Rabbits are released into the woods where there are no other rabbits of this species. The function f(t) can be used to model the population of this new species after t years. Below are four forms of the function that model this situation. Which form most clearly shows the monthly population growth?

Answer:

-6n-20=-2n+4(1-3n)

Solution

The bracket should be expanded

-6n-20=-2n+4-12n

Then we collect the like terms

-6n + 2n+12n = 20+4

8n=24

Now divide both sides by 8

8n/8 =24/8

n = 3

You can now insert 3 into anywhere you see n and see how it goes

-6n-20= -2n + 4(1-3n)

-6(3) - 20 = -2(3) + 4[ 1-3(3)]

-18 -20= -6 + 4(1-9)

-38= -6 -32

-38= - 38

That's all

Step-by-step explanation:

Answer:

19x/14 + 97/56

Step-by-step explanation:

Step-by-step explanation:

Equation of the given line is :

[tex] 2x +12y= - 1\\

\therefore 12y = - 2x - 1\\

\therefore y = \frac {- 2}{12}x - \frac {1}{12}\\

\therefore y = - \frac {1}{6}x - \frac {1}{12}\\[/tex]

Equating above equation with [tex] y= m_1x + c

[/tex] we find:

[tex] m_1 = - \frac{1}{6}[/tex]

Where [tex] m_1[/tex] is the slope of given line:

Let the slope of required line be [tex] m_2.[/tex]

Since lines are perpendicular

[tex] \therefore m_1 \times m_2= - 1\\

\\\therefore - \frac{1}{6} \times m_2= - 1\therefore m_2= 6\\[/tex]

Equation of required line in slope point form is given as:

[tex] y-y_1 =m_2(x-x_1) \\

\therefore y-9 =6(x-0)\\

\therefore y-9 =6x\\

\huge\orange {\boxed {\therefore y =6x+9}} \\[/tex]

Answer: A. Y= -6x+9

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

The complete question in the attached figure

step 1

Find the volume of a typical cereal box

[tex]V=LWH[/tex]

substitute the given values

[tex]V=(2.5)(7.75)(11.75)=227.65625\ in^3[/tex]

Convert to cubic feet

Remember that

[tex]1\ ft=12\ in[/tex]

so

[tex]1\ ft^3=1,728\ in^3[/tex]

so

[tex]227.65625\ in^3=(227.65625/1,728)\ ft^3[/tex]

step 2

Find the volume of all of the boxes of breakfast cereal bought in the united states in one year

Multiply the volume of one box by 2.7 billion boxes

[tex](227.65625/1,728)(2,700,000,000)=355,712,890.625\ ft^3[/tex]

step 3

If the warehouse is 10 feet tall what could the side lengths of the floor be?

Divide the volume by the height to obtain the area of the rectangular base

[tex]A=(355,712,890.625)/10=35,571,289\ ft^2[/tex]

If the floor were a square, the dimensions would be

5,964 ft by 5,694 ft approximate

The area of the warehouse's floor can be calculated by dividing the total volume of cereal boxes by the height of the warehouse, which is given to be 10 feet. The exact dimensions of the floor (length and width) cannot be determined from the information given. Many combinations of length and width can yield the same area.

Given the problem, it is implied we must estimate the size of the warehouse able to contain the volume of all the cereal boxes purchased in the United States in one year. The shape mentioned is a rectangular prism (a box), with known height 10 feet. The area of the warehouse floor (base) would be the total volume divided by the height of the warehouse.

However, the information needed to calculate the exact dimensions of the warehouse's base (length and width) is not provided in the question. Essentially, many combinations of length and width could yield the same area. For example, if the area was 200 sq ft, it could be 20 ft by 10 ft, or 40 ft by 5 ft, and so on.

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No. In fact, you divide it into two.

So let's say the diameter is 10 cm.

To get the radius, you halve it or divide by two.

10 ÷ 2 = 5 cm

The radius of a circle with a 10 cm diameter is 5 cm.

Answer: No

Step-by-step explanation: You have to divide it by two to to have the radius.

1. A line joining the two sides of a circle is called diameter.

2. This line actually divide the circle into halves.

3. The radius of a circle is the length of the circle from the centre position.

5. The radius is half the dimension of diameter.

6. Now we can prove that radius(r) is equal to diameter/2

r=d/2.

To determine the house's value over time, a function can be created using the initial value and an annual growth rate. Specific details about the growth rate are needed for an accurate function, but a generic formula with a constant rate can still be provided.

Creating a Function for House Value Over Time

To write a function that determines the value of a house in thousands of dollars based on the number of years since purchase, we would need additional information about how the house's value appreciates or depreciates over time. This could involve a fixed annual appreciation rate, market trends, renovations, or depreciation.

Without specific data, a generic function can still be proposed, assuming a constant annual percentage increase. Let's call the annual growth rate 'r' (in decimal form) and the original value of the house 'V'. The function would then be:

f(t) = V × (1 + r)^t

For example, if Kyle bought the house at a value of $100,000 (or 100 in thousands of dollars) and the annual growth rate is 3% (or 0.03), the function defining the future value of the house would be:

f(t) = 100 × (1 + 0.03)^t

Using this formula, we can calculate the future value of Kyle's house after any number of years 't'.

The vertical axis of the given ellipse x^2/4 + y^2/16 = 1 is 8 units long, and each semimajor axis for an ellipse with a major axis of 16 cm would be 8 cm. An ellipse with an eccentricity of 0.8 would be considered elongated.

The ellipse given by the equation x^2/4 + y^2/16 = 1 has a vertical major axis. This can be deduced because the larger denominator is under the y^2 term, meaning the ellipse stretches further in the y-direction. In this case, the length of the major axis is 2 times the square root of 16, which is 2 times 4, equaling 8. Therefore, the major axis is 8 units long, and since each semimajor axis is half of the major axis, the semimajor axis would be 4 units long. Consequently, for the given options, the vertical axis of the ellipse is 8.

Considering a different ellipse with a major axis of 16 cm, the semimajor axis would be half of this length, resulting in 8 cm. If such an ellipse has an eccentricity of 0.8, it is more elongated than circular. Typically, ellipses with lower eccentricities (closer to 0) appear more circular, while those with higher eccentricities (closer to 1) appear more elongated.

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Answer:

[tex]x=-15[/tex]

Step-by-step explanation:

Complete question :      In a right triangle other two angles are [tex](0.3x+64)\textdegree\ and\ (0.1x+32)\textdegree[/tex] find the value of [tex]x[/tex].

In a right angle the third angle is [tex]90\textdegree[/tex]

we know that

Sum of angle in a triangle [tex]=180\textdegree[/tex]

[tex](0.3x+64)+(0.1x+32)+90=180\\\\0.3x+64+0.1x+32+90=180\\\\0.4x+96+90=180\\\\0.4x+186=180\\\\0.4x=-6\\\\[/tex]

Dividing [tex]0.4[/tex] both sides

[tex]\frac{0.4x}{0.4}=\frac{-6}{0.4}\\\\x=\frac{-60}{4}\\\\x=-15[/tex]

Final answer:

To solve the equation -2/9m + 12 = -8 for m, subtract 12 from both sides, then multiply by -9/2. The solution is m = 90.

Explanation:

To solve the equation -2/9m + 12 = -8 for m, start by isolating the term involving m. Subtract 12 from both sides of the equation to get:

-2/9m = -8 - 12

-2/9m = -20

Next, multiply both sides by -9/2 to solve for m:

m = (-20) * (-9/2)

m = 180/2

m = 90

Therefore, the solution to the equation is m = 90.

Answer:

2 1/4

Step-by-step explanation:

Each person gets 2 1/4 bread sticks.

9÷4= 2 1/4

Answer:

each person gets

2 1/4 (= 2.25) bread sticks

Step-by-step explanation:

total number of breadsticks = 9

total number of people = 4

assuming everyone gets the same amount of breadsticks

dividing 9 bread sticks by 4 people

= 9/4

= 2 1/4 (= 2.25) bread sticks

Answer:

3 pairs

Step-by-step explanation:

After spending 78 out of 90, Staci has 12 left.

12/4 = 3

Answer:

3

Step-by-step explanation:

90-78=12

4x3= 12

12-12= 0

Answer:

25-a-b=c or also c=25-a-b

Step-by-step explanation:

We need to get "c" by itself.

The equation for the total amount of laps is a+b+c=25

To get c by itself, we subtract a and b from both sides

Thus, we get c=25-a-b

Hope this helped!

Answer:

y=4x-22

Step-by-step explanation:

y-y1=m(x-x1)

y-(-10)=4(x-3)

y+10=4x-12

y=4x-12-10

y=4x-22

Answer:

645/3 = 215

Step-by-step explanation:

You can use long division to find the answer.

x = y + 4 is already done so we will substitute that into the other equation!

3(y + 4) + y = 16

Distribute.

3y + 12 + y = 16

Add the terms.

4y + 12 = 16

Give y its own side.

4y = 4

Divide by 4.

y = 1

Substitute this back into one of the equations.

x = 1 + 4

x = 5

The point for these 2 equations is (5, 1)

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

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To solve the equation, isolate and substitute variable 'y' in the first equation with 'x - 4'. This leads us to find 'x = 5'. Substituting 'x' in the first equation gives us 'y = 1'. Therefore the solution is 'x = 5, y = 1'.

The subject at hand is an algebra problem involving a system of two equations. First, we can select which variable to isolate. In our case, isolating 'y' in the first equation would be easier than it might seem. That would leave us with 'x = y + 4'.

Next, we can substitute 'y' with  'x - 4' in the second equation, giving us '3x + (x - 4) = 16'. We simplify this equation to '4x = 20'. Solving this gives us 'x = 5'. Lastly, we replace 'x' in the first equation with '5', which gives us the value of 'y = 5 - 4', so 'y = 1'.

The solution to the system of equations 'x = y + 4 and 3x + y = 16' therefore is 'x = 5, y = 1'.

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Answer:

C (1/4)

Step-by-step explanation:

Answer:

C 1/4

Step-by-step explanation:

Answer:

2/3 and 3/2

Step-by-step explanation:

I got a problem like that in class today and I got it right lol

The scale factor of the following similar figures is 2/3 or 3/2.

Two figures are said to be similar if they have the same shape and proportional sides.

Therefore the ratio of their corresponding sides are constant. The scale factor is the same as the ratio of their corresponding sides.

From the question:

Hence the scale factor of the following similar figures is 2/3 or 3/2.

Find out more on similar figures at: https://brainly.com/question/2644832

Answer:

2

Step-by-step explanation:

you get 2 because 5 times 2 equals 10 and 6 times 2 equal 12. so you get 10/12

Step-by-step explanation:

[tex]\frac{5}{6} = \frac{5\times 2}{6\times 2} = \frac{10}{12} \\ \\

[/tex]

Therefore, answer is 2.

Answer: The distance from the person on the ground to the bottom of the hotair balloon is 1,649 ft

Step-by-step explanation: Please refer to the attached diagram

From the diagram, the hotair balloon is labelled B. If Marero looks down and forms an angle of depression of 20°, that means he is forming an angle of 70° to point C where one of the two persons are standing. Point B is an angle of 70° (point A cuts point B at a perpendicular, that is, 90°)

With these we can now use the trigonometrical ratio of tangent to calculate the distance marked x on the diagram.

Tan B = opposite/adjacent

Tan 70 = x/600

When we cross multiply, we now have

Tan 70 × 600 = x

2.7475 × 600 = x

1648.5 = x

Rounded to the nearest feet

x = 1,649 feet

Final answer:

To determine the distance of the person from the ground point below the hot-air balloon, we use the angle of depression and the tangent trigonometric ratio. The calculation yields approximately 1648 feet when rounded to the nearest whole number.

Explanation:

To solve for the distance of the person at point C from the point on the ground directly below the hot-air balloon, we need to use trigonometric ratios. To find this distance, which we'll call 'd', we'll use the tangent of the angle of depression. The angle of elevation from the person looking up to the hot-air balloon would also be 20° because alternate interior angles created by a transversal intersecting two parallel lines are congruent. The relationship we use is:

tangent of angle = opposite/adjacent

In this case:

tan(20°) = 600/d

To isolate 'd', we take:

d = 600 / tan(20°)

Using a calculator, we find:

d ≈ 600 / 0.3640 ≈ 1648.35 feet

Rounded to the nearest whole number, the person at C is approximately 1648 feet from the point on the ground below the hot-air balloon.

Answer:

B: The domain represents a 11-month period of flower production.

Step-by-step explanation:

The domain of a Function

It's the set of all the values a function can take in its independent variable. The independent variable (usually x) is represented as the horizontal axis of a graph, where we can know the interval of values considered for values of the function.

In the provided graph, we can see the horizontal axis is labeled 'Months' and its values range from 1 to 11. The vertical axis is labeled "Number of flowers produced" which will be the Range of the function.

From the options presented, we can discard the C and D because they are related to the number of flowers produced, which is not the domain of the function. The option A talks about the months of production but the months range up to 180. Option B is the correct choice.

B: The domain represents a 11-month period of flower production.

Answer:

134

Step-by-step explanation:

They sold 134 hamburgers. The shop sold 268 cheeseburgers. 268 is 2x as much as 134. Divide 402 by 3, and you can find the amount of hamburgers. Times it by 2, and you find the amount of cheeseburgers.

Answer:

b= -8

Step-by-step explanation:

we have: 3y +12 = 6x <=> y + 4 = 2x <=> y= 2x - 4

=> 2y=4x + b

<=> 2(2x-4) = 4x +b

<=> 4x - 8= 4x +b

<=> b = -8

Answer:

1071.8 to 1 decimal point

Step-by-step explanation:

The first thing you would do is multiply the 4/3, 3.14 and the 8^3

So we know that 8^3 is 8X8X8 which is 512

So the first thing you do I 4/3 X 3.14 X 512 = 160768/75 (2143.6 1DP)

Then you would divide this by 2

2143.6/2 = 1071.8

Answer:

24+24x I believe is the answer. Good luck on your test :)

Answer:

D

Step-by-step explanation:

2x2(4x3 - 3x2 + 6x)

= 2x²(4x³ - 3x² + 6x)

= 8x^5 - 6x⁴+ 12x³

Answer:

95%

Step-by-step explanation:

We have that:

The number of potato chips in a bad is normally distributed with a mean of 75 and a standard deviation of 5.

We want to use the empirical rule to solve this:

We know that:

65=75-2(5)

That means

[tex]65 = 75 - 2 \sigma[/tex]

Also, 85=75+2(5)

[tex]85 = 75 + 2 \sigma[/tex]

According to the the empirical rule approximately 95% of the distribution is within 2 standard deviation of the mean

Answer:

28.065

Step-by-step explanation:

Answer: 20.52

Step-by-step explanation:

Answer:20.52

Step-by-step explanation:

A line the decimals on top of each other then add the whole numbers and the numbers outside of the decimal

The distance along the path of the ship be within the range of the torpedoes is 4 kilometers.

Explanation:

The submarine lies 3 km from the target ship.

Let B denotes the target ship and C denotes the submarine.

Let AC denotes the the target ship would be within the range of the torpedoes.

The image attached below illustrates that the distance between submarine and the target ship and the range of the torpedoes.

Let BC denotes the distance between the target ship and the submarine. Let AC denotes the range of the torpedoes.

To determine the length of AB, let us use Pythagorean theorem,

[tex]AC^{2} =AB^{2} +BC^{2}[/tex]

Substituting the values of BC = 3 and AC = 5, we have,

[tex]5^{2} =AB^{2} +3^{2}[/tex]

Squaring the terms, we get,

[tex]25 =AB^{2} +9[/tex]

Subtracting both sides by 9, we have,

[tex]16 =AB^{2}[/tex]

Taking square root on both sides,

[tex]AB = 4[/tex]

Thus, the distance along the path of the ship be within the range of the torpedoes is 4 kilometers.