12g=12(2/3g-1)+ 11 Please solve the equation fully and step by step

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

2 years ago

Someone explain it please

Alina [70]

9514 1404 393

Answer:

∠A = 44°

Step-by-step explanation:

In order to find the measure of angle A, you need to know the value of the variable x. This means you need some relation that you can solve to find x.

Happily, that relation is "the sum of angles in a triangle is 180°." This means ...

84° +(x +59)° +(x +51)° = 180°

(2x + 194)° = 180° . . . collect terms

2x = -14 . . . . . . . . . . divide by °, and subtract 194

x = -7 . . . . . . . . . . . .divide by 2

Now, the measure of angle A is ...

∠A = (x +51)° = (-7 +51)°

∠A = 44°

4 0

3 years ago

Day X = 33; Day Y = 44. What is the percent change from day X to day Y?

Serhud [2]

Answer: 33.3% increase, pretty sure

Step-by-step explanation: Big number- Small number, and then divided by the first number: 44-33=11. 11 divided by 33 ( original) is 0.3333, and then change the decimal to a percent, which is 33.3%.

5 0

2 years ago

Please help me 7th grade

Anon25 [30]

Answer:

4(-80) = -320

Step-by-step explanation:

His elevation decreased by 80 each hour. Since he was walking for 4 hours, the equation would be

4(-80) = -320.

6 0

2 years ago

The graph relates the distance traveled by Train A, in miles, and the time taken, in hours. The table shows the distance travele

melomori [17]

Answer:A)

Yes, the relationship is proportional.

B)

66,000 miles.

Step-by-step explanation:

A)

Yes, the graph represents a proportional relationship.

Since, A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:

y=kx

for some constant k , called the constant of proportionality .

As y=12000x hence the relationship is proportional.

B)

We calculate the equation of the graph with the help of two points on the graph namely (2,24000) and (4,48000) with the help of slope-intercept form of the line.

y=mx+c where m denotes the slope of the line and c denotes the y-intercept of the line.

Here when x=2 y=24000 and when x=4 y=48000

Hence, 24000=2x+c

and 48000=4x+c

on subtracting the above two equations we have:

m=12000 and c=0

Hence, the equation of line is y=12000x

Now the value at x=5.5 is:

y=12000×5.5=66,000

Hence, the number of miles the probe travels in 5.5. hours is 66,000 miles.

Step-by-step explanation:

4 0

2 years ago