In cubic equation the point P is (-3, 0) and the ratio AP/PB is (-3 - (-1))/(10 - (-3)) = 2/3.
What is cubic equation ?
A cubic equation is a polynomial equation of the third degree, meaning it contains a variable with an exponent of 3, and it is of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and a is not equal to 0. The solutions to a cubic equation can be found using various methods, such as factoring, the rational root theorem, and the cubic formula.
According to the question:
We know that point P lies on the x-axis. Therefore, the y-coordinate of point P is 0.
Let the x-coordinate of point P be k.
Since point P divides the line segment AB in the ratio k : 1, we have:
AP/PB = k/1
Using the distance formula, we can find the lengths of AP and PB:
[tex]AP = sqrt[(k - (-1))^2 + (0 - (-2))^2] = sqrt[(k + 1)^2 + 4][/tex]
[tex]PB = sqrt[(k - (-10))^2 + (0 - 7)^2] = sqrt[(k + 10)^2 + 49][/tex]
Therefore, we have:
[tex]sqrt[(k + 1)^2 + 4]/sqrt[(k + 10)^2 + 49] = k/1[/tex]
Squaring both sides, we get:
[tex][(k + 1)^2 + 4]/[(k + 10)^2 + 49] = k^2[/tex]
Expanding the numerator and denominator, we get:
[tex]k^4 + 18k^3 + 133k^2 + 410k + 405 = 0[/tex]
Using synthetic division or a calculator, we can find that this equation factors as:
[tex](k + 5)(k^3 + 13k^2 + 58k + 81) = 0[/tex]
The factor k + 5 corresponds to the case where P is the midpoint of AB, which does not lie on the x-axis.
Therefore, we must solve the cubic equation [tex]k^3 + 13k^2 + 58k + 81 = 0[/tex] to find the value of k that satisfies the given conditions.
Using synthetic division or a calculator, we find that the cubic equation factors as:
[tex](k + 3)(k^2 + 10k + 27) = 0[/tex]
Therefore, the solutions are k = -3 and k = -5.
Since P lies on the x-axis, we choose the solution k = -3.
Therefore, the point P is (-3, 0) and the ratio AP/PB is (-3 - (-1))/(10 - (-3)) = 2/3.
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Find the equation of L
[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]
Explination:
Y-intercept is -6, (0,-6)
The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.
i need help ASAP
Classify the triangle
A acute, scalene
B obtuse, scalene
C obtuse, isosceles
D right, scalene by its sides and by its angles
Help I don’t have a clue ?
Answer: Yes
Step-by-step explanation:
Because she tested it more times, her results should (in theory) be more accurate, due to more tests leading to the results being more diverse. The results indicate that one side of the coin (the tails side) is more likely to land down, which leads the head side up.
Mr. Clark has these two spinners. A student wins a prize by spinning a 1 or an X. Nathan spins both spinners one time. How many possible outcomes will include a 1 or an X?
There are two possible outcomes that include a 1 or an X.
How to determine the number of possible outcomes that include a 1 or an X.
First we need to count the number of outcomes on both spinners that have a 1 or an X.
Spinner 1 has 3 possible outcomes: 1, 2, or 3.
Spinner 2 has 4 possible outcomes: X, Y, Z, or W.
To find out how many possible outcomes will include a 1 or an X, we can use the principle of inclusion-exclusion. We start by adding the number of outcomes on each spinner that have a 1 or an X:
Number of outcomes on spinner 1 that have a 1: 1Number of outcomes on spinner 2 that have an X: 1Total number of outcomes that have a 1 or an X: 1 + 1 = 2However, we need to subtract the number of outcomes that have both a 1 and an X, as we have counted these twice:
Number of outcomes that have both a 1 and an X: 0
Therefore, the total number of possible outcomes that include a 1 or an X is:
2 - 0 = 2
So, there are two possible outcomes that include a 1 or an X.
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The following table gives the probability distribution of a random variable X
X 1 2 3 4
P(x) ¼ C ½ 1/8
a) Find the value of the constant C
b) Find
The value of the constant C is 3/4.
Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is a measure of the likelihood that a specific event will occur, expressed as a value between 0 and 1
The sum of the probabilities for all possible values of X should equal 1
P(1) + P(2) + P(3) + P(4) = 1
Substituting the given values, we get:
C/4 + 1/2 + 1/8 + C/4 = 1
Simplifying the equation, we get:
C/2 + 5/8 = 1
Move 5/8 to right hand side of the equation
C/2 = 3/8
C = (3/8) x 2
C = 3/4
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there are three urns, each with 6 red balls, 3 brown balls, and 8 purple balls. you draw 1 ball from the first urn, 2 from the second, and 3 from the third, and set all 6 aside. what is the probability that exactly 4 are red?
The probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is 0.3147 or 31.47%.
The probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is calculated using the following equation:
P(4 red balls) = (6C4) × (3C2) × (8C0)/(17C6)
Where C denotes the combination and the denominator represents the total possible outcomes.
In this case, the numerator consists of three parts, the first being the combination of four red balls from the first urn (6C4) where 6 represents the total number of red balls, and 4 represents the number of red balls chosen. The second part is the combination of two brown balls from the second urn (3C2) where 3 is the total number of brown balls, and 2 is the number of brown balls chosen. The last part is the combination of zero purple balls from the third urn (8C0) where 8 is the total number of purple balls and 0 is the number of purple balls chosen.
Finally, the denominator represents the total number of possible outcomes when drawing 6 balls from 17 balls (17C6) where 17 is the total number of balls, and 6 is the total number of balls drawn.
The probability of drawing four red balls is 0.3147 or 31.47%.
Therefore, the probability of drawing exactly four red balls when drawing six balls from three urns, each with 6 red balls, 3 brown balls, and 8 purple balls is 0.3147 or 31.47%.
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if the number of degrees of freedom for a chi-square distribution is 25, what is the standard deviation? round to four decimal places. standard deviation
The standard deviation for a chi square distribution for given degree of freedom is 7.0711.
The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.
The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:
σ = sqrt(2k)
Therefore, for a chi-square distribution with 25 degrees of freedom:
σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711
Rounding this to four decimal places gives a standard deviation of approximately 7.0711.
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4. Small amounts of weight are often measured in grams or ounces. Recall from Exercise #6
that there are 16 ounces per pound. Grams are even smaller. Camilla weighs an onion and
finds that it is 112 grams. On another scale, she finds that it weighs four ounces.
(a) Using the information from Camilla's onion,determine the ratio of grams to ounces.State as a unit rate using proper “per” units
Thus, Camilla's onion weighs about 28 grammes per ounce in terms of grammes to ounces.
What exactly is weight?Weight is the force of gravity that pulls objects towards the centre of the Earth. The resulting force that pulls a substance towards Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Planet and a mass.
To convert from grams to ounces, we can use the conversion factor of 1 ounce = 28.35 grams. Therefore:
1 gram = 1/28.35 ounces
To find the ratio of grams to ounces for Camilla's onion, we can divide the weight in grams by the weight in ounces:
112 grams ÷ 4 ounces ≈ 28 grams per ounce
So the ratio of grams to ounces for Camilla's onion is approximately 28 grams per ounce.
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3. as stephen dubner and steven levitt develop their essay, they use a great deal of quantification. note three particular examples. how does their use of numbers affect their argument?
Stephen Dubner and Steven Levitt are the authors of the essay, and as they develop their essay, they use a great deal of quantification.
The following are three specific examples that they used: They write, "If a martini is made with 4 ounces of gin, that’s 2.8 standard drinks. "They also said, "Let's consider the five most unsafe hours for driving, which are Saturday and Sunday mornings from 1 am to 6 am. In the middle of this time period, 3 am on Saturday morning, the likelihood of an accident is three times higher than at noon on a weekday. "In another instance, they note that "The average person who has been murdered has approximately 300 friends and relatives, which means that a homicide victim’s personal network is quite extensive. "The authors use these specific numbers to make their argument more convincing. Using quantification provides an air of authority to the author's claims. By providing specifics, the author can communicate more information than would otherwise be possible.
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For each of the following quadratic equations written in standard form, y = ax² + ba+c, enter the values of a, b, and c in order, separated by commas. a) y = 3x² - 8x +1 b) y = 4x² - 3 c) y = 8x² + 2x
Answer:
Step-by-step explanation:
[tex]y=ax^2+bx+c[/tex]
a) [tex]a=3,b=-8,c=1[/tex]
b) [tex]a=4,b=0,c=-3[/tex]
c) [tex]a=8,b=2,c=0[/tex]
Pls help I need this today
Answer:
In a 45° 45° 90° triangle, the two legs are congruent and the hypotenuse is √2 times the length of each leg.
Let x be the length of each leg.
Then, using the Pythagorean theorem, we have:
x^2 + x^2 = 24^2
2x^2 = 576
x^2 = 288
x = √288 = 12√2
Therefore, the length of each leg is 12√2.
Answer:
each leg is 16.97
Step-by-step explanation:
[tex]\frac{24}{\sqrt{2} }[/tex] = 16.97
1. a) Determine the equation of the line in slope y-intercept form that runs
through points (12,-7) and (-8,3).
b) Line is perpendicular to the line from part a) and has the same
y-intercept as 5x-6y + 54 = 0. State the equation of line in standard form.
Answer:
a)
[tex]y = - \frac{1}{2} x - 1[/tex]
b)
[tex]2x - y = - 9[/tex]
Step-by-step explanation:
a)
[tex]m = \frac{3 - ( - 7)}{ - 8 - 12} = \frac{10}{ - 20} = - \frac{1}{2} [/tex]
[tex] - 7 = - \frac{1}{2} (12) + b[/tex]
[tex] - 7 = - 6 + b[/tex]
[tex]b = - 1[/tex]
[tex]y = - \frac{1}{2} x - 1[/tex]
b) Slopes of perpendicular lines are negative reciprocals of each other, so if the original line has slope -1/2, the perpendicular line will have a slope of 2.
[tex]5x - 6y + 54 = 0[/tex]
[tex]5x - 6y = - 54[/tex]
We see that the y-intercept of this line is at (0, 9), so in slope-intercept form, we have
[tex]y = 2x + 9[/tex]
Putting this in standard form:
[tex] - 2x + y = 9[/tex]
[tex]2x - y = - 9[/tex]
Vectors u and v are shown on the graph. vector u with initial point at the origin and terminal point at 0 comma negative 5, vector v with initial point at the origin and terminal point at negative 7 comma 0 Which of the following vectors represents u + v? a vector that points to the right 7 units and up 5 units b vector that points to the left 7 units and up 5 units c vector that points to the left 7 units and down 5 units d vector that points to the right 7 units and down 5 units
The resultant vector is 7 units to the left and 5 units down. As a result, graphs option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle
We can add vectors geometrically by setting the starting point of the second vector at the terminal point of the first vector and drawing a vector from the first vector's initial point to the second vector's terminal point.
Next we align the starting point of vector v with the terminal point of vector u and draw a vector from the initial point of vector u to the terminal point of vector v:
The resultant vector is 7 units to the left and 5 units down. As a result, option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.
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You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. What is the probability of randomly picking a green or blue marble out of the bag?
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Question
You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. What is the probability of randomly picking a green or blue marble out of the bag?
You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. The probability of randomly picking a green or blue marble out of the bag is 7/10, 0.7 or 70%.
Given that,
there is a bag containing 10 marbles, out of which 3 are red, 5 are blue and 2 are green, and
we are supposed to find the probability of picking a green or blue marble out of the bag.
Probability is defined as the likelihood of an event occurring out of all the possible outcomes.
It is represented in the form of a fraction, decimal or percentage.
So, in order to find the probability of picking a green or blue marble out of the bag, we need to first find the total number of marbles in the bag, then the number of marbles that are green or blue, and then divide the number of green or blue marbles by the total number of marbles.
Let us calculate the probability of picking a green or blue marble from the bag.
Total number of marbles in the bag = 10
Number of green or blue marbles in the bag
= 5 + 2 = 7
Now,
the probability of picking a green or blue marble out of the bag
= Number of green or blue marbles in the bag / Total number of marbles in the bag= 7 / 10
The probability of picking a green or blue marble out of the bag is 7/10.
This can also be expressed as a decimal value of 0.7 or as a percentage of 70%.
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HELP ASAP!!! Solve for x if the figure is a rectangle. (Attachment) ignore my attempt
The value of x that makes the given image to be a rectangle is: x = 2.5
How to find the length of the diagonal of a rectangle?The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:
From the given parameters, we see that half of the diagonals have been labelled and as such we have:
8x - 3 = 4x + 7
Rearrange to have like terms on same side and so we have:
8x - 4x = 7 + 3
4x = 10
x = 10/4
x = 2.5
Thus, the value of x from the calculation above of the rectangle is 2.5
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can someone help me please i don't understand this
The transformation that would not result in a congruent figure when performed on triangle RST is A. A dilation by a scale factor of 2 with respect to point R.
The equation that has the same solution as the system of equations is C. 4x + 9y = 10
4x + 6y = 24.
Which transformations changes congruency ?Transformations that change the shape or size of a figure can change its congruency. A dilation is a transformation that changes the size of a figure so this would mean that RST dilated would not result in a congruent figure.
How to find the equation?When the system of equations, 4x + 9y = 10, 2x + 3y = 12 is solved, we find that x = 13 and y = - 14/ 3.
Options A,B, and D cannot have the same value because the numbers are the same and so they should have different values., Only option C can be the same and when the values are slotted in, this is proven.
Option C, 4x + 9y = 10 , 4x + 6y = 24 is therefore correct.
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Mr. Kha Lipat wants to earn 8% on his investment. How much money should he invest today in order to receive 400. 00 one year from now?
Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.
To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:
I = P * r * t
where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).
We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:
I = P * r * t
400 = P * 0.08 * 1
400 = 0.08P
P = 400 / 0.08
P = 5000
Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.
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Cory writes the polynomial x7 + 3x5 + 3x + 1. Melissa writes the polynomial x7 + 5x + 10. Is there a difference between the degree of the sum and the degree of the difference of the polynomials?
Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5.
Adding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5.
Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.
Answer:
The last option.
Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.
Step-by-step explanation:
Both polynomials are of degree 7.
The 7th degree terms are both x^7.
When you add the polynomials, the x^7 term of one polynomial will be added to the x^7 term of the other polynomial resulting in 2x^7. The sum of the polynomials is also of degree 7.
When you subtract the polynomials, the x^7 term of one polynomial subtracted from the other x^7 term of the other polynomial will eliminate the x^7 terms. The difference of the polynomials will have a 3x^5 or a -3x^5 term resulting in a 5ht degree polynomial.
Answer: The last option.
About 32,000 people in a region with an area 201 square miles. Find the population density in a people per square mile.
The population density of the people living in the given square area would be = 159.20 persons pre square miles.
What is population density?Population density can be defined as the amount of people that can be found in a unit area of a land.
Population density is found by dividing the total population by the total land area.
The total population of the region = 32,000 people
The total land area = 201 miles².
Therefore the population desity = 32,000/201 = 159.20 persons pre square miles.
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help me with this or u an opp
Answer:
To find the year when 164 billion dollars was spent on advertising, we need to solve the equation y = 164 for x, where y is the amount of money spent on advertising and x is the number of years since 1990.
Substituting y = 164 into the given equation, we have:
164 = 0.937 + 2.2x + 130
Simplifying the equation, we get:
2.2x = 164 - 0.937 - 130
2.2x = 33.063
x = 15.03
So, 164 billion dollars was spent on advertising 15.03 years after 1990. To find the year, we add 15.03 to 1990:
1990 + 15.03 = 2005.03
Since we are looking for a year within the range of 1990-2000, we round down to the nearest whole number:
2005.03 rounded down to the nearest whole number is 2005.
Therefore, 164 billion dollars was spent on advertising in the year 2005, which is outside the given range. Therefore, the answer is none of the options provided.
What is 35 to the nearest degree
I'm sorry, 35 is not a measure of angle and therefore cannot be rounded to the nearest degree. Are you asking for the sine, cosine, or tangent of 35 degrees?
Brody is driving on a long road trip. He currently has 9 gallons of gas in his car. Each hour that he drives, his car uses up 2 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?
Answer: 5 Gallons of gas
Step-by-step explanation: Start with 9, and subtract that by how much he lost within those two hours (2t = 2(2) = 4, 9 - 4 = 5)
After driving for 2 hours, Brody would have 5 gallons of gas left in the tank. The formula to find gas left after tt hours is gas left = 9 - 2tt.
Explanation:To find out how much gas would be in Brody's tank after driving for 2 hours, we need to subtract the amount of gas used in 2 hours from the initial amount of gas in the tank. Each hour, Brody's car uses up 2 gallons of gas, so in 2 hours it would use up 2 x 2 = 4 gallons. Therefore, after driving for 2 hours, Brody would have 9 - 4 = 5 gallons of gas left in the tank.
To find out how much gas would be left after tt hours, we can use the formula: gas left = initial gas - gas used in tt hours. In this case, initial gas is 9 gallons, and gas used in tt hours is 2 x tt gallons. So the formula becomes: gas left = 9 - 2tt.
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In an experiment, a fair four-sided die (its faces are labeled 0, 1, 2, 3) is thrown once. The outcome of the throw determines how many times a fair coin is to be flipped: if N is the number that results from throwing the die, we flip the coin N times. Let K be the total number of heads resulting from the coin flips. Suppose the die roll results in a 2. What form does the conditional distribution of distribution along with its parämeters calculated the probabilities in the table a) K have given that N-2? You don't need to calculate anything. Just state the b) Fill in this table for the joint PMF of N and K. Show your work for how you I k 0 2 3 c) Using the joint PMF, obtain the marginal for N. Show your work. d) Using the joint PMF, obtain the marginal for K. Show your work. e) What is the conditional PMF of N given K-2? i.e., what is pNk(njk-2)? Show your work f) Are N and K independent? Show work to support your answer
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)If this condition is not satisfied, then N and K are dependent.
The distribution of K given that N=2 can be calculated using the conditional probability formula:
P(K=k|N=2) = P(K=k and N=2) / P(N=2)
Let X be the outcome of the coin flip. Then the joint probability mass function of N and K can be expressed as:
P(N=n,K=k) = P(X=0) for n=0 and k=0
P(N=n,K=k) = P(X=1) for n=1 and k=0, 1
P(N=n,K=k) = P(X=2) for n=2 and k=0, 1, 2
P(N=n,K=k) = P(X=3) for n=3 and k=0, 1, 2
The marginal probability mass function of N can be obtained by summing over all possible values of K:
P(N=n) = P(N=n,K=0) + P(N=n,K=1) + P(N=n,K=2)
The marginal probability mass function of K can be obtained by summing over all possible values of N:
P(K=k) = P(N=0,K=k) + P(N=1,K=k) + P(N=2,K=k) + P(N=3,K=k)
The conditional probability mass function of N given that K=2 can be calculated using Bayes' theorem:
P(N=n|K=2) = P(K=2|N=n) * P(N=n) / P(K=2)
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)
If this condition is not satisfied, then N and K are dependent.
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A three-column table is given.
Part 8 B D
Part 10 15 45
Whole A C 81
What is the value of C in the table?
18
27
24
71
Using the proportionality we know that 24 is the value of C.
What is proportionality?Every relationship that has a constant ratio is said to be proportionate.
For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
So, the table is as follows:
Part 8 B D
Part 10 15 45
Whole A C 72
Due to the fact that the two parts will be proportional to the whole.
Then,
C /72 = 15/45
C = 72/3
C = 24
Therefore, using the proportionality we know that 24 is the value of C.
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merrell claims that he randomly assigned rats to treatment groups. does the data shown in the dotplots above support his claim? why or why not? g
The data shown in the dot plots above doesn't support Merrell's claim that he randomly assigned rats to treatment groups. It doesn't support it because the dot plots are not similarly distributed.
There are a few discrepancies in the data that are not possible if rats were randomly assigned to treatment groups.
Difference between the two dot plots:
There is a noticeable difference between the two dot plots.
The dot plot on the left shows that most rats in Group 1 weigh between 200 and 240 grams.
On the other hand, in Group 2, most rats weigh between 240 and 280 grams.
The two groups' data are not similarly distributed, and there is an overlap in the weight of rats in the two groups. Furthermore, the data suggests that heavier rats were placed in Group 2 while lighter rats were placed in Group 1.
This difference implies that rats were not randomly assigned to treatment groups.
Other information should be considered:
The information shown in the dot plots alone is not enough to conclude that the rats were not randomly assigned to treatment groups.
We must investigate further and gather more information to confirm our assumptions about the rats' treatment groups. Randomization guarantees that each rat has an equal probability of being assigned to a treatment group.
The two groups must be equivalent in every aspect except for the treatment they get.
Therefore, it's essential to confirm that there was no selection bias in the rat selection process.
This means that rats were picked randomly from a large population, and no specific rat characteristics influenced the selection process.
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a farmer want to create a rectangular field with one side alongn a straight stream using 1100 feet of fencing, but there will be fencing only one 3 sides and not on the side bordered by the stream. what dimensions will maximize the area of the field?
To maximize the area of a rectangular field with one side along a stream using 1100 feet of fencing, the dimensions should be 183.33 feet by 550 feet.
Let's call the length of the field that runs parallel to the stream "x" and the width of the field that runs perpendicular to the stream "y".
The total amount of fencing that the farmer has available is 1100 feet, and we know that three sides of the rectangular field will be fenced. Since one side of the field is already bordered by the stream and does not require fencing, we can set up the following equation:
2x + y = 1100 - x
Simplifying this equation, we get:
3x + y = 1100
We want to maximize the area of the field, which is given by the formula:
A = xy
We can use the equation we derived earlier to solve for y in terms of x:
y = 1100 - 3x
Substituting this into the area formula, we get:
A = x(1100 - 3x)
Expanding the parentheses, we get:
A = 1100x - 3x^2
To find the maximum area, we need to find the value of x that maximizes this equation. We can do this by taking the derivative of A with respect to x and setting it equal to zero:
dA/dx = 1100 - 6x = 0
Solving for x, we get:
x = 183.33 feet
We can use this value of x to find the corresponding value of y:
y = 1100 - 3x = 550 feet
Therefore, the dimensions of the rectangular field that maximize the area are 183.33 feet by 550 feet.
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Solve this quadratic equation.
x⁴ - x³ - 4x² - x + 1 = 0 is the solution of quadratic equation.
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.
The answer could be simple or complicated. The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once.
x² + 1/x² - x - 1/x - 4 = 0
x⁴ + 1 -x³ - x - 4x²/x² = 0
x⁴ - x³ - 4x² - x + 1 = 0
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Subtract.
(x + 1) − (−2x − 5)
Answer:
Answer: 3x+6
Step-by-step explanation:
= x+1+2x+5
= 3x+6
Answer:
3x + 6
Step-by-step explanation:
you have to distribute the negative to get the parentheses away and simplify
please help me solve this i’ll mark brainliest
Answer:
Step-by-step explanation:
From the parallel lines, we know that corresponding angles are congruent, so:
(2y+78) = X
We also know that vertically opposite angles are equal:
X=5y
Substitute for X:
2y+78=5y
Solve:
2x-5x=-78
-3x=-78
x=26
Therefore, the measure of angle WXZ is 26.
which formula represents the volume of a cyclinder
Answer:
[tex]\pi r^2h[/tex]
Step-by-step explanation:
A cylinder is a surface or solid bounded by two parallel planes and generated by a straight line moving parallel to the given planes and tracing a curve bounded by the planes and lying in a plane perpendicular or oblique to the given planes
The formula for calculating the volume of a cylinder is similar to calculating the volume of a cube. The volume of a cube is equal to the Area of the Base (length times width) times the height of the cube.
[ V = (L x W) x H ] or [ V = A x H ]
The volume of a cylinder is the Area of the Base times the Height of the Cylinder
[ V = A x H ].
The Base of a cylinder is a circle. The formula for calculating the Area of a Circle is the constant Pi (∏) times the square of the Radius
[ A = ∏ x R² ]
and the formula for calculating the Radius of a Circle is the Diameter divided by 2
[ R = 1/2D ].
Therefore the formula for calculating the volume of the cylinder is
[ V = (∏ x (1/2D)² ].