Write a mixed number that is equivalent to 16/3

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 book shelly is reading has 235pages. She has already read 110 pages. If she reads 25 pages a day from now on, how many more

saul85 [17]

Answer: If Shelly reads 25 pages a day for 5 days she will finish her book

Step-by-step explanation: 235-110=125

125/25=5

6 0

3 years ago

Read 2 more answers

Find the factors of function g.

SashulF [63]

This will be 2400 cause there is nothing in the ones place

3 0

3 years ago

Xavier is a new student, explain to him what a variable is. Use complete sentences.

Anit [1.1K]

Answer:a symbol, usually a letter, used to represent a number.

Step-by-step explanation:

a math process (like adding, subtracting, multiplying, or dividing)

3 0

3 years ago

American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.4% of American

OLga [1]

The variance of the binomial distribution of the number of households with landline service is 2.

<h3>What is the binomial probability distribution?</h3>

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The variance of the distribution is given by:

V(X) = np(1 - p)

In this problem, the parameters are given as follows:

n = 8, p = 0.504.

Hence the variance is given by:

V(X) = 8 x 0.504 x 0.496 = 2.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

5 0

2 years ago