Find f(100) and show how to solve

Answer:

4 years

Step-by-step explanation:

9% of the population is 1800. subtract that to get 18200. thats 1 year. subtract again to get 16400. thats 2 years. again to get 14600. 3 years. and then again to get 12800 which is less than 13000. so its 4 years.

Final answer:

Using the exponential decay formula, it takes approximately 8 years for a town's population of 20,000 to decrease to fewer than 13,000 at a yearly decrease rate of 9%.

Explanation:

The question involves calculating the number of years it takes for a town's population to decrease to fewer than 13,000 given an initial population of 20,000 and a yearly decrease rate of 9%. To solve this, we use the formula for exponential decay, which is P(t) = P₀[tex]e^{rt}[/tex], where P(t) is the population at time t, P0 is the initial population, r is the rate of decrease, and t is the time in years.

Substituting the given values, we have 13,000 = 20,000[tex]e^{-0.09t}[/tex]. Solving for t, we take natural logarithms on both sides, which gives ln(13,000/20,000) = -0.09t, leading to t = ln(13,000/20,000) / -0.09. This calculation yields t ≈ 8.04 years, meaning the population will be fewer than 13,000 in about 8 years.

This is a practical application of exponential decay in analyzing population dynamics, highlighting how populations decrease over time under consistent negative growth rates.

Answer:

[tex]12+c-2d[/tex]

Step-by-step explanation:

The correct expression of the problem is

[tex]4\left(3 + \dfrac14c - \dfrac12d\right)[/tex]

Applying the distributive property

[tex]4\left(3 + \dfrac14c - \dfrac12d\right)=(4*3)+(4*\dfrac{1}{4} c)-(4*\dfrac{1}{2} d)=(12)+(c)-(2d)[/tex]

therefore

The equivalent expression is equal to

[tex]12+c-2d[/tex]

50 pounds to 35 pound

That is 15 pound decrease and a 15/50 times 100 percent decrease.

15/50 x 100 = 30% decrease

answer: 30% decrease

Answer:

22222222222222222222222224

Step-by-step explanation:

Add 2 to 22222222222222222222222222 and you will get 22222222222222222222222224

Answer:

yassssdiogfodiujtg idosuygi8reodsjgbkfcjnvfdkjmnib

Step-by-step explanation:gy7f76gh8uh7t

Answer:6

Step-by-step explanation:

If you were to divide 8 by 2 you would get 4 and this makes it easier to get the answer. 75% of 4 is 3 so multiple 3 by 2 to get 6.

Answer:

x<21

Step-by-step explanation:

How I always do it is I write down the number that was in the problem. So write down 21. Next I write down less. Then, if it says less, then the inequality sign's open side will face the number. This will be the opposite if the problem says more

The inequality representing a classroom that can accommodate fewer than 21 students is s < 21, which means the classroom can hold any number of students from 1 up to 20.

The question asks which inequality represents the number of students a classroom can accommodate if it can hold fewer than 21 students. To express this mathematically, we use an inequality sign. Since the classroom can accommodate less than 21 students, it means the number of students (let's call this number s) must be strictly less than 21. Therefore, the inequality that correctly represents this condition is s < 21.

This inequality means that any whole number of students from 1 up to 20 can fit in the classroom, as all these values are less than 21. It's crucial to understand that the inequality does not include 21 itself, because it specifies "less than," not "less than or equal to."

Answer:

You have a full amount of chocolate cake and you eat [tex]\frac{1}{3}[/tex] part of the cake and left the remaining amount for the next day. So, what amount of cake that you left for the next day?

Step-by-step explanation:

We have to make a subtraction problem so, that the answer to the problem is [tex]\frac{2}{3}[/tex].

Now, the problem may be described as follows :

You have a full amount of chocolate cake and you eat [tex]\frac{1}{3}[/tex] part of the cake and left the remaining amount for the next day. So, what amount of cake that you left for the next day?

So, the solution is [tex](1 - \frac{1}{3}) = \frac{2}{3}[/tex] amount of the cake. (Answer)

Answer:

his commission would be $6250

Step-by-step explanation:

please give me brainly :)

Answer:

6250

Step-by-step explanation:

The scale will draw UP to a larger dimension.

The width would be 16 and the length would be 24.

When you scale factor. You basically multiply its initial number by the amount of ratio given. Since it said scale factor 4. You multiply the width and length by 4.

Sophia's expression is incorrect because she did not multiply 2 by -1 correctly.

Ursula's expression is incorrect because she cannot simplify 2-4x.

A correct equivalent expression is 6-2+4x.

What can I say? I got this correct on ttm.

Hope you have a great day~

Answer: Yes

Step-by-step explanation: An arithmetic sequence is a sequence that has a common difference. The common difference is the number that is repeatedly added or subtracted to reach the next term in the sequence.

In this sequence, notice that we start with 15. Then, we subtract 2 to reach our next term which is 13. Next, we subtract 2 to get to our next term which is 11. In the same way, we subtract 2 from 11 to reach our next term, 9.

The dot dot dots just mean that this sequence goes on forever so to answer your question, this is indeed an arithmetic sequence.

Eileen was 600 feet away from the finish line before the race began.

Step-by-step explanation:

Step 1; Eileen rode at a speed of 20 feet per second whereas Andrew rode at a speed of 15 feet per second. So for every second that passes the distance in between decreases by 5 seconds. Assume x is the number of seconds at which the distance in between is 0. The distance in between at the beginning of the race is 150 feet due to the headstart.

Distance between them = Decreasing distance every second × x

150 feet = 5 feet/ second × x

x = 150 feet / 5 feet/second = 30 seconds.

So it takes Eileen 30 seconds to cover the distance between her and Andrew and cross the finishing line at the same time.

Step 2; The race lasted for 30 seconds so we can find the distance Andrew and Eileen traveled by multiplying their speed per second with the total number of seconds.

Distance Andrew traveled = speed per second × total number of seconds

= 15 feet per second × 30 seconds = 450 feet

Distance Eileen traveled = speed per second × total number of seconds

= 20 feet per second × 30 seconds = 600 feet

Graph plot;

The X-axis is time with 5 seconds for each cm

the y-axis is distance with 100 feet for each cm.

Eileen's plot (0,0), (5,100), (10,200), (15,300), (20,400), (25,500), (30,600).

Andrew's plot (0,150), (5,225), (10,300), (15,375), (20,450), (25,525), (30,600).

Answer: 200+7 * X=

Step-by-step explanation:

Answer:

sum = addition, times = multiplication, a number = a variable (let's say n)

Use this written out problem to write the algebraic expression?

200 + 7n    or   7n +200   (both are the same)

Step-by-step explanation:

Answer:

x-int: (2, 0)

y-int: (0,8)

(8-0)/(0-2)= 8/-2=  -4

y - 0 = -4(x - 2)

y = -4x + 8

Step-by-step explanation:

Option B: [tex]$\Delta R S T \sim \Delta UV W ; \frac{5}{6}$[/tex]

Explanation:

The polygons are similar because in [tex]$\Delta R S T$[/tex], the measure of ∠R=32°

Also, in [tex]$\Delta U V W$[/tex], the measure of ∠U=32°

Now, we shall find the scale factor,

Since, [tex]$\Delta R S T \sim \Delta U V W$[/tex], then the sides are proportional which is given by,

[tex]\frac{RS}{UV}[/tex]

Substituting the values of RS and UV from the figure, we get,

[tex]\frac{10}{12}[/tex]

Simplifying, we have,

[tex]$\frac{5}{6}$[/tex]

Thus, the scale factor is [tex]$\frac{5}{6}$[/tex]

Hence, Option B is the correct answer.

Answer:

Approximately there are 3,785.6 milliliters in one gallon

Step-by-step explanation:

Let's find out how many milliliters are there in one gallon.

1 US Cup = 236.6 ml (actual equivalence)

Let's recall that:

16 US Cups = 1 US Gallon

Therefore,

1 US Gallon = 16 * 236.6 ml

1 US Gallon = 3,785.6 ml

Approximately there are 3,785.6 milliliters in one gallon

Answer:

24 dollars

Step-by-step explanation:

6$for each one if u multiply then you'll get the number

Answer:

$24.00

Step-by-step explanation:

hope i helped

The vertex is (-1, -16)

x intercepts is : (3, 0) or (-5, 0)

y intercept is (0, -15)

Solution:

Given is:

[tex]y = (x+1)^2 - 16[/tex]

The vertex form of an equation is given as:

[tex]y = a(x-h)^2 + k[/tex]

Where, (h, k) is the vertex

On comparing the above equation with given,

h = -1

k = -16

Thus the vertex is (-1, -16)

To find the x-intercept, substitute y = 0 in given

[tex]0 = (x + 1)^2 - 16\\\\x^2 + 2x + 1 - 16 = 0\\\\x^2 + 2x - 15 = 0\\\\Split\ the\ middle\ term\\\\x^2 - 3x +5x - 15 = 0\\\\(x^2 -3x) + (5x - 15) = 0\\\\x(x - 3) + 5(x - 3) = 0\\\\Factor\ out\ x - 3\\\\(x-3)(x + 5) = 0\\\\x = 3\\\\x = -5[/tex]

Thus x intercepts is : (3, 0) or (-5, 0)

To find the y-intercept, substitute x = 0 in given

[tex]y = (0+1)^2 - 16\\\\y = 1 - 16\\\\y = -15[/tex]

Thus the y intercept is (0, -15)

Answer:

Step-by-step explanation:

B 4C and log 625

Answer: 48

Step-by-step explanation:

You can either add 8 six times or get a calculator and solve.

Answer:

[tex]P(Blue)=0.60[/tex]

Step-by-step explanation:

Probability: [tex]Probability\ of\ an\ event=\frac{favourable\ outcome}{total\ outcome}[/tex]

[tex]Total\ marbles=20\\\\Hence\ total\ outcomes=20\\\\Blue\ marbles=12\\\\Hence\ favourable\ outcomes=12\\\\P(Blue)=\frac{12}{20}\\\\P(Blue)=\frac{2\times 6}{2\times 10}\\\\P(Blue)=\frac{6}{10}\\\\P(Blue)=0.60[/tex]

Answer:

  160 people

Step-by-step explanation:

  (24000 lb)/(150 lb/person) = (24000/150) persons = 160 persons

If the weight could be evenly distributed, it would take about 160 people to lift a diplodocus.

Answer:

The combinations of necklaces and bracelets that the artist could sell for exactly $12.00 are

B: 2 necklaces and 5 bracelets

D: 4 necklaces and 2 bracelets

G: No necklaces and 8 bracelets

Step-by-step explanation:

let the number of necklace be x

the number of  bracelets be y

Then

The cost of one  necklace is $2.25

The cost of one bracelets is $1.50

Thus

x(2.25)  + y(1.50) = 12.00-------------------------(1)

Option A : 5 necklaces and 1 bracelet

(5)(2.25)  + (1)(1.50) = 12.00

11.25 +  1.50  =  12.00

12.75 > 12.00

Option B :2 necklaces and 5 bracelets

(2)(2.25)  + (5)(1.50) = 12.00

4.5 +  7.5 =  12.00

12. 00 = 12.00

Option C:  3 necklaces and 3 bracelets

(3)(2.25)  + (3)(1.50) = 12.00

6.75 + 4.50 =  12.00

11.25 < 12.00

Option D: 4 necklaces and 2 bracelets

(4)(2.25)  + (2)(1.50) = 12.00

9.00 + 3.00 = 12.00

12.00 =  12.00

Option E: 3 necklaces and 5 bracelets

(3)(2.25)  + (5)(1.50) = 12.00

6.75 + 7.5 = 12.00

14.25 >  12.00

Option F: 6 necklaces and no bracelets

(6)(2.25)  + (0)(1.50) = 12.00

13.5  + 0 = 12.00

13.5 > 12.00

Option G: No necklaces and 8 bracelets

(0)(2.25)  + (0)(1.50) = 12.00

0 +12.00= 12.00

12.00 =  12.00

The combinations of necklaces and bracelets that the artist could sell for exactly $12.00.

B: 2 necklaces and 5 bracelets

D: 4 necklaces and 2 bracelets

G: No necklaces and 8 bracelets

Since the artist is selling necklaces at $2.25 each, and bracelets at $1.50 per each, then the corresponding values will be:

2(2.25) + 5(1.50) = 4.50 + 7.50 = 12.00

4(2.25) + 2(1.50) = 9 + 3 = 12.00

0(2.25) + 8(1.50) = 0 + 12 = 12

In conclusion, the correct options are B, D, and G.

Read related link on:

https://brainly.com/question/15007030

Answer:

12

Step-by-step explanation:

y = kx

2⅔ = k(¼)

8/3 = k/4

k = 4×8/3 = 32/3

y = (32/3)x

y = (32/3)(1⅛)

y = (32/3)(9/8)

y = 3×4 = 12

Answer:

17.78 meters

Step-by-step explanation:

Let

x ----> the horizontal distance, in meters, to home plate

[tex]\theta[/tex] ----> the angle of vision

we know that

[tex]tan(\theta)=\frac{40}{x}[/tex] ----> by TOA (opposite side divided by the adjacent side)

we have

[tex]tan(\theta)=\frac{9}{4}[/tex]

substitute

[tex]\frac{9}{4}=\frac{40}{x}[/tex]

solve for x

[tex]x=40(4)/9\\x=17.78\ m[/tex]

Answer:

25x3 + 25x2 - 19x + 7

 —————————————————————

        5x + 2        

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

[tex]\frac{14(5x-2)(x+19)}{-7(x+19)(5x-2)}[/tex] the (x+19) on the numerator and denominator cancel out

[tex]\frac{14(5x-2)}{-7(5x-2)}[/tex] (5x-2)on the numerator and denominator cancel out

[tex]\frac{14}{-7}[/tex] = [tex]\frac{2}{-1}[/tex] =  -2

I hope this helped!

Answer:Perimeter is the limit of any given geometric figure. Circumference is just the name given to a circle’s perimeter, in other words, the circle’s limit, its edge.

The reason for this is because the perimeter is, by definition, the sum of the lenghth of every side of any given geometric figure. A circle has either no sides, or number of sides, so its perimeter has to be treated differently.

Remember that π (Pi) equals 3.141592 approximately. This is a constant, meaning that no matter what circle you are studying, Pi will always have the same value. It is the relation between the diameter and the lenght of its circumference. A circle with diameter xwill travel 3.141592x before it completes a revolution. This is where Pi comes from.

So the difference would be that a “normal” perimeter is only the sum of the sides. A circumference is the perimeter of a circle, given a diameter and the constant value of Pi, that derives from other properties of the circle, and not by its sides (remember a circle has either none or nnumber of sides).

Answer:

B. On Pearson (-1/4) D on Egdenuity(-1/4)

The student erred in calculating the slope for the line perpendicular to the given line. They should have used -1/4 instead of 2. The correct equation is y - 5 = -1/4 * (x + 8).

The error the student made lies in calculating the slope of the line that is perpendicular to given line y = 4x + 2. The slope of this line is 4, therefore the slope of the line perpendicular to it should be the negative reciprocal of 4, which is -1/4, not 2 as the student assumed. We also use the point-slope form of the line which is y - y1 = m(x - x1). Substituting m as -1/4 (the slope of perpendicular line) and the point (-8,5) into the equation, we should get y - 5 = -1/4 * (x + 8).

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Answer:

30% is what was given off the phone

$180 was the deduction price on the phone

Step-by-step explanation:

The price was actually $600

A discount of 20% was given on it

Then late extra 10%

Add of the percentage

20+10=30% off the actual price

30% of $600

30/100*600

18000/100=$180

Answer:

Its 28%

Step-by-step explanation:

I don't know step by step all the others were wrong on here so I picked 28% and it said correct