Ask question

Ask question

All categories

4 years ago

9

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.

1 answer:

Tasya [4]4 years ago

4 0

Answer:

Number of songs played in commercial are 7 and Number of songs played in movie are 5.

Step-by-step explanation:

Let Number of songs played in commercial be x

and Number of songs played in movie be y.

Total number of songs played =12

Hence,

$x+y=12\ \ \ \ equation \ 1$

Also

Cost for songs played in commercial = $50

Cost for songs played in movie = $130

Total Money earned = $1000

Hence,

$\$50x+\$130y=\$1000$

Dividing by 10 on both side we get;

$\$5x+\$13y=\$100\ \ \ \ equation \ 2$

Now multiplying equation 1 by 5 we get;

$5x+5y=60 \ \ \ \ equation \ 3$

Now Subtracting equation 3 from equation 2 we get;

$(5x+13y=100)- (5x+5y=60)\\8y=40\\y=\frac{40}{8}=5$

y = 5

x + y = 12

x + 5 = 12

x = 12 - 5

x = 7

Hence, Number of songs played in commercial are 7 and Number of songs played in movie are 5.

You might be interested in

Use the properties of exponents to rewrite y=3e^-0.6t in the form y=a(1+r)^t or y=a(1-r)^t. Round the value or r to the nearest

vesna_86 [32]

Answer:

$y=3(1-0.451)^t$

The value of r is 0.451

The percentage decrease is about 45.1%

Step-by-step explanation:

The given exponential function is $y=3e^{-0.6t}$

Using the exponent rule, $(x)^{ab}=(x^a)^b$

$y=3(e^{-0.6})^t$

Now the value of $e^{-0.6}=0.5488$

Thus, we can rewrite the function as

$y=3(0.5488)^t$

Therefore, the function in form $y=a(1-r)^t$

$y=3(1-0.451)^t$

The value of r is 0.451

The percentage decrease is about 0.451 ×100 = 45.1%

8 0

4 years ago

Duane and mick are saving their money to build a tree house.Duane adds $5 to their piggy bank every other week.Mick adds $2 ever

miss Akunina [59]

2 + 7 + 2 + 7 + 2 + 7 + 2 + 7 + 2 + 7 = 45
7 = 5 + 2
10 weeks

they have been saving their money for 10 weeks

6 0

3 years ago

Read 2 more answers

What is the vertex for the function f(x) = 3(x – 2)2 + 4?

Gala2k [10]

Answer:

The vertex for the function f(x) = 3(x – 2)2 + 4 is at (2, 4).

Step-by-step explanation:

Find the vertex for f(x) = 3 (x - 2)^2 + 4

f(x) = 3 (x - 2)^2 + 4 can also be written as:

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

To find critical points, first compute f'(x):

d/(dx)(3 (x - 2)^2 + 4) = 6 (x - 2):

f'(x) = 6 (x - 2)

Solve 6 (x - 2) = 0

6x - 12 = 0

6x = 12

x = 2

iI you substitute x = 2 in 3 (x - 2)^2 + 4 then you get:

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

x = 2

y = 3 (2 - 2)^2 + 4

y = 3 (0)^2 + 4

y = 3 (0) + 4

y = 4

Answer: The vertex for the function f(x) = 3(x – 2)2 + 4 is at ( 2, 4 ).

5 0

3 years ago

Country Club Activities At the Avonlea Country Club, 67% of the members play bridge and swim, and 86% play bridge. If a member i

Volgvan

Answer: 0.78

Step-by-step explanation:

Given : P(bridge and swim) = 0.67

P(bridge)= 0.86

Formula for conditional probability :

$P(B|A)=\dfrac{P(\text{A and B})}{P(A)}$

So, $\text{P(swim }|\text{ bridge) = }\dfrac{\text{ P(bridge and swim)}}{\text{P(bridge)}}$

$=\dfrac{0.67}{0.86}\approx0.78$

Hence, the probability that the member swims, given that the member plays bridge = 0.78

3 0

3 years ago

Of 1936 people so came into a blood bank to give blood, 200 people had high blood pressure. Estimate the probability that the ne

Inessa05 [86]

Answer:

person has a 10% chance of having high bp

Step-by-step explanation:

200 out of 1936 equals about 10%

7 0

3 years ago