The domain of the function is given. Find the range.

f(x) = 2x - 1

Domain: {-2, 0, 2, 4}

The probability that the first number is a 3 and the second is a 7 is 1/64

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

spinner had region numbered from 1 to 8

So, the probability on the spinner has an equally likely chance of being selected= 1/8.

P(3) = 1/8

P(7) = 1/8

Thus, probability that the first number is a 3 and the second is a 7

=(1/8) * (1/8)

= 1/64

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Answer:

The rectangular equation that is equivalent to the given polar equation is:

y= -2

Step-by-step explanation:

We know that the polar coordinate of a equation are related to the rectangular coordinates of the equation as:

[tex]x=r\sin \theta\\\\y=r\cos \theta[/tex]

where,

[tex]r=\sqrt{x^2+y^2}[/tex]

Now we are given that:

[tex]r\sin \theta=-2[/tex]

Also,

[tex]\theta=\arctan \dfrac{y}{x}[/tex]

Hence, on converting the given polar equation to the rectangular equation we get:

[tex]y=-2[/tex]

Answer:

The probability that the student is opposed to extending the school day is 0.3666 or 36.67% approx.

Step-by-step explanation:

Arranging the table properly and adding a column of total students.

                          In favor      Opposed      Undecided      Total students

Grade 9                6                4                    8                       18

Grade 10               10               11                   9                       30

Grade 11                12               15                   11                      38

Grade 12                15               6                   14                      35

If the principal randomly selects a student in grade 10 from this survey, this means we will only consider grade 10 students.

The probability that the student is opposed to extending the school day is = [tex]\frac{number of opposed students}{total number of students}[/tex]

There are 11 students who are opposed and total students in grade 10 are 30.

So, probability is : [tex]\frac{11}{30}= 0.3666[/tex] or 36.67% approx.

they  won 1/2 of their games and won 12 games

1/2 = 50% , multiply by 2 to make 100%

 so 12 x 2 = 24 games were played

To calculate the number of games played by the soccer team, multiply the number of games they won (12) by 2, because winning 12 games represents winning [tex]\frac{1}{2}[/tex] of all games played. The soccer team thus played a total of 24 games.

To find how many games the soccer team played in total, we can set up a proportion using the information that they won [tex]\frac{1}{2}[/tex] of their games. This means for every game they won, they played two (since [tex]\frac{1}{2}[/tex] represents one out of two games). If the team won 12 games, and that represents [tex]\frac{1}{2}[/tex] of the total games, we can use a simple equation to solve for the total number of games (T).

The proportion is as follows: [tex]\frac{1}{2}[/tex] = [tex]\frac{12}{T}[/tex], where 12 is the number of games won, and T is the total number of games played.

To solve for T, we multiply both sides of the equation by T to get rid of the fraction: [tex]\frac{T}{2}[/tex] = 12. To find T, we then multiply both sides of the equation by 2 to isolate T on one side of the equation: T = 12 * 2.

Therefore, the team played a total of T = 24 games.

To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.

In order to map ΔABC to ΔXYZ, you can follow these steps:

By performing these steps, you can map one triangle to another.

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Answer:

The correct option is D.

Step-by-step explanation:

The given expression is

[tex]36x^2-49[/tex]

It can be written as

[tex](6x)^2-(7)^2[/tex]

Using the formula

[tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex](6x)^2-(7)^2=(6x+7)(6x-7)[/tex]

Therefore the complete factor form of given expression is (6x+7)(6x-7). The correct option is D.

Answer

Length of rectangular garden = x feet

As, Width is 3 feet less than Length.

Width = (x-3 ) feet

Area of Rectangle = Length × Breadth

Area = 54 square feet

→54 = x × (x-3)

→ x²-3 x-54=0

Splitting the Middle term

→x² - 9  x + 6 x- 54=0

→x × (x-9)+6 × (x-9)=0

→ (x+6)(x-9)=0

→x+6=0 ∧ x-9=0

x≠-6, as length can't be negative.

So, x=9

Length of Rectangular garden = 9 feet

The correct answer is: c. II and III only

To determine which volume formula(s) exhibit joint variation, we need to consider if the volume (V) varies directly with two or more variables. In joint variation, V is directly proportional to the product of two or more variables.

Let's analyze each formula:

I. V = 8^3 → This is not a joint variation as V is solely dependent on the constant 8.

II. V = πr^2h → This shows joint variation as V varies directly with both r and h.

III. V = Bh → This also exhibits joint variation since V varies directly with both B (base area) and h (height).

The variables in this situation are the price of the tickets and the quantity of tickets sold. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand. Diana should lower the price if demand is elastic, raise the price if demand is inelastic, and can maintain the same revenue if demand has unitary elasticity.

The variables in this situation are the price of the tickets and the quantity of tickets sold. These two variables directly affect the total revenue generated by Diana from ticket sales. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand.

If demand for tickets is elastic, Diana should lower the price to increase total revenue. A decrease in price will result in a larger percentage increase in the quantity sold, leading to a higher total revenue. On the other hand, if demand is inelastic, Diana should raise the price to increase revenue. A certain percentage increase in price will result in a smaller percentage decrease in quantity sold, ultimately raising total revenue.

If demand has unitary elasticity, an equal percentage change in quantity will offset a moderate percentage change in price. In this case, Diana can earn the same revenue regardless of a moderate increase or decrease in ticket price.

Answer:

The required number is 604703

Step-by-step explanation:

Consider the provided number 604703.472883

The rule for rounding a number is:

If the number on the right side of rounding digit is 0, 1, 2, 3, 4 then no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.

If the number on the right side of rounding digit is 5, 6, 7, 8, 9 then rounding digit rounds up by one number  and change the rest of the digit right to rounding digit with 0.

The number on the hundred place is 7 and the number on right side is 0.

Thus, no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.

Hence, the required number is 604703

By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.

In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.

x – 2z = 9 so x = 2z + 9

6x – 2y – 5z = 29

–5x + 5y + 3z = –14

Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14

6(2z + 9) – 2y – 5z = 29

12z + 54 - 2y -5z =29

-2y + 7z = - 25 (1st equation)

–5(2z + 9) + 5y + 3z = –14

-10z - 45 + 5y + 3z = -14

5y - 7z = 31 (2nd equation)

Multiply (1st) equation by 5 and (2nd) equation by 2.

-10y + 35z = - 125

10y - 14z = 62

21z = - 63

z = -3

Substitute z = - 3 into x = 2z + 9

x = 2z + 9

x = 2(-3) + 9

x = 3

Substitute x =  3 and z = 3 into 6x – 2y – 5z = 29

6x – 2y – 5z = 29

6(3) – 2y – 5(-3) = 29

18 - 2y + 15 = 29

-2y + 33 = 29

-2y = -4

y  = 2

x = 3, y = 2 and z = -3

Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.

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Answer:

[tex]y = \frac{3}{32}[/tex]

Step-by-step explanation:

Using the exponent rule:

[tex]a^{-n} = \frac{1}{a^n}[/tex]

Given the function:

[tex]y = 6 \cdot (4)^x[/tex]              ......[1]

To evaluate the function rule for x = -3.

Substitute x = -3 in [1] we have;

[tex]y = 6 \cdot (4)^{-3}[/tex]

⇒[tex]y = 6 \cdot \frac{1}{4^3} = 6 \cdot \frac{1}{64}=\frac{3}{32}[/tex]

Therefore, the function rule for the given value when x = -3 is:

[tex]y = \frac{3}{32}[/tex]

Answer:

Answers a little bit more simplified, all credit to the expert :)

E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right

E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis

E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis

E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down

Step-by-step explanation:

Fiona should use 1 cup of butter when using 3 cups of flour, according to the recipe's ratio of 24:8:3 for flour to butter to water.

The question asks how much butter Fiona should use if she's using 3 cups of flour and the recipe calls for flour, butter, and water in the ratio of 24:8:3. To solve this, we take the ratio for butter (which is 8) and divide it by the flour ratio (which is 24), then multiply by the number of cups of flour Fiona is using (which is 3 cups).

Step-by-step Solution: