The work required to pump the sludge is approximately 21449.6 ft-lbs.
To calculate the work required to pump the sludge, we need to determine the volume of the sludge and then multiply it by the weight of the sludge.
First, let's find the volume of the sludge in the tank. Since the tank is formed by rotating the segment between (2, 0) and (4, 4) around the y-axis, it forms a frustum of a cone. The formula for the volume of a frustum of a cone is:
V = (1/3) * π * h * (R^2 + r^2 + R*r),
where h is the height of the frustum, R is the radius of the larger base, and r is the radius of the smaller base.
In this case, the height of the frustum is the difference in y-coordinates between the two points: h = 4 - 0 = 4 ft.
The radius of the larger base, R, is the y-coordinate of the point (4, 4): R = 4 ft.
The radius of the smaller base, r, is the y-coordinate of the point (2, 0): r = 0 ft.
Substituting these values into the volume formula, we have:
V = (1/3) * π * 4 * (16 + 0 + 0) = (4/3) * π * 16 = 67.03 ft^3 (approximately).
Next, we need to calculate the weight of the sludge, which is the volume multiplied by the density:
Weight = Volume * Density = 67.03 ft^3 * 80 lbs/ft^3 = 5362.4 lbs (approximately).
Finally, we can calculate the work required to pump the sludge 4 feet upwards. The work is given by the formula:
Work = Force * Distance,
where Force is the weight of the sludge and Distance is the vertical distance it is pumped.
Work = Weight * Distance = 5362.4 lbs * 4 ft = 21449.6 ft-lbs (approximately).
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help help help help help help !!!!
Answer:
Yes because if you were to continue enlarging the shape it would continue to follow the path/line of 10,1
Step-by-step explanation:
Points C(-4;3), A(6; 1) and T(2; -3) are given.Show that the points C, A and T are the vertices of a right-angled triangle.
Answer:
Step-by-step explanation:
To show that points C(-4, 3), A(6, 1), and T(2, -3) form a right-angled triangle, we can calculate the slopes of the lines connecting these points.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of the lines formed by the points:
Slope of line CA:
m_CA = (1 - 3) / (6 - (-4))
= (-2) / 10
= -1/5
Slope of line CT:
m_CT = (-3 - 3) / (2 - (-4))
= (-6) / 6
= -1
Slope of line AT:
m_AT = (-3 - 1) / (2 - 6)
= (-4) / (-4)
= 1
Since two lines are perpendicular if and only if the product of their slopes is -1, we can check if the product of the slopes of CA and AT is -1. If it is, then the triangle formed by the points C, A, and T is a right-angled triangle.
Product of slopes m_CA and m_AT:
(-1/5) * (1) = -1/5
The product of the slopes is -1/5, which is not equal to -1. Therefore, the points C(-4, 3), A(6, 1), and T(2, -3) do not form a right-angled triangle.
Hence, we can conclude that the points C, A, and T do not form a right-angled triangle based on the slopes of the lines connecting them.
helpp A car manufacturer claims that the average top speed of its newest cars is 145 mph. A sample of 87 cars showed that their average top speed was 150 mph, with a sample standard deviation of 19 mph. Test this hypothesis using a 1% significance level.
a.Reject the null hypothesis. There is not enough evidence to oppose the car manufacturer's claim.
b.Fail to reject the null hypothesis. There is not enough evidence to oppose the car manufacturer's claim.
c.Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
d.Fail to reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
How to find the null hypothesisThe null hypothesis (H0) is that the true average speed is 145 mph, and the alternative hypothesis (H1) is that the average speed is not 145 mph.
Using a z-test, we can calculate the z-score as [tex](150-145)/(19 \sqrt(87)),[/tex]which is approximately 3.67.
For a two-tailed test at the 1% significance level, the critical z-scores are -2.576 and 2.576.
Since the calculated z-score is beyond this range, we can reject the null hypothesis.
Therefore, there is enough evidence to oppose the car manufacturer's claim.
The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.
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The right triangular prisms shown have the same surface area. Find the height of
prism B.
20 cm
Prism A
24 cm
h = cm
3 cm
20 cm
6 cm
Prism B
8 cm
The height of prism B based on the information given will b 22cm.
How to calculate the value of the heightPrisms are transparent optical elements that have at least two flat surfaces and refract light. They are usually made of glass or plastic and are used in a variety of optical applications, including scientific experiments, photography, and surveying. Prisms come in a variety of shapes and sizes, including triangular, rectangular, and pentagonal.
From the information, it should be noted that the surface area of prism A will be
= 60 × 2 + 7+ 384
= 576cm²
The surface area of prism A will be:
48 + 10h + 8h + 6h = 576
48 + 24h = 576
h = 528 / 24
h = 22cm
The height is 22cm
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The right triangular prisms shown have the same surface area. Find the height of prism B.
Prism A:
Height: 24 cm
Base: a right triangle with legs 3 cm and 20 cm
Depth: 6 cm
Prism B:
Height: ?
Base: a right triangle with legs 8 cm and 20 cm
Depth: 3 cm
Both prisms have the same surface area.
for science class, leo is making a poster about constellations. he wants to line the top and bottom edges with shiny star stickers. his poster is 0.75 meters long, and each star sticker is 15 millimeters wide. how many stickers does leo need for his poster?
Leo needs 100 star stickers to line the top and bottom edges of his 0.75-meter-long poster with 15-millimeter-wide stickers. Leo will need 50 star stickers for his poster.
First, we need to convert the length of Leo's poster from meters to millimeters since the width of the star stickers is given in millimeters.
0.75 meters x 1000 millimeters/meter = 750 millimeters
Now we can calculate how many stickers Leo needs by dividing the length of the poster by the width of each sticker:
750 millimeters ÷ 15 millimeters/sticker = 50 stickers
Therefore, Leo will need 50 star stickers for his poster.
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A gum ball machine contains 12 red, 13 green, and 8 yellow gum balls. What is the
least number of gum balls Jack has to buy to be certain he gets 6 gum balls that are
the same color?
Answer:
Jack would have to buy 18 gum balls to be certain he gets 6 gum balls that are the same color.
Answer:
It's 16
Step-by-step explanation:
Imagine taking out 5 reds, after that 5 green ones and then 5 yellow gum balls. So the 16th must be number 6 of any color.
Rewrite each of the following expressions without using absolute value 20 POINTS!
Equation: |z-6|-|z-5| If z<5
A) (6-z)+(5-z)
B) (z-6)-(5-z)
C) (6-z) +(z-5)
After rewriting the final answer will be 1.
Given,
|z−6|−|z−5| , if z<5
Now,
|z-6| will be less than 0 since z is less than 5 and |z-5| will be less than 0 since z is less than 5.
So we can rewrite it as 6-z and 5-z by removing the absolute value signs and converting them in positive .
(6-z) - (5-z)
Further,
6-z-5+z
= 1
Hence Rewriting can be done without absolute values.
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help me please
Which of the following represents the polar equation r = (cot^2 θ)(csc θ) as a rectangular equation?
x2 + y2 = 1
y = 1
y2 = x3
y3 = x2
The rectangular equation that represents the polar equation r = (cot²θ)(csc θ) is y³ = x², which is an option (d).
The polar equation r = (cot²θ)(csc θ) can be written in rectangular form using the relationships x = r cos θ and y = r sin θ.
Substituting these expressions into the polar equation, we get:
r = (cot²θ)(csc θ)
r = (cos θ/sin θ)²(1/sin θ)
r = cos² θ/sin³ θ
x = r cos θ = cos³ θ/sin³ θ
y = r sin θ = cos² θ/sin² θ
As per the variable of x and y,
y³ = x².
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mike pays $2.79 for coffee every weekday morning on his way to work. on saturdays, he goes to visit his mother and takes her out to her favorite coffee shop where he spends $7.83 for two coffees. how much does he spend per week for coffee? $21.78 $26.91 $13.95 $29.61
Answer:
$21.78
Step-by-step explanation:
2.79 X 5 = 13.95
13.95 + 7.83 = 21.78
PLEASE HELPPPPPPPPPPPPPPP
Answer:
Yes
Step-by-step explanation:
If you look at the graph of y = 16x^4 - 81, you see that it intersects the x-axis at two distinct places so there are two real solutions. Whenever a polynomial function intersects the x-axis, there are at least one or more real roots.
I attached a picture of the graph using Desmos, where you'll see that there are two real roots.
there are 14 gods and goddesses but only 12 thrones of olympus. which two do not have thrones on olympus and why?
The twelve thrones of Olympus are occupied by the major gods and goddesses in Greek mythology, including Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and Dionysus. However, there are two gods who are not given a place on the throne - Hades and Hestia.
Hades, the god of the underworld, is not included in the twelve thrones because he rules over the dead in the underworld. As a result, he does not need a place on Olympus. Hestia, the goddess of the hearth, voluntarily gave up her seat to Dionysus, as she preferred to live a peaceful and uneventful life on earth. She is regarded as one of the "lesser" gods but still holds great importance in Greek mythology, as she is responsible for the protection of the home and family.
Overall, while the 14 gods and goddesses play important roles in Greek mythology, only twelve are given seats on Olympus. Hades and Hestia have their own roles to play and, for different reasons, do not have a place on the thrones.
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Chapter 5:
If A and B are mutually exclusive events, then P(A ∩ B) = 0 and the general addition law can be simplified to the sum of the individual probabilities for A and B, the special law of addition.
If A and B are mutually exclusive events, P(A ∩ B) = 0, and the general addition law can be simplified to the sum of the individual probabilities for A and B
Given data ,
If events A and B are mutually exclusive, it means that they cannot occur simultaneously. In this case, the intersection of events A and B, denoted as A ∩ B, would indeed have a probability of 0
And , P(A ∪ B) = P(A) + P(B)
Therefore , if A and B are mutually exclusive, the probability of either event A or event B occurring is equal to the sum of their individual probabilities.
Hence , the probability is solved
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there are 36 students in a class. 1/3 of the class brings lunch and 1/2 of them order lunch. How many of them eat lunch each day
First, we need to find the number of students who bring lunch:
1/3 x 36 = 12 students bring lunch.
Next, we need to find the number of students who order lunch:
1/2 x 12 = 6 students order lunch.
So, the total number of students who eat lunch each day is:
12 (who bring lunch) + 6 (who order lunch) = 18 students.
at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 46 minutes and a standard deviation of 3 minutes. if you visit that restaurant 29 times this year, what is the expected number of times that you would expect to wait between 39 minutes and 53 minutes, to the nearest whole number?
Rounding to the nearest whole number, we would expect to wait between 39 and 53 minutes about 29 times out of 29 visits using standard deviation.
We can use the normal distribution to find the probability of waiting between 39 and 53 minutes for each visit, and then multiply that probability by the number of visits to get the expected number of times waiting in that range.
First, we need to standardize the range of waiting times using the formula:
z = (x - mu) / sigma
where x is the waiting time, mu is the mean waiting time, sigma is the standard deviation, and z is the corresponding z-score.
For the lower limit of 39 minutes:
z1 = (39 - 46) / 3 = -2.33
For the upper limit of 53 minutes:
z2 = (53 - 46) / 3 = 2.33
Next, we can use a standard normal distribution table or calculator to find the probability of waiting between -2.33 and 2.33, which is approximately 0.9902.
Therefore, the expected number of times waiting between 39 and 53 minutes out of 29 visits is:
Expected number = 0.9902 * 29 = 28.68
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A circle has a radius of 2. What is the area of the circle. Round to the nearest tenth
Answer:
The area is 12.57, rounded to the nearest then is 13.
Step-by-step explanation:
A=πr2=π·22≈12.56637
four hundred draws will be made at random with replacement from the box (a) estimate the chance that the sum of the draws will be more than 1,500. (b) estimate the chance that the ticket [3] will be drawn fewer than 90 times.
In both cases, the estimates depend on the specific characteristics of the box and the probabilities associated with each draw.
To estimate the chance that the sum of the draws will be more than 1,500, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.
(b) Similarly, to estimate the chance that the ticket [3] will be drawn fewer than 90 times, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.
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a production process produces 6% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts? 0.0020 0.0299 0.9701 0.9980
The probability that the sample contains exactly two defective parts from a production process with a 6% defect rate is 0.0299. Option B is answer
To find the probability, we can use the binomial probability formula. The formula is P(X=k) = (n C k) * (p^k) * ((1-p)^(n-k)), where n is the sample size, k is the number of successes (defective parts), p is the probability of success (defect rate), and (n C k) represents the combination formula.
In this case, n = 5 (sample size), k = 2 (number of defective parts), and p = 0.06 (probability of a part being defective). Plugging these values into the formula, we get P(X=2) = (5 C 2) * (0.06^2) * ((1-0.06)^(5-2)) = 10 * 0.0036 * 0.8464 = 0.0299.
Therefore, the probability that the sample contains exactly two defective parts is 0.0299 (Option B).
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It’s proportions
Need help with first four
The answers are explained below.
Given are the questions to be solved with the help of proportionality,
Let the unknown values be x,
a) 32 / x = 8 / 6
x = 24
Hence the height of the tree is 24 ft.
b) 3.5 / 5 = x / 3
x = 2.1
Hence the cups of flour needed is 2.1 cups.
c) 2 / 90 = 5 / x
x = 225
Hence 5 cubic ft sand will weigh 225 lbs.
d) 18.50 / 35 = 12.50 / x
x = 23
Hence $12.5 will costs for 23.
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according to a recent study, the weight of male babies less than two months old in the united states is normally distributed with mean 11.9 pounds and standard deviation 2.6 pounds. what proportion of babies weigh more than 10.1 pounds?
The proportion of male babies less than two months old in the United States that weigh more than 10.1 pounds is 0.7554 or approximately 75.54%.
We are given the following information:
Mean = 11.9 pounds
Standard deviation = 2.6 pounds
To find the proportion of babies that weigh more than 10.1 pounds, we need to find the z-score and then find the corresponding area under the standard normal distribution curve.
1: Calculate the z-scoreWe can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the weight of the baby in pounds, μ is the mean weight of male babies less than two months old in the United States, and σ is the standard deviation of the weights of male babies less than two months old in the United States.
Let's plug in the given values:x = 10.1 pounds
μ = 11.9 pounds
σ = 2.6 pounds
z = (10.1 - 11.9) / 2.6z = -0.6923 (rounded to four decimal places)
2: Find the area under the standard normal distribution curve
We can use a standard normal distribution table or a calculator to find the area under the curve for a z-score of -0.6923. Using a calculator, we get:
P(z > -0.6923) = 0.7554 (rounded to four decimal places)
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two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown. a square, a regular pentagon, and a regular $n$-gon, all with the same side length, also completely surround a point. find $n$.
Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point. A square, a regular pentagon, and a regular $n$-gon, all with the same side length, also completely surround a point. n is 20.
A polygon having 5 sides or 5 angles is called a pentagon. The terms "pentagon" and "gonia," which both denote five angles, are the components of the word "pentagon." End to end, the four sides of a hexagon come together to create a shape. The geometric form known as a pentagon has five sides or five angles. In this case, "Penta" stands for five, and "gon" for an angle. One of the several kinds of polygons is the pentagon.
A point has an angle sum of 360 degrees.
The square's internal angles are all 90 degrees.
The regular pentagon has 108 degree internal angles.
Our unidentified polygon's interior angle is 360 - 108 - 90, or 162 degrees.
We can quickly calculate that this polygon's outer angle is 18 degrees.
Any regular polygon's outward angles add up to 360 degrees.
You get 20 times when you divide 360 by 18.
So, the polygon we don't know has 20 sides.
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Name the arc made by the given angle
The required arc made by the angle ∠UQT in the given circle is arc UT.
Given the diagram of circle, which is marked with different line segments.
Arc is the part of the circle. Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.
That implies, the arc made by the angle ∠UQT is arc UT.
Therefore, the required arc made by the angle ∠UQT in the given circle is arc UT.
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What is the value of the coefficient of the x² term when the expression (3.5x2-5+2x) is multiplied by (-5x -0.75) ?
The coefficient of the x² term is
If the value of the coefficient of the x² term when the expression (3.5x²-5+2x) is multiplied by (-5x -0.75) . The coefficient of the x² term is -2.625.
What is coefficient ?When multiplying (3.5x² - 5 + 2x) by (-5x - 0.75), we need to discover the product of the parts that contain x² in order to determine the coefficient of the x² term.
Now let write out the product of the two polynomials:
(3.5x² - 5 + 2x) × (-5x - 0.75)
= -17.5x³ - 2.625x² + 25x + 3.75
So,
The x² term's coefficient which is -2.625 is the coefficient of the term that contains x².
Therefore the coefficient is -2.625.
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you collect a basketball that's worth $150. Each following year it doubles in worth from the previous year. Write a function that shows the worth,w(t), at any given time,t.
Answer:
150(2)^t
Step-by-step explanation:
The function that represents the worth, w(t), of the basketball at any given time, t, can be written as:
w(t) = 150(2)^t
where t is the number of years since the basketball was collected.
This function uses the formula for exponential growth, where the value of the basketball doubles each year. The initial value of the basketball is $150, and the value is multiplied by 2 for each year that passes. Therefore, after one year, the basketball is worth $300 (2 times $150), after two years it is worth $600 (2 times $300), and so on.
By plugging in different values of t, we can calculate the worth of the basketball at any given time.
1. What does God look like?
2. What came first, the chicken or the egg?
3. Where do you go when you die?
4. What are black holes?
5. Why is water wet?
6. Why do people die?
7. How did the world begin?
8. Where do babies come from?
9. Why is the sea salty?
10. Why is the moon sometimes out in the day?
11. How does the internet work?
12. Why is the sky blue?
13. Where does wind come from?
14. Why do we have a leap year?
15. What makes the Earth spin?
16. Why is blood red?
17. What is infinity?
18. How big is the world?
19. Why doesn't the sky fall down?
20. Why does cutting onions make you cry?
21. How do planes fly?
22. How do telephones work?
23. How does TV work?
24. Why am I right/left handed?
25. What is electricity?
26. How do clouds float?
27. How does the car work?
28. How do the sun and moon stay in the sky?
29. Why are people's eyes different colours?
30. How does lightning strike?
Answer: here are my answers.
Step-by-step explanation: Here are some brief answers to your questions:
1. The appearance of God is a matter of personal belief and varies across different religions and cultures.
2. This question is still debated by scientists and philosophers, and there is no clear answer. It is thought that the egg came first, as the evolution of birds and egg-laying animals predates the existence of chickens.
3. Views on what happens after death also vary across different religions and cultures. Some believe in an afterlife, while others do not.
4. Black holes are extremely dense regions in space where gravity is so strong that nothing, not even light, can escape.
5. Water is wet because it has a high surface tension, which allows it to adhere to other surfaces and create a thin film of water.
6. People die due to a variety of factors, including disease, injury, and aging.
7. The origin of the world is a complex question that has been studied by scientists, philosophers, and theologians for centuries. The most widely accepted scientific theory is the Big Bang theory, which suggests that the universe began with a massive explosion approximately 13.8 billion years ago.
8. Babies are formed through the fertilization of an egg by sperm, which occurs during sexual intercourse.
9. The sea is salty due to the presence of dissolved salts and minerals, which come from the weathering of rocks and volcanic activity.
10. The moon is sometimes visible during the day because its orbit around the Earth causes it to appear in different parts of the sky at different times.
11. The internet is a global network of interconnected computers and servers that communicate with each other using standardized protocols.
12. The sky appears blue because of the scattering of sunlight by the gases and particles in the Earth's atmosphere.
13. Wind is caused by differences in air pressure, which are created by variations in temperature, humidity, and other factors.
14. A leap year is a year that contains an extra day (February 29) to keep the calendar year synchronized with the astronomical year, which is approximately 365.25 days long.
15. The Earth spins on its axis due to the conservation of angular momentum from the formation of the solar system.
16. Blood is red because it contains hemoglobin, a protein that binds to oxygen and gives blood its characteristic color.
17. Infinity is a mathematical concept that represents a quantity that is larger than any finite number.
18. The Earth has a diameter of approximately 12,742 kilometers (7,918 miles) and a circumference of approximately 40,075 kilometers (24,901 miles).
19. The sky appears to be above us because the Earth's gravitational field holds the atmosphere in place around the planet.
20. Cutting onions releases a gas called syn-propanethial-S-oxide, which irritates the eyes and causes them to produce tears.
21. Planes fly by generating lift from their wings, which is created by the flow of air over the curved surface of the wing.
22. Telephones work by converting sound waves into electrical signals, which are transmitted over a network of wires or wireless connections.
23. Television works by transmitting images and sound over electromagnetic waves, which are received by a receiver and displayed on a screen.
24. Whether a person is right or left-handed is determined by the dominant hemisphere of their brain.
25. Electricity is a form of energy caused by the movement of electrons through a conductor.
26. Clouds float because they are made up of tiny water droplets or ice crystals that are lighter than the surrounding air.
27. Cars work by converting the energy stored in fuel into motion through a series of processes, including combustion, transmission, and propulsion.
28. The sun and moon appear to stay in the sky due to their position relative to the Earth's rotation and orbit.
29. The color of a person's eyes is determined by the amount and type of pigments in the iris.
30. Lightning is caused by the buildup and discharge of electrical energy in the atmosphere, typically between a cloud and the ground or between two clouds.
how many ways can you place two indistinguisable kings on an empty chess board so that they do not attack each other
The answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.
To answer this question, we need to understand the basic rules of chess. A king can move one square in any direction, including diagonally. So, to ensure that two kings are not attacking each other, we need to place them on two squares that are not adjacent to each other, and not on the same diagonal line.
There are 64 squares on a chess board, and the first king can be placed on any of those squares. The second king, however, has fewer options because it cannot be placed on the same row, column or diagonal as the first king.
The number of ways to place the second king will depend on where the first king was placed. For example, if the first king was placed in one of the corners, then the second king will have only two possible squares to be placed in. On the other hand, if the first king was placed in the center of the board, then the second king will have fewer options.
Overall, there are 32 possible squares for the second king to be placed in, which means that there are 32 possible ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.
In summary, the answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.
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Name the greatest negative integer.
Answer:
The greatest negative integer is the number one less than 0 and the smallest positive integer is the number one greater than 0.
Step-by-step explanation:
simplify the following
[tex]3x( - 2 {x}^{2} - 4x) + 6 {x}^{3} + 5 {x}^{2} [/tex]
Answer:
- 7x²-------------------------
Simplify the expression.
First distribute, then collect like terms:
3x(- 2x² - 4x) + 6x³ + 5x² = - 6x³ - 12x² + 6x³ + 5x² = ( - 6x³ + 6x³) + ( - 12x² + 5x²) = - 7x²the frequency of people with red hair (a recessive trait) in population a is 49% and is 25% in population b. a long-term famine in population a causes a number of people in population a to migrate to population b, where they mate randomly with members of population by. geneticists estimate that in each generation, after migration, 10% of people in population b consist of population a emigrants. what will be the frequency of individuals with red hair in population b after 10 generations of migration?
So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.
We need to use the Hardy-Weinberg equation, which describes how the frequencies of alleles in a population will change over time.
The equation is:
p^2 + 2pq + q^2 = 1
Where:
p = frequency of one allele
q = frequency of the other allele
p^2 = frequency of homozygous dominant individuals
2pq = frequency of heterozygous individuals
q^2 = frequency of homozygous recessive individuals
In this case, the recessive trait is red hair, so we'll use q to represent the frequency of the recessive allele.
In population a, q = 0.49, so p (the frequency of the dominant allele) = 1 - q = 0.51.
In population b, q = 0.25, so p = 0.75.
After the emigrants from population a migrate to population b, the new frequency of the recessive allele in population b will be:
q' = (0.1 x 0.49) + (0.9 x 0.25) = 0.286
This is the new value of q after one generation of migration. To calculate the frequency of red-haired individuals after 10 generations, we need to use the equation:
q^10 = (0.286)^10 = 0.0002
So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.
The frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%. This is based on the assumption that the emigrants from population a mate randomly with members of population b and that the population sizes remain constant over time.
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Is 84 cubed an irrational number?
Answer:Yes, because ∛84 = ∛(2 × 2 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 84 is an irrational number.
Step-by-step explanation:
Answer: i think so
Step-by-step explanation:
Write in factored form then identify the zeros y=(x+1)^2-4
To write the given quadratic equation, y = (x + 1)^2 - 4, in factored form, we can start by expanding the equation using the square of a binomial:
y = (x + 1)(x + 1) - 4
y = (x^2 + 2x + 1) - 4
y = x^2 + 2x + 1 - 4
y = x^2 + 2x - 3
Now, to find the zeros of the equation, we set y = 0 and solve for x:
x^2 + 2x - 3 = 0 To factor this quadratic equation, we need to find two numbers whose product is -3 and whose sum is 2. The numbers that satisfy this condition are 3 and -1:
(x + 3)(x - 1) = 0
Now, setting each factor equal to zero, we can find the values of x:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Therefore, the factored form of the equation y = (x + 1)^2 - 4 is (x + 3)(x - 1) = 0, and the zeros of the equation are x = -3 and x = 1.
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