What is 1 3/10 • 1 1/3

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

Find the island height of a pyramid with a volume of 432 ft^3 if the base is a square with a side length of 12 ft. Round to the

dmitriy555 [2]

So the picture below shows what the slant height is. It also shows that the pyramid can form a right triangle, in which we can use the pythagorean theorem, which is $leg^2+leg^2=hypotenuse^2$ .

But first, we have to find the height of this pyramid. The volume formula for a square pyramid is $A=\frac{lwh}{3}$ . Since we know its a square pyramid, the length and width are going to be the same (12 ft), and we know that the volume is 432 ft^3. Using this info, we can solve for the height:

$432=\frac{12*12*h}{3}\\ 1296=12*12*h\\ 1296=144*h\\ 9=h$

So now we can use the pythagorean theorem (remember to split the 12 by 2, since the right triangle has only half the length of the base). Our equation will be solved as such:

$6^2+9^2=s^2\\ 36+81=s^2\\ 117=s^2\\ 10.8=s$

In short, the slant height is 10.8 ft.

3 0

3 years ago

On a map, 1 inch equals 25 miles.Two cities are 3 inches apart on the map.What is the actual distance between the cities?

SVEN [57.7K]

Answer:

75 miles

Step-by-step explanation:

We are given the scale on the map, which is that 1 inch is 25 miles in real life. We can write that as a ratio of 1 inch: 25 miles. Now say we have two inches, then we have 50 miles because we add on another 25 miles, then we do that again and we get to 75 miles.

Another way to think about it (more complicated):

you can represent ratios as a fraction

so we do 1/25=3/x

To find x, we can do (25*3)/1 which equals 75, if you don't know what I did there then you don't know, sorry!

you can also do it in a different way

same scenario though

you represent it as a fraction

and do 1/25=3/x. We see that the ratio from 1 to 3 is multiplied by 3 so that means the ratio from 25 to x is also going to be multiplied by 3, and 25 multiplied by 3 is 75.

Please let me know if you have any questions.

5 0

3 years ago

Read 2 more answers

Ethan can blow 15 balloons in 20 minutes Junwei can blow 18 balloons in 25 minutes and vishal can blow 16 balloons in 21 minutes

monitta

Answer:

ethan blows fastest

Step-by-step explanation:

5 0

3 years ago

The equations in the system below are equivalent.