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.
45.6 x 10 to the 2nd power
4,560
10 to the 2nd power is = 100
so 100 × 45.6 =
At the fair, you spend $6 for food, then use the rest of your $20 to buy ride tickets. You have
enough money to buy 56 tickets. How much does each ticket cost?
a. $ 0.20 c. $0.35
b. $0.25 d. $ 0.48
Harry ate 6 candies. Jake ate 2 fewer candies than Harry. How many candies did jake eat?
Answer:
4
Step-by-step explanation:
6 - 2 = 4
Jake ate 2 less than 6 which is how many Harry ate.
Answer:
4
Step-by-step explanation:
the answer is 4 because 6 minus 2 would be 4 so the answer is four
A cantaloupe weighs 1/2. A watermelon weighs four times as much as the cantaloupe, how much does the watermelon weighs?
Answer:2
Step-by-step explanation: 1/2=0.5 0.5x4=2
Tim would like to buy a video game that costs $27. He has not saved any money. His parents are willing to pay him $3 for every 2 chores, but will also pay him for completing single chores.
Tim would have to do 18 chores (2 chores 9 times or 1 chore 18 times) to be able to buy the video game.
Step-by-step explanation:
Step 1; Tim's parents will give him $3 for every two chores. This equals $1.50 for a single chore. He wants to save up $27 so that he can buy the video games he wants.
Step 2; The number of times he has to do the chores to be able to but the video game is a division between the money he wants to save up by the money he gets for the chores.
Number of 2 chores he needs to do = Amount of money he wants to save up / money he gets for doing two chores
= $27 / $3 = 9 times.
Number of single chores he has to do =Amount of money he wants to save up / money he gets for doing two chores
$27 / $1.50 = 18 times
Which Fraction is less than 3/5 3/10 3/4 2/3 or 5/3
Answer:
The fraction less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given fractions are
[tex]\frac{3}{5} ,\frac{3}{10} ,\frac{3}{4}, \frac{2}{3}, \frac{5}{3}[/tex]
[tex]\frac{3}{5} =0.6\\\\\frac{3}{10}= 0.3\\\\\frac{3}{4} =0.75\\\\\frac{2}{3}=0.66 \\\\\frac{5}{3}=1.66[/tex]
Arranging the fraction in increasing order of their value
[tex]\frac{3}{10}= 0.3<\frac{3}{5} =0.6<\frac{2}{3}=0.66<\frac{3}{4} =0.75<\frac{5}{3}=1.66[/tex]
So,the fractions less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
Add. What is the answer
(5b^2-3b+2)+(2b-4)
Answer:
5b²-1b-2
Step-by-step explanation:
-3b and +2b are like terms so you combine them together -3b+2b= -1b
+2 and -4 are like terms so +2-4= -2
5b² has no like terms
then you put your answers together to simplify the equation
5b²-1b-2
The polynomials added together give the result 5b^2 - b - 2. The addition is done by combining like terms in the given polynomials.
Explanation:To add these polynomials, you combine like terms. Like terms are the terms in the polynomial that have the same variable and exponent. Here, our terms are 5b^2, -3b, 2, 2b, and -4.
The term 5b^2 does not have a like term, so it remains as is. The terms -3b and 2b add up to -b because -3b + 2b = -b. And finally, the constants 2 and -4 add up to -2. When we combine these results, we have the final answer: 5b^2 - b - 2.
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3 1/2, 3 5/6, 4 2/12, ………………, 4 5/6
What is the missing term?
What rule can you create for this pattern?
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
The sequence is [tex]3\frac{1}{2}, 3\frac{5}{6}, 4\frac{2}{12}, .... , 4\frac{5}{6}[/tex].
So, we have to find the missing term.
The sequence can be written in improper fraction as [tex]\frac{7}{2}, \frac{23}{6}, \frac{25}{6}, ... , \frac{29}{6}[/tex].
Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by [tex]\frac{1}{3}[/tex].
As, [tex](\frac{23}{6} - \frac{7}{2}) = \frac{1}{3} = (\frac{25}{6} - \frac{23}{6})[/tex].
Therefore, the missing number is [tex](\frac{25}{6} + \frac{1}{3}) = \frac{27}{6} = \frac{9}{2} = 4\frac{1}{2}[/tex]. (Answer)
The height y of a jumping frog can be modeled by y = -16x^2+ 4x, where x is the time in
seconds) since the frog jumped from the ground. Find the roots of the equation when y = 0
Explain what the roots mean in this situation.
Answer:
roots: 0, 1/4time when the height is zeroStep-by-step explanation:
The roots are the values of x that make y=0.
0 = -16x^2 +4x = -4x(4x -1)
The values of x that make the factors zero are solutions to this equation:
x = 0
x = 1/4 . . . . . makes the factor (4x-1) equal to zero
The roots of the equation are x=0 and x=1/4.
__
Since y is height and x is time, when y=0, the frog is on the ground. The roots, then, are the times when the frog is on the ground.
The smaller root is the time when the frog leapt.
The larger root is the time when the frog landed.
The roots of the equation y = -16x² + 4x are x = 0 and x = 1/4,
The given equation y = -16x² + 4x models the height y of the frog as a function of time x in seconds.
To find the roots of this equation when y = 0, we need to solve:
0 = -16x² + 4x
This is a quadratic equation.
Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.
In this case, factoring is straightforward:
0 = x(-16x + 4)
This gives us two solutions
x=0
x=4/16=1/4
The roots are x = 0 and x = 1/4 seconds.
Interpreting the Roots
The roots of the equation indicate the times when the frog is at ground level (y = 0). At x = 0, the frog has just jumped, and at x = 1/4 seconds, the frog returns to the ground. Therefore, these roots represent the start and the end of the jump respectively.what is the product of 2/5 and 2/3
Answer:
4/15 or in decimal form its 0.26
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.26
A spherical ball with a volume of 2,304π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answer:
Therefore the volume of the box is 13824 in³
Step-by-step explanation:
Given:
A spherical ball with is packaged in a box that is in the shape of a cube.
Volume of ball = 2304π in³.
Let 'r' be the radius of sphere
To Find:
Volume of Cube = ?
Solution:
Volume of sphere is given by
[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]
Substituting the values we get
[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]
Now we know that diameter is given by
[tex]diameter=2\times r=2\times 12=24\ in[/tex]
it is given that,
The edge length of the box is equal to the diameter of the ball.
Therefore the length of cube = 24 in
Now the volume of the cube is given by
[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]
substituting the values we get
[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]
Therefore the volume of the box is 13824 in³
H E L P ME ASAP! PLEASE I NEED HELP!
Part a) Wayen's saving before he spend $28 is $30
Part b) Steph's saving after she spend $28 is $8
Step-by-step explanation:
Ratio of Wayen's saving to stephs saving: 5:5
After spending $28
Ratio of Wayen's saving to Stephs saving: 1:4
We can write ratio as:
[tex]\frac{W}{S}=\frac{5}{6}\\Cross\,\,multiply\\6W=5S\,\,eq(1)[/tex]
After spending $28
[tex]\frac{W-28}{S-28}=\frac{1}{4}\\Cross\,\,multiply\\4(W-28)=S-28\,\,eq(2)[/tex]
Part a) Find Wayen's saving before he spend $28
Using both equations to find value of W
Putting value of S from eq(1) into eq(2)
6W/5=S
[tex]4W-112+28=S\\4W-84=S\\Putting\,\,value\,\,of\,\,S\\4W-84=\frac{6W}{5}\\ Multiply\,\,both\,\,sides\,\,by\,\,5\\20W-420=6W\\20W-6W=420\\14W=420\\W=420/14\\W=30[/tex]
So, Wayen's saving before he spend $28 is $30
Part b) Find Steph's saving after she spend $28
First Steph's saving before spending $28 is:
[tex]S=\frac{6W}{5}\\S=\frac{6*30}{5} \\S=36[/tex]
Now, After spending $28
S-28 we get:
36-28= $8
So, Steph's saving after she spend $28 is $8
Keywords: Ratio and proportion
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What place is the 4 at in the number 562,347
Answer: tenth place
Step-by-step explanation:
Answer:
The tens place.
Step-by-step explanation:
In order, the numbers would go as follows:
7 would be in the ones place.
4 would be in the tens place.
3 is in the hundreds place.
2 is in the thousands place.
6 is in the hundred thousands place.
5 is in the millions place.
What does 7 1/2 - 2 3/16 - 1 5/8= as a fraction?
Answer:
3 11/16
Step-by-step explanation:
7 1/2 - 2 3/16 - 1 5/8
turn all to same fractions using multiplication
by this i mean to only multiply the fractions (both numerator and denomenator)
7 8/16 - 2 3/16 - 1 10/16
Turn them into improper fractions
120/16 - 35/16 - 26/16 =
And solve
3 11/16
The maximum volume of a cylindrical tank measures 3rs/4 liters. What is one-third of the tank's maximum volume? (1/3)x(3rs/4) (3rs/4) / 1/3 (3rs/4) / 3 9rs/4 rs/4
there is not any slope for this mathematical equation
To find one-third of the tank's maximum volume, multiply the maximum volume by one-third: 1/3 * 3rs/4 = 3rs/12.
Explanation:To find one-third of the tank's maximum volume, we can multiply the maximum volume by one-third:
1/3 × 3rs/4 = 3rs/12
So, one-third of the tank's maximum volume is 3rs/12 liters.
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Your bedroom ceiling is 10 feet high and is 2/3 as high as the living room ceiling. Write and solve an equation to find the height of the living room ceiling
The height of living room ceiling is 15 feet.
Step-by-step explanation:
Given,
Height of ceiling in bedroom = 10 feet
This is 2/3 height of living room ceiling.
Let,
x be the height of living room ceiling.
2/3 of x = 10
[tex]\frac{2}{3}x=10[/tex]
Multiplying both sides by 3
[tex]3*\frac{2}{3}x=10*3\\2x=30[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{30}{2}\\x=15[/tex]
The height of living room ceiling is 15 feet.
Keywords: fraction, division
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The height of the living room ceiling is 15 feet.
Explanation:To find the height of the living room ceiling, we can start by letting 'x' represent the height of the living room ceiling.
Since the bedroom ceiling is 2/3 as high as the living room ceiling, we can write the equation:
10 = (2/3)x
To solve for x, we can multiply both sides of the equation by 3/2:
(3/2)(10) = (3/2)((2/3)x)
15 = x
Therefore, the height of the living room ceiling is 15 feet.
What is the absolute value of | 56-12 |?
Answer: 44! Hope this helps :D
Step-by-step explanation:
Answer:
Step-by-step explanation:
56 - 12 is 44
how do you do linear models?
Answer:
Identify the input and output values.
convert the data to do coordinate pairs.
find the slope.
write the linear model.
use the model to make a prediction by evaluating the function at the given x-value.
use the model to identify an x value that results in a given y value.
Which is larger 17/40 or 8/15
It's easier to figure it out when both fractions have the same denominator, so let's fix that:
17/40*15/15 is 255/600
8/15*40/40 is 320/600
Notice we are multiplying by a factor of 1 to get equivalent fractions
So 8/15 is bigger
Hope this helped!
8/15
when you divide it it comes out to be 0.533 repeating
but when you divide 17/40 it comes out to be 0.425
so .5 is larger then .4
what is the domain
{(-1,2),(4,6), (8,3),(11,-6)
a)D:{-1,4,8,11}
b)-1,4,11
c)-6,2,3,6
d)-1,-6,2,3
Answer:
a
Step-by-step explanation:
the x of each point in order from least to greatest makes up the domain
What ratio is equivalent to 2:9
Answer:
8:36
Step-by-step explanation:
Factors: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36
GCF: 4
8 ÷ 4 = 2 36 ÷ 4 = 9
Can someone please help me first answer gets brainlist
Answer:
9=1.375 10=1.625 11=3.3125 12=4.45
using standard normal distribution tables, the area under the standard normal curve corresponding to Z > -1.62 is:
The area under the standard normal curve corresponding to Z > -1.62 is approximately 0.9474.
Explanation:The question asks for the area under the standard normal curve corresponding to Z > -1.62. Using standard normal distribution tables, we can find this area by finding the area corresponding to Z = -1.62 and subtracting it from 1. Since standard normal distribution tables provide the area to the left of the Z-score, we need to subtract the area from 1 to get the area to the right of the Z-score.
By looking up Z = -1.62 in the standard normal distribution table, we find the area to the left (or below) the Z-score is approximately 0.0526. Therefore, the area to the right (or above) the Z-score is approximately 1 - 0.0526 = 0.9474.
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Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical. 20 students have tickets. Select all the equations that can be used to find the number of students in Bryan’s homeroom.
The equation formed by the given problem statement is 0.5*x + 4 = 20, solving this gives x = 32. Hence, there are 32 students in Bryan’s homeroom.
Explanation:The problem statement says that 'Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical' and '20 students have tickets'. If we denote the total number of students in Bryan’s homeroom by x, we can write the statement as an equation: 0.5*x + 4 = 20. Simplifying this equation gives us 0.5*x = 20 - 4 = 16, so x = 16 * 2 = 32. Hence, there are 32 students in Bryan’s homeroom.
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When 18 is subtracted from 6 times a number the result is -12 what is the number
Answer:
24
Step-by-step explanation:
18-6=12
24=12x2
12-24= -12
Hahn passes the 0 point running 5 meters per second to the right. where will he be 6 seconds later
Answer:
30 meters away
Step-by-step explanation:
each second is equal to 5 meters, hence meters per second
a hose is coiled into circular loops about 30 inches in diameter. the length of each loop is about...
a. 7 ft
b. 8 ft
c .9ft
D. 10ft
Answer:
b. 8 ft
Step-by-step explanation:
We use the formula for the circumference of a circle to find the length of each loop.
Circumference of a circle = 2πr or Dπ
Where: π = pi
r = radius of the circular loops
D = Diameter
π = [tex]\frac{22}{7}[/tex]
D = 30 inches
Use Circumference of a circle = Dπ
Circumference of a circle = 30 x (22/7)
= 30 x 3.142857143
= 94.28571429 inches
Convert 94.28571429 inches to feet (ft)
12 inches = 1 ft
94.28571429 inches = 94.28571429/12
= 7.857142858 ft
≈ 8 ff
An Expression is shown.
1 3 a 2 + b ÷ 2
What is the value of the expression if a = 3 and b = 8?
Answer:
If you're supposed to be multiplying the first four numbers, the answer is going to be 13.
Step-by-step explanation:
Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10
Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x
Which step in solving this equation is justified by the Distributive Property?
A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C) Step 3 ⇒ 8x − 8 = 9x − 10
D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Answer:
A I think is the right one
As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable? What one-variable equation is she left with after adding?
5x + 6y = 18
2x – 3y = 12
Factor:________
Equation:________x=_________
Answer:
Yumiko should multiply the other equation by 3.
If she adds the two equations she would be left with the variable 'x'.
Step-by-step explanation:
Given the two equations are as follows:
[tex]$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $[/tex]
[tex]$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $[/tex]
It is given that she multiplies the first equation by 6. Therefore, (1) becomes
[tex]$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $[/tex]
Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.
The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.
Therefore, Equation (2) becomes:
[tex]$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $[/tex]
Now, we add Equation (a) and Equation (b).
[tex]$ \implies 12x - 18y + 15x + 18y = 72 + 54 $[/tex]
[tex]$ \implies 27x = 126 $[/tex]
Factor: 3
Equation: 27x = 126