The relation R defined on C is not a partial order, as it fails to satisfy reflexivity, antisymmetry, and the Comparability property
To determine whether the relation R defined on the complex numbers C is a partial order, we need to verify three properties: reflexivity, antisymmetry, and transitivity.
Reflexivity: For any complex number z = a + bi, is z R z?
To satisfy reflexivity, we need to check if a² + b² < a² + b² holds true for all complex numbers. Since a² + b² is always equal to a² + b², the condition a² + b² < a² + b² is never satisfied. Therefore, R is not reflexive.
Antisymmetry: For any complex numbers z1 = a1 + b1i and z2 = a2 + b2i, if z1 R z2 and z2 R z1, does it imply that z1 = z2?
To satisfy antisymmetry, we need to show that if a1² + b1² < a2² + b2² and a2² + b2² < a1² + b1², then a1 = a2 and b1 = b2. However, this is not necessarily true, as there can be distinct complex numbers with different values of a and b but with the same magnitude. Therefore, R is not antisymmetric.
Since R fails to satisfy both reflexivity and antisymmetry, it cannot be a partial order for C.
Regarding the comparability property, a partial order requires that any two elements can be compared with each other. In the case of R, the relation is based on the magnitudes of the complex numbers, and it is possible for two complex numbers to have different magnitudes and not be comparable. For example, if we take z1 = 2 and z2 = 3i, both have non-zero magnitudes, but comparing their magnitudes does not establish a clear ordering. Therefore, R does not have the comparability property.
In conclusion, the relation R defined on C is not a partial order, as it fails to satisfy reflexivity, antisymmetry, and the comparability property
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Without loss of generality, we can assume that a1² + b1² > a2² + b2². If we choose c = a1 and d = b1, then we have z1 R z2. On the other hand, if we choose c = a2 and d = b2, then we have z2 R z1. Therefore, R has the comparability property.
To determine if R is a partial order for C, we need to check if it satisfies the following properties:
Reflexivity: For any complex number z = a + bi, we have a² + b² < a² + b², which is false. Therefore, R is not reflexive.
Antisymmetry: Suppose (a + bi) R (c + di) and (c + di) R (a + bi). Then we have a² + b² < c² + d² and c² + d² < a² + b², which implies a² + b² = c² + d². Since the squares of the magnitudes of two complex numbers are equal if and only if the two complex numbers are equal, we have a + bi = c + di. Therefore, R is antisymmetric.
Transitivity: Suppose (a + bi) R (c + di) and (c + di) R (e + fi). Then we have a² + b² < c² + d² and c² + d² < e² + f². Adding these two inequalities, we get a² + b² < e² + f², which implies (a + bi) R (e + fi). Therefore, R is transitive.
Since R is not reflexive, it is not a partial order for C.
To determine if R has the comparability property, we need to check if for any two distinct complex numbers z1 = a1 + b1i and z2 = a2 + b2i, either z1 R z2 or z2 R z1.
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he system of equations shown is solved using the linear combination method
StartLayout 1st row 1st column 6 x minus 5 y = negative 8 right-arrow 2nd column 6 x minus 5 y = negative 8 right-arrow 6x minus 5 y = negative 8 2nd row 1st column negative 24 x + 20 y = 32 right-arrow one-fourth (negative 24 x + 20 y = 32) right-arrow negative 6 x + 5 y = 8 with Bar Underscript 3rd row 3rd column 0 = 0 EndLayout
What does 0 = 0 mean regarding the solution to the system?
The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient.
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
here, we have,
In this case, the system of equations is given as
6x - 5y = -8
6x - 5y = -8
Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8
6x - 5y = -8
(-) 6x - 5y = -8
----------------------
0 = 0
This in other words means that the difference between both equations is 0.
When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions.
Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.
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1) Find the Z-score for the data point X given mean μ and
standard deviation o. Round to two decimal places as needed
x=72
μ=63
0=3
The z score when x=72 , μ=63 , 0=3 is z=3
Why is z-score important?Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.
What is the z-score formula used for?Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.
According to the equation
z=x-u/sigma
we get z=3
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John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles. He reaches home 2 hours later and notes that he has traveled 30 miles. If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
The correct equation for this given situation is,
⇒ d = 9.5t + 11
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles.
And, He reaches home 2 hours later and notes that he has traveled 30 miles.
Now, Let d represents the distance and t represents the time, in hours
So we get;
Let the equation which model this situation,
⇒ d = a t + b
Where a and b are constant.
Let the gas station is the starting point.
So, at gas station t = 0 , d = 11
Hence,
⇒ 11 = 0 × a + b
⇒ b = 11
When he reaches home 2 hours later notes that he has traveled 30 miles.
And, with substituting with b = 20
⇒ 30 = 2 × a + 11
⇒2a = 30 - 11 = 19
⇒ a = 19/2 = 9.5
So, We get the equation,
⇒ d = 9.5t + 11
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An arithmetic sequence begins with 25, 31, 37, 43, 4
Which option below represents the formula for the sequence?
f(n) = 25 + 6(n)
f(n) = 25 + 6(n + 1)
f(n) = 25 + 6(n − 1)
f(n) = 25 + 6(n + 1)
The arithmetic sequence function is c)f(n)=25 + 6(n-1).
What is arithmetic sequence?
An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.
Here the given series 25,31,37,43,...
First term [tex]a_1[/tex]= 25
Now Common difference d = [tex]a_2-a_1[/tex]=31-25 = 6.
Now using arithmetic sequence formula,
[tex]f(n)=a_1+(n-1)d[/tex]
Here putting indicated value [tex]a_1[/tex]= 25 and d=6
=> f(n) = 25 + (n-1)6
=> f(n) = 25 + 6 (n-1)
Hence the correct option is c)f(n)=25 + 6(n-1).
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Answer:
C. f(n)=25 + 6(n-1).
Step-by-step explanation:
got it right on test
A right triangle is shown in the graph.
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (f, g) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (f, g) = (3, –1) and h = 8, determine the domain and range of the circle. (4 points)
Part C: Is the point (10, –4) inside the border of the circle if (f, g) = (3, –1) and h = 8? Explain using mathematical evidence. (3 points)
A) The standard equation of the circle, with center at (f, g) and a point on the circle at (x, y) is; (x - f)² + (y - g)² = h²
B) The domain and range of the circle are respectively;
[-5, 11] and [-9, 7]
C) Yes the point (10, –4) is inside the border of the circle
How to find the domain and range of a circle?A) Using the Pythagorean theorem will generate the equation for a circle as follows;
Sum of squares of sides = square of hypotenuse
From the given image, we have;
(x - f)² + (y - g)² = h² . . . . . . circle centered on (f, g) with radius h
B) The circle is defined for values of x in the domain f ± h, and for values of y in the range g ± h.
Domain: 3 ± 8 = [-5, 11]
Range: -1 ± 8 = [-9, 7]
C) The distance from point (10, -4) to (f, g) calculated as;
h² = (10 - 3)² + (-4 - (-1))²
h² = 7² + (-3)²
h² = 49 + 9 = 58
h = √58 < 8
Thus, the distance to the point is less than h=8 and it implies that the point is inside the circle.
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A study finds that out of every 400 babies born in the world, 20 have some kind of major birth defect. What is the simplest way to assign random numbers to conduct a simulation based on this statistic?
Select the correct choice below and fill in the answer boxes to complete your choice.
Fill in the question mark for the answer you choose
A. Use 1 digit numbers 0-9, let 0- ? Represent babies born with birth defects and #?-? Represent babies born without a major defect
B. Use 1 digit numbers 0-9, let 0- ? Represent babies born with birth defects, #?-? Represent babies born without a major defect, and skip #?-9.
C. Use 2 digit numbers 00-99, let 00-?? represent babies born with birth defects and #??-?? Represent babies born without a major defect.
D. Use 2 digit numbers 00-99, let 00-?? represent babies born with birth defects, #??-?? Represent babies born without a major defect, and skip #??-99
This is equal to 0.04 plus 1.96 into root over 0.04 into 0.96 divided by 400 point. This is equal to 0.059, which is equal to 5.9 percent. Therefore, double 0 to 5.9 percent represent babies born with defect.
What is the Justification for the above?According to one research, 28 out of every 400 kids born in the globe suffer some form of serious birth problem. To execute a simulation based on this data, the easiest approach to assign random numbers is to use 00-06 (7%) to identify the newborns with birth abnormalities.
It is to be noted that:
The sum total of births is: 400
The sum of defective babies = 28
Hence, the fraction or ratio of this is:
28/400
= 7/100
= 7%.
The implication here is that that 07-99 (93%) will represent the babies without birth defects.
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answer?????????????????
Marhall and Vickie are alepeople who earned the ame amount thi week, although Vickie made 6 more ale than Marhall. Marhall earn a bae of $186 plu $15 per ale. Vickie earn a bae of $48 plu $18 per ale. How many ale did Marhall make thi week?
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale. Since both of them earned the same amount, we can set up the equations
Marhall made 9 ales this week.
Step by explanation
We can use an equation to solve this problem.
Let x = number of ales Marhall made
Marhall's Earnings = 186 + (15 x)
Vickie's Earnings = 48 + (18 x)
Since both of them earned the same amount, we can set up the equations and solve for x:
186 + (15 x) = 48 + (18 x)
15x = 138
x = 9
Therefore, Marhall made 9 ales this week.
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale.
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What is inequality Class 6 short answer?
Inequality is a situation in which people do not have the same rights, resources, or opportunities. It can be seen in many aspects of society, including income, education, health care, and access to resources.
InequalityInequality affects people in many different ways. It can limit access to education and employment opportunities, as well as health care, good housing, and basic services.
It can also lead to disparities in income and wealth, which can further limit opportunities for those in disadvantaged social classes. Inequality can have a negative impact on individuals, as it can limit their ability to access resources needed for a better life.
It can also lead to social unrest, as people may feel that they are not being treated fairly. Inequality can also lead to a lack of trust in government and institutions, which can further hinder progress and development. In order to reduce inequality, governments, businesses, and individuals must work together to create a more equitable society.
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What are examples of inequalities?
Examples of inequalities are mathematical statements that compare two expressions and express the relationship between them using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to). Here are a few examples: x + 2 > 5, |x - 2| < 4, sin(x) > 1/2, log2(x) > 3.
Linear Inequality: x + 2 > 5, this inequality states that x is greater than 3.
Quadratic Inequality: x^2 - 3x + 2 < 0, this inequality states that the value of the quadratic expression is less than zero.
Absolute value inequality: |x - 2| < 4, this inequality states that the absolute value of the difference between x and 2 is less than 4.
Rational Inequality: (x + 2)/(x - 3) < 0, this inequality states that the value of the rational function is less than zero.
Logarithmic Inequality: log2(x) > 3, this inequality states that the logarithm base 2 of x is greater than 3.
Trigonometric Inequality: sin(x) > 1/2, this inequality states that the sine of x is greater than 1/2.
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Write down the equation of the function whose graph is shown
To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.
Linear equations with two variables have straight line graphs. There are numerous ways to express linear equations:
Slope-Intercept Formula: y=mx+b
The slope is m and the y-intercept is the point in an equation of the type y = mx + b, such as y = 2x 3. (0, b). Create a table of values (Method 1) or use the slope and y-intercept (Method 3) to graph equations of this kind (see Examples 1 and 6).
Basic Formula: axe + by = c
Find the x- and y-intercepts (Method 2) to graph equations of this type, such as 3x 2y = 6, or solve the equation for y to form y = mx + b and create a table of numbers (see Example 2).
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What is the value of exponential 4?
The value of exponential 4 is 4^4, or 256. it means that 4 should be multiplied by itself 4 times.
In mathematics, an exponential is a number that is multiplied by itself a certain number of times. For example, when 4 is used as an exponential, it means that 4 should be multiplied by itself 4 times. This is written as 4^4, or 4 to the fourth power. This means that 4 is multiplied by itself 4 times, resulting in the value of 256.
Exponentials can be used to calculate the power of a number. For example, in the case of 4^4, 4 is the base number and 4 is the exponent. An exponent is the number of times a base number is multiplied by itself. In this case, the base number (4) is being multiplied by itself 4 times, resulting in a value of 256.
In addition, exponentials can be used to solve equations. For example, if we need to solve for x in the equation 4^x = 256, we can use the exponential 4 to determine the value of x. In this case, x = 4 because 4^4 = 256.
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Bonnie spent a total of $77.77 on new clothes at a clothing store. She Brought 1 pair of sandals, 2 T-Shirts for 11.49 each, 1 pair for $32 The Tax on the purchase was 4.40. How Much did Bonnie pay for the pair of sandals
The total cost of a pair of sandals is given by the equation A = $ 18.39
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of pair of sandals be represented as A
Now , the equation will be
The total amount spent by Bonnie = $ 77.77
The cost of one shirt = $ 11.49
So , the cost of 2 shirts = 2 x 11.49 = $ 22.98
And , the cost of 1 pair = $ 32
The total tax on the purchase = $ 4.40
So , the cost of pair of sandals A = total amount spent by Bonnie - cost of 2 shirts - cost of 1 pair - total tax on the purchase
Substituting the values in the equation , we get
The cost of pair of sandals A = 77.77 - 22.98 - 32 - 4.40
On simplifying the equation , we get
The cost of pair of sandals A = $ 18.39
Hence , the total cost of sandals is $ 18.39
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Solve for X. M<1= (x+13)
M<2=39
M<3=(5x+4)
On solving the provided question, we can say that using properties of triangle, the value of x is 7.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
By using the property of triangle,
The exterior angle of the triangle is the sum of opposite two angle of the triangle.
Hence,
64 + 8x = 18x - 6
10x = 70
x = 7
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What is the length of the hypotenuse of a 45 45 90 triangle?
In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg.
How to find the length of the hypotenuse of a 45 45 90 triangle?Since the triangle's legs are equal, the hypotenuse may be determined using the equation c = a2/. The side length will be equal to a = c2/2 if the value of the hypotenuse is provided. When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. The Pythagorean theorem can frequently be used to locate the missing legs or hypotenuse of 45 45 90 triangles. The sides' to the hypotenuse's ratio.To learn more about hypotenuse refer to:
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Does anyone know how to find this out?? Thank you so much!
The solution set is (A) TV/RS = TQ/ RQ.
What is the similarity of the triangle?
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.
We have given,
Triangle QRS and triangle QTV are similar,
ΔQRS ≈ ΔQTV
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.
so, TV/RS = TQ/ RQ
Therefore, The solution set is (A) TV/RS = TQ/ RQ.
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2 1/3 divided by 1/3
Answer:
Step-by-step explanation:
and 2.3333333333
The top pair of scales are balanced. How many triangles replace the question mark on the bottom scales to make them balance? ?
Answer: 5 triangles
Step-by-step explanation:
we can take the circles out of the top scale and see that 2 triangles equal a square, so we see 2 squares on the bottom so that is 4 triangles plus one extra
How is negative of an image obtained with intensity levels 0 l 1 with r and s being pixel values?
Negative of an image can be obtained by subtracting each pixel values from 1.
What is pixel value?Pixel value is the numerical representation of a color in an image. It is the amount of brightness or darkness of a pixel in an image, usually ranging from 0 (black) to 255 (white). Pixel values are used to determine how an image should be displayed on a monitor or printed on a page.It is usually measure of brightness of pixel with the higher number indicating brighter pixel and lower number indicating darker pixel.
This can be done by subtracting the pixel values r and s from 1, so the new value of each pixel would be 1-r and 1-s. This process of subtracting each pixel value from 1 is known as “inverting”.
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A rockinghorse has a weight limit of 60 pounds what is 95% of that
Answer: 57
Step-by-step explanation:
1. Multiply 95 and 60
2. You get 5700, then you divide by 100
3. 5700/100 = 57
Add the following integer. 1. (-78)(98)=
2. (45)(23)=
3. (67)(56)=
4. (98)(-73)=
5. (-971)(237)=
On adding the integers we get:
206812325-734The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
For, (-78) + (98)
Step 1: Locate the first number, which is -78.
Step 2: Locate the second number, which is 98.
Step 3: Add the two numbers together by starting with the first number and counting up or down according to the sign of the second number. In this case, 98 is positive, so we count up 98 from -78.
Step 4: The answer is 20
Similarly, solving for the rest of the sub-parts we get:
2. 45+23=68
3. 67+56=123
4. 98 + (-73)=25
5. -971+237= -734
Therefore, On adding the integers we get:
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Use the conversions given below to change 63 kg into stones.
Give your answer rounded to 1 dp.
1 kg = 2.2 pounds
1 stone = 14 pounds
Answer:
63kg x 2.2 = 138.6 pounds
138.6 pounds/14 = 9.9 stones
Step-by-step explanation:
Answer:
63kg×2.2=138.6 pounds
138.6 pounds/14=9.9
A rectangle has a width of x centimeters and a perimeter of 8x centimeters a square has sides of length 1/4 that of the length of the rectangle.
Find the perimeter of the square
The perimeter of the square is calculated to be (8 - x) cm
How to find the perimeter of the squareThe perimeter of a square is calculated using the formula
= 4 * length
From the problem we have that the length of the square
= 1/4 length of rectangle
perimeter of rectangle
8 = 2(Length + width)
dividing through by 2
4 = L + w
substituting w = x
8 = L + x
L = 8 - x
length of square = 1/4 * 8- x = (8 - x)/4
perimeter of a square = 4 * (8 - x)/4
perimeter of a square = 8 - x
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Why is the base in the exponential function greater than 1?
The base in the exponential function is greater than 1 because exponential growth is defined as a constant multiplication of the original value, rather than a constant addition as in linear growth. A base greater than 1 results in a growth rate that increases over time, while a base less than 1 results in a growth rate that decreases over time.
THE EXPONENTIAL FUNCTIONThe exponential function is written as bˣ, where b is the base and x is the exponent. The base is the number that is being multiplied by itself a certain number of times, as determined by the exponent.
A base greater than 1 means that the value of the function is increasing at an increasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a larger and larger result. This is known as exponential growth.
On the other hand, a base less than 1 means that the value of the function is decreasing at an decreasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a smaller and smaller result. This is known as exponential decay.
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Henrie play baeball. He hit 80% of the time he bat. If he i up to bat 20 time thi weekend at hi baeball tournament, how many time i he expected to hit
This may be computed by dividing his hitting % by the number of times he bats (20). (0.8). 20 x .8 = 16
Percentage:
a: a part of a whole expressed in hundredths a high percentage of students attended.
b: the result obtained by multiplying a number by a percent the percentage equals the rate times the base.
c: a share of winnings or profits.
If Henrie hits 80% of the time he's at bat, and he is up to bat 20 times this weekend, he is expected to hit 16 times. This can be calculated by multiplying the number of times he is up to bat (20) by his hitting percentage (0.8). 20 x .8 = 16
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Max spends three times as long on his math homework than he does on his science horr spent a total of 64 minutes on math and science homework last night, how long did he math homework?
Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.
What is Equation?Two or more expressions with an Equal sign is called as Equation
Given that,
The time spend on math homework = 3 times time spend on science homework,
Also, total time spent on math and science both homework = 64 minutes.
Let time spend by Max on science homework is t minutes,
Then by given condition, time spend on math homework = 3t
Total time = 64 minutes
t + 3t = 64 minutes
4t = 64 minutes
Divide both sides by t
t = 16 minutes
Hence, Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.
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A car is traveling at a rate of 40 mph. What is the speed in feet per min
Answer:3520.000
Step-by-step explanation:
ft/min =mph * 88.00000
ft/min =40 * 88.00000
ft/min =3520.000
-3(2x+2)<10 solve the inequality and graph the solution ?
Therefore , the solution of the given inequality problem comes out to be
-8/5.
What is a good example of inequality?The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. Finding the x variable values for which the inequality holds true is what we are most interested in.
Here,
Give:
=> -3(2x+2) < 10
=>2x+2>10/3
=>x+1>-10/6
=>> -10/6-1 >1
=> -8/5
Therefore , the solution of the given inequality problem comes out to be
-8/5..
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A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.4 ounces. For the questions that follow, suppose that the company is telling the truth. (a) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, do it. If not, explain why you cannot. (b) A quality control inspector measures the contents of an SRS of 50 cans of the company's soda and calculates the sample mean 7. Calculate the mean and standard deviation of the sampling distribution of x for samples of size n = 50. Interpret the standard deviation. (c) What is the shape of the distribution described in part (b)? Justify your answer. (d) The inspector in part (b) obtains a sample mean of x = 11.9 ounces. Calculate the probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less.
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a. We cannot calculate the probability, because we do not know the shape of the distribution.
b. The mean and standard deviation of the sampling distribution of x are 12 and 0.0566.
c. The shape of the distribution described in part b is symmetrical.
d. The probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less is 0.0386.
We do not know the shape of the distribution, so we cannot calculate the probability that a single randomly selected can contains 11.9 ounces or less. The question given have not told us that the distribution of individual cans was normal, and we cannot assume it is so; therefore, we cannot calculate its probability.
As given information the mean μx = 12.
And standard deviation σx = σ / √n = 0.4 / √50 = 0.566.
The shape of the distribution described in part b is symmetrical, because the two sides of the distribution are a mirror image of each other. Therefore, it is normal distribution.
Since the sample is large n = 50 and 50 > 30, so by CLT (Central Limit Theorem), the distribution of sample means is approximately normal N(12, 0.0566). So, P(x ≤ 11.9) = normalcdf (0, 11.9, 12, 0.0566) = 0.0386.
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Why is 45 a prime number?
No, the given statement 45 is a prime number is false statement as 45 represents the composite number.
As given in the question,
Given number is equal to :
45
Prime numbers represents such numbers which is having only two factors one and the given number itself.
Prime numbers does not get exactly divided by any other integer.
Factors of 45 are equals to :
1, 3, 5, 9, 15, 45
It represents 45 has more than two factors.
And number 45 exactly get divided by 3, 5, 9, 15 .
So it is not a prime number rather it represents the composite number.
Therefore, the given statement 45 is a prime number is false statement as 45 is a composite number.
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