As a result, y = 200 + 160[tex]e^{(0.4t)}[/tex] is the answer to the provided differential equation with starting conditions of y = 40 and t = 0.
What equation of number would that be?A mathematical statement that shows the equivalence of a couple of equations is what an equation at algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The given differential equation is:
dy/dt = 0.4(y - 200)
To solve this differential equation, we need to separate the variables and integrate:
dy/(y - 200) = 0.4 dt
Integrating both sides, we get:
ln|y - 200| = 0.4t + C
where C is the constant of integration.
To determine the value of C, we use the initial condition that y = 40 when t = 0:
ln|40 - 200| = 0.4(0) + C
ln|-160| = C
C = ln(160)
Thus, the equation becomes:
ln|y - 200| = 0.4t + ln(160)
Taking the exponential of both sides, we get:
|y - 200| = [tex]e^{(0.4t+ln(160))}[/tex] = 160[tex]e^{(0.4t)}[/tex]
Simplifying, we get:
y - 200 = ±160[tex]e^{(0.4t)}[/tex]
y = 200 ± 160[tex]e^{(0.4t)}[/tex]
Using the initial condition that y = 40 when t = 0, we can determine the value of the constant of integration:
40 = 200 ± 160[tex]e^{(0.4(0))}[/tex]
40 = 200 ± 160
Solving for the two possible values of y, we get:
y = 360 or y = 40
Therefore, the solution to the given differential equation with the initial condition y = 40 and t = 0 is:
y = 200 + 160[tex]e^{(0.4t)}[/tex]
To know more about Equation visit:
https://brainly.com/question/2228446
#SPJ1
Jill bought 8 pounds of potatoes at a local wholesaler for $18. Her friend Jack bought 6 pounds of potatoes at the supermarket for $15. Jack thinks he got the better deal because $15 is less than $18. Is Jack correct? Why or why not.
Answerer Latoya got a better deal because she paid less than Herman by 25 cents
Step-by-step explanation:
Latoya 18 divided by 8= $2.25
Herman 15 divided by 6= $2.50
So Latoya saves $0.25 cents
A sample of paint contains 3 ounces of blue paint and 8 ounces of yellow paint. If you have a 24ounce can of the blue paint,how much yellow paint should you mix with it in order to make the same color as the sample
We shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
What are Ratiοs?Ratiοs are a way οf cοmparing twο οr mοre quantities by expressing their relative sizes οr amοunts. They can be written in the fοrm a:b οr a/b, where a and b are the quantities being cοmpared. Ratiοs are οften used in mathematics and everyday life tο express prοpοrtiοns, rates, and οther relatiοnships between quantities.
Tο make the same cοlοr as the sample, we need tο maintain the same ratiο οf blue tο yellοw paint.
The ratiο οf blue tο yellοw paint in the sample is 3:8, which simplifies tο 3/8.
If we have 24 οunces οf blue paint, we can use this ratiο tο find the amοunt οf yellοw paint needed:
(3/8) * 24 = 9 οunces
Therefοre, we shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
To learn more about Ratios from the given link
https://brainly.com/question/13419413
#SPJ1
Algebra 1 please help
An exponential function is a function in which the independent variable x appears as an exponent.
a is the y-intercept.
b is the rate of change and common ratio.
The function is exponential growth when b > 1.
The function is exponential growth when b < 1.
y-intercept is the initial value of the function when x is equal to 0.
Asymptote is the line that the function approaches but does not cross.
How to write and determine an exponential function?In Mathematics, an exponential function is typically represented by the following mathematical expression:
f(x) = a(b)^x
Where:
x represent time.a represent the base value, vertical intercept, or y-intercept.b is the slope, common ratio, and rate of change.Based on the given exponential function y = a(b)^x, we can logically deduce that the y-intercept is represented by a, b is the rate of change, and common ratio.
In conclusion, an asymptote is a line which the graph of a given function approaches, but it would neither touch nor cross.
Read more on exponential equation here: brainly.com/question/28939171
#SPJ1
5 times the quantity 4 plus a number c
Answer:
[tex]5(4+c)[/tex]
A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?
(4, 4), (6, 7), (7, 3)
(1, 7), (2, 10), (5, 6)
(1, 1), (2, 4), (5, 0)
(-2, 4), (-1, 7), (2, 3)
Option C. To translate the triangle downward by 3 units, we need to subtract 3 from the y-coordinate of each vertex. This will shift the entire triangle down by 3 units.
The original triangle has vertices (1, 4), (2, 7), and (5, 3):
(1,4)
/ \
/ \
(2,7)----- (5,3)
To translate the triangle downward by 3 units, we subtract 3 from the y-coordinate of each vertex:
(1, 4) -> (1, 1)
(2, 7) -> (2, 4)
(5, 3) -> (5, 0)
The new triangle has vertices (1, 1), (2, 4), and (5, 0):
(1,1)
/ \
/ \
(2,4)----- (5,0)
To learn more about triangle please click on below link.
https://brainly.com/question/26776354
#SPJ1
A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?
A. (4, 4), (6, 7), (7, 3)
B. (1, 7), (2, 10), (5, 6)
C. (1, 1), (2, 4), (5, 0)
D. (-2, 4), (-1, 7), (2, 3)
players per game 10 50 100
prizes awarded 2 6 18
A bag contains blue and yellow chips for a game at a carnival. To play, a person must select a chip from the bag. If the chip is blue, the person receives a prize. If the chip is yellow, the person does not receive a prize. The results after 10, 50, and 100 people played were recorded.
Which set of numbers from the table would give the best estimate of the probability of receiving a prize?
a
10 people and 2 prizes awarded
b
50 people and 6 prizes awarded
c
100 people and 18 prizes awarded
d
we cannot estimate the probability of receiving a prize
The best estimate of the probability of receiving a prize would be the ratio of the number of prizes awarded to the total number of people who played the game.
a) For 10 people, 2 prizes were awarded, so the estimate of the probability of receiving a prize is 2/10 or 0.2 (20%).
b) For 50 people, 6 prizes were awarded, so the estimate of the probability of receiving a prize is 6/50 or 0.12 (12%).
c) For 100 people, 18 prizes were awarded, so the estimate of the probability of receiving a prize is 18/100 or 0.18 (18%).
Therefore, the best estimate of the probability of receiving a prize would be c) 100 people and 18 prizes awarded, which gives an estimate of 0.18 or 18%.
what are the coordinates of the vertex
Answer:
vertex = (- 4, 6 )
Step-by-step explanation:
the vertex is the turning point on the curve.
this is situated at (- 4, 6 )
Answer:
The coordinates of the vertex are:
[tex]\left(\;\boxed{-4}\;,\;\boxed{6}\;\right)[/tex]
Step-by-step explanation:
The graph shows a parabola that opens downwards.
The vertex of a parabola that opens downwards is its maximum point.
From inspection of the graph, the maximum point is (-4, 6).
Therefore, the coordinates of the vertex are (-4, 6).
A six-sided number cube is rolled 12 times, and the number 3 is rolled 2 times. What is the theoretical probability of rolling the number 3?
Answer:
29%
Step-by-step explanation:
PLEASE HELP!! I NEED IT FOR TODAY!! GIVE A GOOD EXPLANATION PLEASE!!
Based on the information given in the histogram, option B. The distribution of the data is asymmetrical, so the mean and the median are likely outside the "1,000-1,099 photocopies" category is the correct statement.
What is histogram?
The histogram shows that the distribution of the data is asymmetrical, with a longer tail towards the right. This means that there are more schools that made a higher number of photocopies than those that made a lower number of photocopies. Therefore, the mean and median are likely to be higher than the midpoint of the "1,000-1,099 photocopies" category, which has the highest frequency.
In a skewed distribution, the mean is typically affected by the outliers, while the median is a better measure of central tendency. Therefore, the median is more likely to be within the "1,000-1,099 photocopies" category, while the mean is likely to be higher.
To know more about histogram, visit:
https://brainly.com/question/30354484
#SPJ1
the distance between (8, 0) and (8, -8)
Answer:
Step-by-step explanation:
The two given points are (8, 0) and (8, -8).
Using the distance formula, the distance between the two points can be calculated as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where x1 = 8, y1 = 0, x2 = 8, and y2 = -8
d = sqrt((8 - 8)^2 + (-8 - 0)^2)
d = sqrt(0 + 64)
d = sqrt(64)
d = 8
Therefore, the distance between the two points is 8 units.
Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
8 + (10 - 7)
7. In the following diagram of AABC it is known that ZA = ZC. If BD bisects ZABC then which two reasons would be needed to show that AB = CB? (1) H.L. and CPCTC (2) A.A.S. and CPCTC (3) S.A.S. and H.L. (4) H.L. and A.S.A. A B D 2 4
Check the picture below.
Helpppppppp 30 point
Step-by-step explanation:
4/25=0.16
6%=0.06
0.1=10%
0.875=7/8
The population in a certain town is increasing linearly each year. The population at time t=3 is 1285 and at time t=8 is 2460, where t is the number of years after 1990.
Answer:
Step-by-step explanation:
We can use the two given data points to find the slope of the line that represents the population growth over time.
The population at time t=3 is 1285, which means that the population has increased by P1 = 1285 - P0, where P0 is the initial population at time t=0 (which is not given). Similarly, the population at time t=8 is 2460, which means that the population has increased by P2 = 2460 - P0.
The time elapsed between t=3 and t=8 is 8-3 = 5 years.
The slope of the line that represents the population growth over time is given by:
slope = (P2 - P1) / (t2 - t1)
where t1 and t2 are the corresponding times.
Substituting the given values, we get:
slope = (2460 - 1285) / (8 - 3)
slope = 235
This means that the population is increasing by 235 people per year.
To find the initial population at time t=0, we can use either of the two given data points. Let's use the population at time t=3:
P1 = 1285 - P0
235 * 3 = 705
1285 - 705 = 580
Therefore, the initial population at time t=0 (i.e., in the year 1990) was 580 people.
We can now use the slope to find the population at any given time t after 1990.
Let P(t) be the population at time t after 1990.
Then, P(t) = P0 + slope * (t - 0)
P(t) = 580 + 235t
For example, the population in the year 2000 (i.e., when t=10) would be:
P(10) = 580 + 235(10) = 3330
Therefore, the population in the year 2000 would be 3330 people.
What is the rectangular form of the parametric equations?
x(t)=t+3,y(t)=2t2−4, where t is on the interval [−4,0].
Enter your answer, in standard form, by filling in the boxes.
y = __,__ where x is on the interval [ , ].
The rectangular form of the parametric equation is given as follows:
y = y = 2x² - 12x + 14, where x is in the interval [-1, 3].
How to obtain the rectangular form of the parametric equation?The parametric equation in the context of this problem is defined as follows:
x(t) = t + 3.y(t) = 2t² - 4.The interval for t is given as follows:
[-4,0].
Hence the bounds of the interval for x are given as follows:
Lower bound: t = -4 -> x = -4 + 3 = -1.Upper bound: t = 0 -> x = 0 + 3 = 3.From the first equation, we can write t as a function of x as follows:
t = x - 3.
Replacing into the second equation, the rectangular form of the equation is given as follows:
y = 2(x - 3)² - 4
y = 2(x² - 6x + 9) - 4
y = 2x² - 12x + 14.
More can be learned about the rectangular form of a parametric equation at https://brainly.com/question/27269624
#SPJ1
Answer: y = "2x^2 - 12x + 14", where x is on the interval ["-1, 3"].
Step-by-step explanation: I took the test.
Males
Females
Total
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d).
Nursing majors
Non-nursing
majors
1016
1728
2744
94
700
794
Question 8 of 11 >
Total
1110
2428
3538
(a) u puudumy L Sharon a un mar
P(being male or being nursing major) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the student is female or not a nursing major.
P(being female or not being a nursing major) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the student is not female or a nursing major.
P(not being female or being a nursing major) =
(Round to the nearest thousandth as needed.)
(d) Are the events "being male" and "being a nursing major mutually exclusive? Explain.
OA. No, because one can't be male and a nursing major at the same time.
OB. Yes, because there are 94 males majoring in nursing.
OC. Yes, because one can't be male and a nursing major at the same time.
This quiz: 11 point(s) possible
This question: 1 point(s) possible
C...
Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):
P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)
From the table, we have:
P(male) = 1110/3538 ≈ 0.314
P(nursing major) = 1016/3538 ≈ 0.287
P(male and nursing major) = 94/3538 ≈ 0.027
Therefore:
P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574
Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.
(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:
P(being female or not being a nursing major) = P(female) + P(not nursing major)
From the table, we have:
P(female) = 2428/3538 ≈ 0.686
P(not nursing major) = 1728/3538 ≈ 0.489
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175
This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):
P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)
From the table, we have:
P(female and nursing major) = 700/3538 ≈ 0.198
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977
Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.
(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:
P(not being female or being a nursing major) = 1 - P(being female or being nursing major)
From part (a), we have:
P(being male or being nursing major) ≈ 0.574
Therefore:
P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426
Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.
(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.
Step-by-step explanation:
please help me find these angles, i dont want a wrong answer.
Answer:
<EAC=75
<BAD=36
<ACD=75
<FAB=75
<CAD=69
<BDA=69
Step-by-step explanation:
EAC= 180-105=75
BAD= CDA
ACD= 75 opposite <s congruent
FAB= 75 vertical <s congruent
CAD=105-36=69
BDA=69 Opposite <s congruent.
Hope this helps! Should be right we just finished this unit.
2. Now, discuss your possible financial goals for the future, that could be related to this career choice.
(Hint: For example: Would you like to purchase a laptop or a car? Do you plan to purchase a condo/house?)
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
What are Stοcks?Stοcks, alsο knοwn as the shares οr equities, represent οwnership in cοrpοratiοn. When yοu buy stοck, yοu are buying small piece οf οwnership in cοmpany. The value οf stοck is determined by supply and demand fοr shares in market, as well as by the cοmpany's financial perfοrmance, industry trends, and οther factοrs.
I can suggest sοme pοssible financial gοals that sοmeοne in a career related tο finance might have:
Saving fοr retirement: A financial prοfessiοnal might set a gοal οf saving a certain amοunt οf mοney each year fοr their retirement.
Investing in stοcks οr οther assets: A finance prοfessiοnal might set a gοal οf investing in stοcks οr οther assets in οrder tο grοw their wealth οver time.
Building an emergency fund: A finance prοfessiοnal might set a gοal οf building an emergency fund tο cοver unexpected expenses οr incοme disruptiοns.
Paying οff debt: A finance prοfessiοnal might set a gοal οf paying οff debt, such as student lοans οr credit card debt, in οrder tο imprοve their financial stability.
Saving fοr a dοwn payment οn a hοme: A finance prοfessiοnal might set a gοal οf saving fοr a dοwn payment οn a hοme in οrder tο purchase a prοperty and build equity.
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
To know more about Amount visit:
brainly.com/question/28825310
SPJ1
Find the Product.
5(cos pi/4 + i sin pi/4) x 3(cos 5pi/3 + i sin 5pi/3)
Answer:
D. 15(cos(23π/12) +i·sin(23π/12))
Step-by-step explanation:
You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).
Complex productThe product is ...
A·cis(a) × B·cis(b) = AB·cis(a+b)
where "cis(x)" means (cos(x) +i·sin(x))
Application5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)
The product is 15·(cos(23π/12) +i·sin(23π/12)).
3: Managing Money
10. Which of the following is kept on record at the bank in order to identify you as the owner of your checking account?
OA. Account verification card
OB. Deposit slip
OC. Signature card
OD. Withdrawal slip
A document that is kept on record at the bank in order to identify you as the owner of your checking account include the following: C. signature card.
What is a checking account?In Economics, a checking account is sometimes referred to as a current account or transaction account and it can be defined as a type of bank account at a financial institution, that allows an accountholder to easily deposit and withdraw his or her money for daily activities.
This ultimately implies that, the use of a debit card is one of the ways through which money in a checking account can be accessed because it allows for deposits and withdrawals of cash at any given time.
In conclusion, a signature card is used by banks to determine the identity and ownership of a checking account (accountholder).
Read more on a signature card here: https://brainly.com/question/30841305
#SPJ1
The document that is kept on record at the bank for identification of the owner of a checking account is a signature card. The correct option is option C.
C. Signature cardWhat is a checking account?A checking account is an operational account which allows;
The deposit and withdrawal of funds when required
Payment of billsPurchase of itemsPayment receiptsA checking account holder is offered a debit card and or a set of cheques, which are then used to withdraw cash or make purchases.
Some of the details that are required to open a checking account are entered into a signature card by new customers.
A signature card includes the personal information of the owner of an account, including;
The signature of the person
The account holders name
The address of the account holder
The account holder identification number
The signature card is a document that is signed when opening a checking account, which the bank use to make references with regards to the account holders transactions.
With the signature card in the record of the bank, the bank can be able to identify a checking account holder's transactions such as issuing of cheque to third party, and also when the account holder makes requests for other banking services.
Learn more on checking accounts here: https://brainly.com/question/1927485
#SPJ1
If the total cost function for a lamp is C(x) =250+ 33x + 0.1x ^ 2 dollars, producing how many units, x, will result in a minimum average cost per unit? Find the minimum average cost.
Aaliyah is in the waiting room for an interview. What should she do while she waits?
a
Bring a book and read until they call her.
b
Apply for other jobs on her phone.
c
Pass the time by checking her social media accounts.
d
Sit and wait patiently.
Answer:
Bring a book and read until they call her.
Step-by-step explanation:
this is a productive and professional way to pass the time while waiting for an interview. It shows that she is prepared and focused on the task at hand. Checking social media or applying for other jobs on her phone may give the impression that she is not fully committed to the interview or is easily distracted. sitting and waiting is also an option, but bringing a book to read is a better use of her time.
hope this helps
D.Sit and wait patiently.
PLEASE HELP !! WILL GIVE BRAINLISET
[tex]-5x+4 = 29 \iff -5x =29-4 \iff -5x = 25\\[/tex]
[tex]x = 25:(-5) \implies \bf x = -5[/tex]
Answer: X = 5
Step-by-step explanation: f(x) is 29, plus it in to f(x)=-5x+4
29=-5x+4
Subtract the 4 with itself and 29
-5x=25
Divide both numbers by -5, you dont want x to be a negative
X = 5
In the circle below, suppose ark KLI = 247 deg and m angle LKJ = 124 deg . Find the following.
The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
What is circle?In geοmetry, a circle is a twο-dimensiοnal shape cοnsisting οf all pοints that are a fixed distance (called the radius) frοm a given pοint (called the center). A circle is a set οf pοints that are equidistant frοm the center. The distance between any pοint οn the circle and the center is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.
The measure of angle JLI can be found using the fact that angles on a straight line add up to 180 degrees. Therefore,
m angle JLI = 180 - m angle LKJ = 180 - 124 = 56 degrees.
The measure of arc JKI can be found using the fact that the measure of an inscribed angle is half the measure of the arc it intercepts. Therefore,
m arc JKI = 2 * m angle JLI = 2 * 56 = 112 degrees.
Therefore, The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
To learn more about Circle from given link.
https://brainly.com/question/29142813
#SPJ1
I need help with some math questions
17. Number of hours, h 10 + 2h Total Cost
1 10 + 2 x 1 12
2 10 + 2 x 2 14
3 10 + 2 x 3 16
4 10 + 2 x 4 18
This is true because as shown in the first example, you have to sub in the number of hours into the "h" value, and multiply it times two. After that, you add ten.
WILL GIVE THE BRAINLIEST PLEASE HURRYY!!!!!!!
Match the equation with the number of solutions for x that are possible.
Column A
1.
:
2.
y+5=12
:
y+5=12
3.
6a+1=9a:
6a+1=9a
4.
5x - 9 = 5x + 5:
5x - 9 = 5x + 5
5.
4(x - 7) +3x = 7x -28:
4(x - 7) +3x = 7x -28
Column B
a.Infinite solutions
b.Three solutions
c.Two solutions
d.One solution
e.There is no way to know
f.No solution
Answer:
1. One solution
2. No solution
3. Infinite solutions
4. Two solutions
5. Three solutions
Step-by-step explanation:
You're welcome ♡
If 5 x 6 = 20+ y,
0 5
0 6
O 10
0 30
what is the value of y?
Answer:
10
Step-by-step explanation:
5×6=20+y
30=20+y
30-20=y
10=y
therefore y=10
the length of PR if PQ is 3x-2 and QR is 5x+6
The length of the line segment PR from the given parameters is: 8x - 8
How to find the length of the Line Segment?The line segment addition postulate is a postulate that states that if we are given two points on a line segment, X and Z, a third point Y lies on the line segment XZ if and only if the distances between the points meet the requirements of the equation XY + YZ = XZ
We are given the parameters:
PQ = 3x - 2
QR = 5x + 6
Thus:
PR = PQ + QR
PR = 3x - 2 + 5x - 6
PR = 8x - 8
Read more about length of Line segment at: https://brainly.com/question/24778489
#SPJ1
1/2%8=p pound of fish is shared equally among aquarium each gets pound of fish food
1. In the calculation, only one pound of fish food is shared equally among one aquarium.
2. Each of the aquarium gets one pound of fish food
How do we solve both problems on the aquarium?To solve the first part of the problem, we need to find the value of P when 1/2 ÷ 8 = P. By doing the calculation by hand, we get:
1/2 ÷ 8 = 0.0625. So, the P = 0.0625.
In the second part of the problem, we know that 1 pound of fish is shared equally among a certain number of aquariums, and we need to find that number.
Since each aquarium gets 1 pound of fish food, and the total amount of fish food is 1 pound, we can set up an equation to solve for the number of aquariums:
1 pound of fish food / X number of aquariums = 1 pound of fish food per aquarium
Simplifying the equation, we get:
X = 1 pound of fish food / 1 pound of fish food per aquarium
X = 1 aquarium
Therefore, the pound of fish food is shared equally among 1 aquarium, and each aquarium gets 1 pound of fish food.
Read more about aquarium
brainly.com/question/28889858
#SPJ1
the explicit formula for this sequence: 21, 17, 13, 9, 5
This is the explicit fοrmula fοr this sequence.
What cοmprises an arithmetic series?An arithmetic series is a set οf integers that are οrdered and have a cοmmοn difference between each fοllοwing wοrd. The cοmmοn difference, fοr instance, between the mathematical series 3, 9, 15, 21, and 27 is 6. An alternative term fοr an arithmetic sequence is an arithmetic prοgressiοn.
The first term is 21 and the cοmmοn difference is -4 (the amοunt added οr subtracted tο get frοm οne term tο the next).
The explicit fοrmula fοr an arithmetic sequence is a n = a + (n - 1)d2, where a is the first term, d is the cοmmοn difference, and n is the term number.
Substituting 21 fοr a and -4 fοr d, we get:
a n = 21 + (n - 1)(-4)
Simplifying, we get:
a n = 21 - 4n + 4
a n = 25 - 4n
This is the explicit fοrmula fοr this sequence.
Learn more about arithmetic series
https://brainly.com/question/16415816?
#SPJ1