Use the function below to find F(3).

Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for each course, the parameters are given as follows:

[tex]n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3[/tex].

Hence the number of ways is given by:

N = 5 x 4 x 4 x 3 = 240.

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Answer:

194.935

Step-by-step explanation:

149.95×30%=44.985

149.95+44.985=194.935 new price

The region in the w-plane into which a rectangular region bounded by the lines x=0, y=0, x=1, y=2 in the z-plane is mapped under the transformation w = (1- i)z + (2 - i)  is mathematically given as

(u, v)=(2,1)

(v, v)=(3,0)

(u, u)=(3,2)

(v, u)=(2,2)

Generally, the equation for is mathematically given as

[tex]&\quad(1-i) 2+(2+i) \\\\&(1-i)(x+y i)+2+i \\\\\&x-x i+y i-1 y+2+i \\\\\&(-x+y+1) i+(x+2) \\\\\[/tex]

Given - that

[tex]&x=0 \\\\&y=0 \\\\\&x=1 \\\\\&y=2 \\\\\&(0,0): v=(-0+0+1): u(0+1) \Rightarrow(u, v)=(2,1) \\\\\&(1,0): v=(-1+0+1): u(1+2) \Rightarrow(v, v)=(3,0) \\\\&(1,2): v=(-1+2+1): u(1+2) \Rightarrow C u, u)=(3,2) \\\\&(0,2): v=(-0+2+1): u(0+2) \Rightarrow(v, u)=(2,2)\\\[/tex]

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Answer:

(c - 2d) (3a - 2b)

Step-by-step explanation:

if you need the steps just ask me in the comments and I’ll type them lol

Answer:

445788

Step-by-step explanation:

OMG too difficult man!!

Thanks to my calculator to solve this hard question

Answer: 16

Step-by-step explanation: 112 is equal to the product of 7 and Raj's score. Therefore, Raj's score score is 112 divided by 7 which is 16.

Answer:

Raj´s score = 16

Step-by-step explanation:

112 = 7R

R = Raj´s score

112/7 = R

R = 16

The expression that can be used to find the area of the tiled floor is 4w² + 200w

Length = 70 Meters

Width = 30 meters

Area = length × width

= 70 × 30

= 2100

Length = 70 + 2w meters

Width = 30 + 2w meters

Area = length × width

= (70+2w) (30+2w)

= 2100 + 140w + 60w + 4w²

= 4w² + 200w + 2100

Area of the tiled floor = Area of new rectangle - area of old rectangle

= (4w² + 200w + 2100) - 2100

= 4w² + 200w + 2100 - 2100

= 4w² + 200w

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Answer:

the answer is A

Step-by-step explanation:

the starting point which is the addition part is 4 dollars for entrance and 3 stands for the price per pound and x is the amount of pounds

Susan investment = $6000

John investement = $4000

Pria investment = $12000

investment proportion of Susan, John and Pria = 6:4:12= 3:2:6

Hence, Pria share in profit = (6/11)*$12000

                                            = $ 6,545.454

Answer:

Pria receives $4941.18 of the profits.

Step-by-step explanation:

• Susan invested $6,000,

• John invested $4000,

• Pria invested $7000.

The ratio of their investments Susan : John : Pria is 6000 : 4000 : 7000 ,

⇒ 6 : 4 : 7

This means that Pria should receive 7/17 th of the total profits.

∴ Pria receives = [tex]\frac{7}{17}[/tex] × $12,000

                         = $4941.18

Answer:

68

Step-by-step explanation:

I did it and it was right

The system of equation that will represent her situation is as follows:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

At store A she will pay a total sum of $50.73 for bread and milk.

At store B she will pay a total sum of $51.63  for bread and milk.

Therefore, the system of equation that will represent her situation is as follows:

where

Therefore,

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

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B and C are the letters from the table which have like terms which is denoted as option B.

This is referred to a type of polynomial which has two terms and is the sum or difference of a monomial.

From the table we can deduce the following:

B and C have a degree of 1 which means they are like terms thereby making them the most appropriate choice.

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Answer:

option 2 is correct

Step-by-step explanation:

The simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

The function is given as:

[tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex]

Expand 108

[tex]f(x) = \frac 14(\sqrt[3]{27 * 4})^x[/tex]

Take the cube root of 27

[tex]f(x) = \frac 14 * 3^x(\sqrt[3]{4})^x[/tex]

Evaluate the product

[tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

Hence, the simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]

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[tex] \frac{2}{5} \: \: and \: \: \frac{3}{2} [/tex]

L.C.M. of 5 and 2 = 10

[tex] \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \\ \\ \frac{3 \times 5}{2 \times 5} = \frac{15}{10} [/tex]

[tex] \frac{5}{10} , \frac{6}{10} , \frac{7}{10} , \frac{8}{10} , \frac{9}{10}, \frac{10}{10} , \frac{11}{10} , \frac{12}{10} , \frac{13}{10} , \frac{14}{10} [/tex]

The 10 rationals numbers are :

[tex] \frac{1}{2} , \frac{3}{5} , \frac{7}{10} , \frac{4}{5} , \frac{9}{10} , \frac{1}{1}, \frac{11}{10} , \frac{6}{5} , \frac{13}{10} , \frac{7}{5} .[/tex]

Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

From the graph;

Using midpoint formula;

[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We substitute in our values

[tex]( \frac{0+2}{2},\frac{4+(-2)}{2}) \\\\( \frac{2}{2},\frac{4-2)}{2}) \\\\( \frac{2}{2},\frac{2}{2}) \\\\( 1, 1 )[/tex]

Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

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Answer:  A rose bush, r, cost $8; one pot of ivy, i, cost $6;

Step-by-step explanation:

[tex]\left \{ {{5r + 3i =58} \atop {5r+10i=100}} \right.[/tex]

We combine them by minus, we get:

    5r + 3i = 58

-    5r + 10i = 100

           - 7i = - 42

               i = 6

We plug in i = 6 to the first equation, we get:

     5r + 3(6) = 58

        5r + 18 = 58

                5r = 40

                  r = 8

The cost of one rose bush is $8 and the cost of one pot of ivy is $6.

Here are the equations to represent the scenario:

Micaela: 5r + 3i = 58

Chelsea: 5r + 10i = 100

Let's solve the system of equations to find the cost of one rose bush (r) and one pot of ivy (i).

Subtracting the first equation from the second equation, we get:

7i = 42

Dividing both sides by 7 we get:

i = 6

The rose bushes will be:

5r + 3i = 58

5r + 18 = 58

5r = 58 - 18

5r = 40.

r = 8

This means that the cost of one rose bush is $8 and the cost of one pot of ivy is $6.

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The exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24

The function is given as:

cos(x) = 24/25, tan(x) < 0

The sine function is calculated using:

sin^2(x) + cos^2(x) = 1

So, we have:

sin^2(x) + (24/25)^2 = 1

Collect like terms

sin^2(x) = -(24/25)^2 + 1

Evaluate the squares

sin^2(x) = -576/625 + 1

Take the LCM

sin^2(x) = (625-576)/625

Evaluate

sin^2(x) = 49/625

Take the square roots

sin(x) = -7/25 --- sin(x) is negative because tan(x) < 0

The tangent function is calculated using:

tan(x) = sin(x)/cos(x)

This gives

tan(x) = (-7/25) / (24/25)

Evaluate

tan(x)= -7/24

Hence, the exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24

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Complete question

Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)

cos(x) = 24/25, tan(x)< 0

sin(x)  =

tan(x) =

Answer:

A. there is exactly one solution. the solution set is {(2, 0)}.

Step-by-step explanation:

3x + 8y = 6

3x - 8y = 6

when we add these 2 equations, we get

6x + 0 = 12

6x = 12

x = 2

now we use one of the original equations to get y :

3×2 + 8y = 6

6 + 8y = 6

8y = 0

y = 0

The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of individual songs and y represent the number of albums, hence:

x + 8y ≤ 50   (1)

x ≤ 30    (2)

y > 2   (3)

The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

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The percent that the cost price is less than the marked price will be 40%.

Let the cost price be 100.

Since the marked price of an article is 40% above the cost price, the marked price is 140.

The percent that the cost price is less than the marked price will be:

= 140 - 100

= 40%

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Answer:

vertex  =  (1/4 , -81/8)

Step-by-step explanation:

f(x) = y

f(x) = 2x²-x-10

a= 2

b= -1

c = -10

-b/2a

-(-1)/(2(2))

1/4

x = 1/4

f(x) = 2x²-x-10

y = 2x²-x-10

y = 2(1/4)²-(1/4)-10

y = 2/16-1/4-10

y = 2/16-4/16-160/16

y = -2/16-160/16

y = -162/16

y = -81/8

Answer:

A centimeters.

Step-by-step explanation:

Answer:3

Step-by-step explanation:because listen 3 is 2 for the side then 9 for the top so 9+9 equals 18 right so then 2+2 equals 4 18+4 does not equal 18

Answer: 14.1 sq meters

Step-by-step explanation:

this question has already been answered

Answer:

4.5

Step-by-step explanation:

1+2+3+4+5+6+7+8= 36

36/8= 4.5

En un triángulo rectángulo con ángulos de 30° -60° -90°, para encontrar la longitud de un lado, debes encontrar la longitud de la hipotenusa.

Es necesario encontrar la longitud del cateto opuesto al ángulo de 30°, también conocido como cateto menor, y luego multiplicarlo por 2, descubriendo así el cateto de la hipotenusa, utilizando la fórmula del teorema de Pitágoras:

Por lo tanto, puedes usar el teorema de Pitágoras para calcular la longitud del lado que falta en un triángulo rectángulo.

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The student that earned a score of 21 or higher on the quiz has a cumulative frequency of 7 and the relative cumulative frequency of 14%

This refers to the pictorial representation of data that is used to show the distribution of numerical data.

From the given image, the histogram shows the quiz scores of students and the frequencies, and the relative cumulative frequency was gotten  by dividing the frequency of each interval by the total number of observations

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