suppose a population of fruit flies increases at a rate of g(t)=5e0.01t, in flies per day. if the initial population of fruit flies is 360 flies, how many flies are in the population after 80 days?
Answers
If the initial population of fruit flies is 360 flies, Therefore, 10,388 fruit flies are in the population after 80 days.
To find the population of fruit flies after 80 days, we need to integrate the given rate function with respect to time from t=0 to t=80 i.e. ∫g(t)dt = ∫5e^(0.01t)dt.
Using integration by substitution, let u=0.01t and du/dt=0.01, so dt = du/0.01
∫5e^(0.01t)dt = ∫5e^udu/0.01 = 500e^(0.01t)/0.01 + C
where C is the constant of integration.
To find C, we use the initial population of 360 flies when t=0:500e^(0.01*0)/0.01 + C = 360
C = 360 - 500 = -140
So the population function is: P(t) = 500e^(0.01t)/0.01 - 140
To find the population after 80 days, we plug in t=80:P(80) = 500e^(0.01*80)/0.01 - 140 ≈ 10388
Therefore, there are approximately 10,388 fruit flies in the population after 80 days.
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Related Questions
There are 16 dominos in the center of the table to play the game. There are four players who are playing the game.
Which equation can be solved to find the number of dominos each player will receive if they each receive the same
number of dominos?
Answers
y varies jointly as x and z. y = 36 when x= 3 and z=3. Find y when x=5 and z=2.y=
Answers
Where k is a constant
When y = 36 , x = 3 , z=3
\(\begin{gathered} k\text{ = }\frac{y}{xz} \\ k=\text{ }\frac{36}{3\times3}\text{ =}\frac{36}{9}\text{ = 4} \end{gathered}\)\(\begin{gathered} y\text{ = 4xz} \\ x=\text{ 5 , z = 2} \\ y\text{ = 4 }\times5\times2=40 \end{gathered}\)The value of y is 40
P Q P⊃Q
T T T
T F F
T F T
F T T
Going from top to bottom, how would you fill in that column?
a. TFFF
b. TTFF
c. TFTF
d. TFTT
Answers
When P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT. The correct answer is option d. TFTT.
The given truth table for the compound proposition P ⊃ Q is: P Q P⊃QT T T T T F FT F T T F
The conditional P ⊃ Q implies that whenever the antecedent P is true, then the consequent Q is true as well.
This implies that the only time the conditional P ⊃ Q is false is when the antecedent is true, but the consequent is false.
Since we see in the truth table that when P is true, and Q is true, the proposition P ⊃ Q is also true.
However, when P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT.
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Can someone please help me ASAP?? It’s due tomorrow!! I will give brainliest If It’s correct.
Answers
Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:
A. Perpendicular to the base: Rectangle
B. Parallel to the base: Triangle with dimensions equal to the base
C. Diagonal from vertex to vertex: Triangle with unknown dimensions
he lengths of the sides of a rectangle are and where the sum of the lengths of the two shorter sides and one of the longer sides of the rectangle is 36. what value of maximizes the area ofthe rectangle?
Answers
The maximum area of the rectangle is A = xy = 12 * 12 = 144 square units.
Let's assume the two shorter sides of the rectangle are x and y, where x ≤ y, and the longer side is z. According to the given information, we have the following equations:
x + y + z = 36 (Equation 1)
x ≤ y
To maximize the area of the rectangle, we need to find the maximum value of xy.
From Equation 1, we can express z as z = 36 - (x + y).
The area of the rectangle, A, is given by A = xy.
Substituting z in terms of x and y, we have:
A = xy = x(36 - (x + y)) = 36x - x² - xy (Equation 2)
To find the value of x that maximizes the area, we can differentiate Equation 2 with respect to x and set the derivative equal to zero:
dA/dx = 36 - 2x - y = 0
Since x ≤ y, we can substitute y with x in the equation above:
36 - 2x - x = 0
Simplifying the equation, we get:
36 - 3x = 0
3x = 36
x = 12
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
12 + y + z = 36
y + z = 24
Since the sum of the lengths of the two shorter sides and one longer side is 36, and x = 12, we can deduce that y = 12.
Therefore, the sides of the rectangle are x = 12, y = 12, and z = 12 (since z = 36 - (x + y) = 12). This means we have a square.
In a square, all sides are equal. Therefore, the maximum area of the rectangle is obtained when all sides are equal, i.e., when x = y = z = 12.
The maximum area of the rectangle is A = xy = 12 * 12 = 144 square units.
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A tank in the shape of a hemisphere has a radius of 7 feet. if the liquid that fills the tank has a density of 93 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid that filled the hemispheric tank to the nearest full pounds is 66775 pounds.
What is the volume of an hemisphere?An hemisphere is half of a sphere. Therefore,
volume = 2 / 3 πr³
where,
r = radiusTherefore,
r = 7 feet
volume = 2 / 3 × 3.14 × 7³
volume = 2 / 3 × 3.14 × 343
volume = 2154.04 / 3
volume = 718.013333333
volume = 718.013
Therefore,
density = mass / volume
93 = mass / 718.013
mass = 718.013 × 93
mass = 66775.24
mass ≈ 66775 pounds
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If C = x – 9x^2 and D = -x + 3, find an expression that equals 3C – D in
standard form.
Answers
stay home stay safe
hope you understand
Expand the binomial using the binomial theorem: (3x-4)^5
Can someone explain how you solve this?
Answers
Answer:
Step-by-step explanation:
We worry about 2 things:
-terms power
-coefficient for each term
(3x-4)^5, has 2 terms 3x and -4
-Start with the first term to the highest power 5 and second term to the lowest power 0, then the high power goes down and low power increases until the first term has the lowest power 0 and the second term has the highest power 5.
-The coefficients for each term we take it from the Pascal triangle.
For the the power 5 the coefficients are 1, 5, 10, 10, 5, 1
\((3x-4)^{5} = 1*(3x)^{5} *(-4)^{0} +5*(3x)^{4} *(-4)^{1} +10*(3x)^{3} *(-4)^{2}+10*(3x)^{2} *(-4)^{3}+5*(3x)^{1} *(-4)^{4}+1*(3x)^{0} *(-4)^{5}\)
Simplify:
\((3x-4)^{5} = 3^{5} x^{5} -20*3^{4} x^{4} +160*3^{3} x^{3}-640*3^{2} x^{2}+1280*3x-1024\)
\((3x-4)^{5} = 243 x^{5} -1,620x^{4} +4,320 x^{3}-5,760x^{2}+3,840x-1024\)
0.3(4 − x) = x − 1.4?
Answers
Answer:
x is equal to 2
Step-by-step explanation:
simplify the equation
distribute the 0.3
0.3*4-0.3x=x-1.4
1.2-0.3x=x-1.4
get x by itself on one side
1.2+1.4=x+0.3x
simplify
2.6=1.3x
2=x
Find each unit rate. Round answers to hundreds
3) $57 for 6 hours of work
Answers
The unit rate is $9.50 per hour
A unit means one of several things. A unit rate means a rate for one thing. We write it as a ratio with the denominator being one.For example, if you run 70 meters in 10 seconds, on average you have run 7 meters in 1 second. Both rates, 70 meters in 10 seconds and 7 meters in 1 second, are ratios, but 7 meters in 1 second are unit rates. The unitary method is a method in which you find the value of one unit and then the value of a required number of units.Suppose you go to the market to buy 6 apples. The trader tells you that he is selling 10 apples for Rs 100. In this case, the number of apples is the unit and the price of the apples is the value.
As the rate for 6 hrs. is $57,
the rate is 57/6=(3×19) / (3×2)
=19/2
=9.50
The unit rate is $9.50 per hour
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Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 1+i, 1 The polynomial function in expanded form is f(x) =
Answers
The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.
A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.
Using the zero-product property, that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:
f(x) = (x - (1+i))(x - (1-i))(x - 1)
Expanding this expression,
f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)
= ((x - 1)² - i²)(x - 1)
= ((x - 1)² + 1)(x - 1)
= (x² - 2x + 1 + 1)(x - 1)
= (x² - 2x + 2)(x - 1)
= x² - 2x² + 2x - x² + 2x - 2
= x² - 3x²+ 4x - 2
.
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A candy company puts 8 gumdrops in each bag. How many gumdrops will the company need to fill 3,234,642 bags?
Answers
The company will need 25,877,136 gumdrops to fill 3,234,642 bags.
Explanation:
If a candy company puts 8 gumdrops in each bag, we need to find the total number of gumdrops the company needs to fill 3,234,642 bags.
Step 1: Calculate the total number of gumdrops in one bag.
The company puts 8 gumdrops in each bag.
So, the total number of gumdrops in one bag is 8.
Step 2: Calculate the total number of gumdrops the company needs to fill 3,234,642 bags.
To calculate the total number of gumdrops the company needs to fill 3,234,642 bags, we need to multiply the number of gumdrops in one bag (8) by the number of bags (3,234,642).
Therefore, the calculation is:
Total number of gumdrops = 8 × 3,234,642
Total number of gumdrops = 25,877,136
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find the probability of the given event. a single fair die is rolled. the number on the die is greater than 2.
Answers
The probability to get the numbers greater than 2 from the outcomes of the event of rolling a single fair die is equal to P(A) = 2/3.
As given in the question,
Event is rolling a single fair die.
Number of fair die to be rolled = 1
Possible outcomes = { 1, 2, 3, 4, 5, 6 }
Total number of possible outcomes = 6
Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }
Number of favourable outcomes = 4
Probability of getting a number greater than 2
= (Number of favourable outcomes) / (Total number of outcomes)
= 4 / 6
= 2 / 3
Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.
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Given f(x) = 3x + 2 and g(x) = 2x - 1, find (g(x))2.
1- 2x2 - 4x + 1
2- 6x²+x-2
3- 4x2 - 4x + 1
4- 9x2 + 12x + 4
Helpppp plzzz
Answers
Answer:
C (if the sign after the digit 1,2,3,4 is not minus !!!)
Step-by-step explanation:
\(f(x)=3x+2\\\\g(x)=2x-1\\\\\\g^2(x)=(gog)(x)=g(g(x)=g(2x-1)=2(2x-1)-1=4x-2-1=4x-3\\\\\\if \ you\ means \ g(x)*g(x)\ then\\\\(g(x))^2=(2x-1)^2=4x^2-4x+1:\ answer \ C\)
Will give brainliest! :)) need asap
Answers
Answer:
D. -3 for every 1 to the right, in goes down 3.
E. 0, the graph could represent no change over time.
F.
assume the point on the graph is the origin, you can graph these
(2,-4)
(1,-2)
(0,0)
(-1,2)
(-2,4)
(-3,6)
Step-by-step explanation:
7. suppose a binary digit (0 or 1) needs to be transmitted across a series of 4 channels. each time, the digit is transmitted correctly to the next channel with probability 0.9, and is transmitted incorrectly (meaning that 1 is transmitted as 0, and 0 is transmitted as 1) with probability 0.1. if the digit 0 is sent, what is the probability that the digit that is received (after having been transmitted across the 4 channels) is a 0?
Answers
The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645
In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.
In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.
Using Bayes' theorem, we can rewrite this as:
P(CCCC | 0 received) x P(0 received) / P(CCCC)
Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:
P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)
Substituting the given probabilities, we get:
P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561
Similarly, we can calculate the probability of receiving a 0 in general as:
P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)
where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:
P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001
Substituting the given probabilities, we get:
P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281
Finally, we can calculate the denominator P(CCCC) as:
P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)
where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:
P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729
Substituting the given probabilities, we get:
P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645
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Gathering data from the first 25 people you encounter at a local mall is an example of ________. A. random sampling B. convenience sampling C. stratified sampling D. systematic sampling
Answers
Answer: B. convenience sampling
Explanation: You are simply taking the first 25 people you see and sampling them, which is your most convenient option. More reliable sampling methods would involve different sampling methods.
what types of deviations from ideal pronunciation of individual words occurs when words are strung together
Answers
When words are strung together in speech, deviations from ideal pronunciation can occur due to various factors such as coarticulation, assimilation, elision, and reduced vowel sounds.
When words are spoken in rapid succession, coarticulation plays a significant role in shaping the pronunciation of individual words. Coarticulation refers to the influence of neighboring sounds on the production of a particular sound. For example, in the phrase "black cat," the /k/ sound in "black" may be influenced by the following /k/ sound in "cat," resulting in a slight modification or assimilation of the sound.
Assimilation occurs when sounds become more similar to nearby sounds. For instance, in the phrase "handbag," the /n/ sound in "hand" may assimilate to the /b/ sound in "bag," making it nasal (as in "hambag") or even causing complete elision of the /n/ sound. Elision refers to the omission or deletion of sounds, often in unstressed or weak positions, such as the reduction of the /ə/ vowel sound in "a" or "the" to a schwa sound, as in "uh" or "thuh."
Additionally, when words are strung together, certain vowel sounds may be reduced or shortened to accommodate the natural rhythm of speech. This reduction can result in changes to the stress patterns and lengths of vowels within words. Overall, these deviations from ideal pronunciation in connected speech are a natural part of spoken language and contribute to the fluidity and efficiency of communication.
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plz help :) and thank you.
Answers
Answer:
what is the question? there's no attachment
Solve for x.
(13x-32)
S
T
V
(7x + 22)°
U
Answers
Answer:
x=9
Step-by-step explanation:
13x-32 and 7x+22 are equal to each other (angles) so
13x-32=7x+22
13x-7x=22+32
6x=54
x=54/6
x=9
Si los conjuntos:
K = {a; x + y}
L = {a + 1; x – y}
Son iguales, halla el valor de ( x - a) a la 2Y
Answers
Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answers
Answer:
52.5
Step-by-step explanation:
because you do 15 x 3.5
this gets 52.5
Answer:
52.5
Step-by-step explanation:
because you do 15 x 3.5
this gets 52.5
Step-by-step explanation:
f(x)=2x -7, What is x when f(x)=-15?
Answers
Answer:
x = -4
Step-by-step explanation:
Plug in -15 into the equation:
f(x) = 2x - 7
-15 = 2x - 7
Solve for x:
-15 = 2x - 7
-8 = 2x
-4 = x
Number six please help!
Answers
Answer:
#6
Use ratios of corresponding sides to find the value of x.a)
(2x - 18)/ 24 = 8/ 482x - 18 = 24/62x - 18 = 42x = 22x = 11b)
(x + 4)/18 = 25/30x + 4 = 18*5/6x + 4 = 15x = 11Which transformation produces congruent figures?
PLEASE HELP, ANYONE!!! HOMEWORK IS DUE TODAY!!!
Answers
Answer:
Last option
Step-by-step explanation:
If you have a plain translation (moving figures up/down/left/right), it doesn't change the size or shape of the object.
Same with reflection, it doesn't change the size or shape.
Hope this helped!
Siggi's utility function is U(q
1
,q
2
)=4(q
1
)
−0.03
+q
2
Calculate the substitution, income, and total effects for a change in the price of q
1
on the demand for q
1
. The substitution effect for a change in p
1
is ε
∗
=, the income effect is θξ=, and the total effect is ε= (Round your responses to 2 decimal places and include a minus sign as necessary.)
Answers
The substitution effect, denoted by ε*, measures the change in quantity demanded of q1 due to the relative price change, while the income effect, denoted by θξ, measures the change in quantity demanded of q1 due to the change in purchasing power. The total effect, denoted by ε, combines both the substitution and income effects.
To calculate the substitution effect, we need to evaluate the price elasticity of demand for q1, which measures the responsiveness of quantity demanded to a change in price. The income effect depends on the income elasticity of demand, which measures the responsiveness of quantity demanded to a change in income. These elasticities can be calculated using the given utility function, but specific price and income data are required.
Without the actual price and income data, it is not possible to provide the exact numerical values for the substitution, income, and total effects. The effects can only be determined with the necessary information and by performing the appropriate calculations using the utility function. The values of ε*, θξ, and ε will depend on the specific price and income changes that are considered.
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A sleep specialist believes that the more caffeine a person consumes per day, the more episodes of restless sleep that person experiences. What are her null and alternative hypotheses
Answers
The null and alternative hypotheses in this case would be formulated as follows:
Null Hypothesis (H0): There is no relationship between caffeine consumption per day and episodes of restless sleep.
Alternative Hypothesis (HA): There is a positive relationship between caffeine consumption per day and episodes of restless sleep.
In other words:
H0: β (slope coefficient) = 0
HA: β (slope coefficient) > 0
The null hypothesis assumes that there is no association or correlation between caffeine consumption and episodes of restless sleep. The alternative hypothesis, on the other hand, suggests that there is a positive relationship, indicating that higher caffeine consumption is associated with a greater number of episodes of restless sleep.
These hypotheses would be tested using statistical methods, such as regression analysis, to determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
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Consider the following data drawn independently from normally distributed populations: (You may find it useful to appropriate table: z table or t table)
xˉ1 = −17.1
s1^2 = 8.4
n1=22
xˉ2 = −16.0
s2^2 = 8.7
n2 = 24
a. Construct the 90% confidence interval for the difference between the population means. Assume the population va unknown but equal. (Round final answers to 2 decimal places.)
confidence interval is __ to __
Answers
The 90% confidence interval for the difference in the population means is -2.51 to 0.31
Calculating the 90% confidence interval for the population mean differenceFrom the question, we have the following parameters that can be used in our computation:
xˉ₁ = −17.1
s₁² = 8.4
n₁ = 22
xˉ₂ = −16.0
s₂² = 8.7
n₂ = 24
Calculate the pooled variance using
P = (df₁ * s₁² + df₂ * s₂²)/df
Where
df₁ = 22 - 1 = 21
df₂ = 24 - 1 = 23
df = 22 + 24 - 2 = 44
So, we have
P = (21 * 8.4 + 23 * 8.7)/44
P = 8.56
Also, we have the standard error to be
SE = √(P/n₁ + P/n₂)
So, we have
SE = √(8.56/22 + 8.56/24)
SE = 0.86
The z score at 90% CI is 1.645, and the CI is calculated as
CI = (x₁ - x₂) ± z * SE
So, we have
CI = (-17.1 + 16.0) ± 1.645 * 0.86
This gives
CI = -1.1 ± 1.41
Expand and evaluate
CI = (-2.51, 0.31)
Hence, the confidence interval is -2.51 to 0.31
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Three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. What must be the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite comer?
Answers
Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.
The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square
The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.
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A glass vase is shaped like a cylinder and has a radius of 2.5 inches. The vase holds 170 cubic inches of water. How tall is the vase? Use 3.14 for pi. Round your answer to the nearest hundredth.
A.8.66 inches
B. 9.78 inches
C. 10.35 inches
D. 12.50 inches
Answers
Answer: The answer would be 8.66 when rounded to the nearest hundredth.
Step-by-step explanation: