the function f(x)=18000(0.7)^x represents the penguin population on an island x years after it was first studied.what was the original population of the penguins on island?​

For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 2 + 2 = 4. One of the triangles has height of 6 and the other has height of 7.

So, the total area is given by:

[tex]A = \frac {1} {2} * 4 * 6 + \frac {1} {2} * 4 * 7\\A = \frac {1} {2} 24+ \frac {1} {2} 28\\A = 12 + 14\\A = 26[/tex]

So, the kite area is 26

ANswer:

Option D

Answer:

  B)  one solution

Step-by-step explanation:

The ratio of x-coefficient to y-coefficient is different in the two equations, so the lines have different slopes. Two lines with different slopes will always have exactly one point of intersection. You don't need to graph the equations to know there is ...

  one solution

__

A graph is attached. As it happens, the two lines are perpendicular. The solution is (2, 0).

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = [tex]253x-2x^2[/tex]

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

                      = 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= [tex]253x-2x^2 - (3x + 6972)[/tex]

= [tex]253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\[/tex]

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

[tex]-2x^2+250x-6972=0\\[/tex]

now we have to solve the above equation for x

Dividing both sides by -2 we get

[tex]x^2-125x+3486=0[/tex]

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

[tex]x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\[/tex]

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

The cost function is C(x) = 3x + 6972, the revenue function is R(x) = 253x - 2x², and the profit function is P(x) = 250x - 2x²- 6972. The smallest break-even point occurs at 16 bins.

To solve the given problem, let's break it down step-by-step:

      The cost function includes both the fixed cost and the variable cost.            The fixed cost is $6972, and the unit cost to produce one bin of cat food is $3. Therefore, the cost function C(x) where x is the number of bins is:

C(x) = 3x + 6972

The price-demand function is given by p(x) = 253 - 2x. Revenue R(x) is the product of the price per bin and the number of bins sold, so:

R(x) = x * (253 - 2x) = 253x - 2x²

The profit function is the revenue function minus the cost function. So, the profit function P(x) is:

P(x) = R(x) - C(x) = (253x - 2x²) - (3x + 6972) = 250x - 2x² - 6972

To find the smallest break-even point, we need to solve the equation where profit equals zero:

0 = 250x - 2x² - 6972

Rewriting the equation, we get:

2x² - 250x + 6972 = 0

Solving this quadratic equation using the quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a, where a = 2, b = -250, and c = 6972:

x = [250 ± sqrt(62500 - 4*2*6972)] / 4

x = [250 ± sqrt(62500 - 27888)] / 4

x = [250 ± sqrt(34612)] / 4

x = [250 ± 186.01] / 4

So, the two solutions for x are approximately:

x = (250 + 186.01) / 4 = 109

x = (250 - 186.01) / 4 = 15.997 ≈ 16

The smallest break-even point is at a quantity of 16 bins.

The cost function is C(x) = 3x + 6972, the revenue function is R(x) = 253x - 2x², and the profit function is P(x) = 250x - 2x² - 6972. The smallest break-even point occurs at 16 bins.

Answer:

Its B ''In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.''

Hence, in step [tex]2[/tex] she did the mistake.

What is the multiplication?

Multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here given that,

Step 1: [tex]\frac{1}{8}=\frac{?}{100}[/tex]

Step 2: [tex]8[/tex] divided by [tex]100 = 0.08[/tex]

Step 3: [tex]0.08[/tex] multiplied by [tex]1 = 0.08[/tex]

Step 4: [tex]0.08[/tex]

She did the mistake in step [tex]2[/tex] it would be,

[tex]\frac{100}{8}=12.5[/tex]

Hence, in step [tex]2[/tex] she did the mistake.

To know more about the multiplication

https://brainly.com/question/5992872

#SPJ5

Answer:

Option C) [tex]0 \leq x \leq 9[/tex]

Step-by-step explanation:

We are given the following information in the question:

The number of users of a cell tower  increased by a factor of 1.5 every year from 2010 to 2019.

[tex]f(x) = 5000(1.5)^x[/tex]

where f(x) is the number of cell tower users and x is the years from the year 2010.

We have to find the domain for the given function.

Domain of a function is defined as the possible values of x the function can take, so that the function is defined.

Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.

x takes the value of years after 2010.

Thus  for year 2010, x = 0 and for year 2019, x = 9

Thus, the domain of the given function is given by:

[tex]0 \leq x \leq 9[/tex]

Answer:

D

Step-by-step explanation:

Given the 2 equations

2x - 3y = 14 → (1)

5x + 3y = 21 → (2)

Adding the 2 equations term by term will eliminate the y - term

(5x + 2x) + (- 3y + 3y) = (14 + 21)

7x = 35 ( divide both sides by 7 )

x = 5 → D

If we want to find when the population of species A will be equal to the population of species B, we need to see when the two equations for the population of each species are equal, ie. equate them and solve for t. Thus:

2000e^(0.05t) = 5000e^(0.02t)

(2/5)e^(0.05t) = e^(0.02t) (Divide each side by 5000)

2/5 = e^(0.02t) / e^(0.05t) (Divide each side by e^(0.05t))

2/5 = e^(-0.03t) (use: e^a / e^b = e^(a - b))

ln(2/5) = -0.03t (use: if b = a^c, then loga(b) = c )

t = ln(2/5) / -0.03 (Divide each side by -0.03)

= 30.54 (to two decimal places)

Therefor, the population of species A will be equal to the population of species B after 30.54 years.

I wasn't entirely sure about the rounding requirements so I've left it rounded to two decimal places.

Answer:

Jamie spent $39.36 in total.

Step-by-step explanation:

First, add the money spent for the sandwich, beverage, and fruit together.

4.75 + 1.25 + .56 = 6.56

Then, multiply the amount spent for one friend by six to find the total.

6.56 x 6 =39.36

I hope this helped you!

Answer:

  1.25 gallons of alcohol

Step-by-step explanation:

Let x represent the amount of alcohol to add to the mix. Then the total amount of alcohol in the mix is ...

  0.15×20 + x = 0.20×(20 +x)

  3 +x = 4 + 0.2x . . . . simplify

  0.8x = 1 . . . . . . . . . . add -3-0.2x

  x = 1/0.8 = 1.25 . . . . divide by 0.8

1.25 gallons of alcohol should be added to make 21.25 gallons of 20% alcohol.

Answer:

t = 2489 years

Step-by-step explanation:

The equation you need for this is

[tex]N=N_{0}e^{kt}[/tex]

where N is the amount AFTER the decomposition, N-sub-0 is the initial amount, k is the decomposition constant and t is time in years.

If we are told that the tusk LOST 26% of its carbon-14, that means 74% of it remains from the initial 100% it had.

Filling in:

[tex]74=100e^{-.00012097t}[/tex]

Begin by dividing both sides by 100 to get a decimal of .74:

[tex].74=e^{-.00012097t}[/tex]

The goal is to get that t out of the exponential position in which it is currently sitting.  Do this by "undoing" the e.  Do THAT by taking the natural log of both sides because a natural log "undoes" an e.  This is due to the fact that the base of a natural log is e.  

[tex]ln(.74)=ln(e^{-.00012097t})[/tex]

The ln and the e disappear on the right side, leaving

ln(.74) = -.00012097t

Plug ln(.74) into your calculator to get

-.3011050928 = -.00012097t

t = 2489

Answer:

Length: 13 feet,

Width: 4 feet.

Step-by-step explanation:

Let w represent width of bulletin board.

We have been given that the length is 3 feet less than 4 times the width. So the length of the bulletin board would be [tex]4w-3[/tex].

We have been given the area of a bulletin board is 52 square feet. We know that a bulletin board is in form of rectangle, so its area would be length times width.

We can represent this information in an equation as:

[tex]w(4w-3)=52[/tex]

Let us solve for w.

[tex]w(4w-3)=52[/tex]

[tex]4w^2-3w=52[/tex]  

Use quadratic formula:

[tex]w=\frac{-(-3)\pm\sqrt{(-3)^3-4\cdot 4\cdot (-52)}}{2\cdot 4}[/tex]

[tex]w=\frac{3\pm\sqrt{9+832}}{8}[/tex]

[tex]w=\frac{3\pm\sqrt{841}}{8}[/tex]

[tex]w=\frac{3\pm29}{8}[/tex]

[tex]w=\frac{3-29}{8}\text{ (or) }w=\frac{3+29}{8}[/tex]

[tex]w=\frac{-26}{8}\text{ (or) }w=\frac{32}{8}[/tex]

[tex]w=\frac{-13}{4}\text{ (or) }w=4[/tex]

Since width cannot be negative, therefore, width of the bulletin board is 4 feet.

Substitute [tex]w=4[/tex] in expression [tex]4w-3[/tex] to find length of bulletin board.

[tex]4w-3\Rightarrow 4(4)-3=16-3=13[/tex]

Therefore, length of the bulletin board is 13 feet.

Answer:

To better understand the data you're working with

Step-by-step explanation:

Note that, the sample is a subset of your whole population (population here is a general definition, it could be a population of cars for example), which means that if you want to understand your population your best "bet" would be using a sample to try to estimate some unknown characteristics of your population. Let's suppose you want to estimate the true mean of your population, then you would need a sample, and if this sample is big enough you could approximate the estimative to the true mean.

It's hard to say exactly what this survey could mean, but the general idea is to understand your data a little more, see if there is any pattern, if a certain value occurs more than others, to calculate the sample mean, median and standard deviation, and so on...

Hope it helped!

Answer:

For b, the answer is that your trying to find out what the type of funtion may be. It could be either exponential, linear, or quadratic.

Step-by-step explanation:

That's what the lesson in edg is all about.

Answer:

At t = 1s, The instantaneous velocity will be -9

Step-by-step explanation:

The position is given by

s(t) = -8 - 9t

If we find the derivative, we get the expression for the velocity

d(s(t))/dt = v(t) = -9

The velocity of the object is constant.

At t = 1s, it will be -9

The three-dimensional figure that is formed by the rotation is (a) an hemisphere

From the figure, we can see that the line is rotated along the y-axis.

And the length of rotation reduces as the rotation moves downward

This rotation would create an hemisphere

The option (a) represents an hemisphere

Hence, the three-dimensional figure that is formed by the rotation is (a) an hemisphere

Read more about rotation at:

https://brainly.com/question/4289712

#SPJ2

Answer:

it's definitely a positive nonlinear graph

Step-by-step explanation:

Hello There!

In an experiment, The independent variable is the variable that the person doing the experiment changes on purpose so they can see if it affects another variable in the experiment. Independent variables are also called "The Manipulated Variables"

I Hope This Helped You!

Have Great Day!

Be Safe,

TheBlueFox

Answer:

Z = 27°

Step-by-step explanation:

The sum of the internal angles of a triangle is always equal to 180 °. Note that the triangle shown whose angles are z and 63 ° is a right triangle. Therefore it has an angle of 90 °. Then we can write the following equation:

[tex]z + 63\° +90\°= 180\°\\\\z = 180\° - 63\°-90\°\\\\z = 27\°[/tex]

Finally z = 27°

ANSWER

[tex]z = 27 \degree[/tex]

EXPLANATION

The diagonals of a rhombus bisect each other at right angles.

Hence each of the four angles at the center by are 90° each.

This means that:

[tex]z + 63 + 90 = 180[/tex]

Sum of interior angles of a triangle.

[tex]z + 153= 180[/tex]

[tex]z = 180 - 153[/tex]

This simplifies to.

[tex]z = 27 \degree[/tex]

Answer:

5.25 miles - 3 miles = 2.25 miles

2.25 miles is the extra miles.

2.25 miles x $1.20 = $2.7

Total:

$2.7 + ($1.5 x 3 miles)

=$2.7 + $4.5

=$7.2

5.5 miles will cost $2.7.

Answer:

B

Step-by-step explanation:

[tex]P(A)=0.995\\P(A')=0.005[/tex]

So [tex]P(A')[/tex] is pretty much unlikely.

Answer:

[tex]d =\sqrt{(b-0)^2 +(c-a)^2}[/tex]

Step-by-step explanation:

We know that the distance between two points is calculated using the following formula

[tex]d =\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

In this case we look for the RS distance

Then

The starting point is: (0, a)

The final point is (b, c)

So

[tex]x_2 = b\\x_1 = 0\\y_2 = c\\y_1=a[/tex]

The distance is:

[tex]d =\sqrt{(b-0)^2 +(c-a)^2}[/tex]

Answer:

h(8q²-2q) = 56q² -10q

k(2q²+3q) = 16q² +31q

Step-by-step explanation:

1. Replace x in the function definition with the function's argument, then simplify.

h(x) = 7x +4q

h(8q² -2q) = 7(8q² -2q) +4q = 56q² -14q +4q = 56q² -10q

__

2. Same as the first problem.

k(x) = 8x +7q

k(2q² +3q) = 8(2q² +3q) +7q = 16q² +24q +7q = 16q² +31q

_____

Comment on the problem

In each case, the function definition says the function is not a function of q; it is only a function of x. It is h(x), not h(x, q). Thus the "q" in the function definition should be considered to be a literal not to be affected by any value x may have. It could be considered another way to write z, for example. In that case, the function would evaluate to ...

h(8q² -2q) = 56q² -14q +4z

and replacing q with some value (say, 2) would give 196+4z, a value that still has z as a separate entity.

In short, I believe the offered answers are misleading with respect to how you would treat function definitions in the real world.

Mean means average.

To find the average, add the data then divide it by the amount of individual data you have.

(6.5 + 5 + 3 + 2 + 2 + 3.5 + 5)/2 = mean

27/2 = mean

13.5 = mean

13.5 miles is the mean distance that Jim jogged.

Answer:

120*pi in^3

Step-by-step explanation:

We are given

Radius of cone=r=6 in

Height of cone=h=10 in

We know that the formula for finding the volume of cone is:

[tex]V=\frac{1}{3}\pi *(r)^{2}*h[/tex]

Putting the values of radius and height:

[tex]V=\frac{1}{3}\pi *(6)^{2}*10\\=\frac{1}{3}\pi *36*10\\=\frac{360}{3}\pi\\=120\pi[/tex]

So, the volume of cone in terms of pi is 120pi cubic in^3 ..

Answer:

The volume of cone = 120π cubic inches

Step-by-step explanation:

Points to remember

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here r = 6 in and h = 10 in

Volume = (πr²h)/3

 = (π * 6² * 10)/3

 = (π * 36 * 10)/3

 = 360π/3

 = 120π cubic inches

Therefore volume of cone = 120π cubic inches

Answer:

  168/(x² +7x)

Step-by-step explanation:

The height of each window is 14/(x+7), and the width of each window is 12/x. The area of each window is the product of its height ans width:

  area = (14/(x+7))(12/x) = 168/(x(x +7))

  area = 168/(x² +7x)

_____

Comment on the problem

There is not enough information given to determine suitable values for x. If x is 42, each window is a square 3 3/7 inches on a side.

Answer:

3/4

Step-by-step explanation:

a1 = (-1/3)^0 = 1

r = -1/3

Hence S = 1/(1+1/3) = 1/(4/3) = 3/4

Answer:

0.75.

Step-by-step explanation:

The common ratio = -1/3 and the first term = (-1/3)^0 = 1.

Sum to infinity =  1 / (1 - (-1/3))

= 1 / 4/3

= 3/4

= 0.75.

Answer:

2

Step-by-step explanation:

f(x) = 3х^2 + 5x

Let x = -2

f(-2) = 3(-2)^2 + 5(-2)

      = 3*4 -10

      = 12-10

       =2