Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.

The given angles 76.2°, 81.7°, and 22.1° can make a triangle, as the sum of these angles is exactly 180°, aligning with the geometric rule that the sum of the interior angles of a triangle must be 180°.

To determine whether the given angles can make a triangle, the law in geometry states that the sum of the measures of the interior angles in a triangle must add up to 180 degrees. To see if the angles 76.2°, 81.7°, and 22.1° can make a triangle, we add them up. The sum is 76.2 + 81.7 + 22.1 = 180 degrees. Thus, yes, these three angles can form a triangle because their sum is exactly 180°.

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Final answer:

The rule for determining the cost based on the number of tickets is Cost = 30 × Tickets. Using this rule, the cost for 10 tickets is calculated to be 300 dollars.

Explanation:

The question requires us to determine a rule for the output based on the given input of tickets and then use this rule to find the cost for 10 tickets. By examining the input and output values provided, we see a consistent pattern: the cost increases by 30 dollars with each additional ticket. Given this pattern, the rule can be formulated as an algebraic expression: Cost = 30 × Tickets.

Applying this rule to an input of x tickets, the expression becomes Cost = 30 × x. To find the cost for 10 tickets, we replace x with 10: Cost = 30 × 10 = 300 dollars.

Final answer:

After 60 years, with an initial deposit of $370 at a 2% interest rate compounded quarterly, the amount in the savings account would be approximately $996.26. This amount does not triple the initial savings, as it is less than $1110.

Explanation:

To calculate the amount of money in the savings account 60 years later with an initial deposit of $370, an interest rate of 2% compounded quarterly, we use the compound interest formula:
A = P(1 +  rac{r}[tex]{n})^{nt}[/tex]
Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for in years.

In this case:

P = $370

r = 0.02 (2% as a decimal)

n = 4 (since the interest is compounded quarterly)

t = 60

So, the equation becomes:

A = 370(1 +  rac{0.02}[tex]{4})^{4 imes 60}[/tex]
A = 370[tex](1 + 0.005)^{240}[/tex]
A = 370[tex](1.005)^{240}[/tex]
A = 370(2.69259) = $996.26 (rounded to two decimal places)

So, after 60 years, the amount in the account would be approximately $996.26. To check if the savings have tripled:

370 imes 3 = $1110

Since $996.26 is less than $1110, the savings have not tripled.

x+y=19 and 6.5x+3y=74.5 can be used to determine the number of gifts wrapped and number of giftbags prepared where x represents the wrapped gifts and y represents giftbags.

Step-by-step explanation:

Let,

x be the gift wrapped with wrapping paper.

y be the gifts in gift bag.

Time for wrapping one gift = 6.5 minutes

Time for doing 1 gift bag = 3 minutes

Total gifts = 19

Total time = 74.5 minutes

According to given statement;

x+y=19

6.5x+3y=74.5

x+y=19 and 6.5x+3y=74.5 can be used to determine the number of gifts wrapped and number of giftbags prepared where x represents the wrapped gifts and y represents giftbags.

Keywords: linear equation, addition

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Answer:753

Step-by-step explanation:

The value of [tex]n^{th}[/tex] term can be calculated by,

[tex]T_{n} = a+(n-1)d\\[/tex]

where,

a = first number of the series

d = constant difference between the numbers

So, according to the question,

a = -6

d = 11

n = 70

hence, by substituting,

[tex]T_{n} = (-6)+(70-1)11\\T_{n} = 753[/tex]

Final answer:

The 70th term of the arithmetic sequence -6, 5, 16 is calculated using the formula for the nth term of an arithmetic sequence, resulting in the 70th term being 753.

Explanation:

The student is asking for the 70th term of the arithmetic sequence -6, 5, 16. In an arithmetic sequence, the difference between consecutive terms is constant. This difference is referred to as the common difference "d". The formula for finding the nth term an of an arithmetic sequence is:

an = a1 + (n - 1)d

Using the provided sequence, we can find the common difference by subtracting the first term from the second term:

d = 5 - (-6) = 11

Now, apply the formula to find the 70th term:

a70 = a1 + (70 - 1)  imes d

a70 = -6 + 69  imes 11

a70 = -6 + 759

a70 = 753

Therefore, the 70th term of the given arithmetic sequence is 753.

Answer:

c=29/20

d=13/5

Step-by-step explanation:

4c+2d=11   A

7d=82-44c  7d+44c=82     B

The first equation multiply by 11

and we get 44c+22d=121   C

C-B=44c+22d-7d-44c=39

15d=39

d=39/15=13/5

so c= 29/20

Answer:

18

Step-by-step explanation:

108/12=9

18/2=9

---------------

9+9=18

Answer:

Right-triangle

Step-by-step explanation:

Take a right triangle for example, then twist it 360 degrees, keeping the longest leg at the center of rotation. It will then form a cone.

Answer:

the answer is an isosceles triangle

Answer:

a. $1.60

b. $8/3 which is about $2.67

Step-by-step explanation:

a. five friends in total. 8/5 = 1.6

b. three friends left. 8/3 =~ 2.67

Hence, for

(A) Each person have to pay is $[tex]1.6[/tex].

(B) Each person's share of the $[tex]8[/tex] tolls now is [tex]2.67[/tex].

What is the division?

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Here given that,

Eric and four of his friends are taking a trip across the New York State

Thruway. They decide to split the cost of tolls equally.

(A)

If the total cost of tolls is $[tex]8[/tex], how much will each person have to

pay

So, five friends in total cost of trolls is

[tex]\frac{8}{5}=1.6[/tex]

(B)

Just before leaving on the trip, two of Eric's friends have a family

emergency and cannot go.

So, three friends left then,

[tex]\frac{8}{3}=2.67[/tex]

Hence, for

(A) Each person have to pay is $[tex]1.6[/tex].

(B) Each person's share of the $[tex]8[/tex] tolls now is [tex]2.67[/tex].

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Answer:

Step-by-step explanation:

Return rate, r = 3% = 0.03

x = initial investment

b = final balance

After 1 year, the balance i

b = initial investment + interest

b = x + r*x = (1 + r)*x

Because r = 0.03,

b = 1.03x   (after 1 year)

Answer:

The total  number of votes 6976 votes

Explanation:

We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.

Let no. of yes votes be equal to x

So we can write 3:5 = x:4360

total number of yes votes can be obtained by Solving for x

[tex]x = \frac{(4360\times 3)}{5}[/tex]

= 2616

Now total number of votes =

sum of total number of yes votes and total number of no votes

= 2616 + 4360

= 6976

Hence, 6976 is the total number of votes of the residents

Answer:

The total  number of votes 6976 votes

Explanation:

We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.

Let no. of yes votes be equal to x

So we can write 3:5 = x:4360

total number of yes votes can be obtained by Solving for x

= 2616

Now total number of votes =

sum of total number of yes votes and total number of no votes

= 2616 + 4360

= 6976

Hence, 6976 is the total number of votes of the residents

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Step-by-step explanation:

Answer:

x=6, y=4. (6, 4).

Step-by-step explanation:

x+y=10

x-y=2

----------

x=y+2

y+2+y=10

2y+2=10

2y=10-2

2y=8

y=8/2=4

x+4=10

x=10-4=6

It will take 12.8047 years for Jari's investment to double

Step-by-step explanation:

The formula for compound interest, including principal sum is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:

Jari invests in a CD with an annual interest rate of 5.45% compounded quarterly. We need to find how many years it will take for Jari's investment to double.

∵ The annual interest rate is 5.45%

∴ r = 5.45% = 5.45 ÷ 100 = 0.0545

∵ The interest rate is compounded quarterly

∴ n = 4

∵ The Jari's investment is doubled in t years

∴ A = 2P

- Substitute these values in the rule above

∵ [tex]2P=P(1+\frac{0.0545}{4})^{4t}[/tex]

- Divide both sides by P

∴ [tex]2=(1+\frac{0.0545}{4})^{4t}[/tex]

∴ [tex]2=(1+0.013625)^{4t}[/tex]

∴ [tex]2=(1.013625)^{4t}[/tex]

- Insert ㏒ to both sides

∴ [tex]log(2)=log[(1.013625)^{4t}][/tex]

- Remember [tex]log(a)^{n}=nlog(a)[/tex]

∴ ㏒(2) = 4t ㏒(1.013625)

- Divide both sides by 4 ㏒(1.013625) to find t

∴ t = 12.8047 years

It will take 12.8047 years for Jari's investment to double

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Answer the answer is in the attachment

To solve for h in the given equation A = (1/2)(ah/bh), divide both sides by (a/b) to isolate h, resulting in h = 2A/b.

Solve for h:

Start with the given equation A = (1/2)(ah/bh).

Divide both sides by (a/b) to isolate h.

Therefore, h = 2A/b.

Answer:

D. 27:1331

Step-by-step explanation:

The volume ratio for the two solids is the side length ratio raised to the third power.

3 to the 3rd power = 27

11 to the 3rd power = 1331

The ratio of their volumes is 27/1331.

Option D is the correct answer.

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

Similar pyramids are pyramids that have the same shape but may differ in size. If two pyramids are similar, then the ratio of the lengths of their corresponding edges (also called sides or heights) is proportional to the ratio of their volumes.

Let's say we have two similar pyramids with corresponding edges a and b, and their volumes are V1 and V2, respectively.

Then, we have:

a/b = k, where k is a constant (the ratio of the lengths of their corresponding edges).

The ratio of their volumes is then:

[tex]V_1/V_2 = (a/ b)^3 = k^3[/tex]

The ratio of their volumes is proportional to the cube of the ratio of their corresponding edges.

This means that if the ratio of the lengths of the corresponding edges is 3:11, then the ratio of the volumes of the two pyramids will be:

[tex](3/11)^3 = 27/1331.[/tex]

Therefore,

The ratio of their volumes is 27/1331.

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Answer:

perimeter =3200cm

Step-by-step explanation:

l=12m=1200cm

w=400cm

perimeter=2(w+l)

=2(1200+400)

=2(1600)

=3200cm

The perimeter of a rectangle in cm that has a length of 12 meters and a width of 400cm is 3200 cm

perimeter of a rectangle = 2(l + w)

where

l = length

w = width

Therefore,

let's convert meters to centimetres

1m = 100 cm

12m = ?

cross multiply

length = 1200 cm

width = 400 cm

perimeter of the rectangle = 2(1200 + 400)

perimeter of the rectangle = 2(1600)

perimeter of the rectangle = 3200 cm

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Answer:

3(x-4)(x+1)

Step-by-step explanation:

Step-by-step explanation:

[tex](3x - 12)(x + 1)[/tex]

Answer:

The number which satisfy the given statement is 7 .

Step-by-step explanation:

Given statement as :

If the sum of twice a number and -12 is multiplied by 2 the result is 11 greater than the opposite  of the number find the number

Now, Let The number be x

So, As per statement

2 × [2 x + ( - 12 ) ] = 11 + ( - x )

Or, 2 × 2 x - 2 × 12 = 11 - x

Or, 4 x - 24 = 11 - x

Or, 4 x + x = 11 + 24

or, 5 x = 35

∴  x = [tex]\frac{35}{5}[/tex]

I.e x = 7

so, number is x = 7

Hence The number which satisfy the given statement is 7 . Answer

Answer:

50, 60, 50, and 60

Step-by-step explanation:

xy = 3000

2x + 2y = 220

Rewrite the second equation

y = -x + 110

Substitute this into the first equation.

x(-x + 110) = 3000

-x^2 + 110x - 3000

Divide by -1

x^2 - 110x + 3000

(x - 60) (x - 50)

x = 60, 50

When x = 60, y = 50 and vice versa, so the sides are 50, 60, 50, and 60.

Answer:

Step-by-step explanation:

Do you still need help

Answer:

9/10

Step-by-step explanation:

you find the lowest common denominator in this case is 10

then you take 1/2 and multiply it by 5 both the bottom and top and then you should get 5/10

next you do the same with 2/5 but this time to the get the denominator to 10 you multiply by 2 again multiply both bottom and top and you should get 4/10

now you just add 4/10 and 5/10 together and you get 9/10 or 0.9 as a decimal

The 9/10 of the group's video games are either at Jerome's house or Mario's house.

To determine what fraction of the group's video games is either at Jerome's house or Mario's house, we add Jerome's fraction to Mario's fraction. Jerome has 1/2 and Mario has 2/5. To add these two fractions, we need a common denominator. Multiplying the numerator and denominator of Mario's fraction by 2, we get 4/10. We can also express Jerome's fraction as 5/10. Now we can add them:

5/10 (Jerome) + 4/10 (Mario) = 9/10

Answer:

77

Step-by-step explanation:

0.18*430=77.4

Answer:

37.5 miles

Step-by-step explanation:

4in = 25 miles

1in = 25/4

4 + 2 = 6

6 = 25 +(6.25*2)

6 = 37.5

To find the distance represented by a line segment on a scale drawing, set up a proportion and solve for x.

To determine the distance represented by a line segment on the scale drawing, we can set up a proportion using the given information. Since 4 inches represents 25 miles, we set up the proportion 4/25 = 6/x, where x represents the distance represented by the line segment. To find x, we can cross-multiply and solve for x: 4x = 150, and dividing both sides by 4 gives x = 37.5. Therefore, the line segment represents a distance of 37.5 miles.

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Answer:

It's -6

ur welcome

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

Let the total bill be "x"

Now,

Anna paid 40% (40/100 = 0.4) of the bill, that means

Cassie paid 100 - 40 = 60% of the bill, that is 60/100 = 0.6

Anna paid 0.4x  &  Cassie paid 0.6x

Cassie's amount is 8 dollar more, so we can write:

0.6x - 8 = 0.4x

Now, we solve for x:

0.6x - 0.4x = 8

0.2x = 8

x = 8/0.2

x = 40

THe total bill is $40

Answer:

[tex]\$16,990.62[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]  

substitute in the formula above

[tex]A=15,000(1+\frac{0.025}{4})^{4*5}[/tex]  

[tex]A=15,000(1.00625)^{20}[/tex]  

[tex]A=\$16,990.62[/tex]  

The right answer is Option B.

Step-by-step explanation:

Let,

Number of songs = x

Price of 1 song = $0.99

Membership fee = $19.99

Total amount paid = $21.97

According to given statement;

0.99x+19.99=21.97

Subtracting 19.99 from both sides

[tex]0.99x+19.99-19.99=21.97-19.99\\0.99x=1.98[/tex]

Dividing both sides by 0.99

[tex]\frac{0.99x}{0.99}=\frac{1.98}{0.99}\\x=2[/tex]

Lauren bought 2 songs.

The right answer is Option B.

Keywords: Linear equation, subtraction

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Answer:

2.1

Step-by-step explanation:

3.4-2.8d+2.8d-1.3

3.4-1.3=2.1

Answer:

27

Step-by-step explanation:

9x3

Answer:

x = 3.576 and x = - 3.076

Step-by-step explanation:

Two functions are given to be, g(x) = 2x² + 3x + 10 and k(x) = 2x + 16.

Now, we have to solve the equation g(x) = 2k(x)  

⇒ 2x² + 3x + 10 = 4x + 32

⇒2x² - x - 22 = 0

The expression in the left hand side can not be factorized and therefore we have to use Sridhar Acharya formula which gives the solutions of the equation in the form ax² + bx + c = 0 are given by  

[tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} - 4ac} }{2a}[/tex]

Therefore, the solutions of the given equation are  

[tex]x = \frac{-(- 1) + \sqrt{(- 1)^{2} - 4 (2)(-22)}  }{2(2)} = 3.576[/tex]

and [tex]x = \frac{-(- 1) - \sqrt{(- 1)^{2} - 4 (2)(-22)}  }{2(2)} = -3.076[/tex] (Answer)

Final answer:

To solve the equation g(x) = k(x) for x, we simplify it to 2x² + x - 6 = 0 and factor it, resulting in x = 1.5 or x = -2. The method used is factoring due to the simplicity of the equation.

Explanation:

To solve the equation g(x) = k(x) algebraically for x, we set the given functions equal to each other. Given the functions g(x) = 2x² + 3x + 10 and k(x) = 2x + 16, the equation becomes 2x² + 3x + 10 = 2x + 16. To solve for x, we must first simplify the equation by moving all terms to one side and then using the quadratic formula or factoring, if possible.

Step 1: Subtract 2x and 16 from both sides to obtain the quadratic equation 2x² + x - 6 = 0.

Step 2: Factor the quadratic equation if possible. In this case, it factors to (2x - 3)(x + 2) = 0, so the possible solutions for x are x = 1.5 or x = -2.

The chosen method for solving this quadratic equation is factoring because the equation simplifies nicely and the factors are easily observable.

Answer:

No image is included. Please create another question and include the image and details about the question! :)

Step-by-step explanation: