Suppose in one year, total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in a certain country amounted to $21 million. Pop/rock music brought in twice as much as the other two categories combined and $10 million more than tropical music. How much revenue was earned from digital sales in each of the three categories?

Answers

Answer 1

Answer:

You can use the fact given that pop/rock music is twice as much as the other two categories combined and $10 million more than tropical music to form the equations to find the revenue earned by each of the three categories.

The revenue earned by each of the three categories is

Pop/rock: $10,500,000
Tropical: $500,000
Latin: $10,000,000

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How to get revenue earned by each music category?

(For the given context)

Let the tropical music earned 'x' amount from digital sale.
Let the Latin music earned 'y' amount from digital sale.
Let the pop/rock music earned 'z' amount from digital sale

Then, by given description, we have:

Pop/rock music brought in twice as much as the other two combined

$z = x + y$

Pop/rock music brought in $10 million more than tropical music

$z = 10,000,000 + x$

And that all of them together earned $21 million

$x + y + z = 21,000,000$

Putting value of z in second equation, we get

$z = 10,000,000 + x\nx + y = 10,000,000 + x\n\n\text{Subtracting x from both the sides}\n\ny = 10,000,000$

Thus, Latin music earned y = $10 million from digital sale.

Putting z in place of x + y (as both are equal as stated in first equation) in the third equation,

$x + y + z = 21,000,000\nz + z = 21,000,000\n2z = 21,000,000\n\n\text{Dividing by 2 on both the sides}\n\nz = 10,500,000$

Thus, pop/rock music earned $10,500,000 from digital sale.

Putting this value in second equation, we get

$z = 10,000,000 + x\n10,500,000 = 10,000,000 + x\n500,000 = x$

Thus, tropical music earned $500,000 from its digital sale.

Thus,

The revenue earned by each of the three categories is

Pop/rock: $10,500,000
Tropical: $500,000
Latin: $10,000,000

Learn more about system of equations here:

brainly.com/question/13722693

Answer 2

Answer:

Answer:

Pop/Rock sold $14 million
Tropical music sold $3 million
Reggaeton sold $4 million.

Step-by-step explanation:

First let's write the music genre as follows:

X = Pop/Rock
Y = Tropical
Z = Reggaeton

$\left \bigg \{ {{X + Y + Z = 21 (1) } \atop {X=2(Y + Z) (2)}} \text{; } \left \bigg \{ {{X + Y + Z = 21 (1)} \atop {X= Z + 10 (3)}$

Let's use $(2)$ in $(1)$ :

$X + Y + Z = 21 \Rightarrow 2(Y + Z) + Y + Z = 21 \Rightarrow\n3(Y+Z) = 21 \Rightarrow Y+Z = 7$

Then,

$X + 7 = 21 \Righarrow X = 14$

Now let's solve for Z,

$14 = Z +10 \Rightarrow Z = 4$

Finally, let's solve for Y,

$14 = 2(Y + 4) \Rightarrow Y + 4 = 7 \Rightarrow Y = 3$

So Pop/Rock sold $14 million, Tropical music sold $3 million and Reggaeton sold $4 million.

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Which ratio forms a proportion with 16/20

Answers

Answer:

4/5 forms a proportion with 16/20.

Step-by-step explanation:

We are given an rational number as 16/20.

we have to find another rational number which is equivalent to it.

as both 16 and 20 are multiple of 4 we could also represent the ratio 16/20 as:

$(16)/(20)=(4 * 4)/(4*5)$

we cancel 4 on both the numerator and denominator to get $(4)/(5)$ .

Hence, the ratio $(4)/(5)$ is proportion with $(16)/(20)$ .

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Jenny James has score of 78 89 90 and 96 on her first four test what score should she make out of 100 points in order to have at least an average of 90

Answers

Answer:

Jenny James would need to have a score of 97 out of 100 points in order to have an average of 90.

Step-by-step explanation:

Given that:

Scores of four tests

78, 89, 90 and 96

Let,

x be the score on fifth test.

Average is the sum of quantities divided by total number of quantities.

Average = 90

Average = $(Sum\ of\ scores)/(No.\ of scores)$

Putting the values in the formula;

$90=(78+89+90+96+x)/(5)\n90=(353+x)/(5)\n90*5=353+x\n450=353+x\n450-353=x\nx=97$

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Jenny James would need to have a score of 97 out of 100 points in order to have an average of 90.

Log 5 plus log 2 equals?

log5 + log2 =

Answers

The sum of logs = the log of the product .

   log(5) + log(2) = log(5·2) = log(10)

If these are all logs to the base 10, then log(10) = 1

   log(5) + log(2) = 1

Let's try it out !

According to my calculator ...

   log(5) = 0.69897...

   log(2) = 0.30103...

Log(5) + log(2) = 0.99999... yay ! not bad

The solution of the equation log5 + log2 using the properties of Logarithm is log(10) or 1.

Logarithms are used to solve exponential equations by converting them into simpler forms.

A number that represents the power to which a fixed number (the base) must be increased in order to get a specific number is called as logarithm.

The property of logarithms states that:

log(a) + log(b) = log(ab).

Applying this property, we get:

log5 + log2

= $\log(5*2)$

= log(10)

Logarithm base 10 (log) gives the power to which 10 must be raised to obtain the given value. So, log(10) represents the exponent required to obtain 10, which is 1.

Thus, the solution of log5 + log2 is equal to log(10) or 1.

Learn more about Logarithm here:

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Determine whether the two triangles are similar

Answers

if 2 of their angles are congruent it would make them similar, or if their sides match up proportionately

The difference between two integers x and -12 is -15. Find the value(s) of x.

Answers

Answer:

x = 3

Step-by-step explanation:

-12–x = -15

15 - 12 = x

x = 3

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Answers

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