1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Romashka [77]
3 years ago
7

Meg initially has 3 hours of pop music and 2 hours of classical music in her collection. Every month onwards, the hours of pop m

usic in her collection is 5% more than what she had the previous month. Her classical music does not change. Which function shows the total hours of music she will have in her collection after x months?a. f(x) = 2(0.05)x + 3b. f(x) = 3(0.05)x + 2c. f(x) = 2(1.05)x + 3d. f(x) = 3(1.05)x + 2
Mathematics
1 answer:
zlopas [31]3 years ago
3 0

Answer:  Option 'd' is correct.

Step-by-step explanation:

Since we have given that

Number of hours of pop music = 3

Number of hours of classical music = 2

According to question, Every month onwards, the hours of pop music in her collection is 5% more than what she had the previous month. Her classical music does not change.

Rate of increment = 5% = 0.05

Let the number of months be 'x'.

So, our required function becomes,

f(x)=3(1+0.05)x+2\\\\f(x)=3(1.05)x+2

Hence, Option 'd' is correct.

You might be interested in
In which pair do both decimals represent rational numbers?
Assoli18 [71]

Answer:

its A

Step-by-step explanation:

Trust me

3 0
3 years ago
Item 7
Mariulka [41]

Answer:

A = 74.7^\circ

B = 42.5^\circ

C = 62.8^\circ

Step-by-step explanation:

Given

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2

For AB

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

d = \sqrt{(-1 - 2)^2 + (2 - 8)^2

d = \sqrt{(-3)^2 + (-6)^2

d = \sqrt{45

So:

AB = \sqrt{45

For BC

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

BC = \sqrt{(2 - 4)^2 + (8 - 1)^2

BC = \sqrt{(-2)^2 + (7)^2

BC = \sqrt{53

For AC

A = (-1,2) \to (x_1,y_1)

C = (4,1) \to (x_3,y_3)

AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2

AC = \sqrt{(-5)^2 + (1)^2

AC = \sqrt{26

So, we have:

AB = \sqrt{45

BC = \sqrt{53

AC = \sqrt{26

By representation

AB \to c

BC \to a

AC \to b

So, we have:

a = \sqrt{53

b = \sqrt{26

c = \sqrt{45

By cosine laws, the angles are calculated using:

a^2 = b^2 + c^2 -2bc \cos A

b^2 = a^2 + c^2 -2ac \cos B

c^2 = a^2 + b^2 -2ab\ cos C

a^2 = b^2 + c^2 -2bc \cos A

(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A

53 = 26 +45 - 2 * 34.21 * \cos A

53 = 26 +45 - 68.42 * \cos A

Collect like terms

53 - 26 -45 = - 68.42 * \cos A

-18 = - 68.42 * \cos A

Solve for \cos A

\cos A =\frac{-18}{-68.42}

\cos A =0.2631

Take arc cos of both sides

A =\cos^{-1}(0.2631)

A = 74.7^\circ

b^2 = a^2 + c^2 -2ac \cos B

(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B

26 = 53 +45 -97.67 * \cos B

Collect like terms

26 - 53 -45= -97.67 * \cos B

-72= -97.67 * \cos B

Solve for \cos B

\cos B = \frac{-72}{-97.67}

\cos B = 0.7372

Take arc cos of both sides

B = \cos^{-1}(0.7372)

B = 42.5^\circ

For the third angle, we use:

A + B + C = 180 --- angles in a triangle

Make C the subject

C = 180 - A -B

C = 180 - 74.7 -42.5

C = 62.8^\circ

8 0
2 years ago
Gabriel purchases a rug priced at $475. With sales tax, the total comes out to $513. What is the sales tax percentage?
Degger [83]

Answer:

The tax is 8%

Step-by-step explanation:

Take the final price and subtract the original price

513-475 = 38

Divide by the original price

38/475 =.08

Change to percent form

8%

The tax is 8%

8 0
2 years ago
Read 2 more answers
How do you write x+y=9 in y=mx+b?
Alina [70]
Y=-x+9 is the correct answer
4 0
3 years ago
Read 2 more answers
Rewrite this expression using a positive exponent.<br> -7<br> 5
Sergio [31]

Answer:

1/5^7

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Over the last 50 years, the average cost of a car has increased by a total of 1,094%. If the average cost of a car today is $31,
    14·1 answer
  • 196 divided by 3.5=_____
    14·2 answers
  • What is the easiest way to show my 11 year old to simplify fractions?
    14·1 answer
  • Central Park is a rectangular park in New York City. A map of Central Park in New York City. The measured length is 12.5 centime
    14·1 answer
  • The graph of the equation y=-2 is a line Explain your answer 1) parallel to the x-axis 2)parallel to the y-axis 3)passing throug
    15·1 answer
  • SOMEONE PLZ HELP FAST AND SHOW UR WORK ILL MARK BRAINLIEST IF YOU SHOW UR WORK AND ANSWER CORRECTLY
    7·1 answer
  • Lin was putting up lights for the holidays around the house. She put up 48 lights in her house and 36 of the lights were green.
    13·2 answers
  • Pls answer
    11·1 answer
  • PLEASE HELP!!!
    7·1 answer
  • What is the range of the function y = 2sin x?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!