In 2006,500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded.

c. If this trend continues at the same rate, how many songs will be legally downloaded in 2020 ?

Answer:

Step-by-step explanation:

[tex]\frac{x}{5} +1=\frac{1}{15}[/tex]

[tex]\frac{x}{5} = \frac{1}{15} -1[/tex]

[tex]\frac{x}{5} = \frac{1-15}{15}[/tex]

[tex]\frac{x}{5} = \frac{-14}{15}[/tex]

multiply both sides by 5

[tex]5*\frac{x}{5} = \frac{-14}{15} *5[/tex]

[tex]x=-\frac{14}{3}[/tex]

Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

Given the data in the question;

A bisector divides a line or angle into two equal halves.

Hence

Segment JM = Segment MK

7x + 5 = 8x

Solve for x

8x - 7x = 5

x = 5

Now, numerical value of segment JM will be;

Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40

Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80

Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.

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Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.

Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.

It is expressed as;

I = prt

Given the data in the question;

Plug the given values into the formula above and solve for I.

I = p × r × t

I = $625 × 0.025 × 0.5

I = $7.81

Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.

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The 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

According to the given question.

We have,

A formual for finding the gereral term of the sequence i.e.

an = n²/{n+1}.

Since, we have to find the 4th, 5th, 6th, and 7th term of the sequence.

Therefore,

4th term of the sequence is given by

[tex]a_{4}[/tex]  = (4)^2/{4 + 1) = 16/5

5th term of the sequence is given by

[tex]a_{5}[/tex]  = (5)^2/{5 + 1}  = 25/6

6th term of the sequence is given by

[tex]a_{6}[/tex]  = 6^2/{6 + 1} = 36/7

7th term of the sequence is given by

[tex]a_{7}[/tex] = 7^2/{7 + 1} = 49/8

Hence, the 4th, 5th, 6th,and 7th terms of the sequence an = n²/{n+1} are 16/5, 25/6, 36/7, and 49/8 respectively.

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Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096

Step-by-step explanation:

You just mutiply the number with 2

The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

The sequence we are provided is 2, 4, 7, 10, …

Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 4 and [tex] a_{3}[/tex] = 7.

A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on

Now, in the given sequence

⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 4 - 2

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2

⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 7 - 4

[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 3

⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 10 - 7

[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 3

Since, the difference between the given sequence of terms are not same.

∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.

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Answer:

81 feet & 19 feet

Step-by-step explanation:

The numbers in the order of least to greatest is :

₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121

Given, the numbers are in decimal and fraction form.

1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1

we need to convert the fractions and then arrange the numbers in the ascending order.

Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.

for 1/2:

1/2 = 0.5

for ₋1/4:

₋1/4 = 0.25

now arrange the numbers according to the least to greatest form.

we have numbers:

0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1

least to greatest form:

₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121

i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121

Hence we get the required form.

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Answer:

[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]

[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]

[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]

Step-by-step explanation:

Long Division Method of dividing polynomials

Divide the first term of the dividend by the first term of the divisor and put that in the answer.

Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.

Repeat until no more division is possible.

Write the solution as the quotient plus the remainder divided by the divisor.

[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]

Solution

[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]

[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Solution

[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]

[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]

Solution

[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]

The quadratic equation which has solutions x = 8 and x = -1 is [tex]\bold{x^2-7x-8}[/tex] = 0.

An equation of degree 2 is called a quadratic equation. That is, the highest power of x in the equation will be two. It has at most two solutions.

Given the solutions are x = 8 and x = -1.

If x = a is a solution, then (x-a) is a factor for the equation.

So here, x-8 and x+1 are factors of the required quadratic equation.

Thus, the quadratic equation will be, (x-8)(x+1) = [tex]\bold{x^2-7x-8}[/tex] = 0.

We can check if x = 8 and x = -1 are the solutions. Put x = 8 in [tex]\bold{x^2-7x-8}[/tex]

Then, 8 x 8 - 7 x 8 - 8 = 0 and -1 x -1 - 7 x -1 - 8 = 0.

So [tex]\bold{x^2-7x-8}[/tex] = 0 is the quadratic equation with solutions x = 8 and x = -1.

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The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.

The formula of the n-th term of a geometric sequence is:

a(n) = a₁ . r^(n-1)

Where:

a₁ is the first term

r  is the ratio = a(n)/a(n-1)

Parameters given in the problem:

a₁ =1024, r=0.5

Plug these parameters into the formula, then we get the explicit formula of the n-th term:

a(n) = 1024 . (0.5)ⁿ⁻¹

The first 5 terms:

a₁ = 1024

a(2) = 1024 . (0.5)²⁻¹

       = 1024 . (0.5)¹ = 512

a(3) = 1024 . (0.5)³⁻¹

       = 1024 . (0.5)² = 256

a(4) = 1024 . (0.5)⁴⁻¹

       = 11024 . (0.5)³ = 128

a(5) = 1024 . (0.5)⁵⁻¹

       = 1024 . (0.5)⁴ = 64

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The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

The given arithmetic series is 6+7.4+8.8+ . . .

The summation notion of given series is ∑6+1.4n , here n starts from 0.

The sum of arithmetic series can be written as,

[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]

n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.

We have, n=11, [tex]a_{1}[/tex] = 6

To calculate sum of arithmetic series, we need to find [tex]a_{11}[/tex] .

[tex]a_{11} = a_{1} + (n-1)d[/tex]

d = 1.4 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get

[tex]a_{11}[/tex] = 6 + (11-1)(1.4)

[tex]a_{11}[/tex] = 6 + 14 = 20

On substituting values in sum of arithmetic series formula, we get

[tex]S_{7}[/tex] = (11(6 + 20))/2 = 143

The summation notion of given series is ∑6+1.4n , here n starts from 0 and the sum of given arithmetic series is 143.

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Answer:

m∠FQR = 23°

Step-by-step explanation:

Since m∠KQF = 90°, it's a complementary angle and is equal to 90°

Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°

(3x - 23)° + (2/3x + 3)° = 90

3x - 23 + (2/3)x + 3 = 90

Combine like terms

multiply the denominator by 3. (3 × 3) = 9 + 2 = 11

(11/3)x - 20 = 90

          + 20   +20

(11/3)x = 110

÷(11/3)  ÷(11/3)

x = 30°

Step 2: Find m∠FQR

m∠FQR = ((2/3)x + 3))

(2/3)(30) + 3

20 + 3 = 23

m∠FQR = 23°

I hope this helps!

Answer:

Step-by-step explanation:

(2/3x+3) + (3x-23)=90

(2/3+3)x -20 =90

11/3x =90 + 20

x= 110 * 3/11 =30

FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23

Answer:

-11.

Step-by-step explanation:

h(x) = -4x - 3, find h(2).​

Replace the x by 2:

h(2) = -4(2) - 3

       = -8 - 3

       = -11.

In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y

The given series is:

    3x + (3 x-2 y) + (3x-4y) + ......

Notice that this is an arithmetic series with:

the first term, a(1) = 3x

the second term, a(2) = 3x - 2y

the 3rd term, a(3) = 3x - 4y

Hence, the common difference is:

     d = (3x - 2y) - 3x = -2y

Recall that the nth term of an arithmetic series is given by:

a(n) = a(1) + (n -1) . d

Substitute n = 15, a(1) = 3x, and d = -2y:

a(15) = 3x + (15 - 1) . (-2y)

a(15) = 3x - 28y

The sum of the first n terms in an arithmetic series is given by:

S(n) = n/2 [a(1) + a(n)]

Substitute n = 15

S(15) = 15/2 [a(1) + a(15)]

S(15) = 15/2 . (3x + 3x - 28y)

S(15) = 15 . (3x - 14y) = 45x - 210y

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Answer:

The answer is 2

Step-by-step explanation:

According to the question, when die is rolled check the number is greater than two and it should be [tex]6[/tex].

The total number of outcomes : [tex]n(E)= {1,2,3,4,5,6}[/tex]

And getting a number greater than [tex]2[/tex] [tex]= {3,4,5,6}[/tex]

Finally, getting a number as [tex]6 = {6}[/tex]

Therefore, the probability can be written as:

[tex]P(E) = \frac{1}{6}[/tex]

Hence, the calculated probability is [tex]\frac{1}{6} .[/tex]

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer:24939.5 i think

Step-by-step explanation:

Answer:

0.245

Step-by-step explanation:

Divide both the numerator and denominator by 2.

49/200 will be 24.5/100

If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245

The portion of wooden strip that is left from the original strip is 1/4

Samantha is using a wooden strip that measures 7/8 yard

Samantha cuts off a piece of the wood that is 3/4 long

The fraction that represents the proportion of the original strip that is left can be calculated as follows

7/8 - 3/4

The LCM of both fractions is 8

7 - 6/8

= 2/8

convert to the lowest term

1/4

Hence the proportion of the original wooden strip that remains is 1/4

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Answer:

7

Step-by-step explanation:

(2t+3r) divide 4

so if r=2 and t=11 the new equation will be :

(2times11 + 3times 2) divide 4

(22+6) divide 4

= 28 divide 4 = 7

The simplified answer to 5.3. √2 will be 7.495.

It should be noted that we are to find the simplified answer to 5.3. √2 .

This means that we have to multiply them. This will be:

= 5.3 × ✓2

= 5.3 × 1.1414

= 7.495

Note that the options given aren't complete.

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Answer: 37°  53°  90°

Step-by-step explanation:

Given:

ΔABC    m∠C=90°    

Solution:

m∠A+m∠B+m∠C=180°

m∠A+m∠B+90°=180°

m∠A+m∠B+90°-90°=180°-90°

m∠A+m∠B=90°

Let m∠A=x°

Hence,

m∠B=(x+16)°

Thus,

x°+(x+16)°=90°

(2x)°+16°=90°

(2x)°+16°-16°=90°-16°

(2)(x)°=74°

Divide both parts of the equation by 2:

x°=m∠A=37°

m∠B=37°+16°

m∠B=53°

Answer:

y = 1100 - 115x

Step-by-step explanation:

Let the monthly payment be $p

In two months Zach would have paid 2p dollars

Balance would be  1100 - 2p = y

We know after 2 months, balance y was actually 870

Substituting y = 870 we get
1100 - 2p = 870

Subtract 1100 on both sides

1100 - 1100 - 2p = 870 -1100

==> -2p = - 230

Divide by -2 on both sides

-2p/-2 = -230/-2

p = 115 which represents the monthly payment .

So the balance y after m months is given by the equation
y = 1100 - 115x

We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent

The value of h based on the information illustrated is 24 1/2.

It should be noted that the fraction given is illustrated as:

3/4h - 12 = 8 5/8

Add 12 to both sides

3/4h - 12 + 12 = 8 5/8 + 12

3/4h = 20 5/8

Multiply both side by 4/3

3/4h × 4/3 = 20 5/8 × 4/3

h = 165/8 × 4/3

h = 27 1/2

Therefore, the value of h is 24 1/2.

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 The final answer is the combination of both solutions   x = 3,− 3.

What are quadratic in math?

Use the quadratic formula to find the solutions

x = - b + √b² - 4ac / 2a

Substitute the values

a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.

x = 0  +  √ 0² - 4 . ( 1 . 9 ) / 2. 1

Simplify

    The final answer is the combination of both solutions.

          x = 3,− 3

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The percent of 16, which is equal to the 80 percent of 42 is 210.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

Let x be the percent of 16, which is equal to the 80 percent of 42.

80% of 42 = x % of 16

80/100 [tex]*[/tex] 42 = x/100 [tex]*[/tex] 16

80(42)/100 = 16/100 [tex]*[/tex] x

Multiplying both sides of the equation by 16/100, then we get

80(42)/100 [tex]*[/tex] (16/100) = 16/100 [tex]*[/tex] x [tex]*[/tex] (16/100)

simplifying the above equation, we get

80(42)/100 [tex]*[/tex] (16/100) =  x

80(42)/16 =  x

210 = x

The value of x = 210.

Therefore, the correct answer is option b. 210.

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Answer:

210

Step-by-step explanation:

We can start by finding 80% of 42:

80% of 42 = (80/100) x 42 = 33.6

So, the question now becomes: what percent of 16 is 33.6?

Let's call the unknown percentage "x".

We can set up the following equation:

x/100 x 16 = 33.6

Multiplying both sides by 100/16, we get:

x = (33.6 x 100)/16

x = 210

There are 190 more birds than expected at the refuge.

The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:

There are 175 birds in all.

According to the inquiry, it is rising by 3%.

Number of birds = (175)(3%) = 5.25 at this point.

As a result, given the data, the anticipated enhanced data is as follows:

Added birds is 175 + 5 + 5 + 5 = 190.

190 more birds are therefore expected in the refuge.

The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.

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