what is 1.18 repeating as a fraction

the equation of g(x) after stretching the graph of f(x) vertically by a factor of 2. Therefore, the equation of g(x) is g(x) = 4(3)^x+1 + 8.

To stretch the graph of (f(x)) vertically by a factor of 2 to form the graph of ( g(x)), we need to multiply the entire function (f(x)) by 2.

Given:

[tex]\[ f(x) = 2(3)^{x+1} + 4 \][/tex]

To stretch the graph vertically by a factor of 2, we multiply the function by 2:

[tex]\[ g(x) = 2 \cdot f(x) \][/tex]

Substitute the expression for [tex]\( f(x) \):[/tex]

[tex]\[ g(x) = 2 \cdot [2(3)^{x+1} + 4] \][/tex]

Now, distribute the 2 inside the brackets:

[tex]\[ g(x) = 4(3)^{x+1} + 8 \][/tex]

This is the equation of [tex]\( g(x) \)[/tex] after stretching the graph of [tex]\( f(x) \)[/tex] vertically by a factor of 2.

Therefore, the equation of [tex]\( g(x) \) is \( g(x) = 4(3)^{x+1} + 8 \).[/tex]

Final answer:

The area per person served by a 12-inch quiche, it was determined that a 10-inch quiche can indeed feed 4 people with the same serving size, as the area available per person in the 10-inch quiche is sufficient.

Explanation:

To determine whether a quiche with a diameter of 10 inches can feed 4 people at the same serving size as a 12-inch quiche that feeds 6 people, we need to compare the areas of the two quiches. The area of a circle is calculated using the formula A = πr² where A is the area and r is the radius. Since the radius is half of the diameter, the 12-inch quiche has a radius of 6 inches and the 10-inch quiche has a radius of 5 inches.

For the 12-inch quiche:
A12 = π(6²) = 36π

For the 10-inch quiche:
A10 = π(5²) = 25π

So, the 12-inch quiche has an area of 36π square inches and the 10-inch quiche has an area of 25π square inches. To find out if the smaller quiche can serve 4 people, we calculate the area per person for the larger quiche: 36π/6 = 6π square inches per person.

Now, we check to see if the 10-inch quiche provides at least that much area for 4 people: 25π/4 ≈ 6.25π square inches per person. Since 6.25π is greater than 6π, we can conclude the 10-inch quiche can indeed feed 4 people with the same serving size as the 12-inch quiche fed 6 people.

Answer:

set of all real numbers (-∞,∞)

Step-by-step explanation:

Solve each inequality

[tex]4p+1>-7[/tex]

Subtract 1 from both sides

[tex]4p>-8[/tex]

Divide by 4 on both sides

[tex]p>-2[/tex]

[tex]6p+3 <33[/tex]

Subtract 3 from both sides

[tex]6p<30[/tex]

Divide both sides by 6

[tex]p<5[/tex]

[tex]p>-2[/tex] or [tex]p<5[/tex]

The graph is attached below

The number 98984 rounded to one significant figure is 100000

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the number be N

The value of N = 98984

Now , the number N has 5 significant numbers

So , the next higher number where N can be rounded is

Now , the number N can be rounded to one significant figure by

The nearest number which the number N can be rounded of to is 100000

So , Let the number 100000 = M

Now , the number M has only 1 significant number and is close to 98984

Therefore , the value of M is 100000

Hence , The number 98984 rounded to one significant figure is 100000

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The statement 'six is greater than or equal to the quotient of a number y and 2.5,' can be converted into the inequality 6 >= y/2.5. Solving for y by multiplying both sides by 2.5 gives y <= 15. Therefore, any number y that is 15 or less will satisfy this inequality.

The question provided, 'six is greater than or equal to the quotient of a number y and 2.5,' requires manipulation of an inequality in mathematics to find the potential values of y. To represent this in mathematical terms, one could write the inequality as 6 ≥ y/2.5. From here, it is a simple matter of isolating y by multiplying both sides of the inequality by 2.5, which results in y ≤ 15. Therefore, any number y that is less than or equal to 15 satisfies the inequality.

Inequality, Isolating variables and Mathematical terms are vital concepts for understanding and solving problems in algebra.

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The ordered pairs lie on the graph of the exponential function [tex]\rm f(x) = 4(5)^{2x}[/tex] is (2,2500) and this can be determined by using the arithmetic operations.

Given :

Exponential Function  ---  [tex]\rm f(x) = 4(5)^{2x}[/tex]

The following steps can be used in order to determine the ordered pairs lie on the graph of the exponential function:

Step 1 - Write the exponential function.

[tex]\rm f(x) = 4(5)^{2x}[/tex]

Step 2 - Substitute the value of (x = -1425) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times -1425}[/tex]

[tex]\rm f(x) = 4(5)^{-2850}[/tex]

By simplifying the above function it does not give the value of f(x) = -1425, therefore, option (A) is incorrect.

Step 3 - Substitute the value of (x = 0) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times 0}[/tex]

f(x) = 4

Therefore, option (B) is also incorrect.

Step 4 - Substitute the value of (x = 1) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times 1}[/tex]

f(x) = 100

Therefore, option (C) is also incorrect.

Step 5 - Substitute the value of (x = 2) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times2}[/tex]

f(x)  = 2500

Therefore, option (D) is correct.

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x^2 +6^2 = 10^2

x^2 + 36 =100

x^2 = 64

x = sqrt(64)

x = 8

To find the side of the original square, we can set up an equation and solve for x.

To solve this problem, let's assume that the side length of the original square is 'x'. If we double it, the new side length would be '2x'. Adding 7 to it gives us '2x + 7'.

The new perimeter of the square is 8 more than 3 times the old perimeter, so we can set up the equation: 2(2x + 7) = 3(4x).

Simplifying this equation, we get 4x + 14 = 12x. By rearranging the equation, we find that 8x = 14, which leads to x = 1.75.

Therefore, the side length of the original square is 1.75 units.

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Scientific notation is the way of writing a large number between 1 to 10 with a power of 10.

The mass of one atom is 6.65 x [tex]10^{-24}[/tex]

The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].

The scientific notation to express the mass of 250 helium atoms is

1.6625 x [tex]10^{-21}[/tex].

It is the way of writing a large number between 1 to 10 with a power of 10.

Example:

1.2 x 10² is in scientific notation.

9.1 x 10³ is in scientific notation.

We have,

Mass of one atom of helium = 6.65 x [tex]10^{-24}[/tex]

Mass of 250 atoms of helium:

= 250 x 6.65 x [tex]10^{-24}[/tex]

= 1662.5 x [tex]10^{-24}[/tex]

Now,

We will make 1662.5 into a number between 1 and 10.

1662.5

= (1662.5/1000) x 1000

= 1.6625 x 10³

Now,

= 1.6625 x 10³ x [tex]10^{-24}[/tex]

= 1.6625 x [tex]10^{3 - 24}[/tex]

= 1.6625 x [tex]10^{-21}[/tex]

Thus,

The mass of one atom is 6.65 x [tex]10^{-24}[/tex]

The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].

The scientific notation to express the mass of 250 helium atoms is

1.6625 x [tex]10^{-21}[/tex].

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Answer:

20%

Step-by-step explanation:

(765 - 153)/765*100

(612)/765*100

0.8*100

80% of original

100% - 80% = 20% reduction

By using equations to represent the relationship between Kevin and Daniel's ages, we can determine that Kevin is 24 years old.

Kevin is 3 times as old as Daniel. Let's denote Kevin's age as K and Daniel's age as D. From the information given, we can form two equations:

K = 3D

K - 4 = 5(D - 4)

3D - 4= 5D -20

16 = 2D

D = 8

K = 24

Solving these equations simultaneously gives the age of Kevin, therefore, Kevin is 24 years old.

Answer:

Step-by-step explanation:

In the image you can observe that the third choice doesn't appear to be congruent to the given one, beacuse it's smaller.

On the other hand, choice A, B and D, have figures that apparently are the same size and shape to the given one, they were just rotated, which is a rigid transformtion, that is, they just move, their size or shape doesn't shape.

Therefore, the right answer is C figure.

Answer:

5.4

Step-by-step explanation:

We are given that

[tex]5\frac{4}{9}[/tex]

We have to find the value which is equivalent to given fraction number.

[tex]5\frac{4}{9}=\frac{45+4}{9}[/tex]

[tex]5\frac{4}{9}=\frac{49}{9}[/tex]

When we divide 49 by 9 then we get

[tex]\frac{49}{9}=5.4444[/tex]

It can write as 5.4

Hence, [tex]5\frac{4}{9}=5.4[/tex]

Answer:5.4

The correct answer to the given expression 2(b+3c) is 'None of the above' as none of the provided options represent an equivalent expression after the application of distributive property.

The expression 2(b+3c) cannot be transformed into any of the given options directly. If we use distributive property, we expand 2(b+3c) to get 2b + 6c, which is equivalent to the original expression.

The options provided, such as 3(b+2c), (b+3c) +(b+3c), or 'None of the above', do not simplify or represent an equivalent expression to 2(b+3c). The correct answer is 'None of the above'. It's important to note that the commutative property of addition, A+B = B+A, and the associative property, (A+B) + C = A +(B+C), suggest that we can regroup or reorder terms in an addition expression without changing its value. However, none of these properties help in finding an equivalent expression among the given options for 2(b+3c).

To guarantee a team, you would need 13 persons, and to guarantee two teams, you would need 24 persons.

The number of persons needed to guarantee that they can raise a team is one more than the number of months in a year. This is because there are 12 months in a year, and to ensure that all team members have birthdays in the same month, you would need at least one person for each month. Therefore, you would need 13 persons to guarantee a team.

To guarantee that there are two teams, you would need a total of 24 persons. This is because each team needs at least one person for each month, and there are 12 months in a year. So, for the first team, you would need 13 persons, and then you would need an additional person for each month to form the second team. This would give you a total of 24 persons to guarantee two teams.

Final answer:

To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. To guarantee that two teams can be formed, you would need at least two people born in each month of the year.

Explanation:

To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. Since there are 12 months, you would need a minimum of 12 people to ensure that a team can be formed.

To guarantee that two teams can be formed, you would need at least two people born in each month of the year, as each team needs five members. So, you would need a minimum of 24 people to ensure that two teams can be formed.

The solution is Option A.

The distance between the base of the ladder and the wall is 9 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the height of the wall = 12 feet

The measure of AB = 12 feet

The length of the ladder = 15 feet

The measure of AC = 15 feet

Now , the distance between the base of the ladder and the wall = BC

The measure of BC is given by the Pythagoras Theorem , where

Hypotenuse² = base² + height²

AC² = AB² + BC²

Substituting the values in the equation , we get

15² = 12² + BC²

Subtracting 12² on both sides of the equation , we get

BC² = 15² - 12²

BC² = 225 - 144

BC² = 81

Taking square roots on both sides of the equation , we get

BC = 9 feet

Therefore , the value of BC is 9 feet

Hence , the distance is 9 feet

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Answer: The equation that shows y=(3/4)x-5/2 is standard form is:

Second option: 3x-4y=10

Solution:

y=(3/4)x-5/2

Standard form of the equation Ax+By=C, with A, B, and C integer numbers

The coefficient of "x" and the independent term are fractions. To simplify them, let's multiply both sides of the equation by 4:

4y=4 [ (3/4)x-5/2]

4y=4(3/4)x-4(5/2)

4y=(4/1)(3/4)x-(4/1)(5/2)

4y=[(4*3)/(1*4)]x-(4*5)/(1*2)

4y=(12/4)x-20/2

4y=3x-10

The two variables must be in the same side of the equation and the independent term in the other side, but the coefficient of "x" must be positive, then subtracting 4y and adding 10 both sides of the equation:

4y-4y+10=3x-10-4y+10

10=3x-4y

3x-4y=10

Answer:

its B i took the test explanation:

Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,

The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.

Number of horses and ponies combined:
22 horses + 18 ponies = 40

Number of rabbits and hares combined:
18 rabbits + 37 hares = 55

Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair