a music store buys instruments and then sells them for more than they paid. during a off sale, the store offers a clarinet for . how much did the store pay for the clarinet?

Answer:

-7

Step-by-step explanation:

The identification process of direct proportion, inverse proportion and partitive proportion is show below.

Proportion is comparison of things or magnitudes in terms of size, amount.

In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.

In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.

Partitive proportion is when the division of a quantity into two or more equal or unequal parts.

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2/5÷2 3/4

0.4 / 2.75

= 0.14545...

The number of balcony seats sold is 110

Finding Unknown quantity using Linear equation:

The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.  

Here we have

Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.

There are 400 seats on the main floor, which are sold out for the evening performance  

The total revenue from ticket sales was $5060.

Here we don't know the number of balcony seats.

Let us assume that number of balcony seats = x

Then total revenue = 400(11) + 6x = 5060

=> 4400 + 6x = 5060

=> 6x = 5060 - 4400

=> 6x = 660

=> x = 110  

Therefore,

The number of balcony seats sold = 110

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a) In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.

The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.

Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.

b)  The probability of an event is equal to the events relative frequency in the population of possible events that can occur.

An event’s relative frequency is a number between 0 and 1, so the event’s probability is from 0 to 1.

For example, when someone says that the probability it raining today is high, you understand that they mean that there is a high chance that it will rain.

But what if someone says that the probability of something happening is very low? You understand that the person means that the event may not occur at all. In mathematics, we define probability in a similar sense.

What is Probability?

Probability is the measure of uncertainty of any event (any phenomenon happened or bound to happen).

What is event?

In probability, the set of outcomes from an experiment is known as an Event.

What is random events?

An event with a probability of occurrence determined by some probability distribution.

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The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

the graph of the line is shown below .

In the question ,

point on the line and slope of the line is given

So , equation will be

Part(1)

(-6, -3), m = -1

(y -(-3)) = -1(x -(-6))

y + 3 = -1(x + 6)

y + 3 = -x - 6

y = -x -6 -3

y = -x -9

the equation is y = -x -9  .

Part(2)

(-7, 6), m = 0

(y - 6) = 0(x -(-7))

y - 6 = 0(x + 7)

y - 6 = 0

y = 6

the equation is y = 6

Part(3)

(-2, 11), m=4/3

(y - 11) = (4/3)(x -(-2))

y - 11 = (4/3)x + 8/3

y = (4/3)x + 8/3 + 11

y = (4/3)x + 41/3

the equation is y = (4/3)x + 41/3

the graph of all the three equations are shown below .

Therefore , The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

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A total of 549 of people at the convention are bored by the cable news

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

Not bored = 122

Bored = 9/11 of the people

This means that

Not bored = 1 - Bored

So, we have

Not bored = 1 - 9/11

Evaluate

Not bored = 2/11

Recall that Not bored = 122

So, we have

2/11 * x = 122

Where x = the number of people

This gives

x = 122 * 11/2

Evaluate

x = 671

Recall that

Bored = 9/11 of the people

So, we have

Bored = 9/11 * 671

Evaluate

Bored = 549

Hence, the number of people at the convention that are bored is 549

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The ratio of frames to honey is the same as in a smaller beehive. 200 pounds of honey can be found in Bert's new beehive.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given data:

Number of frame beehives = 6

Pound of honey = 40

Current Frame beehive = 30

The first step is to formulate an equation and then use the formulated equation to find  the number of honey

E = 40 × 30 ÷ 6

E = 40 × 5

E = 200 honey

Therefore the number of honey is 200.

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The time taken for Wilson to paint the bookcase is 50 minutes.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4

Therefore, the time taken to paint the whole bookcase will be:

= Number of minutes / Percentage painted

= 20 / 0.4

= 50

He'll use 50 minutes.

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The measure of ∠ YXR is 55 degrees.

Given that:-

m∠ XOY = 110 degrees

XR is a tangent to circle O at X.

We have to find the measure of ∠ YXR.

Draw the radii XO and OY to form the isosceles triangle XOY.

We know that the radius of the circle is perpendicular to the tangent.

Hence,  ∠OXR = 90 degrees.

Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.

Let, ∠ OXY = OYX = x

Hence,

110 + x + x = 180 degrees

2x = 70 degrees

x = 35 degrees

Now, we know that,

∠ OXR = ∠ OXY + ∠ YXR

90 = 35 + ∠ YXR

∠ YXR = 90 - 35 = 55 degrees.

∠ YXR = 55 degrees.

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The amount of energy that the ball will have at 10 m/s is; 600 J

From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.

If we take the square of the velocity, we get 2² = 4.

Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.

Similarly;

For velocity equal to 3 m/s, the energy is given as:

E = 6 * 3²

E = 54 J

Thus, the general formula to find the energy is given as:

E = 6 * v²

where;

E is the energy

v is the velocity

Now, for velocity equal to 10 m/s, energy is given as;

E = 6 * 10

E = 60 J

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The volume of a frustum is equal to 445.3785 cubic units.

Mathematically, the volume of a cone can be calculated by using this formula:

Volume of a cone = 1/3 × πr²h

Where:

For the volume of the large cone, we have the following:

Volume of large cone = 1/3 × πr²h

Volume of large cone = 1/3 × 3.142 × 6² × 12

Volume of large cone = 3.142 × 36 × 4

Volume of large cone = 452.448 cubic units.

Since the height of the small cone is quarter of the height of the large cone, we have:

Height of small cone = 1/4 × 12 = 3 units.

Radius of small cone = 12/18 = 3/2 = 1.5 units (similar triangles by AAA).

For the volume of the small cone, we have the following:

Volume of small cone = 1/3 × πr²h

Volume of small cone = 1/3 × 3.142 × 1.5² × 3

Volume of small cone = 3.142 × 2.25

Volume of small cone = 7.0695 cubic units.

Mathematically, we know that the volume of a frustum is made by subtracting the volume of a small cone from the volume of a similar large cone cone:

Volume of the frustum = Volume of large cone - Volume of small cone

Volume of the frustum = 452.448 - 7.0695

Volume of the frustum = 445.3785 cubic units.

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The final balance is $97,920.

Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.

Given this, The principal is $3000.

Interest rate = 4.8%

Time = 2 years We must find the final balance.

The end balance formula is

C = P[ 〖(1+r)〗^n – 1]

C = 3000[ 〖(1+4.8)〗^2 – 1]

C = 3000 [ 〖(5.8)〗^2 – 1]

C = 3000 [ 33.64 – 1]

C = 3000 ( 32.64)

C = 97,920

Therefore the ending balance is $97,920

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Answer:

A/ 80 grams

Step-by-step explanation:

We know that 430 - 280 = 150,  so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams

Answer:

-30

Step-by-step explanation:

Distribute

5 x -4= -20 2 x -2= -4

-20+(-6)+(-4)

Add together

-20 + -6= -26

-26 + (-4)

Add again

-26 + -4= -30

-30

The equation of the graph is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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Answer:

X=

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−84=108x

Step 1: Subtract 108x from both sides.

2x−84−108x=108x−108x

−106x−84=0

Step 2: Add 84 to both sides.

−106x−84+84=0+84

−106x=84

Step 3: Divide both sides by -106.

−106x

−106

=

84/−106x=−42/53

Answer:16 minutes

Step-by-step explanation:

64 errors / 8 errors = 8

8 x 2 minutes = 16 minutes

The x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) =  (x-1)²/x²-1

To find the x-intercept where y = 0

or f(x) = 0

0 =  (x-1)²/x²-1

x ≠ ±1

x - 1 = 0

x = 1

Thus, the x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

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In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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The number of terms in the expression 5x - 2 is 2

The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be

The terms can be like terms or unlike terms

The two terms given is separated by the subtraction operator and are both unlike terms

The first term 5x consist of

The second term is just a constant which is 2

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Answer:

  2.4

Step-by-step explanation:

You want the average rate of change on the interval [-9, -4] for the graphed function.

The average rate of change (m) is the slope of the line between the points at the ends of the interval. For function f(x) on interval [a, b], this is ...

  m = (f(b) -f(a))/(b -a)

For the function f(x) on the interval [-9, -4], the average rate of change is ...

  m = (f(-4) -f(-9))/(-4 -(-9)) = (-4 -(-16))/5 = 12/5 = 2.4

The average rate of change of f(x) on [-9, -4] is 2.4.

The length of the line segment defined by two endpoints; negative 3 comma 10 to 4 comma negative 1 as required in the task content is; 13.04.

It follows from the task content that the length of the line segment whose endpoints are as given in the task content is to be determined.

Recall; The length of a line segment whose endpoints are defined by; (x1, y1) and (x2, y2) is given as;

Length = √{ (y2 - y1)² + (x2 - x1)² }

Therefore, since the given endpoints are; (-3, 10) and (4, -1), it follows that the length of the line segment in discuss is;

Length = √{ (-1 - 10)² + (4 - (-3))² }

Length = √(121 + 49)

Length = √170

Length = 13.04.

Ultimately, the length of the line segment as required is; 13.04.

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Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

2 + [tex]\frac{3}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number

Answer:

[tex]1.8 \times {10}^{2} = 180[/tex]

Step-by-step explanation:

[tex] \frac{9 \times {10}^{5} }{5 \times {10}^{3} } = \frac{9}{5} \times \frac{ {10}^{5} }{ {10}^{3} } = 1.8 \times {10}^{2} = 1.8 \times 100 = 180[/tex]

The hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the defective sets.

As per the stated question.

You can select five television from a possible twelve in the sample space.

To acquire at least 2 faulty, therefore:

¹²C₅ = 12!/(7!)(5!) =12*11*10*9*8/(5*4*3*2*1)

¹²C₅ = 11*9*8

Obtaining two or three defective items. (At least 2).

2 defective items are-

(³C₂)(⁹C₄) = 3*9*8*7*6/(4!)

(³C₂)(⁹C₄) =9*7 =63

Three defective items equal -

(³C₃)(⁸C₂) = 1*8*7/2!

(³C₃)(⁸C₂) = 56

Total defective items is 63+56= 119 ways.

Probability = 119/(11*9*8)

Probability = 119/792

Thus, a hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the flawed sets.

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The phrase [tex]f (x)[/tex] denotes a formula with [tex]x[/tex] serving as its input variable. Not multiply f and x, though!

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .

The x in [tex]f(x)[/tex] is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation [tex]f(2)[/tex].

Hence,  the phrase [tex]f (x)[/tex] represents a formula with [tex]x[/tex] serving as its input variable.

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The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ 32z - 48

The expression can be rewritten as,

⇒ 32z - 48

⇒ 16 · 2z - 16 · 3

⇒ 16 (2z - 3)

The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

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