Harry buys a sofa set that costs $2000.00. He pays for it by installments at an interest rate of 5% per year. What is the total amount he has to pay at the end of the one year?

1L = 1000ml

 14L = 14000ml

14000-9500 = 4500ml left

If the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.

A number system is defined as a system of writing to express numbers.

We have to find the number for the absolute value of a nonzero real number is equal to the opposite of the number

The absolute value of a number is its numerical value without regard to its sign.

So if the absolute value of a number is equal to the opposite of the number, it means that the sign of the number must be negative.

Hence, if the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.

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The sum of the probabilities of any event and its complement is always 1.

The student's question involves probability and arrangement of objects, which falls under the subject of mathematics. More specifically, the problem relates to permutations and the fundamental counting principle, combined with basic probability concepts.

Statement 36: The sample space is the set of all possible outcomes that can occur. Since there are 12 different books, the sample space consists of these 12 unique titles, where 8 are fiction (F1 to F8) and 4 are nonfiction (N1 to N4). The sample space is therefore: {F1, F2, F3, F4, F5, F6, F7, F8, N1, N2, N3, N4}.

Statement 37: The sum of the probabilities of an event and its complement is always 1. This is because an event and its complement together cover all possible outcomes in the sample space.

When two dice are rolled, there are 6 feasible outcomes out of 36 that will sum to '7', hence the probability is 1 out of 6, or approximately 0.167.

In the field of probability, when you roll two dice, there are 6 possible outcomes for each die, hence giving us 36 possible outcomes altogether (6*6=36). Out of these 36 possible outcomes, there are 6 combinations that can total to '7'. These combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the probability of rolling a '7' with two dice is 6 out of 36, which simplifies to 1 out of 6, or approximately 0.167, when rounded to three decimal places.

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We are given that:

fabric required = 3 3/5 yards

costumes = 5

We can write fabric required as a fraction in the form of:

(3 * 5) + 3 = 18

fabric required = 18 / 5 yards

So total fabric required is = (18 / 5 yards) * 5 = 18 yards

Answer:

18 yards

The value of ( g o f ) (0) is -3.

Here,

The function is given as;

[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]

We have to find the value of ( g o f ) (0).

What is Composite function?

Composite function is an operation that takes two functions f and g and produces a function k such that k (x) = g(f(x)).

Now,

The function are;

[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]

Simplify ( g o f ) (0) as;

⇒ [tex]( g o f ) (0) = g ( f (0)) = g (0) = 0-3 = -3[/tex]

Hence, The value of ( g o f ) (0) is -3.

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The function g(x) = –7x² + x³ is the reflection of the function f(x) = 7x² – x³ about the x-axis. This is observed by the change in signs of each term in the function's equation after performing the reflection.

By observing the given equation, f(x) = 7x² – x³ and g(x) = –7x² + x³, it is clear that the function f(x) reflects about the x-axis to create function g(x). This is indicated by the change of signs of each term in the equation of the function.

To elaborate, a reflection about the x-axis sees a function's equation change y(x) to -y(x). In our example, f(x) becomes -f(x) or –(7x² – x³), which after simplifying gives us –7x² + x³ = g(x). Therefore, g(x) is the reflection of f(x) about the x-axis.

Furthermore, to identify a reflection about the y-axis, observe if the equation changes from f(x) to f(-x). An even function or a function symmetric about the y-axis would not change with this transformation. Conversely, an odd function would change signs, just like our function did when reflecting over the x-axis.

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The simplified form of cos C is sqrt(2)/2.

"Cos is the cosine function of a right triangle in trigonometry. Cos function is the ratio of adjacent side and hypotenuse. It helps us to find the length of the sides of the triangle, irrespective of given angle.

Suppose we have a right triangle and α is the angle between adjacent side and hypotenuse, then as per the cos function, we can write

Cos α = Adjacent Side/Hypotenuse"

Here, given the base of the triangle is = 5

and hypotenuse is = 5sqrt2

So, [tex]cos C = 5/5\sqrt2 = 1/\sqrt2[/tex]

Multiplying both numerator and denominator by sqrt2

We get [tex]\sqrt2/2[/tex].

Hence, the value of cos C is [tex]\sqrt2/2[/tex]

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To get the perfect square when a is greater than 1 divide the whole equation by a.

When a given expression is simplified to the square of a sub-function is called a perfect square.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let's presume with an example,
ax² + bx + c =0
In order to get the perfect square the whole equation must be divided by a for a greater than 1

x² + b/a x + c/a = 0

Thus, to get the perfect square when a is greater than 1 divide the whole equation by a.

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The coordinates of the midpoint of segment VW are (x/2, (y-3)/2).

To find the coordinates of the midpoint of segment VW, we can use the midpoint formula.

The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

Given the endpoints V(-2, -6) and W(x+2, y+3), we can find the x-coordinate of the midpoint by taking the average of the x-coordinates: (-2 + (x+2))/2.

Similarly, we can find the y-coordinate of the midpoint: (-6 + (y+3))/2.

So the coordinates of the midpoint are (x/2, (y-3)/2).

Answer:

The value of [tex]\frac{b}{a}=4[/tex] .

Step-by-step explanation:

As given in the question

[tex]\frac{2a}{b}=\frac{1}{2}[/tex]  

Now find out the value of [tex]\frac{b}{a}.[/tex]

[tex]\frac{b}{a}=\frac{2\times 2}{1}[/tex]

[tex]\frac{b}{a}=2\times 2[/tex]

[tex]\frac{b}{a}=4[/tex]

Therefore the value of [tex]\frac{b}{a}=4[/tex] .

The value of b/a from the equation; 2a/b=1/2 is; 4

The given equation is;

Divide both sides of the equation by 2; we have;

Hence, the inverse of a/b is b/a and;

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The density of the cube is calculated to be 2 g/cm³ by dividing the mass (250 grams) by the volume of the cube (125 cm³).

To calculate the density of a substance, you divide its mass by its volume. In the given problem, the cube has a mass of 250 grams and each side of the cube is 5 cm. The volume of a cube is calculated by taking the cube of the side length, which in this case is 5^3 = 125 cm³.

By substituting the given mass and computed volume in the formula, we find that the density of the cube is 250 grams ÷ 125 cm³ = 2 g/cm³.

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Answer:

Cost of living is the amount of money needed for fixed expenses such as housing, food, taxes, and health care, as well as variable expenses. Big cities tend to have a higher cost of living than smaller cities.

Step-by-step explanation:

Answer:

1. D. 30

2. C. [tex]\frac{5}{14}[/tex]

3.  [tex]\frac{5}{9}[/tex]

4. D. [tex]\frac{8}{15}[/tex]

5. A. [tex]\frac{12}{9}, \frac{11}{9}[/tex]

Step-by-step explanation:

1. LCD or lowest common denominator for a set of fractions is lowest common multiple of all the denominators in that set of fractions

∴ for [tex]\frac{3}{5}[/tex] and [tex]\frac{1}{6}[/tex] LCD will be 5×6 = 30

2. [tex]\frac{3}{7} - \frac{1}{14}  = \frac{6-1}{14} = \frac{5}{14}[/tex]

3. [tex]\frac{1}{3} - \frac{2}{9}  = \frac{3+2}{9} = \frac{5}{9}[/tex] = [tex]\frac{5}{9}[/tex]

4. [tex]\frac{2}{15} + \frac{1}{15} = \frac{1}{5}\\\\\frac{2}{15} + \frac{8}{30} = \frac{2}{5}\\\\\frac{2}{15} + \frac{5}{15} = \frac{7}{15}\\\\\frac{2}{15} + \frac{8}{15} = \frac{2}{3}[/tex]

5. [tex]\frac{12}{9} - \frac{11}{9} = \frac{1}{9} \\\\\frac{34}{7} - \frac{21}{7} = \frac{13}{7} \\\\\frac{24}{5} - \frac{11}{3} = \frac{17}{15}\\\\\frac{27}{9} - \frac{11}{3} = \frac{-6}{9}[/tex]

Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

The number of miles driven varies directly with the number of hours in the car.

Billy drives 171 miles in 3 hours.

Then the number of miles he can drive in 4.5 hours will be

Let x be the number of miles covered in 4.5 hours.

The speed remains constant.

Then we have

x / 4.5 = 171 / 3

x = 256.5 miles

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Billy could drive 256.5 miles in 4.5 hours.

To find the number of miles Billy could drive in 4.5 hours, we will use the concept of direct variation. Direct variation states that when two variables are directly proportional, their ratio is constant.

Given that Billy drives 171 miles in 3 hours, we can set up a proportion:

Miles driven / Hours in the car = Miles driven / Hours in the car

Using the given values, we have:

171 / 3 = x / 4.5

To solve for x, cross multiply:

3x = 171 * 4.5

Divide both sides by 3:

x = (171 * 4.5) / 3

Simplifying the right side of the equation gives us:

x = 256.5

Therefore, Billy could drive 256.5 miles in 4.5 hours.

Answer:

If a staff member notices behavioral changes in the child it could improve the situation if a staff member subtly questioned the child not alarming anything and if the child is aware of abuse the staff member could quickly respond and seek help from a higher person.

If the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²

Let x represent the surface area of the cube

Hence:

Surface area of a cube of edge x =6x²  

Surface area of the cube =6(25cm)²

Surface area of the cube=150cm²

Inconclusion if the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²

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