The equation of the relationship between glucose left (g) and time elapsed (t) is found and intercepts are also found.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Given, the drip rate of glucose = 1.02 cc/min
Total glucose given = 120cc
Time taken to given 120cc glucose = 120/1.02 = 117.6 minutes ≈ 118 minutes
a) We will use g for glucose left and t for the time in minutes.
When t = 0 , g = 120
When t = 20, g = 120 - (1.02 * 20) = 99.6cc
when t = 40, g = 120 - (1.02 * 40) = 79.2cc
Similarly, we fill up the table as below:
t 0 20 40 60 80 100 120
g 120 99.6 79.2 58.8 38.4 18 0
b) We know in 1 minute = 1.02 cc glucose is used
So the glucose left after 1 minute = 120 - 1.02 * 1
From option (a), we can see that for 20 minutes
g = 120 - (1.02 * 20)
So for t minutes, glucose left can be represented by the equation:
g = 120 - 1.02t
c) from the above equation, we can find :
t intercept
g = 0
0 = 120 - 1.02t
120 = 1.02t
t = 117.6 minutes
g- intercept
t = 0
g = 120 - 1.02*0 = 120 cc
Now the graph is a straight line passing through (0,120) and (117.6,0).
Therefore the equation of the relationship between g and t is found and intercepts are found.
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Explain how the tiles show that 2s + 3s² is not
equivalent
to 5s.
The size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expressions are 2s+3s² and 5s.
Here, 2s+3s²≠5s
Substitute s=-1 in 2s+3s²≠5s, we get
2(-1)+3(-1)²≠5(-1)
1≠-5
Substitute s=2 in 2s+3s²≠5s, we get
2(2)+3(2)²≠5(2)
16≠10
Therefore, the size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
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"Your question is incomplete, probably the complete question/missing part is:"
Is 2s+3s² equivalent to 5s? Use math tiles to model 2s+3s² and 5s.
s+s s²+s²+s² s+s+s+s+s
2s 3s² 5s
The expression 2s+3s² is not equivalent to 5s. Explain how that tiles show that 2s+3s² is not equivalent to 5s.
please help meee.
step by step please
here is the picture please help me.
The domain of function fog (x) is [-2, 3].
From the case, it was given that:
f(x) = √(6 - x)
g(x) = x² - x
Domain of fog (x) ?
First, we need to find the form of function fog (x):
fog (x) = √(6 - (x² - x)
fog (x) = √(6 - x² + x)
fog (x) ≤ 0 --> to be rational
√(6 - x² + x) ≤ 0
To find the domain of function fog(x), we need to find the value of x where fog (x) equals to zero (0):
√(6 - x² + x) = 0
6 - x² + x = 0
(-x + 3) (x + 2) = 0
x = 3 or x = -2
Next, we need to chose random number above, between, and below 3 and -2 to find the domain of fog (x):
-2 < x < 3; x = 0
fog (0) = √(6 - (0)² + (0))
fog (0) = √6 --> rational
x < -2; x = -3
fog (-3) = √(6 - (-3)² + (-3))
fog (-3) = √(6 - 9 - 3)
fog (-3) = √(-6) --> irrational
x > 3; x = 4
fog (4) = √(6 - (4)² + (4)
fog (4) = √(6 - 16 + 4)
fog (4) = √(-6) --> irrational
Hence, the value of x should be -2 ≤ x ≤ 3 to make fog (x) function rational.
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Expand. Your answer should be a polynomial in standard form. ( � − 3 ) ( � − 4 ) = (x−3)(x−4)=
The polynomial in standard form after expansion is x² - 7x + 12.
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
The given expression is (x - 3) (x - 4).
We have to expand this as a polynomial in standard form.
Standard form of a polynomial with degree n is,
a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻¹ + aₙ xⁿ
(x - 3) (x - 4) = x (x - 4) - 3 (x - 4)
Applying the distributive property,
= x² - 4x - 3x + 12
= x² - 7x + 12
This is a standard form of a second degree polynomial.
Hence x² - 7x + 12 is the expansion of the given expression.
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Levels of Measurement!
What type of measure scale is being used? Nominal, Ordinal, interval or Ratio.
1. A satisfaction survey of a social website by number:
1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied.
2. The colors of crayons in a 24-crayon box.
3. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
4. The distance in miles to the closest grocery store.
5. High school men soccer players classified by their athletic ability:
Superior, Average, Above average.
1) A satisfaction survey of a social website by number is Ordinal.
2) The colors of crayons in a 24-crayon box are nominal.
3) The baking temperatures for various main dishes are interval.
4) The distance in miles to the closest grocery store is Ratio
5) High school men soccer players classified by their athletic ability are Ordinal.
The satisfaction survey scale is ordinal since the numbers are used to indicate the order of satisfaction (i.e., very satisfied is higher than somewhat satisfied, which is higher than not satisfied), but the difference between each level is not known.
The colors of crayons are nominal since they are categorical and do not have an inherent order or numeric value.
The baking temperatures are interval, as the differences between the values are meaningful, but there is no true zero point (i.e., 0 degrees does not indicate the absence of temperature).
The distance to the closest grocery store is ratio, as it has a true zero point (i.e., 0 miles means no distance), and the differences between distances are meaningful and measurable.
The classification of high school soccer players by athletic ability is ordinal since the categories are ordered, but the differences between them are not known.
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Using the graphing tool, write the exponential function that best modes the number of trees infected
The exponential function that best modes the number of trees infected [tex]y = a * e^{bx}[/tex]
what is exponential function ?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex] where "a" is a constant called the base, and "x" is the exponent. The base "a" is usually a positive number greater than 1, although it can be any positive number, including fractions and decimals.
Given by the question:
Assuming that the number of infected trees follows an exponential growth pattern, we can use the following equation:
[tex]y = a * e^{bx}[/tex]
where y is the number of infected trees at a given time, x is the time elapsed, a is the initial number of infected trees, and b is the rate of growth.
To find the values of a and b that best fit the data, we can use regression analysis techniques. We would need to input the data into a statistical software program, such as R or Excel, and run a regression analysis to estimate the values of a and b.
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What is the value of the function at x = -2?
Answer:
f(-2) = 2
Step-by-step explanation:
Value of the function at x = -2.
Go to x=-2 and then read what the y value is at x=-2
y = 2 at x = -2.
f(-2) = 2
for
6. Tami multiplies two fractions. The first fraction is greater than -1 but less than 0. The
notei
second fraction is greater than 0 but less than 1.
Which statement describes the product of the two fractions Tami multiplied?
The product of the two fractions Tami multiplied will be a negative number between 0 and -1.
How to find the product of the multiplicationSince the first fraction is negative greater than -1 but less than 0
and the second fraction is positive, greater than 0 but less than 1, their product will be negative.
This is because when a negative number multiplies a positive number the product is a negative number
Moreover, since both numbers are in fraction and less than whole their multiplication will also be a reduction tending towards zero
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Does Stephanie have enough to cover the property damages
Since Stephanie carries a 100/300/100 liability policy, Stephanie's insurance can cover up to $100,000, therefore Stephanie have enough coverage to cover the property damages.
What is Property Damage?Property damage is any harm or destruction to real or tangible personal property that is brought on by carelessness, intentional obliteration, or a natural disaster.
A more serious form of property damage known as destruction of property involves physical harm to items that are either beyond repair or would be very expensive to replace.
We see that Stephanie has an insurance policy and because she has a 100/300/100 liability policy, she can cover for the damage because it is less than $100,000
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PLEASE ANSWER ASAP!!!!
Sorry about the random numbers throughout the text. I had to censor some words due to brainly being scared of Macbeth.
Read the excerpt from act 1, scene 7 of The Tragedy of Macbeth.
Macbeth. He’s here in double trust:
First, as I am his k1nsman and his subject,
Strong both against the deed; then, as his host,
Who should against his murd3r3r shut the door,
Not bear the kn1fe myself. Besides, this Duncan
Hath borne his faculties so meek, hath been
So clear in his great office, that his virtues
Will plead like angels trumpet-t0ngu’d against
The deep d4mnation of his taking-off;
And p1ty, like a nak3d new-born babe,
Striding the blast, or heaven’s cherubin, hors’d
Upon the sightless couriers of the air,
Shall blow the horr1d deed in every eye,
That tears shall drown the wind. I have no spur
To pr1ck the sides of my intent, but only
Vaulting ambition, which o’er-leaps itself
And falls on the other.
Which statement best describes why Macbeth’s use of both logic and emotion is appropriate in this scene?
A. The use of logic causes Macbeth to envision himself as king, and the use of emotion leads him to think about those who would mourn Duncan’s death.
B. The use of logic causes Macbeth to reconsider his thoughts of killing the king, and the use of emotion leads him to question his motives.
C. The use of logic causes Macbeth to reevaluate Duncan’s capable leadership, and the use of emotion leads him to realize that his plan is justified.
D. The use of logic causes Macbeth to ponder the consequences of murder, and the use of emotion leads him to recommit to the promise he made to his wife.
The correct answer is: The use of logic causes Macbeth to ponder the consequences of murder, and the use of emotion leads him to recommit to the promise he made to his wife.
What is probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a numerical measure of the uncertainty of an event, represented as a fraction, decimal, or percentage between 0 and 1. An event with a probability of 0 means that it is impossible for the event to occur, while an event with a probability of 1 means that it is certain to occur. In probability theory, events can be independent or dependent. Independent events have no effect on each other, so their probabilities are multiplied to find the probability of both events happening. Dependent events are those in which the outcome of one event affects the outcome of another event, so their probabilities must be multiplied differently to find the probability of both events happening.
Here,
The use of both logic and emotion in this scene highlights Macbeth's internal conflict and the struggle between his moral and immoral desires.
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Two buses are traveling towards each other, planning to meet in the middle. The first bus travels at 30 mph for 2 hours, then the second bus starts moving at 50 mph. How many hours after the first bus' departure do the buses meet up with one another?
Answer:
21
Step-by-step explanation:
The buses meet up with one another 2 hours after the first bus's departure.
The first bus travels at 30 mph for 2 hours, so it travels a distance of 30 * 2 = 60 miles.
The second bus starts moving at 50 mph, so it travels at a relative speed of 50 + 30 = 80 mph.
Let x be the number of hours after the first bus's departure that the buses meet up.
The total distance traveled by the two buses is 60 + 80x.
Since the distance traveled by the two buses is equal, we have 60 + 80x = 60 + 80x.
Solving for x, we get x = 2 hours.
Here is the solution in steps:
The first bus travels at 30 mph for 2 hours, so it travels a distance of 30 * 2 = 60 miles.
The second bus starts moving at 50 mph, so it travels at a relative speed of 50 + 30 = 80 mph.
Let x be the number of hours after the first bus's departure that the buses meet up.
The total distance traveled by the two buses is 60 + 80x.
Since the distance traveled by the two buses is equal, we have 60 + 80x = 60 + 80x.
Solving for x, we get x = 2 hours.
Therefore, the buses meet up with one another 2 hours after the first bus's departure.
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when two or more objective function coefficients are changed simultaneously, further analysis is necessary to determine whether the optimal solution will change.
The domain of the function f(x)= -long(5-x)+b is all real numbers except for x = 5.
What is function?Function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.
The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.
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The complete question is: Will changing two or more objective function coefficients simultaneously affect the optimal solution?
Suppose you surveyed 30 people and asked them whether they are white (W) white (N), and how many traumas (serious accidents, rapes, or crimes) they have enced in the past year. You also asked them to tell you whether they perceive theme as being in the upper, middle, working, or lower class. Your survey resulted in the data presented in the table below: a. Identify the level of measurement for each variable. b. Construct raw frequency tables for race. c. What proportion of the 30 individuals is nonwhite? What percentage is white?
a. The level of measurement for each variable are Race: Nominal, trauma: Ratio, Social Class: Ordinal.
b. Raw frequency tables for race:
Race Frequency
W 21
N 9
c. The proportion of the 30 individuals who are nonwhite is: 9/30 = 0.3
So, 30% of the individuals are nonwhite.
The percentage of individuals who are white is: 21/30 x 100% = 70%
So, 70% of the individuals are white.
Race is a nominal variable because it is a categorical variable that does not have any inherent order or ranking. The two categories are "W" for white and "N" for nonwhite.
Trauma is a ratio variable because it is a quantitative variable that has a meaningful zero point. This means that a value of zero indicates the absence of the thing being measured, and values greater than zero indicate a greater quantity of the thing being measured.
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Factor 2x^3+3x^2+8x+12
Fill in answer
(2x+_) (x^2+_)
(2x+3) (x+2) (x−2) thats the answer
Figure order is a rectangle what are the coordinates of point Q
The coordinates of point Q in the rectangle named QRST is (5, 5).
What are Coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given:
We have the Graph having coordinate T(5, 2).
and, length of QT = 3 unit
As, the vertical distance shows the y coordinate then the y coordinate of Q is 3.
and, the x coordinate is same as T.
Then, the Coordinate of Q is (5, 2+3) or (5, 5).
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Re-write the quadratic function below in Standard Form y = 4(x−7)(x+3)
plsssssssss help
The quadratic function y = 4(x−7)(x+3) is re-written in standard form as
4x²- 16x - 84 = 0
How to write the standard formThe general formula for a quadratic function is expressed as;
ax² + bx + c = 0
From the information given, we have;
y = 4(x−7)(x+3)
expand the bracket, we get;
(x−7)(x+3)
x²+ 3x - 7x - 21
add or subtract the like terms
x² - 4x - 21
Multiply by 4, we have;
4(x² - 4x - 21)
4x²- 16x - 84 = 0
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a water cooler contains 5 gallons of water there are 24 students who drink one cup each from The Jug how many pints of water are left in the cooler
The number of pints of water left in the cooler will be 28 pints
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A water cooler contains 5 gallons of water there are 24 students who drink one cup each from the Jug.
In 5 gallons of water, there are 40 pints of water. And in 1 cup of water, there are 0.50 pints.
Then the number of pints of water left in the cooler is given as,
⇒ 40 - 24 x 0.5
⇒ 40 - 12
⇒ 28 pints
The number of pints of water left in the cooler will be 28 pints
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Use the given points to write a system of two linear equations with the two unknowns being the slope and y-intercept of the line. Solve the system to identify those parameters and write the equation for the line passing through the two points in slope-intercept form.
(2, 5) and (6, 2)
(-1, 3) and (0, -2)
(-2, -4) and (2, 1)
The equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
(2, 5) and (6, 2):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (2 - 5) / (6 - 2)
= -3/4
We may write the following using the equation of a line in the point-slope form:
y - y1 = m(x - x1)
Choosing point (2, 5) as (x1, y1), we get:
y - 5 = (-3/4)(x - 2)
Simplifying this equation, we get:
y = (-3/4)x + 11/2
So the equation of the line passing through (2, 5) and (6, 2) in slope-intercept form is y = (-3/4)x + 11/2.
(-1, 3) and (0, -2):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (-2 - 3) / (0 - (-1))= -5
We may write the following using the equation of a line in the point-slope form:
y - y1 = m(x - x1)
Choosing point (-1, 3) as (x1, y1), we get:
y - 3 = (-5)(x + 1)
Simplifying this equation, we get:
y = -5x - 2
So the equation of the line passing through (-1, 3) and (0, -2) in slope-intercept form is y = -5x - 2.
(-2, -4) and (2, 1):
The two points are connected by a line that has the following slope:
m = (y2 - y1) / (x2 - x1)
= (1 - (-4)) / (2 - (-2))
= 5/4
We may write the following using the equation of a line in the point-form:slope
y - y1 = m(x - x1)
Choosing point (-2, -4) as (x1, y1), we get:
y + 4 = (5/4)(x + 2)
Simplifying this equation, we get:
y = (5/4)x - 9/4
So the equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.
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Assume that the conditions for bucket sort are satisfied. the probability that a particular bucket contains more than 5 is at most 1/16.a. Trueb. False
The statement can be true under certain conditions. The probability that a particular bucket contains more than 5 elements will depend on the size of the bucket and the distribution of the elements.
However, if we assume that the distribution is uniform and the number of elements is much larger than the number of buckets, we can estimate the probability using the following formula:
P(bucket > 5) = 1 - P(bucket <= 5) = 1 - (5/n)
Where n is the number of elements to be sorted, and 5 is the maximum number of elements that can fit in a bucket. If we assume that there are 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16 if:
1 - (5/n) <= 1/16
Solving for n, we get:
n >= 80
This means that if we have at least 80 elements to be sorted, and we distribute them uniformly among 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16. Therefore, the statement can be true under certain conditions.
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In 2020, of a random sample of votes cast, 12 out of 25 were cast for Candidate A and 23 out of 50 were cast for Candidate B.
What fraction of ballots were cast for someone other than
Candidate A or Candidate B?
The fraction of ballots that were cast for someone other than Candidate A or Candidate B is given by the equation q = 3/50
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the fraction of ballots that were cast for someone other than Candidate A or Candidate B be represented as q
Now , the equation will be
The fraction of ballots cast for Candidate A = 12/25 = 24/50
The fraction of ballots cast for Candidate B = 23/50
So , the total fraction of ballots casts for Candidate A and Candidate B = fraction of ballots cast for Candidate A + fraction of ballots cast for Candidate B
Substituting the values in the equation , we get
The total fraction of ballots casts for Candidate A and Candidate B is given by p = ( 24 + 23 ) / 50
p = 47/50
Now , fraction of ballots that were cast for someone other than Candidate A or Candidate B = 1 - p
The value of q = 1 - p
q = 1 - ( 47/50 )
q = 3/50
Hence , the fraction is 3/50
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Packages of 500 sheets of printer paper 216 mm × 279 mm × 45 mm are available
packaged in cases 216 mm × 279 mm × 270 mm. Jacinta needs to order 7,000
sheets for a small office but can only order full cases. How many cases should they
order, and why?
To determine how many cases of printer paper Jacinta should order, we first need to calculate the number of sheets in one case:
The volume of one ream of paper is: (0.216 m) x (0.279 m) x (0.045 m) = 0.00239 cubic meters
Since there are 500 sheets in a ream, the volume of one sheet of paper is 0.00239 / 500 = 4.78 x 10^-6 cubic meters
The volume of one case is: (0.216 m) x (0.279 m) x (0.27 m) = 0.0161 cubic meters
The number of sheets in one case is therefore: 0.0161 / 4.78 x 10^-6 = 3360 sheets
Since Jacinta needs 7,000 sheets and can only order full cases, she will need to order at least 2 cases:
2 cases would contain 2 x 3360 = 6720 sheets, which is more than Jacinta needs
1 case would only contain 3360 sheets, which is not enough for Jacinta's needs
Therefore, Jacinta should order 2 cases of printer paper.
Find the surface area of the composite figure.
5 cm
4 cm
4 cm
Hint: Area of a
Triangle = b.h
SA = [?] cm²
4 cm
If you'd like
The surface area of the figure is 56 square units
What is the surface area of the figure?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Net of right rectangular pyramid
The surface area of the figure is calculated as
Area = sum of individual areas
Using the above as a guide, we have the following:
Area = 4 * 4 + 4 * 1/2 * 4 * 5
Evaluate the expression
Area = 56
Hence, the area is 56 square units
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From Laura's results, what is the probability of rolling an even number
The probability of rolling an even number based on Laura's results is 40%.
We can tell from Laura's outcomes that she rolled the die 10 times and recorded the results. There are 4 even outcomes (numbers 2, 4, 6, and 8) and 6 odd results out of a possible 10 results (1, 3, 5, 7, 9, and 10).
We must divide the number of even possibilities by the total number of potential outcomes in order to calculate the chance of rolling an even number. Given that there are four even outcomes out of a possible ten, the likelihood of rolling an even number is as follows:
probability of rolling an even number = number of even outcomes / total number of outcomes
probability of rolling an even number = 4/10
probability of rolling an even number = 2/5
When rolling an even number, the probability = 0.4.
probability of rolling an even number = 40%
As a result, 40% of the time, depending on Laura's results, an even number will be rolled.
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suppose we roll two six-sided dice. consider event a as getting an odd number on die 1, event b as getting an even sum for the two dice. are event a and b independent?
The events A and B are dependent. P(A and B) is not equal to 1/4, as it is less than that.
The probability of getting an odd number on the first die is 3/6 = 1/2.The probability of getting an even sum is 18/36 = 1/2.The probability of getting an odd number on the first die and an even sum is 9/36 = 1/4.If A and B were independent, we would expect P(A and B) = P(A)P(B) = 1/2 * 1/2 = 1/4. However, P(A and B) is not equal to 1/4, as it is less than that. Therefore, A and B are dependent events.
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In a very large population, a quantitative trait has the following distribution pattern. If there is no gene flow, the curve shifts to the left or to the right, and the population size consequently increases over successive generations, which of the following is most likely occurring?
The distribution of a quantitative trait in a population can have important implications for the size and composition of the population over time.
Quantitative traits are characteristics that can be measured and quantified, such as height or weight. These traits often have a normal distribution pattern in large populations, meaning that most individuals fall within a certain range and there are fewer individuals at the extremes.
The normal distribution of a quantitative trait is often represented by a bell curve. This curve shows the frequency of individuals at different values of the trait, with the majority of individuals falling near the middle of the curve and fewer individuals at the extremes. The mean, or average, of the trait is located at the peak of the curve, and the standard deviation determines the width of the curve.
If the distribution shifts to the left, this means that there are fewer individuals with high values of the trait and more individuals with low values. This could occur if there is selective pressure against individuals with high values, or if there is a genetic mutation that affects the trait in a negative way.
As a result, the population size may increase, as individuals with low values of the trait are more likely to survive and reproduce.
Conversely, if the distribution shifts to the right, this means that there are fewer individuals with low values of the trait and more individuals with high values.
This could occur if there is selective pressure in favor of individuals with high values, or if there is a genetic mutation that affects the trait in a positive way.
As a result, the population size may also increase, as individuals with high values of the trait are more likely to survive and reproduce.
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What's the possible values of z when t = 81
( be it real or complex number )
[tex] {z}^{2} = \sqrt{t} [/tex]
So annoying ~
Answer:
[tex]\boxed{\mathrm{z=\pm 3}}[/tex]Step-by-step explanation:
[tex]\mathrm{z^2=\sqrt{t}, \; when, \; t=81}[/tex]
Substitute t with 81:-
[tex]\mathrm{z^2=\sqrt{81}}[/tex]
Since 9*9 =81, square of 81 is 9:-
[tex]\mathrm{z^2=9}[/tex]
Take the square root of both sides.
[tex]\mathrm{z=\pm \sqrt{9} }[/tex]
and since 3*3 = 9 the square root of 9 will be 3.:-
[tex]\mathrm{z=\pm 3}[/tex]
_____________________
Hope this helps!
Locate and classify all the critical points of the function. (Order your answers by their ordered pairs, from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) t(x, y) = x^3 − 12xy + y^3
The critical points of the function t(x,y) are:
(0,0)
(4,16)
To find the critical points of the function t(x,y), we need to find the points where the gradient is equal to zero or undefined.
Let's begin by computing the partial derivatives of t(x,y):
t_x = 3x^2 - 12y
t_y = 3y^2 - 12x
Now, we can set these partial derivatives equal to zero and solve for x and y:
3x^2 - 12y = 0
3y^2 - 12x = 0
Simplifying these equations, we get:
x^2 - 4y = 0
y^2 - 4x = 0
Multiplying the first equation by 4x and the second equation by 4y, we get:
4x^3 - 16xy = 0
4y^3 - 16xy = 0
Adding these equations together, we obtain:
4x^3 + 4y^3 - 32xy = 0
Dividing by 4, we get:
x^3 + y^3 - 8xy = 0
This is the equation of a curve known as the "folium of Descartes". It has a cusp at the origin and two other branches that intersect the x-axis and y-axis, respectively.
To find the critical points, we need to solve the system of equations:
x^2 - 4y = 0
y^2 - 4x = 0
x^3 + y^3 - 8xy = 0
From the first equation, we get:
x^2 = 4y
Substituting this into the second equation, we get:
y^2 - 16y = 0
This gives us two possible values for y: y = 0 or y = 16.
If y = 0, then x = 0 from the first equation. Substituting into the third equation, we get:
x^3 = 0
So the critical point is (0,0).
If y = 16, then x = 4 from the first equation. Substituting into the third equation, we get:
64 + 16^3 - 8(4)(16) = 0
Simplifying, we get:
64 + 4096 - 512 = 3648
So the critical point is (4,16).
We can classify these critical points by computing the Hessian matrix of t(x,y) and evaluating it at each critical point:
H = [t_xx t_xy]
[t_xy t_yy]
where t_xx, t_xy, and t_yy are the second partial derivatives of t(x,y).
At (0,0), we have:
t_xx = 6x = 0
t_xy = -12
t_yy = 6y = 0
So the Hessian matrix is:
H = [-12 0]
[ 0 -12]
The determinant of H is 144, which is positive, and the trace of H is -24, which is negative. Therefore, the critical point (0,0) is a saddle point.
At (4,16), we have:
t_xx = 6x = 24
t_xy = -12
t_yy = 6y = 96
So the Hessian matrix is:
H = [ 24 -12]
[-12 96]
The determinant of H is 2112, which is positive.
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Julia is using this figure to prove that triangle ABC is an isosceles triangle. First, she used the converse of the perpendicular bisector theorem and the definition of perpendicular lines to determine that CE is the perpendicular bisector of AB.
A horizontal line A B, and a vertical line C D are intersecting at point E. The points A B C form an isosceles triangle.
What could be the next step of a valid proof?
A.
AC = BC because of the perpendicular bisector theorem
B.
CE = BC because of the perpendicular bisector theorem
C.
CE = AB because of the perpendicular bisector theorem
D.
AE = CE because of the perpendicular bisector theorem
Answer:
A. AC = BC because of the perpendicular bisector theorem
Step-by-step explanation:
You want the next step in the proof that ∆ABC is isosceles.
ChoicesThe correct answer choice is the only one that is a true statement:
A. AC = BC because of the perpendicular bisector theorem
__
Additional comment
We're not clear on how this proof starts, because the converse of the perpendicular bisector theorem tells you that CD is a perpendicular bisector of AB if and only if every point on CD is equidistant from A and B. That is, you have to assume that ABC is isosceles before the converse of the perpendicular bisector theorem can apply.
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describe two ways to graph the equation 4x - 6y = 18
Answer:
Using the slope-intercept form, the y-intercept is −3 .
Evaluate 2x + 3y if x =2 and y = 8
What’s 10 more than triple P
The value of mathematical expression is,
⇒ 10 + 3P
What is Mathematical expression?Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 10 more than triple P.
Now, We can simplify mathematical expression as;
Triple P = 3P
Hence, We get the expression as;
⇒ 10 more than triple P.
⇒ 10 + 3 × P
⇒ 10 + 3P
Therefore, We get;
The value of mathematical expression is,
⇒ 10 + 3P
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