The exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
What is exponential ?
an exponential function is a function of the form:
f(x) = a^{x}
where a is a positive constant called the base, and x is the exponent. The base represents the factor being repeatedly multiplied, while the exponent represents the number of times the base is being multiplied by itself.
To model the decreasing population of catfish in Athena Lake, we can use an exponential function of the form:
P(t) = P0 × e^{-rt}
where:
P(t) is the population at time t
P0 is the initial population
r is the annual growth rate (in this case, a negative value representing a decreasing population)
e is the mathematical constant e (approximately 2.71828...)
t is the time elapsed (measured in years)
In this case, we know that the initial population P0 is 800, and that the current population P(1) is 760 (since Franklin started monitoring one year ago and estimates the population has decreased to 760). So we can use these values to solve for the annual growth rate r:
760 = 800 × e^{-r}
Dividing both sides by 800, we get:
0.95 = e^{-r}
Taking the natural logarithm (ln) of both sides, we get:
ln(0.95) = -r
Solving for r, we get:
r ≈ 0.0513
So the exponential model for the population of catfish in Athena Lake is:
P(t) = 800 × e^{-0.0513t}
where t is the time elapsed (measured in years).
To learn more about exponential visit the link:
https://brainly.com/question/11975096
#SPJ9
he tapes the edge with special tape.how much tape will each coaster required
Answer: 5% Of Tape
there is going to be 5% of tape for the coaster
Solve for y.
2y - 8x = 20
y = [ ? ]x + {?}
Answer:
y = 4x + 10
Step-by-step explanation:
2y - 8x = 20 ( add 8x to both sides )
2y = 8x + 20 ( divide through by 2 )
y = 4x + 10
Answer: y=4x+10
Step-by-step explanation:
If a item is $30 and the is 20% off the regular price how much would it be
Answer:
20 percent off depends on the original cost: Take the original number and divide it by 10. Double your new number. Subtract your doubled number from the original number. You have taken 20 percent off! For $30, you should have $24.
Step-by-step explanation:
Which number is a perfect square
Responses
2
8
16
20
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
There are 19 animals in the field. Some are cows and some are ducks. There are 60 legs in all. How many of each animal are in the field?
Answer:
There are 11 cows and 8 ducks
Step-by-step explanation:
x will represent number of cows and (19-x) will represent ducks
[tex]4x+2(19-x)=60[/tex]
multiply 2 with (19-x)
[tex]4x+38-2x=60[/tex]
add your x's
[tex]2x+38=60[/tex]
subtract 38 on both sides
[tex]2x=22[/tex]
then divided 2 on both sides
[tex]x=11[/tex] cows
now to find ducks subtract
[tex]19-11[/tex]
your answer will be 8
So there are 11 cows and 8 ducks
to double check do this
[tex]11*4 + 8*16\\=44+16\\=60[/tex]
The table represents an exponential function. What is the multiplicative rate of change of the function?
The multiplicative rate οf change οf the given expοnential functiοn is 1/5.(1st οptiοn).
What is expοnential functiοn?An expοnential functiοn is a Mathematical functiοn which is οf the fοrm
f (x) = aˣ, where “x” is variable here and a real number and “a” is a cοnstant which is called the base οf the functiοn where a shοuld be greater than zerο.
The expοnential functiοn is given here in tabular fοrm.
Here frοm the table οf expοnential functiοn we get when x= 2 then
y= 2/5
again when x= 3 then y= 2/25
sο (2/5)×(1/5) = 2/25
again fοr x= 4 , y= 2/125
(2/25)×(1/5) = 2/125
sο every time the expοnential functiοn is multiplied by 1/5 and we get the next result.
Hence, The multiplicative rate οf change οf the given expοnential functiοn is 1/5.
To know more about exponential function
https://brainly.com/question/30241796
#SPJ1
A train is moving at a rate of 65 miles/hour toward a railroad marker located 200 miles away. Which equation could be used to find the time it will take for the distance between the train and the railroad marker to be 4 miles apart, where h represents the time in hours?
The distance d between the train and the railroad marker can be expressed as:
d = 200 - 65h
where 200 represents the initial distance between the train and the marker, and 65h represents the distance the train has covered after h hours, assuming a constant speed of 65 miles per hour.
To find the time it will take for the distance between the train and the marker to be 4 miles apart, we can set d to 4 and solve for h:
4 = 200 - 65h
65h = 196
h = 196/65
So the equation to find the time it will take for the distance between the train and the railroad marker to be 4 miles apart is:
200 - 65h = 4
or
65h = 196
or
h = 196/65
Solve and graph the inequality.
-4 < 4x < 20
The solution of the given inequality is x ∈ (-1,5). The graph has been plotted and attached below.
What is an inequality?
In mathematics, an inequality is a relationship that unfairly compares two numbers or other mathematical expressions. Size comparisons between two numbers on the number line are most usually made.
We are given an inequality as -4 < 4x < 20.
Now, on splitting the inequality, we get two inequalities which are:
-4 < 4x and 4x < 20.
On solving -4 < 4x, we get
⇒ -4 < 4x
⇒ -1 < x
Similarly, on solving 4x < 20, we get
⇒ 4x < 20
⇒ x < 5
So, we get -1 < x < 5 which means x ∈ (-1,5).
The graph of the inequality has been plotted and attached below.
The red part represents -1 < x and the blue part represents x < 5.
Hence, the solution of the given inequality is x ∈ (-1,5).
Learn more about inequality from the given link
https://brainly.com/question/30238989
#SPJ1
Which relationships describe angles 1 and 2?
Select each correct answer.
vertical angles
complementary angles
adjacent angles
supplementary angles
Answer:
Step-by-step explanation:
Supplementary Angles and Adjacent Angles
Answer: It would be both supplementary and adjacent angles
Step-by-step explanation: both of the angles add up to 180 degrees
I need help on this asap!
In linear equation, 0.75x + 2y ≤ 16 , 2x + 4y ≤ 40 are the solution represent .
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
if the small pair is x, the large pair is y.
45 minutes = 0.75 hour
120 minutes = 2 hour
so, 0.75x + 2y ≤ 16
2x + 4y ≤ 40
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
olympic gold medal has a gram of 586 grams. what is the mass of a 2018 olympic gold medal in hectograms
The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.
First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.
To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.
To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.
The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.
To know more about hectograms, refer here:
https://brainly.com/question/1058206#
#SPJ11
if a value has a z-score of positive 2, what does this tell us about the value compared to the mean? if a value has a z-score of -1.5, what does this tell us about the value compared to the mean? write 2-3 sentences.
As a general rule, a Z-score of - 3.0 to 2.0 recommends that a stock is exchanged inside three standard deviations of its mean.
A Z-Score is a statistical estimation of a score's relationship to the mean in a gathering of scores.
A Z-score can uncover to a merchant on the off chance that worth is normal for a predefined informational collection or on the other hand assuming it is abnormal.
As a general rule, a Z-score of - 3.0 to 2.0 recommends that a stock is exchanged inside three standard deviations of its mean.
Merchants have created numerous techniques that utilize z-score to distinguish connections between's exchanges, and exchanging positions, and assess exchanging systems.
The higher (or lower) a z-score is, the further away from the mean the fact is. This isn't really positive or negative; it just shows where the information lies in a regularly conveyed test. This implies it comes down to inclination while assessing speculation or opportunity. For instance, a few financial backers utilize a z-score scope of - 3.0 to 3.0 on the grounds that 99.7% of regularly conveyed information falls here, while others could utilize - 1.5 to 1.5 in light of the fact that they favor scores nearer to the mean.
to know more about mean click here:
https://brainly.com/question/1136789
#SPJ4
39 of the 52 students in choir A like musicals. 35 of the 44 students in choir b like musicals. Was there a higher percentage of students that like musicals in choir A or B?
Choir B has a higher percentage of students who like musicals.
what is percentage ?
Percentage is a way of expressing a proportion or a fraction out of 100. It is a widely used concept in mathematics, finance, statistics, and other fields. For example, if 20 out of 100 students in a class like pizza, we can say that the percentage of students who like pizza is 20%. To calculate the percentage, we usually multiply the given fraction by 100. For instance, if 3 out of 5 students like math, we can calculate the percentage of students who like math as follows:
(3/5) x 100 = 60%
Thus, 60% of the students in the class like math.
To determine which choir has a higher percentage of students who like musicals, we need to calculate the percentage of students in each choir who like musicals.
For choir A, 39 out of 52 students like musicals:
39/52 = 0.75 or 75%
For choir B, 35 out of 44 students like musicals:
35/44 = 0.795 or 79.5%
Therefore, choir B has a higher percentage of students who like musicals.
To know more about percentage visit :-
https://brainly.com/question/24877689
#SPJ1
which answer refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time? group of answer choices
The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.
Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.
Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.
Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.
Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.
See more about prevalence at: https://brainly.com/question/16865966
#SPJ11
Compounds angles identities
Answer:
Compound angle identities are trigonometric identities that relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles.
The main compound angle identities are:
1. sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
2. cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
3. tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))
where A and B are any two angles.
These identities can be used to simplify trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities.
For example, we can use the compound angle identity for sin(A + B) to find sin(π/4 + π/6):
sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)
sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)
sin(π/4 + π/6) = (√6 + √2) / 4
Compound angle identities are an important part of trigonometry and are used in various fields such as physics, engineering, and mathematics.
jason is making a concrete driveway. he mixes dry cement and water in the correct ratio. the table shows how much dry cement to mix with different amounts of water. jason says a graph of the relationship includes the point (63, 140). is jason correct?
Jason is correct when he says that a graph of the relationship includes the point (63, 140).
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The relationship is defined according to the equation presented as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one, which is also the constant ratio of the relationship.
From the table given at the end of the answer, when x = 54, y = 120, hence the constant is given as follows:
k = 120/54
k = 2.2222.
Hence the equation is:
y = 2.2222x.
When x = 63, the output of the function is given as follows:
y = 2.2222 x 63
y = 140.
Hence Jason is correct when he says that a graph of the relationship includes the point (63, 140), as when x = 63, the output of the function is of y = 140.
Missing InformationThe table is given by the image presented at the end of the answer.
More can be learned about proportional relationships at https://brainly.com/question/7723640
#SPJ1
an online buying club offers a membership for $245, for which you will receive a discount of 10 percent on all brand-name items you purchase. how much would you have to buy to cover the cost of the membership?
You would have $2,450 to buy to cover the cost of the membership.
An online buying club offers a membership for $245, for which you will receive a discount of 10 percent on all brand-name items you purchase.
We have to determine how much you would have to buy to cover the cost of the membership.
You have to buy to cover the cost of the membership = An online buying club offers a membership/Receive a discount
You have to buy to cover the cost of the membership = $245/10%
You have to buy to cover the cost of the membership = $245/0.10
You have to buy to cover the cost of the membership = $2,450
To learn more about cost of the membership link is here
brainly.com/question/15014708
#SPJ4
Please help!! Determine what line the angle below has been reflection across. Justify your answer
The line of reflection for the given angle is corresponding vertices.
1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.
In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.
This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles
for such more questions on reflected angle
https://brainly.com/question/27243531
#SPJ11
14 , 28, 56 as product of their prime factors
Answer:
14 = 2 x 7
28 = 2² x 7
56 = 2³ x 7
In P, answer the following:
A. Name a radius
B. Name a diameter
C. Name a cord
D. Name a central angle
E. Name a tangent to the circle
Answer:
radius=PC
diameter=AB
chord=AC
central angle=angleAPC
tangent=AD
what would happen if 300 people were sampled instead of 200, and the confidence level remained the same?
If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.
Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.
To learn more about sampling refer :
https://brainly.com/question/6979326
#SPJ11
What is p(8 or less than 7) write answer as a whole number
The expression "p(8 or less than 7)" suggests that we are looking for the probability of an event that satisfies one of two conditions: either the outcome is 8 or the outcome is less than 7. However, we need to know the specific probability distribution or situation in which this function p is being used to calculate a meaningful answer.
For example, if p represents the probability of rolling a certain number on a fair six-sided die, then p(8 or less than 7) would be 0, because 8 is not a possible outcome and all outcomes less than 7 are equally likely. However, if p represents the probability of a certain event occurring in a particular situation, then we would need more information about the nature of the event to calculate the probability.
Find out more about the probability distribution
brainly.com/question/14210034
#SPJ4
Question 8 of 10
Floyd's brick house is located in the suburbs. If his building property
insurance is $652.50 per year, how much is his house worth?
Annual Premium per $100 of coverage
Brick
Steel
Area
rating
Building Contents
Building Contents
City
0.39
0 43
Suburb 0.45
0.52
Rural 0.6
0.69
OA. $185,000
OB. $145,000
OC. $125,000
O D. $95,000
05
0.56
0.71
0.54
0.63
0.8
Mixed
Building Contents
0.55
0.72
0.89
0.65
0.74
0.91
Wood
Building Contents
0.66
0.83
1
0.76
0.85
1.02
The right answer is (B), which is $145,000, given that his building property insurance costs $652.50 annually.
what is interest ?In mathematics, interest usually refers to the sum of money that is charged or made over the course of a given period of time on a principal sum of money. In finance and economics, interest—which can be basic or compound—is frequently used to calculate borrowing costs and return on investment. The principal sum, the interest rate, and the duration for which the interest is being charged or earned are the three factors used to compute simple interest.
given
We are informed that Floyd's home is situated in a suburban area, where building property insurance costs $0.45 for every $100 of coverage.
Assume Floyd's home is worth x. Then, the yearly payment for his home's building property insurance is:
0.0045x = $652.50
After finding x, we obtain:
x = $652.50 ÷ 0.0045
x ≈ $145,000
Floyd's home is therefore currently worth about $145,000.
The correct response is (B ) $145,000 as his building property insurance is $652.50 per year.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
Two square pyramids are joined at their bases.
Each base is 28 cm long. The distance between the
vertices of the combined pyramids is 21 cm. What
is the volume of the solid formed?
The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.
Let V be the volume of the solid formed.
⇒ volume of the solid formed - V = 2 ( [tex]\frac{1}{3} *B*h[/tex] )
Now substitute the values,
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * [tex]28^{2}[/tex] * 10.5 )
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * 784 * 10.5 )
⇒V = 2 ( 261.3 * 10.5 )
⇒V = 2 ( 2,743.65 )
⇒V = 5,487.3 unit ²
Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
Learn more about Volumes:
https://brainly.com/question/12798020
#SPJ1
deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
To know more about probability:
https://brainly.com/question/30034780
#SPJ11
need help with part B i send you the screenshot of my work bc i dont know where to place the words
4 divided by 1/5=20
1st
you change the 4 to 4/1
2nd
you change the 1/5 to 5/1
3rd
multiply 4/1x5/1 which gives you 20
how many ways can we place three rooks on a four by five board so that no rook is threating another?
There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.
To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.
Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.
Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.
To know more about total number of arrangements refer here:
https://brainly.com/question/1179123#
#SPJ11
what is the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud?
There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:
[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]
where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.
We know that p=0.15, so we can plug in the values:
[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]
So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
Learn more about Probability:
https://brainly.com/question/24756209
#SPJ4
PLSSSS HELP IF YOU TURLY KNOW THISSS
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
__________________
hope it helps ⸙
if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
For such more question on deposit
https://brainly.com/question/1438257
#SPJ11