In the population of peas in arizona, initially at equilibrium, a new species of bird is introduced. the birds eat peas of both colors, but prefer to eat yellow peas. it is estimated that yellow peas have a 60% chance to be eaten, while green peas have a 20% chance to be eaten. after the introduction of the birds, what fraction of the next generation of peas do you expect to be yellow
Answers
After the introduction of the birds, we can expect a decrease in the number of yellow peas as they are preferred by the birds. Therefore, the fraction of the next generation of peas that will be yellow will be lower than what it was initially.
The introduction of the new bird species will create a shift in the selective pressures acting on the pea population. Since the birds prefer to eat yellow peas, there will be a higher chance that yellow peas will be consumed, leaving behind more green peas to reproduce. This will lead to a decrease in the frequency of the yellow pea allele in the next generation.
To estimate the fraction of the next generation of peas that will be yellow, we can use the Hardy-Weinberg equilibrium equation. Let p represent the frequency of the yellow pea allele and q represent the frequency of the green pea allele in the initial population. Since the population is initially at equilibrium, we can assume that p = 0.5 and q = 0.5. After the birds are introduced, the selection pressure on the yellow pea allele will cause a decrease in its frequency.
The probability of a yellow pea being eaten is 0.6, so the probability of a yellow pea surviving to reproduce is 0.4. Similarly, the probability of a green pea being eaten is 0.2, so the probability of a green pea surviving to reproduce is 0.8. We can use these probabilities to calculate the frequency of the alleles in the next generation.
The frequency of the yellow pea allele in the next generation can be calculated as:
p' = (0.4 * p) / (0.4 * p + 0.8 * q)
Substituting p = 0.5 and q = 0.5, we get:
p' = (0.4 * 0.5) / (0.4 * 0.5 + 0.8 * 0.5) = 0.25
Therefore, we can expect that 25% of the next generation of peas will be yellow. This represents a decrease from the initial frequency of 50%. The remaining 75% of the next generation will be green peas.
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Related Questions
What is mechanical energy? Give an
example,
Answers
Answer:
mechanical energy ✨ is a form of energy it is all the energy that an object has because of it motion
Step-by-step explanation:
like an bow and arrow or hitting a hammer on a nail
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
Answers
Minimize z=5x1+4x2 Subject to: 6x1+2x2≤24 x1+2x2≤6 −x1+x2≤1 x2≤2
Answers
By substituting the corner points into the objective function, we can compare the values of z and identify the minimum. The corner point with the lowest z value will give us the optimal solution.
To solve the given linear programming problem completely, we will follow the steps mentioned earlier. Let's go through the process in more detail:
Step 1: Identify the decision variables:
Let x1 and x2 be the decision variables representing the values we want to find that minimize z.
Step 2: Formulate the objective function:
The objective function is given as z = 5x1 + 4x2.
Step 3: Formulate the constraints:
The given constraints are:
6x1 + 2x2 ≤ 24
x1 + 2x2 ≤ 6
-x1 + x2 ≤ 1
x2 ≤ 2
Step 4: Combine all the constraints:
To combine the constraints, we rewrite them in standard form:
6x1 + 2x2 ≤ 24 ---> 6x1 + 2x2 + 0x3 + 0x4 = 24
x1 + 2x2 ≤ 6 ---> x1 + 2x2 + 0x3 + 0x4 = 6
-x1 + x2 ≤ 1 ---> -x1 + x2 + 0x3 + 0x4 = 1
0x1 + x2 ≤ 2 ---> 0x1 + x2 + 0x3 + 0x4 = 2
Step 5: Solve the linear programming problem:
To solve this linear programming problem, we can use various methods such as the Simplex method or graphical method. Here, we'll use the graphical method to find the optimal solution.
First, let's plot the feasible region by graphing the equations of the constraints:
Plotting 6x1 + 2x2 = 24:
x1 | x2
0 | 12
4 | 0
Plotting x1 + 2x2 = 6:
x1 | x2
0 | 3
6 | 0
Plotting -x1 + x2 = 1:
x1 | x2
-1 | 0
0 | 1
Plotting x2 = 2:
x1 | x2
0 | 2
Next, we need to find the feasible region by considering the overlapping shaded area formed by the inequalities. However, I cannot provide a visual representation here. Please refer to a graphing tool or software to plot the equations and find the feasible region.
Finally, we evaluate the objective function z = 5x1 + 4x2 at the corner points of the feasible region to determine the minimum value of z. Each corner point represents a specific combination of x1 and x2 within the feasible region.
By substituting the corner points into the objective function, we can compare the values of z and identify the minimum. The corner point with the lowest z value will give us the optimal solution.
Please note that without the graphical representation, I am unable to provide the exact numerical solution. I recommend using a graphing tool or linear programming software to visualize the feasible region and determine the optimal values of x1 and x2 that minimize z.
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Two congruent squares and a parallelogram were used to form the figure shown. 3 m C I 2.8 m 6 m What is the area of the figure in square meters? A 25.8 m² 2 B 40.8 m² 34.8 m² D 28.8 m² 3 m
Answers
Answer: The table that could be the data the student collected is table D.
Step-by-step explanation: What is an electromagnet?
An electromagnet is described as a type of magnet in which the magnetic field is produced by an electric current and usually consist of wire wound into a coil.
If student builds an electromagnet using a variable power source and 40 turns of wire. We have it that the student changes the voltage and counts the number of paper clips that are picked up. The table described below could perfectly described the scenario.
This is Table D
Voltage (V)
3
6
9
12
Number of paper clips
9
18
27
36
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What would you use to graph the inequality y ≥ 4 ?
The coordinate plane
A number line
The origin
This inequality cannot be graphed.
Answers
A number line use to graph the inequality y ≥ 4.
How do you graph an inequality?Treat the,, >, or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.Pick a point that is not on the line next. Verify if the inequality is satisfied by this point. The area containing that point should be shaded if it satisfies the inequality. Shade the area that does not contain that point if it does not satisfy the inequality. Every point in the shady area satisfies the inequality.Explanation :
y = − 4 is a horizontal line at -4, since
y ≥ − 4, the area above -4 will be shaded and the line will be solid since it is greater than AND equal to:
graph{y>=-4 [-10, 10, -5, 5]}
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-Cuántos números 2 veras si cuentas de del 10 al 22?
Answers
Answer:
12
Step-by-step explanation:
For the Adjusted R Squared, which of the following is true: a. Is the same R 2
as in the simple linear regression b. Can decrease if the addition of another X regressor does not lower SSR enough relative to the impact of the increase of k by another X regessor. c. Is between 0 and 1 d. Measures the ratio of the sum of squared residuals compared to the total sum of squares
Answers
The correct statement is c. The Adjusted R-squared is a measure used in multiple regression analysis that is between 0 and 1. It is different from the R-squared value in simple linear regression.
The Adjusted R-squared can decrease if the addition of another X regressor does not sufficiently lower the sum of squared residuals (SSR) relative to the impact of increasing the number of predictors (k). It measures the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size, rather than the ratio of the sum of squared residuals to the total sum of squares. It provides a measure of how well the regression model fits the data, and it ranges between 0 and 1. A value closer to 1 indicates that a higher proportion of the variance in the dependent variable is explained by the predictors.
Adding another X regressor to the multiple regression model can impact the Adjusted R-squared. If the additional regressor does not significantly contribute to reducing the sum of squared residuals (SSR) relative to the increase in the number of predictors (k), the Adjusted R-squared can decrease. This means that the added regressor does not improve the model's ability to explain the variance in the dependent variable adequately.
However, the Adjusted R-squared does not directly measure the ratio of the sum of squared residuals to the total sum of squares. Instead, it represents the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size. It penalizes models with a large number of predictors that may overfit the data, thereby providing a more reliable measure of the model's goodness of fit.
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3. Suppose you are looking over this fabric, trying to find defects, yard by yard. What is the probability you will observe more than 10 yards before finding the first defect
Answers
The probability of observing more than 10 yards before finding the first defect is 0.3487.
The problem belongs to the geometric probability distribution. This probability distribution is concerned with the probability of finding the first occurrence of success in a sequence of Bernoulli trials in which the probability of success is constant across each trial and the trials are independent of one another. We know that, Let Y represent the number of yards that will be examined before the first defect is found, which is geometrically distributed with p = 0.1. That is, p(Y > 10) = (1-p)10 = (1-0.1)10 = 0.9 10 = 0.3487. This probability can be explained by saying that there is a 34.87 percent chance that more than 10 yards will be examined before the first defect is observed. Therefore, the probability of observing more than 10 yards before finding the first defect is 0.3487.
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The midpoint of AB is M (4, 4). If the coordinates of A are (2, 1), what are the
coordinates
of B?
Answers
Answer:
(6,7)
Step-by-step explanation:
Let B(x,y).
By the midpoint formula,
4 is the average of 2 and x, so x = 6.Similarly, y = 7.So, the coordinates of B are (6,7).
5 people want to split a bag that holds 36 pounds of rice equally. Which fraction shows how much each person will get?
Answers
Answer:
7.2 = 7 1/5
divide five by 36
Historically, a part's length has been normally distributed with a mean of 4.1 inches and a standard deviation of 0.15 inches. Suppose that we take samples of size 92 parts and find the sample mean of the length of the parts in the sample. What is the expected value of the sample mean?
Answers
The expected value of the sample mean is 4.1 inches when the sample size is 92
Given that the part's length is normally distributed with a mean of 4.1 inches and a standard deviation of 0.15 inches and we need to find the expected value of the sample mean when the sample size is 92. We know that the formula to calculate the expected value is given as;Expected Value (E) = µwhere µ is the population mean and represents the expected value of a population.So, the expected value of the sample mean when the sample size is 92 is given as;E = µ = 4.1 inchesHence, the expected value of the sample mean is 4.1 inches when the sample size is 92.
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look at the adjoining figure and write 2 pairs of intersecting lines.
Answers
Answer:
Line AB and Line GHLine CD and Line FFConcept:
Intersecting lines are lines that overlap upon only one point. The number of lines can be two or more.
Intersecting lines can intersect at any angle.
Solve:
There are in total four intersecting points in the given figure.
As we can see from the figure, any two lines would intersect each other
Therefore, 2 pairs of intersecting lines can be any pairings of lines that are not in the same orientation.
Line AB and Line GHLine CD and Line FFHope this helps!! :)
Please let me know if you have any questions
Tell whether the angels are adjacent or vertical. Then find the value of x.
(please show how you solved the problem!)
Answers
Answer:
Angles: adjacent
x = 18
Step-by-step explanation:
Adjacent Angles: angles that border each other to the left/right
Vertical Angles: opposite set of angles that are congruent
Given these definitions, these angles are not only adjacent, but also right angles. Right angles add to 90°.
Thus, 3x + 2x = 90Step 1: Combine like terms.
\(3x + 2x = 90\) \(5x = 90\)Step 2: Divide both sides by 5.
5x ÷ 5 = 90 ÷ 5x = 18Therefore, the answer is adjacent and x = 18.
EMERGENCY!!!!!
What is the slope and Y intercept of (-2,0) (4,1)??!?!!??
Answers
Answer:
Slope= 1/6 Y-intercept= 1/3
Step-by-step explanation:
1-0=1
4-(-2)=6
Slope = 1/6
y-0= 1/6 (x-(-2))
y-0= 1/6x + 1/3
Y intercept is 1/3
given coordinates: (-2,0) (4,1)
\(\sf slope \ formula:\dfrac{y2-y1}{x2-x1}\)
→ \(\dfrac{1-0}{4--2}\)
→ \(\dfrac{1}{6}\)
equation:
→ \(\sf y - 0 = \dfrac{1}{6} ( x- -2)\)
→ \(\sf y = \dfrac{1}{6} x + \dfrac{1}{3}\)
To find y-intercept, put x as 0.
→ \(\sf y = \dfrac{1}{6} x +\dfrac{1}{3}\)
→ \(\sf y = \dfrac{1}{6} (0) +\dfrac{1}{3}\)
→ \(\sf y = \dfrac{1}{3}\)
LaTeX: \frac{27.50\:gallons}{5\:buckets}
Answers
Explanation:
Solve:
determine the intervals on which the graph of =()y=f(x) is concave up or concave down, and find the points of inflection.
Answers
the graph of f(x) = x^3 - 3x^2 - 9x + 5 is concave down on the interval (-∞, 1), concave up on the interval (1, +∞), and has a point of inflection at x = 1.
To determine the intervals on which the graph of a function is concave up or concave down, we need to analyze the second derivative of the function. The concavity of a function can change at points where the second derivative changes sign.
Here's the step-by-step process to find the intervals of concavity and points of inflection:
Find the first derivative of the function, f'(x).
Find the second derivative of the function, f''(x).
Set f''(x) equal to zero and solve for x. The solutions give you the potential points of inflection.
Determine the intervals between the points found in step 3 and evaluate the sign of f''(x) in each interval. If f''(x) > 0, the graph is concave up; if f''(x) < 0, the graph is concave down.
Check the concavity at the points of inflection found in step 3 by evaluating the sign of f''(x) on either side of each point.
Let's go through an example to illustrate this process:
Example: Consider the function f(x) = x^3 - 3x^2 - 9x + 5.
Find the first derivative, f'(x):
f'(x) = 3x^2 - 6x - 9.
Find the second derivative, f''(x):
f''(x) = 6x - 6.
Set f''(x) equal to zero and solve for x:
6x - 6 = 0.
Solving for x, we get x = 1.
Therefore, the potential point of inflection is x = 1.
Determine the intervals and signs of f''(x):
Choose test points in each interval and evaluate f''(x).
Interval 1: (-∞, 1)
Choose x = 0 (test point):
f''(0) = 6(0) - 6 = -6.
Since f''(0) < 0, the graph is concave down in this interval.
Interval 2: (1, +∞)
Choose x = 2 (test point):
f''(2) = 6(2) - 6 = 6.
Since f''(2) > 0, the graph is concave up in this interval.
Check the concavity at the point of inflection:
Evaluate f''(x) on either side of x = 1.
Choose x = 0 (left side of x = 1):
f''(0) = -6.
Since f''(0) < 0, the graph is concave down on the left side of x = 1.
Choose x = 2 (right side of x = 1):
f''(2) = 6.
Since f''(2) > 0, the graph is concave up on the right side of x = 1.
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Simplify the following. Do not write multiplication signs in your answers.
a) p×q×q×r×r×q×q×r=
b) t×t×t×t×u×u×t×t×t×u×u=
Answers
Answer:
q⁴r³p
t⁷u⁴
Step-by-step explanation:
hope this is the answer
A minor league hockey team had the following scores for the start of the season for the start of the season 3,6,2,1,2,3,0,4,5,1,5,4. What is the MODE score of the hockey team?
Answers
The given data set is:
\(3,6,2,1,2,3,0,4,5,1,5,4\)It is required to find the mode.
Recall that the mode is the value in a set of data that has the most occurrences.
Note that the mode is not unique and a data set may have no mode.
The value that has the most occurrences in the set is not unique.
Hence, the data set has no mode score
¿por que en los mapas se respeta la misma escala? Ayudenme por favor esta es otra pregunta ¿qué pasaría si una parte del mapa se convirtiera en escala y otra parte a una escala diferente?
Answers
Answer:
Ok, supón que conoces exactamente tu posición en un mapa, y también sabes a donde quieres ir.
Podes ver en ese mapa la distancia entre tu posición y el lugar al que quieres ir, ahora, si la escala del mapa es conocida (por ejemplo 1cm = 1km) y constante, entonces vos podes medir la cantidad de centímetros entre tu posición y tu destino, y multiplicar ese numero por la escala, de esta forma conociendo la distancia real entre tu posición y tu destino.
Ahora, si la escala no es constante, entonces es imposible saber exactamente la distancia entre nuestra posición y nuestro destino, entonces este mapa no sirve realmente para ubicarnos/guiarnos, entonces no funciona como un mapa.
En el caso de que una parte este en una escala y otra parte en otra, en la primera parte un centímetro en el mapa equivaldría a una distancia X en la realidad, y en la otra zona un centímetro en el mapa equivaldría a una distancia Y en la realidad.
Donde X es diferente de Y, ahora, cuando queremos calcular la distancia entre dos lugares tendríamos que saber exactamente en que lugar se da el cambio de escala (para saber si usamos X o Y). Lo que hace que leer este mapa sea bastante mas difícil que leer un mapa normal.
When we are using the strategy "closest to", we look to see what tidy number our number is closest to. Is 67 closer to 60 or 70?
Answers
When using the "closest to" strategy, we would round 67 to 70 because the absolute difference between 67 and 70 is smaller than the absolute difference between 67 and 60.
To determine which tidy number 67 is closer to using the strategy "closest to," we can look at the distance between 67 and 60 as well as the distance between 67 and 70. The distance between 67 and 60 is 7, while the distance between 67 and 70 is 3. Since 67 is closer to 70 than 60, we would say that 67 is closer to 70 using the "closest to" strategy.
This is because the goal of the "closest to" strategy is to find the tidy number that minimizes the distance from the given number, and in this case, 70 is closer to 67 than 60.
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2. In the real-world, humans hear sound as an analog signal. This means the signal is a continuous
waveform, which is completely processable by human ears. However, machines 'hear' sound a little
differently, as they process sound digitally, which is a discrete waveform.
When sound is recorded or transmitted electronically, the continuous (analog) waveform is sampled to
convert it to a discrete (digital) sequence. Sampling is the process of reducing a continuous-time signal
to a discrete-time signal. As the sampling rate increases, the sound quality of the recording or
transmission will improve.
The graphs below represent two different samples of a pure tone. Sample 1 is taken 8 times per unit of
time. Sample 2 is taken 16 times per unit of time.
a) why would sample 2 reproduce a better replication of the pure signal?
b) write a sinusoid model for sample 2.
Answers
Answer:
a) Sample 2 records at a more frequent rate, so compared to 1 it's a continuous waveform.
b) y = 7.75 • cos(π/8(x))+7.75
Step-by-step explanation:
that other guy wasn't very nice for not giving the answer, screw him
PLS PLS PLS PLS PLS HELP
Answers
Answer:
304.5 cm2
Step-by-step explanation:
Think imaginatively, we got two congruent triangles and two rectangles with different dimensions.
S.A. of 2 triangles = 2*( 1/2 x B x H)
= 2*( 1/2 x 10.5 x 14) = 147 cm2
Rectangle 1 = 5*17.5 = 87.5 cm2
Rectangle 2 = 5*14 = 70 cm2
Total = 147 + 87.5 + 70 = 304.5 cm2
A playing card has a perimeter of 28 centimeters. Its area is 45 square centimeters. What are the dimensions of the playing card?
Answers
Step-by-step explanation:
A playing card is in the form of a rectangle whose perimeter is equal to 28 cm and area is 45 cm².
If l and b are length and breadth of the rectangle.
Area,
\(A=lb\)
\(45=lb\\\\l=\dfrac{45}{b}\ .....(1)\)
Perimeter,
\(P=2(l+b)\\\\28=2(l+b)\\\\14=(l+b)\ ....(2)\)
Put the value of l from equation (1) to equation (2). So,
\(14=\dfrac{45}{b}+b\\\\14=\dfrac{45+b^2}{b}\\\\14b=45+b^2\\\\b^2-14b+45=0\\\\b^2-9b-5b+45=0\\\\b(b-9)-5(b-9)=0\\\\b=5\ cm, 9\ cm\)
Put the value of b in equation (1),
If b = 5 cm
\(l=\dfrac{45}{5}=9\ cm\)
If b = 9 cm
\(l=\dfrac{45}{9}=5\ cm\)
So, the dimensions of the playing card is 9 cm by 5 cm.
Find the sum of squares of the deviations from the mean of a series of ACT scores listed below.31, 22, 24, 15, 23The sum of squares is(Type an integer or a decimal.)
Answers
Solution
Given the following scores below
\(31,22,24,15,23\)To find the sum of squares of the deviations,
Firstly, we find the mean, the formula to find the mean of ungrouped data is
\(\begin{gathered} \bar{x}=\frac{\sum_X}{n} \\ Where\text{ n is the number of terms} \end{gathered}\)Where n = 5
Substitute the given data into the formula to find the mean of ungrouped data
\(\begin{gathered} \bar{x}=\frac{31+22+24+15+23}{5} \\ \bar{x}=\frac{115}{5}=23 \\ \bar{x}=23 \end{gathered}\)Secondly, we subtract the mean from each of the values given as shown below
\(\begin{gathered} 31-23=8 \\ 22-23=-1 \\ 24-23=1 \\ 15-23=-8 \\ 23-23=0 \end{gathered}\)Then, to find the sum of squares of the deviations
We add the square of each of the deviations deduced above
\(\begin{gathered} =(8)^2+(-1)^2+(1)^2+(-8)^2+(0)^2 \\ =64+1+1+64+0 \\ =130 \end{gathered}\)Hence, the sum of squares is 130
f(x) = 5x2 + 4x – 6
g(x) = 3x2 – 9
Answers
Answer:
f=5x2+4x−6
g=3x2−9
Roderick earns $8.25 per hour at his new job. On his first day of work
Roderick earned $49.50, and on his second day he earned $41.25. How
many total hours did he work on his first two days?
A 5
B. 6
C. 10
D. 11
Answers
Answer:
Roderick worked a total of 11 hours on his first 2 days at work.
Step-by-step explanation:
If he earns 8.25$ per hour, divide the total money for each day by 8.25.
1st day :$49.50
Total hours:
?
Solve :
Step 1: Divide the day total by the hourly pay) 49.50/ 8.25
Step 2: Get the total) 49.50/ 8.25 = 6
Step 3: The total is equal to the hours worked that day.
Total hours of day 1:
6
2nd day :$41.25
Total hours:
?
Solve :
Step 1: Divide the day total by the hourly pay) 41.25/ 8.25
Step 2: Get the total) 41.25/ 8.25 = 5
Step 3: The total is equal to the hours worked that day.
Total hours of day 2:
5
The sum of 2 times a number and 4 is 8. Translate the sentence into an equation. Use the variable x for the unknown number
Answers
Let:
x = Unknown number
The sum of 2 times a number and 4 can be expressed as:
\(2x+4\)Since the result is 8, the equation is given by:
\(2x+4=8\)Solve for x:
Subtract 4 from both sides:
\(\begin{gathered} 2x+4-4=8-4 \\ 2x=4 \end{gathered}\)Divide both sides by 2:
\(\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}\)Answer:
x = 2
What are the numbers in the eighth group in the pattern
below?
(1, 3, 6) (2, 6, 9) (3, 9, 12) …
Answers
Answer:
50,2500, 127500
Step-by-step explanation:
(1, 1, 2) (2, 4, 12) (3, 9, 36)
x, x², x²*(x+1)
when x=50
50, 2500, 127500
Write the slope-intercept form of an equation that passes through the
point (-2,3), and is parallel to y=-x+5. *
Answers
What is the unit rate for meters per second if a car travels 374 meters in 17 seconds?
Answers
Answer:
22 meters per second.
Step-by-step explanation:
374 divided by 17 = 22.
Answer:
22
374meters. 17
(/). divided by (/)
17seconds 17
Equals 22 meters per second
Step-by-step explanation:
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