The total cost of sand to fill the sandbox is $59.48. Lauren and 3 friends divide the cost equally. How much does each person pay?

Part 1) Finding the inverse

Let x = r and y = H(r)

We have the equation y = 6240(1 + x/100)^t which is the same as saying y = 6240(1 + 0.01x)^t since 1/100 = 0.01

From here, swap x and y to get the equation x = 6240(1+0.01y)^t

Let's solve for y

x = 6240(1+0.01y)^t

6240(1+0.01y)^t = x

(1+0.01y)^t = x/6240

1+0.01y = (x/6240)^(1/t)

0.01y = (x/6240)^(1/t)-1

100*0.01y = 100*((x/6240)^(1/t)-1)

y = 100*((x/6240)^(1/t)-1)

y = 100*(x/6240)^(1/t) - 100

This becomes r = 100*(H/6240)^(1/t) - 100 after we replace y with r and x with H. Note the r and H swapped places, just like x and y did. Earlier we had H isolated on the left, but now r is isolated on the left.

We could write r(H) = 100*(H/6240)^(1/t) - 100 to mean the same thing.

So what exactly does this inverse function do? Well the original function tells us the number of households for any given growth rate, which is r.

The inverse function swaps things around to allow us to find the growth rate if we know how many households there are. We're working backwards. In both cases, t is held to some constant fixed value.

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Part 2) Finding the growth rate if the number of households is 7800 after 3 years.

We're going to plug in H = 7800 and t = 3 into the inverse function we found to determine the value of r, or r(H)

r(H) = 100*(H/6240)^(1/t) - 100

r(7800) = 100*(7800/6240)^(1/3) - 100

r(7800) = 7.72173450159419

You'll need your calculator to get this approximate value. After rounding to two decimal places, we get r(7800) = 7.72

Since r = 7.72, this means the growth rate is 7.72%

$2816.80 is the raise

21 is 30% of 70

Answer: 25.81

Step-by-step explanation:

We can see its a right triangle and then with Squareroot(21^2 + 15^2) = 25.81

Answer:

In mathematics, a variable is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions. In science, there is a independent and dependent variable.

Step-by-step explanation:

Answer:

VARIABLE MEANING: A variable is a letter used to describe an unknown number. A quantity that can change or vary, taking on different values. A letter or symbol representing a varying quantity.

CO EFFICIENT MEANING: A number next a variable behind the letter examples: 4m -3x 6y 5w

EXPRESSION MEANING: An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.

TERM MEANING: It's either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by divide.

Answer:

5000 N

Step-by-step explanation:

Given:

Mass m = 1000 kg

Acceleration a = 5 m/s^2

Force F =?

By Newton's first law of motion:

F = ma

F = 1000 * 5

F = 5000 N

(N = Newton, unit of force is Newton and is written as N. )

This value is approximate because pi = 3.14 is approximate

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Work Shown:

r = 4 = radius

pi = 3.14 approximately

C = circumference

C = 2*pi*r

C = 2*3.14*4

C = 25.12

The circumference is approximately 25.12 meters.

Side note: The circumference is the same as the perimeter of a circle.

Answer:

P=15

Step-by-step explanation:

Answer:

P=15

Step-by-step explanation:

first:

98-38=60

4p=60

60÷4=15

P=15

hope that helped :)

Answer:

82,300

Step-by-step explanation:

last numbers is 345

so if 350 it would go to 400

but it is under so it goes to 300.

Answer:

1. Hundred is 82,300

2. Hundreths is 82,345.57

3. Tens is 82,350

4. Tenths is 82,345.6

Step-by-step explanation:

Hope this helps you!!

Answer:

r = -1

Step-by-step explanation:

-3(1+6r)=14-r

Distribute the -3

-3*1 -3*6r = 14-r

-3 -18r = 14 -r

Add 18r to each side

-3-18r+18r = 14-r+18r

-3 = 14+17r

Subtract 14 from each side

-3-14 = 14+17t-14

-17 = 17r

Divide by 17

-17/17 = -17r/-17

-1 =r

Answer:

well we don't don't know...because x is unknown

Answer:

There no problem but 5<=x in equation form

Step-by-step explanation:

That way because x can either be five or higher

Answer:

---> --->  

WS  DS

Step-by-step explanation:

Answer:

ok have a nice time

Step-by-step explanation:

Answer:

I totally agree *brainly don't take down my answer pls*

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

It is half of 8

A dozen is 12 if there's 2 that's 24 cakes

If they ate 3 now it's 21

Decide that by 3 now it is 8

Answer:

that looks hard sorry i cant help you good luk .

Step-by-step explanation:

perimeter = sum of all sides of figure

perimeter = 18cm + 18cm + 8cm + 18cm + 30cm + 18cm + 18cm + 4cm

perimeter = 132cm

plz follow me

Answer:

B and C

Step-by-step explanation:

It is going down

Answer:

let's define:

x = number of dimes

y = number of quarters.

Then the total amount of money that he has is:

x*$0.10 + y*$0.25

Now we know that:

"He has no more than 24 coins"

Then:

x + y ≤ 24

"...worth at least $3.50 combined"

x*$0.10 + y*$0.25 ≥ $3.50

Then we have two inequalities:

x + y ≤ 24

x*$0.10 + y*$0.25 ≥ $3.50

To graph these, it is easier to write them as linear equations in the slope-intercept form.

Then we need to isolate the y-variable in both equations.

we will get:

y ≤ 24 - x

y ≥ $3.50/$0.25 - x*$0.10/$0.25

In the first equation we have:

"y is smaller or equal than the line"

Then this is graphed with a solid line, and we shade all the region below the line

For the second equation, we have the inverse case, then it will be graphed with a solid line and we need to shade all the region above the line.

The solutions for the system will be all these values that are in both shaded regions.

The graph can be seen below.

In the graph, we can see that one acceptable solution can be:

x = 5

y = 15

or

x = 6

y = 16

The only other restriction we should add is:

x ≥ 0

y ≥ 0

Because Lincoln can not have a negative number of coins, so we can only find solutions in the first quadrant.

Answer:

lol hard!

Step-by-step explanation:

Answer:

-1=n I believe would be the answer.

Answer:

x= 1

Step-by-step explanation:

2x1=2+3=5

Answer:

x is equals to 1..........

Answer: 21

Step-by-step explanation: 21.7659574 would be the exact awnser but to estimate you can just say 21

Answer:

It is actually 20.

Step-by-step explanation:

Answer:

Two x's can have the same y, but an x cannot have different y's. For example, [(2,3)(-2,4)(3,3)(5,18)] is a function because all of the x's have a specific y, and there is not more than one y to an x. However, [(2,3)(-3,7)(2,-4)] is not a function because one of the x's has more than one y.

Step-by-step explanation:

(hope this helps-you can just put the first sentence...the rest is kinda wordy :P)

Answer:

B

Step-by-step explanation:

(f – g)(x) = f (x) – g(x)=

[tex]3 {x}^{2} - 4x + 3 \\ - 2 {x}^{2} + 6x + 4 \\ = 5 {x}^{2} - 10x - 1[/tex]

Answer: 40 + t =58

I just did the problem and the other ones don’t make sense