Find the greatest common factor of the two numbers.
12,39

The probability that George will win is 1/10 and the probability that Julia will win is 1/20.

So, calculate the probability as follows:

We know,

(A) George's probability of winning:

(B) Julia's probability of winning:

Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.

Know more about probability here:

https://brainly.com/question/28924396

#SPJ13

Answer:

Multiply and divide by √2 . You'll get √22

Step-by-step explanation:

The expression (2/3)² when simplified by repeated multiplication is 4/9

From the question. the expression is given as

(2/3)²

We start by rewriting the expression using repeated multiplication

This in other words means that:

We rewrite the (2/3)² as repeated multiplication

To do this, we apply the exponent rule of indices

This rule states that:

a^m = a * a * a .... in m places

So, we have

(2/3)² = (2/3) x (2/3)

Evaluate the products

(2/3)² = 4/9

Hence, the equivalent expression is 4/9

Read more about repeated products at

brainly.com/question/28771184

#SPJ1

The required expression is 3h(150) + h(270) which is the correct answer would be an option (D).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Since each house will have 3 smaller bedrooms that required 150 square feet of carpet

⇒ 3 × 150

Each house will have 1 larger bedroom that requires 270 square feet of carpet.

⇒ 270

So, (3 × 150 + 270) × h

⇒ 3h(150) + h(270)

Thus, The required expression is 3h(150) + h(270).

Hence, the correct answer would be an option (D).

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

The question seems to be incomplete the completed part has been attached below

Answer:

depends on how many sections there are

Step-by-step explanation:

if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.

The given points gives us a line with constant slope of -2.

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

The points are in the form of ( x, y) , where y= g(x)

Plot these points on the graph and join the points through a line.

Refer to the attachment for the graph.

The slope is constant.

consider any 2 points:

(x,y) = (0,7)

(m,n) =(2,3)

Slope = change in y values/ change in x values

         = (7-3)/(0-2) = 4/-2 = -2

The given points gives us a line with constant slope of -2.

To learn more about the coordinates from the given link

https://brainly.com/question/17206319

#SPJ1

[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]

[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]

[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]

Answer:

Step-by-step explanation:

The speed of the aircraft is 682 mph

Given that: A speed of 60 mph is equal to 88 ft/sec

If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit  ratio of

of mph to ft/s, that is:

60/88 = m/1000

m = 6x1000/ 88 = 60000/88 = 682 mph

Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph

Learn more about speed on:

https://brainly.com/question/2681210

#SPJ1

Answer:

2

Step-by-step explanation:

This is because yes. If you add 1 and 1 (use your fingers) and count the two, you simply get 2.

The amount of profit made by JMP is 102000.

Given,

In the question;

JMP made a profit of $85,000 last year.

If the profit margin increased by 20% this year.

To find the amount of profit made by JMP.

Now, According to the question:

Based on the given condition:

Formulate:

= 85000 x (20% + 1)

Calculate;

85000 x (0.2 + 1)

Calculate the sum or difference

85000 x 1.2

= 102000

Hence, The amount of profit made by JMP is 102000.

Learn more about Profit at:

https://brainly.com/question/15522319

#SPJ1

The solution to the equation given as 2x + 4y = 6x − y has the ordered pair of (3, 4)

From the question, we have the following equation that can be used in our computation:

2x+4y=6x−y

Solving further, we need to collect the like terms

So, the equation becomes

2x - 6x = -4y - y

Next, we evaluate the like terms in the above equation

So, we have the following representation

-4x = -3y

Divide both sides by -3

The equation becomes

x = 3/4y

At this point, we assume any value for y and then solve for x

Assume that the value of y is 4

So, we have the following representation

x = 3/4 * 4

Evaluate the products

x = 3

So, we have

x = 3 and y = 4

Express as ordered pairs

(x, y) = (3, 4)

Hence, the ordered pair of the solution is (3, 4)

Read more about ordered pair at

https://brainly.com/question/1528681

#SPJ1

Answer:

12 ft, 13 ft , 17 ft

Step-by-step explanation:

let x be the length of the second side , then

one side is x + 1

third side is x + 5

the perimeter P is the sum of the 3 sides, then

P = x + x + 1 + x + 5 ← collect like terms

P = 3x + 6

given P = 42 , then equating gives

3x + 6 = 42 ( subtract 6 from both sides )

3x = 36 ( divide both sides by 3 )

x = 12

x + 1 = 12 + 1 = 13

x + 5 = 12 + 5 = 17

the 3 sides are 12 ft, 13 ft , 17 ft

The equation of the line perpendicular to the given line is, y = 3x + 1.

What is slope of the line?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

Consider, the given equation of line

[tex]y = -\frac{1}{3}x+4[/tex]

We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.

Here, the point is (-2, 5).

First to find the slope of the line.

Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.

Here, the slope of given line is, -1/3.

So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]

Therefore, the slope of the line is 3.

Now to find the equation of the line.

Consider, the point - slope form of the line

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

Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]

⇒

[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]

Hence, the equation of line in slope - intercept form, is y = 3x + 1.

To know more about slope of the line, click on the link

https://brainly.com/question/27212023

#SPJ1

The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The given point K(-2,-5)

If we reflect a point(x,y) along the y-axis then the coordinate after reflection converts as K'(-x,y)

The reflection of K(-2,-5) along the y-axis will be  K'(2,5).

Hence "The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5)".

For more about coordinates,

brainly.com/question/7869125

#SPJ1

The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.

Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.

Given,

Ellipse given,

x²+ xy + y ² = 7

Differentiating:

dy/dx

x²+ xy + y² = 7

d/dx(x² + xy + y²) = d/dx(7)

2x + 1y + x dy/dx + 2y dy/dx = 0

dy/dx = 2x + y/ x + 2y

dy/dx = 0

2x + y = 0

x + 2y = 0

Now, we have 2 equations,

x² + xy + y² = 0

y = -2x

Solving equations by substitution method,

x² + x(-2x) + (-2x)² = 7

x² - 2x² + 4x² = 7

3x² = 7

x = ±√21/3

Using y = -2x

Points are:

( -2√21/3 , √21/3) and (2√21/3 , -√21/3)

±√21/3 = ±1.528

x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}

To learn more about differentiation, visit:

https://brainly.com/question/24898810

#SPJ1

The value of f(2) is 2.

What is graph function?

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.

All y-coordinates of the graph function are an output of the graph function.

All x-coordinates of the graph function are an input of the graph function.

f(2) is an output of the function.

Here find the y-coordinates of the point on the graph when the value of x is 2.

(2,3) is a point on the graph.

Thus f(2) = 3

To learn more about function, click on below link:

https://brainly.com/question/5975436

#SPJ1

Answer: 25.949%

Step-by-step explanation:

Answer:

3x  + 12

Step-by-step explanation:

3(x+1)+9

= 3x  + 3 + 9

= 3x  + 12

The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The computed table is:

x  | y  

-3   8

-1,   2

To complete a table of values, we can plug in the known value of each of the ordered pairs that are represented in a table into the given equation that models the relationship, then find the value of the missing variable.

The equation that represents the relationship between x and y is given as y = -3x - 1.

Find the value y in the ordered pair (-3, y) by substituting x = -3 into y = -3x - 1:

y = -3(-3) - 1 = 8

y = 8

Find the value x in the ordered pair (x, 2) by substituting y = 2 into y = -3x - 1:

2 = -3x - 1

Add 1 to both sides

3 = -3x

Divide both sides by -3

x = 3/-3

x = -1

The ordered pairs with the missing values are: (-3, 8) and (-1, 2).

The table would be computed as:

x  | y  

-3   8

-1,   2

Learn more about equation on:

https://brainly.com/question/18114672

#SPJ1

⇒[tex]3x^{2} -13x-10\\=3x^{2} -15x+2x-10\\=(3x^{2} -15x)+(2x-10)\\=3x(x-5)+2(x-5)\\=(x-5)(3x+2)[/tex]

⇒The answer is  (x-5)(3x+2)

The passage of journal entries to record the transactions, using the perpetual system of inventory with the First-in, First-out (FIFO) method, is as follows:

Account Titles                                 Debit        Credit

Inventory                                     $300,000

Accounts Payable (Indiana International) $300,000

Accounts Receivable

(Ceridian Corporation)            $100,000

Sales Revenue                                           $100,000

Cost of goods sold                   $60,000

Inventory                                                    $60,000

Cash                                       $275,000

Sales Revenue                                        $275,000

Cost of goods sold               $150,000

Inventory                                                 $150,000

Accounts Payable

(Indiana International)       $300,000

Cash                                                       $300,000

Inventory                            $360,000

Cash                                                      $360,000

Cash                                     $60,000

Sales Revenue                                     $60,000

Cost of goods sold            $30,000

Inventory                                              $30,000

Inventory $300,000 Accounts Payable (Indiana International) $300,000

Accounts Receivable (Ceridian Corporation) $100,000 Sales Revenue $100,000

Cost of goods sold $60,000 Inventory $60,000

Cash $275,000 Sales Revenue $275,000

Cost of goods sold $150,000 Inventory $150,000

Accounts Payable (Indiana International) $300,000 Cash $300,000

Inventory $360,000 Cash $360,000

Cash $60,000 Sales Revenue $60,000

Cost of goods sold $30,000 Inventory $30,000

Thus, with the perpetual system using FIFO, inventory movements are recorded in the Inventory account as they occur and not at the period's end.

Learn more about journalizing transactions at https://brainly.com/question/17201601

#SPJ1

The solution to the given inequality 3 - x ≤ 19

or - x ≥ 24 is x ≥ -16 or x ≤ -24

An inequality is a statement that is of two quantities; one is specifically less than or greater than another. Inequality symbols are:

3 - x ≤ 19

or

- x ≥ 24

3 - x ≤ 19

-x ≤ 19 - 3

- x ≤ 16

divide both sides by -1

x ≤ 16/-1

x ≥ -16

or

- x ≥ 24

x ≥ 24/-1

x ≤ -24

In conclusion, the solution to the inequality is given by x ≥ -16 or x ≤ -24

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

Answer:

A,C,D

Step-by-step explanation: