Answer: from generation 19 to 20.
Step-by-step explanation:
The greatest percentage increase will occur from generation 19 to 20 as the exponential power will be highest.
What is exponential growth?
Exponential growth happens once the larger in size you're the quicker you grow that causes you to even larger in size. it's the expansion characterised by interest, or growth. it's known as exponential growth as a result of it will solely be delineate mathematically by inserting time within the exponent or power of the bottom. Population then is adequate to the population at the current times some discretional range to the facility of the expansion rate times the time. The discretional range is sometimes two then the expansion rates is given because the reciprocal of the doubling time.
Main body:
initial population = 25
Total generation = 20
growth rate = 0.2
General formula of exponential function = aˣ
here a = 25 and x = 0.2
⇒25⁰°²
= 1.9
hence total population = 25+2 = 27
So it is clear that in 19 to 20 generation , growth will be highest.
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Finn has a piece of bamboo stick that is 50 cm long. He cuts the stick once into two pieces and used it to build a rhombus-shaped kite; he used a textile 288cm^2 in area along with the sticks. How long were the two sticks?
The lengths of the bamboo sticks obtained using the quadratic formula are;
33.06 cm and 16.94 cm
What is the quadratic formula?The quadratic formula used to find the solution of quadratic equations can be presented as follows;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4\times a \times c} }{2 \times a}[/tex]
The area of the rhombus = 280 cm²
The length of the stick = 50 cm
Let x represent a length of the sticks , therefore;
The length of the other stick = 50 - x
The rhombus consists of two triangles
The height of the triangles is half the length of the diagonal of the rhombus, therefore;
Area = x × (50 - x) × 0.5 = 280
-0.5·x² + 25·x = 280
x² - 50·x + 560 = 0
x = (50 ± √((-50)² - 4 × 1 × (560))/(2)
x ≈ 33.06, or x ≈ 16.94
The lengths of the bamboo sticks are;
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13.
(a) What fraction of this square is shaded?
(b) What decimal part of this square is not shaded?
Answer to question 1:
2/5
Explanation:
This square is a 10 by 10 graph, meaning there is 100 total blocks, and 40 of the squares are shaded in, making 40/100 of the squares shaded. 40/100 is then simplified to 2/5.
Answer to question 2:
0.6
Explanation:
As previously stated, the graph has a total of 100 squares, and 60 of the squares are not shaded, making it 60/100 squares unshaded. 60/100 is then converted to a decimal of 0.6.
what is the half-life of a radioactive substance that decays at a continuous rate of 11% per minute? (round to one decimal places.)
5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).
Define the half-life of a radioactive substance?A radioactive sample's half-life is the amount of time it takes for half of its atomic nuclei to spontaneously transform into another nuclear species and emit particles and energy.When we use the formula A = A0(1 - r)t,
where A is the quantity of a substance we have at any given moment (t), A₀ is the quantity we have at the beginning (at t = 0), and r is the rate of decay, we may state the following:(1/2)A₀ = A₀(1 - 0.11)t
[Divide both sides by A₀ results in:
1/2 = (0.87)t
Using the log of both sides;:
log(1/2) = log(0.87)t
Using a logarithm property, we can bring the "t" to the front, giving us:
log(1/2) = t.log(0.89)
[Dividing both sides with log(0.89) gets us:
t = log(1/2)/log(0.89)
Using calculator for soling the values.
t = 5.94 seconds
Thus, 5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).
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The angles of a quadrilateral are 3y+25, 2y+30, 2y-5, y+30. The value of y is
Answer:
y=35
Step-by-step explanation:
3y+25+2y+30+2y-5+y+30=360
Combine like terms then you will get
8y+80=360
8y=280
y=35
Answer:
35°
Step-by-step explanation:
the sum of the angles in a quadrilateral is 360 degrees
let 's make and solve the equation
3y + 25 + 2y + 30 + 2y - 5 + y +30 = 360
Combine like terms then you will get
(3y + 2y + 2y + y) + (25 + 30 - 5 + 30) = 360
8y + 80 = 360
8y + 80 - 80 = 360 - 80
8y = 280
y = 280:8
y= 35
madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random. what are the odds in favor of her selecting a red marble? (type answer in form a:b) 5:30
The odds in favor of her selecting a red marble = 6/7
Here, Madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random.
We need to decide the odds in favor of her selecting a red marble.
Total number of marbles = 30 + 5
Total number of marbles = 35
So, the odds in favor of her selecting a red marble would be,
p = number of favourable outcomes / total number of outcomes
p = 30/35
p = 6/7
Therefore, the probability that she select a red marble is 6/7
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Describe the error in the work shown. 62 + 3 + 5 x 2 36 + 8 x 2 36 + 16
this is due tomorrow pls help
The error is not using PEMDAS in right order and the answer is 75.
What is PEMDAS?PEMDAS is a method of operation in which operations are done in the order of parentheses first , then exponents, multiplication, division, addition and subtraction in the respective manner.
Given expression, 62 + 3 + 5 x 2
By using PEMDAS,
Step.1 - Firstly do the multiplication;
62 + 3 + 5 x 2 = 62 + 3 + 10
Step.2 - Now add the remaining terms;
62 + 3 + 10 = 75
Therefore, the answer is 75 .
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find the distance between the two points (7,4) (3,3)
Applying the distance formula, the distance between the two points (7, 4) and (3, 3) is: 4 units.
How to Find the Distance Between Two Points?If we have two given points with their coordinates, to find the distance between these two points, apply the distance formula that is expressed as:
d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Given the two points:
(7, 3) = [tex](x_1, y_1)[/tex]
(3, 3) = [tex](x_2, y_2)[/tex]
Substitute the values into the distance formula:
d = √[(3−7)² + (3−3)²]
d = √[(−4)² + (0)²]
d = √16
d = 4 units.
The distance is: 4 units.
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Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.69 and standard deviation 0.74. in USE SALT (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.69 and 3.00? (Round your answers to four decimal places. at most 3.00 between 2.69 and 3.00 (b) How large a sample size would be required to ensure that the first probability in part (a) is at least 0.99? (Round your answer up to the nearest whole number.)
The formula to convert the sample mean to a z score is, z = (x−μ)/σ/√n
a) Probability that the sample average sediment density is at most 3 is 0.9525 and probability between 2.69 and 3.00 is 0.4525..
b) Large Sample size is approx. 4 ..
We have given that,
Suppose the sentiment density of a randomly selected specimen from a certain region is normally distributed with
Sample mean , X-bar = 2.69
Sample size , n = 25
Standard deviations, σ = 0.74
a) we have to see what's the probability that the sample average setiment is at most 3 and then we're going to calculate between 2.69 and 3 point, so the firstly we have to calculate the standard error.
standard error = σ/√n = 0.74/√25
=> standard error = 0.148
the probability that x is between 2.69 and 3 in the probability of 2.69, i.e P (2.69<z <3)
P(at most 3 ) = P( X-bar <3) = P( X-bar - u /σ /√n<( 3 - 2.69) /0.74/5 )
=> P(z< 1.67) = 0.9525
P (2.69<z <3) = P( 2.69 - 2.69/0.74/5<z< 1.67)
=> P( <z< 1.67) = 0.4525
b) A large sample size is needed to make sure the first probability is 0.99.
If P(X-bar <3) = 0.99
=> P( 0<z<(3-2.69)/0.74/√n ) = 0.99
=> (3 - 2.69 )/0.74 /√n = 2.33
=> 0.31 √n /0.25 = 2.33
=> n = ( 2.33×0.25/0.31)² = 3.5 ~ 4
Hence, sample size is 4 and P( <z< 1.67) is 0.4525
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If Amy is tardy, then she will get a detention
Write the CONVERSE of this statement
Answer:
Amy will get detention if she is tardy
Step-by-step explanation:
each year, more than 2 million people in the united states become infected with bacteria that are resistant to antibiotics. in particular, the centers of disease control and prevention have launched studies of drug-resistant gonorrhea.† suppose that, of 221 cases tested in a certain state, 14 were found to be drug-resistant. suppose also that, of 322 cases tested in another state, 6 were found to be drug-resistant. do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? use a 0.02 level of significance. (let p1
Yes, These data suggest a statistically significant difference between the proportions of drug-resistant cases in the two cities.
In first city, the drug-resistant proportion is significant while In other city, It is not significant.
What is Ratio and proportion ?
A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another.
Let the first city to be City A and the other city as City B.
In city A, 14 cases are of drug-resistant out of total 221 cases.
In city B, 6 cases are of drug-resistant out of total 322 cases.
We'll find the proportion of drug-resistant cases of both cities,
City A = 14 / 221 = 0.06 > 0.02
City B = 6 / 322 = 0.018 < 0.02
If use a 0.02 level of significance then,
City A has significant drug-resistant cases while City B does not have significant cases.
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A recent college graduate is planning to take the first three examinations in the coming summer. She will take the first exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam is 0.9. If she passes the first exam, then the conditional probability that she passes the second one is 0.8, and if she passes both the first and the second exams, then then the conditional probability that she passes the third exam is 0.7.
The recent college graduate upon passing her exam with a probability will be as follows:
(a) Let the event where she passes the exam be denoted as [tex]E_{i}[/tex] and by i-th exam.
P(passes all exams) = P([tex]E_{3} E_{2} E_{1}[/tex]) = P([tex]E_{3} | E_{2} E_{1}[/tex])P([tex]E_{2} | E_{1}[/tex])P([tex]E_{i}[/tex])
= (0.7)(0.8)(0.9)
= 0.504
(b) By calculating,
[tex]P (E_{1} E_2^{c} | (E_{1} E_{2} E_{3})^{c})[/tex] = [tex]\frac{P (E_{1} E_2^{c} | (E_{1} E_{2} E_{3})^{c})}{P((E_{1} E_{2} E_{3})^{c})}[/tex]
= [tex]\frac{P(E_{1} E^{c}_{2}) }{P((E_{1} E_{2} E_{3})^{c})}[/tex]
= [tex]\frac{P(E^{c}_{2} | E_{1)}P(E_{1 )} } {{P((E_{1} E_{2} E_{3})^{c})}}[/tex]
= [tex]\frac{(1- P (E_{2}|E_{1})) P(E_{1})}{1-P(E_{1} E_{2} E_{3} }[/tex]
= [tex]\frac{(1-0.8) X 0.9}{1-0.504}[/tex]
where we know the denominator from part (a)
≈ 0.3629
Probability theory deals with numerical representations of the likelihood that an event will happen or that a statement is true. A probability is a number between 0 and 1, where 0 essentially signifies an event's impossibility and 1 generally denotes certainty. The likelihood that something will happen is what is commonly referred to as probability. We can talk about the likely of one outcome, or the likelihood of a few outcomes, when we don't know how an event will turn out. An event's probability distribution is studied in statistics.
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Six adult tickets to a movie at the theater cost
$52.50. Find the price for one ticket.
Answer:
$8.75 for one ticket
Step-by-step explanation:
Since this is just plain division, you'd divide 52.50 by 6 and get your answer of 8.75.
Hope I helped!
1400 people signed up for a bike sharing program. This represents 8% of the people who live in Divyas town. 75% of the people who signed up for the program also own cars.
Answer:
what is the question??????
A baseball player made 9 errors in 60 games. How many errors would we expect the player to make in 100 games
The basketball player made 15 errors in 100 games as of the given condition.
Given that,
A baseball player made 9 errors in 60 games, how many errors would we expect the player to make in 100 games is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Let the error be x, for 100 games,
Now, according to ot the question,
9/60= x / 100
x = 15
Thus, the basketball player made 15 errors in 100 games.
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You are planning a cookout and figure that you will need at least 3 packages of hot dogs and hamburgers. A package of hot dogs, x, costs $4 and a package of hamburgers, y, costs $5. You can spend a maximum of $20 on hot dogs and hamburgers.
a. Write a system of linear inequalities for the number of packages of each that can be bought.
A system of linear inequalities for the number of packages of both hot dogs and hamburgers that can be bought is as follows:
x + y ≥ 3.
4x + 5y ≤ 20.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of hot dogs.Let the variable y represent the number of packages of hamburgers.Since you will need at least 3 packages of both hot dogs and hamburgers, the linear inequality to represent this is as follows:
x + y ≥ 3.
For the cost of both hot dogs and hamburgers, and the maximum amount you can spend;
4x + 5y ≤ 20.
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Lauren runs 2100 meters in 6 minutes. How many meters can Lauren run in one minute?
Answer: 350 meters
Step-by-step explanation: if she can run 2100 meters in 6 minutes to get 1 minute you can to divide by 6. so 6 minutes turn to 1 minute and 350 meters.
Monica deposits $100 into a savings account that pays a simple interest rate of 3.3%. Paul deposits $200 into a savings account that pays a simple interest rate of 2.1%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
[tex]~~~~~~ \stackrel{\textit{\LARGE Monica}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (100)(0.033)(1) \implies I = 3.3 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\LARGE Paul}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 2.1\%\to \frac{2.1}{100}\dotfill &0.021\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.021)(1) \implies I = 4.2[/tex]
well, Monica needs to check more closely what was in that last cup of coffee she drank, she's hallucinating.
What estimate can i do for 3.5x0.4
Answer:
The answer is 1.4
1/2x+3/4y=10
3/4х-y=4
Answer:
ONE:1/2x+3/4y=10
ANS:
x=
−3
2
y+20
EXPLANATIONLet's solve for x.
1
12
12x+
12x+3
12x+34
12x+34y=10
Step 1: Add (-3)/4y to both sides.
1
12
12x+
12x+3
12x+34
12x+34y+
12x+34y+−3
12x+34y+−34
12x+34y+−34y=10+
12x+34y+−34y=10+−3
12x+34y+−34y=10+−34
12x+34y+−34y=10+−34y
12x+34y+−34y=10+−34y1
12x+34y+−34y=10+−34y12
12x+34y+−34y=10+−34y12x=
12x+34y+−34y=10+−34y12x=−3
12x+34y+−34y=10+−34y12x=−34
12x+34y+−34y=10+−34y12x=−34y+10
Step 2: Divide both sides by 1/2.
1
2
x
x1
x12
x12=
x12=−3
x12=−34
x12=−34y+10
x12=−34y+101
x12=−34y+1012
x12=−34y+1012x=
x12=−34y+1012x=−3
x12=−34y+1012x=−32
x12=−34y+1012x=−32y+20
Answer:
Answer:x=
Answer:x=−3
Answer:x=−32
Answer:x=−32y+20
srry I can't understand the secondquestion
KINDLY CORRECT ME IF IM WRONG ❕4800 people attended a football game. If 10% of the people who attended were teenagers, how many teenagers attended the game?
Answer: 480 are teenagers
Step-by-step explanation:
To find a percentage of a number, I like to convert the percentage into its decimal form, so I do...
10% = .1 because a percentage is out of a whole number. 100% = 1.
Next, multiply your sum by the percentage you are looking for, so...
[tex]4800*.1=480[/tex]
Bella used 24 cm of tape to wrap 8 presents. How much tape will bella need in all if she has to wrap 13 presents? Solve using unit rates.
Answer:39cm
Step-by-step explanation:
(3x +33)"
(4x+8)
Find B
Answer: B=90 degrees maybe
Step-by-step explanation:
9 - (-21) =
PLEASE HELP
Answer:
30
Step-by-step explanation:
9-(-21) = 9+21 = 30
what is the GCF sum of 6+18
Answer:
GCF = 6; sum = 6(1 +3)
Step-by-step explanation:
You want the greatest common factor of 6 and 18.
GCFThe greatest common factor is the largest factor common to both numbers. Here, we can factor the numbers as ...
6 = 6·1
18 = 6·3
The factor 6 is common to both numbers. (Other numbers, such as 1, 2, and 3 are also common factors, but 6 is the largest.)
The GCF is 6.
In terms of the GCF, the sum can be written ...
6 +18 = 6(1 +3)
__
Additional comment
If the smaller number is not a factor of the larger, then the next value to check is the difference between the larger and smaller.
Euclid's algorithm tells you the remainder from division of the larger by the smaller will be zero when the divisor is the GCF. Otherwise, the remainder can be used to replace the larger number for trying again.
Here, 18/6 = 3 r 0, so 6 is the GCF.
Write x^5/x^7 as a single exponential expression
Answer:
Usually we write the final answer with positive exponents.
[tex]\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{x^{5} }{x^{7} }[/tex]
When we are dividing powers with the same bases, we subtract the exponents.
[tex]x^{5-7}[/tex] = [tex]x^{-2}[/tex] or [tex]\frac{1}{x^{2} }[/tex]
consider a list of randomly generated 2-letter ""words"" printed on a paper. the letters cannot be repeated. 1) how many different words are there? 26*25 2) at least how many of these ""words"" should be printed to be sure of having at least 7 identical ""words"" on the list? 26*25*7 3) at least how many identical ""words"" are printed if there are 5201 ""words"" on the list?
1) the maximum number of different 2 letter words = 650
2) 3901 words that should be printed to be sure of having at least 7 identical words on the list.
3) if there are 5201 words on the list, then there are 11 identical words
In this question, we have been given a list of randomly generated 2-letter words printed on a paper and he letters cannot be repeated.
1)the maximum no. of different 2 letter words would be,
using permutation,
^(26)P_2 = 650
2) the least number of words that should be printed to be sure of having at least 7 identical words on the list.
650 * 6 = 3900
3900 + 1 = 3901
to sure 7 identical words 3901 words should be printed.
3) the least number of identical words are printed if there are 5201 ""words"" on the list.
5201 = (520 * 10) + 1
so, there are at least 11 identical words.
Therefore, 1) the number of different 2 letter words = 650
2) the least number of words that should be printed to be sure of having at least 7 identical words on the list = 3901
3) if there are 5201 words on the list, 11 identical words should be printed.
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a portfolio has a 3-year standard deviation of 18.1%. what is the 1-year standard deviation? group of answer choices 8.69% 11.80% 10.45% 6.39%
The one - year standard deviation is, 10.45%.
what is standard deviation?
The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.
Given:
A portfolio has a 3-year standard deviation of 18.1%.
We have to find the one - year standard deviation.
One - year SD = Variance / number of years.
Here,
Variance = square of standard deviation = (18.1)^2 = 327.61
So,
One - year SD = 327.61 / (3/1)
One - year SD = 109.20
Now,
(109.2)^(1/2) = 10.45%
Hence, the one - year standard deviation is, 10.45%.
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 170 engines and the mean pressure was 7.7 lbs/square inch. assume the standard deviation is known to be 0.8. if the valve was designed to produce a mean pressure of 7.6 lbs/square inch, is there sufficient evidence at the 0.01 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
The null hypothesis is that the mean is equal to 7.6 lbs while the alternate hypothesis of the valve is that it is not equal to 7.6lbs.
What is a Hypothesis in statistics?
This term is used to refer to a statement which is made that is tested to be true or untrue during the study.
The Null hypothesis
H0: μ = 7.6
The alternate hypothesis:
H1: μ ≠ 7.6
The null hypothesis says the valve produces a mean pressure of 7.6 lbs. The alternate hypothesis on the other hand says that it does not equal to 7.6lbs.
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Answer:
H0: μ=7.6
Ha: μ>7.6
1. Which number has an absolute value greater than 8?
a) 9
b) -8
c) 0
d) 8
Answer:
b)-8
Step-by-step explanation:
Because the absolute value of -8 is 8 and it will have an greater number then all of them
PLEASE HELP ASAP!!!!
Answer:
11.3
Step-by-step explanation:
Angles A & B are each 45 degrees because if you subtract 90 from 180 and divide that by 2 you get 45 then you do:
sin(45) times 16 which is 11.3
SIN = opposite over hypotenuse.