Suppose you are able to download 1 free song to your tablet daily and each additional download costs $0.59. If your monthly bill is $15.34, how many songs did you download if you download 28 free songs? Write an equation and solve for the unknown variable

The fraction ( 8/10 ) when converted into a decimal number is equal to 0.8.

The decimal number system is frequently used to express both integer and non-integer quantities. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system.

The number of shots fired by Marlin should be expressed as a decimal number.

We know that,

Marlin made 8 shots out of 10 shots which is in fraction, it is 8/10.

However, since we are dividing by 10, we shall shift the decimal point of 0.8 to the left (the zero is not really important as it only represents a place value )

Or,

( 8 /10) = ( 4 / 5 ) = 0.8

Therefore, the fraction of the shots Marlin made is 0.8.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 5x + 6}\\\mathsf{f(x) = 5(-7) + 6}\\\mathsf{f(x) = -35 + 6}\\\mathsf{f(x) = -29}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{f(x) = -29}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

$30.75

Step-by-step explanation:

Since the sale was 20% off, the tennis racket is 80% of its original price.

[tex].8p = 24.60[/tex]

[tex]p = 30.75[/tex]

The diameter of circle is 10.0 feet.

We are given the area of circle. The formula of area with respect to diameter is as follows -

Area = 1/4πd², where d represents diameter of circle.

Taking the value of π as 3.14.

Rewriting the equation according to diameter -

d² = (area×4)÷π

Now, keep the values in formula to find the diameter of circle.

d² = (79×4)÷3.14

Performing multiplication on the Right hand side of the equation

d² = 316÷3.14

Performing division on the Right hand side of the equation

d² = 100.6

d = √100.6

Taking square root on the Right hand side of the equation

d = 10.03 feet

Rounding to nearest tenth -

d = 10.0 feet

Hence, the diameter of circle is 10.0 feet.

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The evaluation of the given functions are as follows;

1. f(x) = 3 - x

g(x) = -2•x

Therefore;

g(fx) = -2 × f(x)

Which gives;

-2 × (3 - x) = -6 + 2•x = 2•x - 6

g(fx) = 2•x - 6

B. 2•x - 6

2. f(x) = 3 - x

g(x) = -2•x

f(g(x)) = 3 - (-2•x) = 3 + 2•x

f(g(x)) = 3 + 2•x

f(g(2)) = 3 + 2×2 = 7

The correct option is therefore;

C. 7

3. f(x) = 3 - x

g(x) = -2•x

Therefore;

g(fx) = 2•x - 6

g(f-1) = 2×(-1) - 6 = -8

C. -8

4. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²

F(G(x)) = 2•(3•x + 2) - 1 = 6•x + 3

F(G(x)) - F(x) = 6•x + 3 - (2•x - 1) = 4•x + 4

A. 4•x + 4

5. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²

G(H(x)) = 3•x² + 2

G(H(1)) = 3×1² + 2 = 5

A. 5

6. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²

F(G(H(x))) = 2•(3•x² + 2) - 1 = 6•x² + 3

F(G(H(2))) = 6×2² + 3 = 27

B. 27

7. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²

H(x + a) - H(x) = (x + a)² - x² = 2•a•x + a²

B. a² + 2•a•x

8. (H(x + a) - H(x))/a = (a² + 2•a•x)/a

(a² + 2•a•x)/a = a + 2•x = 2•x + a

A. 2•x + a

9. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²

F(x) + G(x) + H(x) = 2•x - 1 + 3•x + 2 + x² = x² + 5•x + 1

C. x² + 5•x + 1

10. f(x) = 2•x² - 3•x + 1

f(3) - f(2) = 2×3² - 3×3 + 1 - (2×2² - 3×2 + 1) = 7

B. 7

11. G(x) = 5•x - 2

G^(-1)(x) = (G(x) + 2)/5

Which gives;

G^(-1)(x) = (x + 2)/5

A. (x + 2)/5

12. f(x) = 2/(x - 6)

The inverse is therefore;

(2/f(x)) + 6

The inverse of f(x) is therefore;

(2/x) + 6

13. g(x) = (5•x - 5)/4

(4•g(x) + 5)/5 = (4/5)•g(x) + 1

The inverse of g(x) is therefore;

(4/5)•x + 1 = f(x)

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Answer:

x=2/7 - 6y/7

Step-by- explanation:

The numerical length of line segment AC is 25.

A line segment refers to a straight line connecting two points.

If point B is on line segment AC, then point B divides the line segment into segments AB and BC.

AB + BC = AC

Given that AB =2x + 10, BC = x, and AC = 5x, substitute these expressions in the equation AB + BC = AC.

AB + BC = AC

2x + 10 + x = 5x

3x + 10 = 5x

5x - 3x = 10

2x = 10

x = 5

To determine the numerical length of line segment AC, substitute the value of x in the equation AC = 5x.

AC = 5x

AC = 5(5)

AC = 25

Hence, the numerical length of line segment AC is 25.

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According to the question, the probability of the event in which all the students went to prom except one. For this, the probability of the complement rule is used.

Out of [tex]100[/tex] students, [tex]91[/tex] went to prom.

So, the probability that students went to prom = [tex]\frac{91}{100} =0.91[/tex]

Now, P(both went to prom) = [tex](0.91)(0.91)=0.8281[/tex]

Using standard probability formula:

P(at least one did not went to prom) = 1-P(both went to prom)

                                                               [tex]1-0.8281=0.1719=17.2%[/tex]

The probability that at least one student did not went is [tex]17.2[/tex] percentage.

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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The amount paid for 0.4 pounds of much after deducting $0.50 coupon is $1.58. option B

Cost of mulch : pounds of mulch

5.20 : 1 = x : 0.4

5.20/1 = x/0.4

5.20 × 0.4 = 1 × x

2.08 = x

Cost of 0.4 pounds of mulch = x = $2.08

Amount paid for 0.4 pounds of much after deducting $0.50 coupon

= $2.08 - $0.50

= $1.58

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Answer:

b) $1.58

Step-by-step explanation:

Now we have to,

→ find the amount the customer must pay.

One pound of mulch costs,

→ $5.20

Then 0.4 pounds of mulch costs,

→ $5.20 × 0.4

→ 5.20 × 0.4

→ $2.08

Total cost after reducing $0.50,

→ 2.08 - 0.50

→ $1.58

Hence, customer must pay $1.58.

By elimination, the solution of the system of equations, x + y = 12 and x - y = 2, is (7 , 5).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable y.

x + y = 12     (equation 1)

x  - y = 2    (equation 2)

2x + 0y = 14

x = 7

Substitute the value of x to any of the two equation and solve for y.

x + y = 12     (equation 1)

7 + y = 12

y = 12 - 7

y = 5

Hence, the solution of the system of equations is (7 , 5).

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Answer: 16/45

Step-by-step explanation:

[tex]\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}[/tex]

Answer:

x

2

−4x−5=0

All equations of the form ax

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±

b

2

−4ac

​

​

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x

2

−4x−5=0

This equation is in standard form: ax

2

+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,  

2a

−b±

b

2

−4ac

​

​

.

x=

2

−(−4)±

(−4)

2

−4(−5)

​

​

Square −4.

x=

2

−(−4)±

16−4(−5)

​

​

Multiply −4 times −5.

x=

2

−(−4)±

16+20

​

​

Add 16 to 20.

x=

2

−(−4)±

36

​

​

Take the square root of 36.

x=

2

−(−4)±6

​

The opposite of −4 is 4.

x=

2

4±6

​

Now solve the equation x=

2

4±6

​

 when ± is plus. Add 4 to 6.

x=

2

10

​

Divide 10 by 2.

x=5

Now solve the equation x=

2

4±6

​

 when ± is minus. Subtract 6 from 4.

x=

2

−2

​

Divide −2 by 2.

x=−1

The equation is now solved.

x=5

x=−1

On simplifying, x(x2 + 7x + 1) is the final expression.

The provided simplification expression can be solved, per the question, by moving the variable terms to one side and the normal terms to the other.

As a result, the phrase may be expressed more succinctly as:

(3x^3+4x^2) - (2x^3 + 3x^2 -x)

x^3 + 7x^2 + x

x(x^2 +7x + 1)

Consequently, x(x2 + 7x + 1) is the right solution via simplification.

A technique to make the phrase less complex is simplification. And the variables' calculations became simple. Problems with simplification can be resolved by using mathematical characteristics.

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Three angles make compose a triangle.

They'll be known as a°, b°, c°.

If we total everything up:

a° + b° + c = 180

The triangle's horizontal line may be drawn farther to the right, creating a new angle. Call this angle "d°" for short.

a° + b° Equals d°

Give this some values:

a° = 60° b° = 70°

c° = 50°

Do should be 130° since c and d create 180° with c° 50°.

Additionally, because:

A + B + C Equals 180, and C + D = 180.

Because the cremains in both cases are the same, a + b = d.

Any of these fit the bill.

Let's call this f° if you will just extend the triangle's horizontal line to the left.

So, b + c Equals f.

So, if a F Equals 120° since f = 60° and a + f = 180.

We established that b + c Equals f in this instance.

Let's now make the line longer and give it the name angle g°.

B being equal to 70°, the angle next to it is 110°.

Consequently, a + c = g.

All inner angles added together equal 180 degrees.

Additionally, the total of the other two inside angles is equal to the outer angles.

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The Simplification of 2x +26

simplify:

4(× + 5) - 2(x - 3)

4x + 20 - 2x +6

2x +26

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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[tex]\displaystyle\\Answer:\ p=-\frac{1}{q}[/tex]

Step-by-step explanation:

A perfect square has equal sides

Hence, px²+2x-q has equal roots (D(discriminant)=0)

[tex]\displaystyle\\D=2^4-4*p*(-q)\\D=2*2+4pq\\D=4+4pq\\D=0\\\Rightarrow\ 0=4+4pq\\Divide\ both\ parts\ of\ the \ equation\ by\ 4:\\0=1+pq\\0-1=1+pq-1\\-1=pq\\Divide\ both\ parts\ of\ the \ equation\ by\ q(q\neq 0):\\-\frac{1}{q}=p\\ Thus,\\p=-\frac{1}{q}[/tex]

Answer:

Step-by-step explanation

Equation: y=3.5x

Constant of proportionality:

The constant ratio of one variable quantity to another to which it is proportional.

Answer: 3.5

The reason is for 3.5 cakes you need this amount of milk.

the angles are the same as their pair

the pairs are

1 and 5

2 and 6

4 and 8

3 and 7

The missing angles in degrees are-

In the given figure;

∠g = 29°, as ∠g and ∠29° are vertically opposite to each other. Both will be equal.

Similarly,

∠k = 61°, as ∠k and ∠61° re vertically opposite to each other. Both will be equal.

From the linear pair;

∠h + ∠g = 180

∠h = 180 - 29

∠h = 151°

Similarly,

∠m + ∠k = 180

∠m = 180 - 61

∠h = 119°

Thus, the missing values of the angles are found.

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The expression that is equivalent to 4 ^ 3 would be an expression that equals 4 ^ 3

4 ^ 3 = 4 x 4 x 4 = 16 x 4 = 64

Answer:

4^3 =

4 x 4 x 4 x4 = 64

Answer:

no worry I'll help u out

Step-by-step explanation:

90+55=145

180-145=35

z=35°

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The final price of the smart phone if you use the store credit card is $375.15.

A discount is when the price of an item is marked down. An item becomes cheaper when it is discounted.

Percentage is the fraction of an amount expressed as an amount out of 100. Percentage is a measure of frequency. The sign used to represent percentage is %.

Price of the smartphone after 35% is discounted : (1 - percentage decrease) x original price

(1 - 0.35) x 679

0.65 x 679 = $441.35

Purchase price after you buy with your credit card : (1 - percentage decrease) x discounted price

(1 - 0.15) x  $441.35

0.85 x  $441.35

= $375.15

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The statement "The arithmetic mean of two numbers is the positive square root of the product of the numbers." is False.

And the true sentence is "The geometric mean of two numbers is the positive square root of the product of the numbers."

Arithmetic Mean:

The arithmetic mean, is also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.

Given,

Here they given the sentence, "The arithmetic mean of two numbers is the positive square root of the product of the numbers.".

We need to find this one is true or not and we also need to replace the underlined word or phrase to make a true sentence.

Based on the definition of arithmetic mean, the given statement is false.

And the correct sentence is

"The geometric mean of two numbers is the positive square root of the product of the numbers.".

Because geometric mean is average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.

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Answer:

89.4

Step-by-step explanation:

89.9,89.6 are more than five so we'll be using the lowest number as the nearest thenth

Answer:

You have to use the distance formula

d=√(x2-x1)^2 + (y2-y1)^2

replace the points and get 10

To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.

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Answer:

The other number is (-18/7)

Step-by-step explanation:

Let the other rational number be 'x'.

  [tex]\sf x * \dfrac{7}{9}= \dfrac{-14}{7}[/tex]

       [tex]\sf x = \dfrac{-14}{7} \div \dfrac{7}{9}[/tex]

Now, use KCF method.

       [tex]\sf x = \dfrac{-14}{7}*\dfrac{9}{7}\\\\x = -2* \dfrac{9}{7}\\\\x = \dfrac{-18}{7}[/tex]

Answer:

-18/7

Step-by-step explanation:

let the unknown no be y

7/9×y= -14/7

7y/9= -14/7

cross multiply

-14×9=7y×7

divide both sides by 7

-2×9=7y

-18=7y

divide both sides by the coefficient of y which is 7

y= -18/7

hope this helps

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The annual percentage rate on a loan with a stated rate of 2.75 percent per quarter is 11%.

It was given that the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter.

It should be noted that quarter means that the value was divided by 4.

Therefore, the annual percentage will be:

= 2.75 × 4

= 11%.

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For given data set, The value of mean is 6.02.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The formula to calculate mean is = sum of all observations / total number of observations

x = 4     5    6    7    8  

f = 12     1     8   18   4        ∑f = 43

fx = 48  5   48  126  32    ∑fx = 259

The formula of mean = ∑fx /  ∑f

= 6.02

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