, 4, 6, x, y, and 10.

The center value is x. Therefore, the median of the data set is x.

The mean of the data = (4 + 6 + x + y + 10)/5

The mean of the data = (20 + x + y)/5

The mean and the median are equal, therefore:

(20 + x + y)/5 = x

20 + x + y = 5x

20 + y = 5x - x

20 + y = 4x

The value of x cannot be less than 6, if x = 7, we woud have:

20 + y = 4(7)

20 + y = 28

y = 28 - 20

y = 8

The values of x = 7, y = 8.

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Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.

Let  be Mike's bill and   be Joe's bill.

(10/100) *m = 2

M = 20

(20/200 )*j = 2

J = 10

So the desired difference is

m-j = 20 – 10

= 10

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By using a linear equation, it is obtained that

Distance farther Daniel's car travel in 1 gallon of gas than Bo's car =

3 miles

What is linear equation?

At first, it is important to know about equation.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The equation y = 31.5x represents the number of miles, y, that Daniel can drive his car for every x gallons of gas

Distance driven by Daniel in 1 gallon of gas = [tex]31.5 \times 1 = 31.5 \ miles[/tex]

Bo uses 9 gallons of gas to drive 256.5 miles in his car.

Bo uses 1 gallon of gas to drive [tex]\frac{256.5}{9}[/tex] miles in his car.

Bo uses 1 gallon of gas to drive 28.5 miles in his car.

Distance farther Daniel's car travel in 1 gallon of gas than Bo's car =

31.5 - 28.5 = 3 miles

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Complete Question

The complete question has been attached here.

The formula for w in terms of p and l is w = (p - 2l)/2

Numbers, symbols and operators grouped together that show the value of something.

Given that, an expression p = 2l + 2w

Solving for w, we get,

w = (p - 2l)/2

Hence, The formula for w in terms of p and l is w = (p - 2l)/2

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Answer:

x=6

Step-by-step explanation:

x-8=-2

x=-2+8

x=6

Answer:

x = 6

Step-by-step explanation:

x - 8 = -2

x - 8 + 8 = -2 + 8

x + 0 = 6

x = 6

Check:

6 - 8 = -2

Let the lemonade and fruit be Mixed in x ratio.

[tex]\therefore[/tex] Total mixture of fruit punch [tex]= 1\times x \ + \ 3\times x = 4x[/tex]

She needs to make 35 liters of punch.

Requirement of ingredients :

Fruit juice to be added [tex]= \frac{x}{4x} \times 35 = 8.75[/tex] liters of fruit juice

If 8.75 liters of fruit juice is to be added,

then,

lemonade required[tex]=35\ litres - 8.75\ litres = 26.25\ litres .[/tex]

Now ,

According to question she wants to make more fruit punch,

so , given that she had 2 liters of fruit juice.

Here ,

⇒x become 2.

⇒Lemonade required =[tex]2\times x[/tex]

⇒Lemonade required = [tex]2\times3 = 6\ liters[/tex]

There total fruit punch =  [tex]6 + 3=9\ liters[/tex]

[tex]\therefore\\[/tex] ratio of fruit juice to lemonade in the second batch = 6:9 = 2:3.

What is ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

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The length of side GF from the similar triangles shown is GF = √10 units

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.

In a similar triangle, DE = GF, Hence:

GF/DF = GH/DE

GF / 5 = 2 / GF

GF² = 10

GF = √10

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Answer:

x = 53°

Step-by-step explanation:

Forming the equation,

→ x + (2x + 21°) = 180°

Now the value of x will be,

→ x + (2x + 21°) = 180°

→ 3x = 180° - 21°

→ x = 159°/3

→ [ x = 53° ]

Hence, the value of x is 53°.

Answer:

9x3

Step-by-step explanation:

x+9

/4

9x=8

x=2

+2=4

x=1+4234

Answer:

Step-by-step explanation:

Put the value of a in equation 2. b² = 6² + a². b² = 36 + (81 / 4 ). b = √(225 / 4). b = 15 / 2. Therefore, the value of a and b will be 9.

Answer:

(2x)-8 is the correct answer

Step-by-step explanation:

Hope this helps

The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48

An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.

Words can be expressed algebraically.

The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48

Let the number be x.

Five-halves of x is: 5/2x

So the difference between  and 17 is:

5/2x - 17 = 48 or 17 - 5/2x = 48

Combine both expressions

[tex]| 17 - \frac{5}{2}x|[/tex] = 48

Hence, the required expression is:  [tex]| 17 - \frac{5}{2}x|[/tex] = 48

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We deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x). The best choice is C.

A diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

Right-shift a function

Inside the function's argument, subtract. For instance, is essentially moved b units to the right.

You go to the right while subtracting from the parameter of the function.

Accordingly, f(x) is moved two units to the right in g(x) = f(x - 2).

also to advance a function

Outside of the function, add. For instance, is essentially shifted up units.

G(x) = f(x - 2) + 3 hence says that f(x) is shifted up by 3 units.

Overall, then, using two transformations, we deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit upswing in the graph of g(x).

Therefore, choice C is right.

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The inequality represented by the graph is y ≥ -x + 2

A graph is a pictorial representation of data and the graph presented represents inequality data

The graph shows a linear function written in the form

y = mx +c

where slope, m calculated as

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (0. 2)  (1, 1)

m = (y₂ -y₁) / (x₂ - x₁)

substituting the values

= ( 2 - 1 ) / ( 0 - 1 )

= 1 / -1

= -1

y intercept, c this is a point where the graph cuts the y axis

c = 2

The two points result greater than or equal to written with the symbol ≥

hence the equation is

y ≥ -x + 2

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Step-by-step explanation:

[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]

The fractions of sixth graders that reached their goal after each day are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

In which the technical terms related to x and y are as follows:

The fraction can be represented by bars, in which:

As shown by the image at the end of the answer, the fractions are given as follows:

The image is given at the end of the answer.

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Answer:

A

Step-by-step explanation:

It is perpendicular because it forms a right angle with the second line

Using the principle of proportional relationship, the total recommended daily amount of fiber is  34.4 grams

Let x be the recommended daily amount ( in grams ) of the fiber,

So, 32% of x = [tex]\frac{32}{100}x[/tex] = 0.32x

According to the question,

11 grams is 32% of the recommended daily amount of fiber,

That is, 0.32x = 11

x = 11/0.32 = 34.4 grams

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Answer:

- (4x+1) (x-9)

Step-by-step explanation:

-4x^2+35x+9

Factor out the 1:

-(4x^2-35x-9)

Factor:

-(4x+1)(x-9)

The table showing the possible value of S and their possibilities is attached below,

The probability that a player moves their counter forward more than 2 spaces is 0.5.

The Probability is the ratio of favorable outcomes to total number of outcomes. The probability of an event must be less than 1 as the sum of all probabilities of events is equal to 1.

Here, If the number on the dice is even, S is half that number; if it is not even, S is double that amount. The table showing the possible value of S and their possibilities is attached below,

Now, finding the probability that a player moves their counter forward more than 2 spaces,

As seen from the table, the number of favorable outcomes where the player moves the counter more than 2 spaces is 3.

The total number of outcomes is 6. so, the probability will be,

Probability [tex]=\frac{3}{6}[/tex]

[tex]=\frac{1}{2} \\\\=0.5[/tex]

Hence, the probability that a player moves their counter forward more than 2 spaces is 0.5.

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