At a local grocery store, 7 lb of squash cost $14.00
and 4 lb of tomatoes cost $10.00.

The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.

The given parameters are:

[tex]\mathbf{a =10000}[/tex] --- the initial population

[tex]\mathbf{r =0.3\%}[/tex] -- the declining rate

Population are always modelled using exponential function.

This is represented as:

[tex]\mathbf{y = a(1 - r)^x}[/tex]

Where y represents the population in x years.

So, we have:

[tex]\mathbf{y = 10000(1 - 0.3\%)^x}[/tex]

[tex]\mathbf{y = 10000(1 - 0.003)^x}[/tex]

[tex]\mathbf{y = 10000(0.997)^x}[/tex]

When the population reaches half, then y = 5000.

So, we have:

[tex]\mathbf{5000 = 10000(0.997)^x}[/tex]

Divide both sides by 10000

[tex]\mathbf{0.5 = 0.997^x}[/tex]

Take logarithm of both sides

[tex]\mathbf{log(0.5) = log(0.997)^x}[/tex]

Apply law of logarithm

[tex]\mathbf{log(0.5) = xlog(0.997)}[/tex]

Make x the subject

[tex]\mathbf{x = log(0.5) \div log(0.997)}[/tex]

[tex]\mathbf{x = 230.7}[/tex]

This means that the population will become half the original population in 230.7 years.

The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.

Read more about exponential function at:

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Answer:

4

Step-by-step explanation:

8x - 4 = 4x + 12

Add 4 to both sides:

8x = 4x + 16

Subtract 4x from both sides:

4x = 16

Divide by 4 from both sides"

x = 4

Answer:

I have attached my answer below.

Step-by-step explanation:

Sorry, I was not able to do the last one as I don't know how to do it.

Hopefully this helps!!

Answer:

25 times 58

Step-by-step explanation:

guessed

Linear Equation in two variables?

Answer:

NO

Step-by-step explanation:

Answer:

y2-y1 over x2-x1, typically the second or set of the higher numbers would be #2 so im taking 0,11 as #2

Step-by-step explanation:

7 i believe

Answer:

y2-y1/x2-x1

11-4/1-0

7/1

slope = 7

Answer:

14

Step-by-step explanation:

70/5 = 14

Answer:

Given:f(x)=2x^2-3x-1

Then,f(-1)=2(-1)^2-3(-1)-1

f(-1)=2(1)+3-1

f(-1)=5-1

f(-1)=4

Step-by-step explanation:

Answer:

yes because it does not have a exponent

Step-by-step explanation:

Answer:

33 1/3%

Step-by-step explanation:

Answer:

33.3%

Step-by-step explanation:

We can also work this out in a simpler way by first converting the fraction 1/3 to a decimal. To do that, we simply divide the numerator by the denominator:

1/3 = 0.33333333333333

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.33333333333333 x 100 = 33.3333%

(Hope this helps can I pls have brainlist (crown)☺️)

The Scale used on blueprint is 1 inches represents 4/3 feet

Scaling is the increase or decrease in size of a figure or object so as to create an image of that object.

Since on the blueprint, the walls measure 10 feet by 12 feet but on the blue print it measures 7.5 inches by 9 inches. Hence:

Scale used on blueprint is 7.5 inches = 10 feet or 9 inches = 12 feet

1 inches = 4/3 feet

The Scale used on blueprint is 1 inches represents 4/3 feet

Find out more at: https://brainly.com/question/20095188

Answer:

The system has no solutions.

Step-by-step explanation:

Let's write it in a more traditional form

[tex]\left \{ {{x-y=7} \atop {6x-6y=-7}} \right. \\[/tex]

Try staring at it for a bit, and then realize what you are being asked: find two numbers whose difference is - at the same time, 7, and -7/6. That's impossible.

Same result you get by elimination. Multiply the first by 6 and either add or subtract - your choice the second. In either case you will get 0 = 35 or 0=49, which are obviously absurd

Answer:

P = - 3

Step-by-step explanation:

For the equation to have no solutions the the coefficient of x on both sides must be the same.

5 - 3x = Px + 7 ← P = - 3 , then

5 - 3x = - 3x + 7 ( subtract 5 from both sides )

- 3x = - 3x + 2 ( add 3x to both sides )

0 = 2 ← not possible

Meaning the equation has no solutions

Answer:

30

Step-by-step explanation:

7+(4*8)-9

Multiply first inside the parentheses

7+(32)-9

Then add and subtract from left to right

39 - 9

30

Answer:

If x is a variable then the answer is 4x⁸ - 2

If x is a multiplication representation then the answer is 30

Step-by-step explanation:

If x is a variable:

1) Eliminate redundant parentheses

[tex]7+(4x^{8} )-9\\7+4x^{8} -9[/tex]

2) Subtract the numbers

[tex]7+4x^{8} -9\\-2+4x^{8}[/tex]

3) Rearrange Terms

[tex]-2+4x^{8} \\4x^{8} -2[/tex]

Answer:

5 - 35n.

Step-by-step explanation:

5(1 - 7n)

Using the Distributive Law:

= 5*1 + 5 *-7n

= 5 - 35n.

Answer:

x = 8°

y = 21°

Step-by-step explanation:

27 + 3y = 90

3y = 63

y = 21°

x + 8x + 18 = 90

9x = 72

x = 8°

Answer:

2 years

Step-by-step explanation:

casue if you multilpy 2 x 11,500 you get 23,000

Step-by-step explanation:

when you do an arithmetic operation to functions, you do it for the defining expressions.

so,

(f+g)(x) = (x + 3) + (4x + 4) = x + 3 + 4x + 4 = 5x + 7

(f*g)(x) = (x+3)*(4x+4) = 4x² + 12x + 4x + 12 = 4x² + 16x + 12

= 4(x² + 4x + 3)

(f-g)(4) = (4+3) - (4×4+4) = 7 - (16+4) = 7 - 20 = -13

Answer:

k = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

5k - 2 = 2k + 4

Step 2: Solve for k

Answer:

k=2

Step-by-step explanation:

5k-2=2k+4

add 2 to both sides

5k=2k+6

subtract 2k to both sides

3k=6

divide both 3k and 6 by 3 to get k by itself

k=2

Answer:

I think this is it 2/36=1/18

Step-by-step explanation:

if x = 2/3 then you will multiply by the reciprocal of 12 which is 1/12.

2/3x1/12= 2/36

simplified 1/18

Answer:

Length of floor = 5 m and breadth of floor = 4 m

Area of floor = length x breadth

= 5 m x 4 m = 20 m.sq

Now, Side of square carpet = 3 m

Area of square carpet = side x side = 3 x 3 = 9 m.sq

Area of floor that is not carpeted = 20 m – 9 m = 11 m.sq

Answer:

Step-by-step explanation:

Given ,

Length of a floor = 5 m

Width of the floor = 4 m

Therefore,

Area of the floor

= l × b

= 5m × 4m

[tex] = 20 {m}^{2} [/tex]

Given,

Sides of a square carpet = 3 m

Therefore,

Area of the carpet

= s × s

= 3m × 3m

[tex] = {9m}^{2} [/tex]

Now,

Area of the floor that is not carpeted is

= Area of the floor - Area of the carpet

[tex] = {20m}^{2} - {9m}^{2} [/tex]

[tex] = 11 {m}^{2} (ans)[/tex]

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

Same as last time, take any 2 points you want:

(0, 3) and (4, 1)

Use the slope formula to calculate the slope:

[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]

On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.

Answer:

PQ≅ST; QR ≅TW; PR ≅SW

Step-by-step explanation:

Area of one triangle = [tex]A = \frac{a·b}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9 {cm}^{2} \\ [/tex]

For 5 triangles = [tex]9 \times 5 = 45 {cm}^{2} [/tex]

- BRAINLIEST answerer

Answer:

13

Step-by-step explanation:

Use the distance formula to solve for the distance between two points.

[tex]d=\sqrt{(x2-x1)^2 + (y2-y1)^2[/tex]

Plug in your coordinate points.

[tex]d=\sqrt{(7-(-5))^2 + (2-7)^2[/tex]

[tex]d=\sqrt{(12)^2 + (-5)^2[/tex]

[tex]d=\sqrt{144 + 25[/tex]

[tex]d=\sqrt{169[/tex]

d= 13

Answer:

d.

took the test

Step-by-step explanation: