List the perfect cubes between 1000 and 3000 that are even numbers

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

3 years ago

the ratio of cats and dogs at the city pound is 92 to 144.which statement descrbes this relationship?

Alexeev081 [22]

Answer:

There are 23 cats for every 36 dogs at the city pound

Step-by-step explanation:

This means that for every group of 92 cats at the city compound there is a group of 144 dogs. So it also means that for every group of 23 cats there is a group of 36 dogs.

92 to 144 or 92/144 = 23/26 or 23 to 36

<h2>Hope This Helps Out</h2>

5 0

2 years ago

Read 2 more answers

You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that

Brrunno [24]

It would be $\frac{10}{38}$ , or, in simplest form, $\frac{5}{19}$ .