The population of growth of a town is 20,000 it decreased at a rate of 9% per year in about how many years will the population be fewer than 13,000
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.
Which expressions are equivalent to the one below? Check all that apply.
logg 5 + logs 125
Answer:
Step-by-step explanation:
B 4C and log 625
Two cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the end of 4 hours, the two cars are 520 miles apart. Find the average speed in mph of the other car. (Enter an exact number.
Final answer:
The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance apart, and then dividing by the time elapsed. The second car has an average speed of 50 mph.
Explanation:
The student is asking for help to find the average speed of the second car when two cars, starting at the same point and traveling in opposite directions, end up being 520 miles apart after 4 hours. The first car travels at an average speed of 80 mph.
To solve this, we need to calculate the total distance covered by both cars in the time frame given. We already know the total distance apart is 520 miles.
The first car travels at 80 mph for 4 hours, covering 80 mph * 4 h = 320 miles. To find out how far the second car traveled, subtract the distance covered by the first car from the total distance apart: 520 miles - 320 miles = 200 miles.
Finally, to find the average speed of the second car, divide the distance traveled by the time. Thus, the second car's average speed is 200 miles / 4 h = 50 mph.
Final answer:
To find the average speed in mph of the other car, divide the total distance traveled by the time. Subtract the first car's average speed from the total speed to find the other car's average speed.
Explanation:
To find the average speed in mph of the other car, we need to determine the total distance traveled. Since the two cars are 520 miles apart at the end of 4 hours, we can divide the total distance by the time to find the average speed.
The first car has an average speed of 80 mph, so the total distance traveled by both cars is 80 mph * 4 hours = 320 miles.
The other car's average speed can be found by subtracting the first car's average speed from the total speed: 320 miles - 80 mph = 240 mph.
Dante decided to spent only $20.00of his allowance and save the rest for later. Can he buy 12 packs of baseball cards?Why or why not
Answer:
yessssssssssssssssssssssssss
assume that y varies directly with x, then solve.
if y=2 2/3 when x=1/4, find y when x=1 1/8.
y=?
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
group of baseball fans can see home plate from a 40 meter tall building outside the stadium. The angle of vision has a tangent of
9
4
. What is the horizontal distance, in meters, to home plate?
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]
What is the equation of the line that has an x-intercept of 2 and a y-intercept of 8?
A y= 2x + 10
B y= 2x + 5
C y= -2x + 10
D y= -2x + 5
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:
The sum of a number and two is equal to negative seven. Translate this sentence to an equation and then find the number.
-5
5
-9
9
Answer:
-9 is correct
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
<3
Please hurry! (include graph for both)
1: Graph h(x)=2sin(2x)−3 . Use 3.14 for π .
2: Graph g(x)=4cos(2x)−2 . Use 3.14 for π .
See the graphs below
Explanation:FOR GRAPH 1:
Let's take:
[tex]f(x)=sin(x)[/tex]
Let's transform this function as follows:
Step 1. Horizontal compression by 1/2:
[tex]f(x)=sin(2x)[/tex]
Step 2. Vertical stretch:
[tex]f_{1}(x)=2sin(2x)[/tex]
Step 3. Vertical shifting 3 units down
[tex]f_{2}(x)=2sin(2x)-3[/tex]
Finally:
[tex]h(x)=f_{2}(x)=2sin(2x)−3[/tex]
The graph is shown in the First Figure below.
FOR GRAPH 2:
Applying a similar method we get:
Step 1. Horizontal compressionStep 2. Vertical stretchStep 3. Vertical shifting
The graph is shown in the Second Figure below.
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To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, multiply the sine and cosine functions by 2 and 4 for amplitude, adjust the period by halving it due to the 2x factor, and shift vertically by -3 and -2 respectively.
Explanation:To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, you can follow these steps:
Plot the basic sin(x) and cos(x) functions, remembering that for sine, the maximum and minimum values are 1 and -1, and the function starts at 0. For cosine, the function starts at its maximum value of 1.Multiply the sine and cosine values by their respective coefficients, 2 for h(x) and 4 for g(x), to stretch the amplitude accordingly.Incorporate the period change by understanding that the coefficient 2 in front of x will make the functions complete their cycles twice as fast, effectively halving the period to π instead of 2π.Finally, shift each graph vertically by the constants -3 for h(x) and -2 for g(x).The resulting graphs will show sine and cosine waves with adjusted amplitudes, periods, and vertical shifts. Remember to use 3.14 as an approximation for π to determine the x-values where key points like maxima, minima, and intercepts occur.
Two angles are supplementary. If one angle measures 56 degrees, what is the measure of the second angle? A. 34 degrees B. 44 degrees C. 114 degrees D. 124 degrees
Supplementary angles add up to 180 degrees. If one angle measures 56 degrees, the other supplementary angle equals 180-56 which equals 124 degrees. So, the second angle measures 124 degrees.
Explanation:Supplementary angles are two angles that add up to 180 degrees. Therefore, if one of these angles measures 56 degrees, the other one must be the value that when added to 56 completes 180. We can find it by using the formula for supplementary angles: angle B = 180 - angle A.
So, to find the measure of the second angle, we subtract the measure of the first angle (56 degrees) from 180 degrees.
Angle B = 180° - 56° = 124°.
Therefore, the second angle measures 124 degrees (Choice D).
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Two students were given the expression shown to simplify. Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent. 6 - (2 - 4x)
Sophia: 6+2+4x
Sophia's expression is incorrect/correct because ______.
Ursula: 6−(−2x)
Ursula's expression is incorrect/correct because _______.
Equivalent Expression
A correct equivalent expression is ______.
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~
Eileen and her brother Andrew had a bicycle race. Eileen Rode at a speed of 20 ft per second while Andrew Rode at a speed of 15 ft./s. To be fair, Eileen decided to give Andrew a 150 foot Headstart. The race ended in a tie how far away was the finish line from where Eileen started include a graph to support your solution
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).
how old am I if 20 reduced by two times my age is 16
Answer:
20-2x=16
Divide all by 2
10-x=8
x=2,
Step-by-step explanation:
The first equation in the following system gives the
company's cost of making x purses. The second
equation gives the company's income for selling x
purses.
What are the solutions to the system of
equations?
(-23,400, 3,400) and (-1,170, 170)
(-1,170, -23,400) and (170, 3,400)
(274, 726) and (5,480, 14,520)
(274, 5,480) and (726, 14,520)
DONE
y=-0.01(x - 500)2 + 4.489
y = 20x
You used substitution to obtain the equation
0 = -0.01x2-10x+1,989 from the system
Intro
Answer:
option 2: (-1,170, -23,400) and (170, 3,400)
Step-by-step explanation:
correct answer for e2020
Answer:
B. (-1,170, -23,400) and (170, 3,400)
Step-by-step explanation:
The sum of 200 and 7 times a number
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:
What subtraction problem has a value of 2/3
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)
Which situation is an example of an observational study?
a.) Having a randomly selected group of students take a pen and paper test and comparing the results with another randomly selected group of students who took the same test on the computer?
b.) Polling voters about their favorite candidates in upcoming elections.
c.) Recording the reaction time of participants in a study who were asked to press a button as soon as they see a certain picture on a screen.
d.) Asking kids in a kindergarten classroom about the average number of pieces of fruit they eat each day.
Answer:
Step-by-step explanation:
C! hopes this helps
Apply the distributive property to create an equivalent expression.
4\left(3 + \dfrac14c - \dfrac12d\right) =4(3+
4
1
c−
2
1
d)=
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]
What helper fact did you double to solve 8 x 6
Answer: 48
Step-by-step explanation:
You can either add 8 six times or get a calculator and solve.
One cup equals approximately 236 ml. Approximately how many ml are there in one gallon
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
Bill spent less than 26$ on a magazine and five books. The magazine cost 4$
Write an inequality to represent the situation. Be sure to define your variable.
Solve the inequality to find the maximum cost each book.
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
Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. How many pounds of macadamia nuts and how many pounds of almonds should dude use for the mixture to cost $7.75 per pound to make
Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.
Step-by-step explanation:
Step 1:
Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.
Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.
Step 2:
Form an equation using the above information.
⇒ 9x + 5.25 (12-x) = 12 × 7.75
⇒ 9x + 63 - 5.25x = 93
⇒ 9x - 5.25x = 30
⇒ 3.75x = 30
⇒ x = 8
Number of macadamia nuts is 8 pounds.
Step 3:
Calculate number pounds of almonds
⇒ Number of pounds of almonds = 12 - x = 4 pounds.
EASY MATH 10 PTS + BRAINLIEST
If (6^2)^p = 6^10, what is the value of p?
a. 2
b. 3
c. 4
d. 5
Answer:
d. 5
Step-by-step explanation:
Can someone explain the difference between the perimeter and the circumference?
REAL ANSWER PLEASE WILL GIVE BRAINLIEST
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).
An irregular polygon is shown below:
The area of the irregular polygon is
square units.
Answer:
15 units²
Step-by-step explanation:
The figure is composed of 2 rectangles.
The rectangle on the left has
A = 4 × 3 = 12 units²
The rectangle on the right has
A = (3 - 2) × (7 - 4) = 1 × 3 = 3 units²
Thus area of figure = 12 + 3 = 15 units²
To find the area of an irregular polygon, divide it into regular shapes and sum their areas. The area of a square is simple: side length squared. When scaling, areas of similar shapes increase by the square of the scaling factor.
Explanation:Understanding Area CalculationTo calculate the area of an irregular polygon, we often need to divide it into regular shapes such as triangles, rectangles, or squares. Once we do that, we can calculate the area of each shape and then sum all the areas to find the total area of the irregular polygon. For instance, if an irregular shape fits within a square of side a, its area is less than a² based on the premise that the area of a circle inscribed in a square is smaller than the square's area yet larger than half. For a square, the calculation is relatively straightforward with the formula for area being side length squared (a²).
Calculating the area becomes even more important when applied to real-life examples, such as surveying land parcels which can have highly irregular outlines. The concept is similar to understanding the relationship between the area of a square and its side length when measuring larger plots of land like a state or a carpet on a house's blueprint. We use scales or conversion factors to translate a drawn measurement to actual size.
The comparison of areas can also be seen in the example where Marta's larger square's area is four times that of the smaller one because areas of similar shapes scale by the square of the scaling factor (in this case, 2).
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Solve the equation for x. For each step, describe the operation and/or property used.
5(2x - 4) - 11 = 4 + 3x
PLEASE HELP
Answer:
x = 5
Step-by-step explanation:
Start by distributing the 5 to remove parentheses. To do this multiply the numbers and variable in the parentheses by 5.
10x - 20 - 11 = 4 + 3x
Next. you want to get the variables to one side. This is done by subtracting 3x from both sides.
7x - 20 - 11 = 4
Now solve the -20 - 11.
7x - 31 = 4
You need to have the variable all by itself. To do this, first add -31 to both sides.
7x = 35
Finally divide by 7.
x = 5
Hope this helped.
B. Factor the polynomial 64x + 27y. If the
polynomial cannot be factored, write prime.
Answer:
PRIME
Step-by-step explanation:
the GCF of 64 and 27 is 1
>therefore the polynomial is already factored and can’t be factored further.
You randomly draw a marble out of a bag that contains 20 total marbles. 12 of the marbles in the bag are blue.
What is P(draw a blue marble)?
If necessary, round your answer to 2 decimal places.
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]
100 points What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
A rectangle with a short side of 6. An arrow points to a smaller rectangle with a short side of 1.5
Answer:
0.25
Step-by-step explanation:
Scale factor = ratio of the sides
Assuming the first rectangle is with shorter side 6,
Scale factor = 1.5/6 = 15/60 = 1/4 = 0.25
Divide the new length by the original length:
The arrow points from 6 to 1.5, so the new length is 1.5 and the original length was 6.
1.5 / 6 = 0.25. The scale factor was 0.25
what is 29/4 simplyfied?
Answer:
7 and 1/4 or 7.25
Step-by-step explanation:
28/4 = 7
1/4 = 0.25
7 + 0.25 = 7.25
Answer:
[tex]\frac{29}{4}[/tex] or [tex]7\frac{1}{4}[/tex]
Step-by-step explanation:
29/4 is the most simplified it can get, if you want it as a mixed fraction then it is 7 1/4.