By using the concept of complex number, it can be calculated that
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
What is a complex number?
Any number of the form a+ib where, a and b are real numbers and i = [tex]\sqrt{-1}[/tex] are called complex number.
Let z = x + iy
[tex]|z - 1|^2 = |z + 1|^2 = |z - i|^2[/tex]
[tex]|x + iy - 1|^2 = |x+iy + 1|^2 = |x+iy - i|^2\\(x-1)^2+y^2 = (x+1)^2+y^2 = x^2+(y -1)^2[/tex]
So the point (x, y) is equidistant from (1, 0), (-1, 0) and (0, 1)
(0, 0) is the only point which is equidistant from (1, 0), (-1, 0) and (0, 1)
z = 0 is the only complex number which satisfies |z – 1| = |z + 1| = |z – i|
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
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A line through (7, 1) and (4, 8) is parallel to the line through (2, x) and (x,-2). What is the value of x?
After solving the equation the value obtained for x will be equal to 5.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information in the question,
The equation of the line passing through the given coordinates will be,
m = (y2 - y1)/(x2 - x1)
The given points are (7, 1) and (4, 8)
Then,
(8 - 1)/(4 - 7) = -7/3
Slope of the line passing through the points (2, x) and (x, -2) then,
(-2 - x)/(x - 2)
Now, we have -7/3 = [tex]-\frac{2+x}{x-2}[/tex]
7x - 14 = 6 + 3x
4x = 20
x = 5
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a study of 26 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.87. a. state the decision rule for 0.025 significance level: h0: rho ≤ 0; h1: rho > 0. (round your answer to 3 decimal places.) b. compute the value of the test statistic. (round your answer to 3 decimal places.) c. can we conclude that the correlation in the population is greater than zero? use the 0.025 significance level.
The value of the test statistic using correlation coefficient and sample size is equal to 8.776 ( round up to 3 decimal places.)
As given in the question,
Sample size 'n' = 26
Correlation coefficient 'r' = 0.87
Significance level 'α' = 0.025
a. Decision rule for the system of hypothesis are:
Null hypothesis : H₀ : ρ ≤0
Alternative hypothesis: H₁ : ρ > 0
Value of the test statistic 't'
= r√n-2 / √1 - r²
= (0.87√ 26 - 2) / √1- 0.87²
= 4.3 / √0.2431
= 4.3 / 0.49
= 8.776
Therefore, value of the test statistic using the given values is equal to 8.776.
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Find the slope of table
Answer:
Slope is 4
Step-by-step explanation:
Easy! Just take the first four points on the table. So, (0,6) and (1,10). Then plug those points into y₂ - y₁ over x₂ - x₁ and you'll get your final answer.
Use a graphing calculator to graph y² = x-5 and x² + y² = 49 in the same viewing window. Use the intersect feature to find the coordinates of the intersections of the graphs. Round your answer to the nearest hundredth. Intersections points:
The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y² = x - 5 ...1
x² + y² = 49 ...2
From equations 1 and 2, then we have
x² + x - 5 = 49
x² + x - 54 = 0
Use the formula method to calculate the value of 'x'. Then we have
x = [- 1 ± √(1² - 4 · 1 · -54)] / 2
x = [- 1 ± √(1 + 216)] / 2
x = (- 1 ± 14.7309) / 2
x = (- 1 - 14.7309) / 2, (- 1 + 14.7309) / 2
x = -7.865, 6.865
Then the value of the variable 'y' is given as,
y² = x - 5
y² = 6.865 - 5
y² = 1.865
y = ± 1.366
The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366). And the graph is given below.
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In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 44 inches?
Answer:
22√3 inches
Step-by-step explanation:
You want to know the length of the longer leg of a 30°-60°-90° triangle when the hypotenuse is 44 inches.
Side lengthsThe ratios of side lengths in a 30°-60°-90° triangle are ...
1 : √3 : 2
This means the longer leg is (√3)/2 times the length of the hypotenuse.
ApplicationIn the given triangle, the longer leg is ...
(44 in)(√3)/2 = 22√3 in
c8 q8 v1: a random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 62.25. suppose that the population standard deviation is known to be 4.5. which of the following is correct? (note that you can answer these questions from understanding gleaned in lecture and lab, but may find r helpful.)
99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
Given, the mean of the final grades of the sample be 62.25 and the standard deviation be 4.5
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
808/8 = 101 per hour
60 minutes = 1 hour so:
101 * 1 = 101
You are interested in how well people recall visual details based on type of scene;SO you compare recall scores for a group of people who view a humorous scene,a dramatic scene, and scary scene_ between-subjects ANOVA independent samples t test related samples t test within-subjects ANOVA
The statistical techniques of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are used to test the validity of the hypothesis regarding the comparison of group mean values.
The term "parametric approach" refers to a statistical technique used to compare the means of two normally distributed continuous variables.
In contrast to ANOVA, which is used to compare the means among three or more groups, the Student's t test (also known as the T test) is used to compare the means between two groups.An ANOVA test with a significant P value identifies at least one pair in which the mean difference was statistically significant.
The post-hoc test (multiple comparisons) is utilized to determine whether pair(s) are significant. When at least one covariate (continuous variable) in an ANOVA test is altered to eliminate confounding variables from the outcome, the procedure is known as an ANCOVA. Because inferences about means are made by analyzing variance, the ANOVA test (F test) is referred to as "Analysis of Variance" rather than "Analysis of Means."
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Find the volume of the olid obtained by rotating the region bounded by y=2x^2, x=0, and y=0 about the x-axi
the volume of the region bounded by y = 2x² is 4π/5unit³
What is volumes of Solids?
We shall encounter several solids and their corresponding volumes when discussing the concept of the volume of a combination of solids. As is common knowledge, the surface areas and volumes of all three-dimensional shapes depend on their dimensions. As we can see in reality, numerous shapes are created by fusing a variety of shapes. For instance, the combination of cone and cylinder shapes creates a tent. Similar to how a cone and a hemisphere combine to form an ice cream cone. As a result, the volume of the solids combined will equal the total of volume of the individual solids.
Given, region y = 2x²
Volume will be V = π/2 ∫(r²) dr
So we have 1/3 π * r² * h
So V = 4π (1/5)
V = 4π/5unit³
Hence, the volume of the solid is 4π/5unit³
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Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. Be sure to factor out any common factors in your final answer.
log5(125/ x^{2}-576)
Answer:
ok you deleted my other answer
Step-by-step explanation:
im just finishing this challenge and you are the last question i need to answer
Lin runs 5 laps in 6 minutes
How many minutes per lap is that.
Answer:
0.83 laps per minute
Answer: 0.83 laps per minute.
Step-by-step explanation:
hello! please help me with this, it’s due tomorrow (picture)
Answer:
[tex]\frac{8}{b^{30} }[/tex]
Step-by-step explanation:
Start within the parentheses
1. Divide coefficients
6/3 = 2
2. Divide variables
When dividing exponents with the same base, in this case b, you subtract.
b^20 - b^30 = b^-10
3. Exponent outside parentheses
When there's an exponent on an exponent, you multiply the exponents.
(2b^-10)^3
8 b^-30
4. Simplify?
This step isn't necessary, but when you have a negative exponent on a variable, the variable can be put in the denominator with a positive exponent.
8b^-30 can become 8/b^30
Tom bought a bag full of coal. After one week the bag was 2 3 full. During the next week he used 1 4 of the remaining coal. What fraction was left in the bag?.
We conclude that there is zero (0) fraction of coal left in the bag with Tom.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
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.
So, a fraction of coal left in the bag:
After 1 week the was 2/3 full. So, we have:
1 - 2/3 = 1/3
Next week, he used the remaining 1/3 coal. Now, we have:
1/3 - 1/3 = 0/0
Therefore, we conclude that there is zero (0) fraction of coal left in the bag with Tom.
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Correct question:
Tom bought a bag full of coal. After one week the bag was 2/3 full. During the next week, he used 1/3 of the remaining coal. What fraction was left in the bag?
F(x) = 6x^3-29x^2+19x+4 and x-4 is a factor of f(x), then find all of the zeros of f(x) algebraically
The zeros of the given function are x= -1/6, x=1 and x= 4
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Divide the polynomial [tex]6x^3-29x^2+19x+4[/tex]by the factor (x-4) using long division method to find other 2 factors:
x-4) [tex]6x^3-29x^2+19x+4[/tex] ( [tex]6x^2-5x-1[/tex]
[tex]6x^3-24x^2[/tex]
______________________
[tex]-5x^2+19x+4[/tex]
[tex]-5x^2+20x[/tex]
__________________________
[tex]-x+4[/tex]
[tex]-x+4[/tex]
__________________________
0
Factors of [tex]6x^2-5x-1[/tex] are (6x+1)(x-1)
Find zeros by equating 3 factors to zero:
(6x+1)(x-1) ( x-4) = 0
=> (6x+1)=0, (x-1) =0 , ( x-4) =0
=> x= -1/6, x=1 and x= 4
Thus, the zeros of the given function are x= -1/6, x=1 and x= 4
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Adriel buys 7 bottles of apple juice at the corner store for a total cost of $5.25. If each bottle costs the same amount, how much is each bottle of juice?
Answer:
$5.25 = 525 cents
525/7=75
each bottle is 75 cents or $0.75
When selecting from unbiased estimators, an estimator with small bias may be preferred over the minimum variance unbiased estimator when the variance of the estimator with bias is less than for the MVUE
yess it is true because of unbiased estimator
what is variance?
Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean when the data are more dispersed
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There is a new ride share service that charges a rate of $5 for the
first 5 miles, then charges $0.50 per mile after that.
If you want to spend $12 or less, what is the maximum number of
miles you could go using the ride share service?
The maximum number of miles you could go using the ride share service for $12 or less is 14 miles
How to find the miles to go with $12The problem is solved by generating the equations
assuming x represents the number of extra miles
$5 is charged for the first 5 miles and $0.50 per mile after that
This can be represented using the equation
total cost, y = $5 + $0.5x
$0.50 for the extra miles
Having $12 the number of miles is calculated as below
$12 = $5 + $0.5x
0.5x = 12 - 5
0.5x = 7
x = 7 / 0.5
x = 14 miles
The number of miles that can be paid for using $12 is 14 miles and this is the maximum number since the amount will result to lesser miles
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2 Determine whether the table represents a linear relationship. If so, state the slope of
the line.
X
2
3
4
5
сл
y
14
21
28
35
X
-2
-1
0
1
y
10
5
0
-5
x
2
3
4
5
y
48
72
90
114
Answer:
Tables A and B represent linear relationship-------------------------
Table Ax = 2, 3, 4, 5 Difference is 1y = 14, 21, 28, 35 Difference is 7This is linear and the slope is 7Table Bx = -2, -1, 0, 1 Difference is 1y = 10, 5, 0, -5 Difference is - 5This is linear and the slope is - 5Table Cx = 2, 3, 4, 5 Difference is 1y = 48, 72, 90, 114 Difference is inconsistentThis is not linearJoe ha eaten 4/5 of a pizza. Jane ha eaten 1/4 of a pizza how many time more pizza ha joe eaten then Jane
By conducting simple mathematical operations, we know that Joe eats 11/20 times more pizza than Jane.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.
We can recall the PEMDAS steps in the following order: parentheses, exponents, multiplication, and division (from Left to right), addition, and subtraction (from left to right).
So, we know that:
Jow eats 4/5 of the pizza.
Jane eats 1/4 of the pizza.
Times Joe eats more pizza than Jane:
4/5 - 1/4
4(4) - 5(1)/20
16 - 5/20
11/20
Therefore, by conducting simple mathematical operations, we know that Joe eats 11/20 times more pizza than Jane.
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14. Ronny is taking a jar with 50 dimes and
quarters to CoinMaster to redeem for dollar
bills. The total value of his jar is $8.
a. Write a system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar.
b. Solve the system to determine the number of
quarters and dimes in the jar.
The system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar is
d + q = 50
0.10d + 0.25q = 8
The number of quarters and dimes in the jar is 20 and 30 respectively.
How to determine the number of quarters and dimes?Let
number of quarters = qthe number of dimes = dd + q = 50
0.10d + 0.25q = 8
From (1)
d = 50 - q
Substitute into equation (2)
0.10d + 0.25q = 8
0.10(50 - q) + 0.25q = 8
5 - 0.10q + 0.25q = 8
- 0.10q + 0.25q = 8 - 5
0.15q = 3
divide both sides by 0.15
q = 3/0.15
q = 20
Substitute q = 20 into (1)
d + q = 50
d + 20 = 50
d = 50 - 20
d = 30
In conclusion, the given situation can be solved using simultaneous equation where number of dimes and quarters are 30 and 20 respectively.
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when solving a system of linear equations algebraically, how do you know when the system has no solution
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
How do you tell if a system of equations has no solution algebraically?
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
What does a system look like if it has no solution?
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
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define two variables and translate the sentence into an inequality. the number of grams of saturated fat is more than seven times the number of grams of unsaturated fat
After translating sentence in to inequality we get x > 7*y.
Let us suppose two variables are x and y.
First let's understand what inequality means?
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal symbol ≠" to indicate that two values are not equal. But various inequalities are used to compare the values and determine whether they are less than or greater than.
Assume x as grams of saturated fat.
Assume y as grams of unsaturated fat.
Given as grams of saturated fat is more than seven times
grams of unsaturated fat.
[tex]x > 7*y[/tex].
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Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week. How many weeks will it take leonardo to pay off the ring?.
It will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
Given, Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week.
So, he made a down payment of 10% of $600 i.e. $60
remaining amount to pay be,
600 - 60 = 540
Let he will take x weeks to pay the remaining amount.
Now, if he pay $65 per week
then, 65x = 540
x = 540/65
x = 8.31
So, it will take approx. 8 - 9 weeks to completely pay the remaining amount after the down payment.
Hence, it will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
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Answer:
9 weeks
Step by step explanation:
It’s right.
A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
The shortest length of fence that the rancher can use is 6000 ft.
What is meant by length?
The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.
Main Body:
x = width of rectangle
y = length of rectangle
A = area of rectangle = xy = 1500000 ft^2
L = length of fencing needed = 2(x + y) + x = 3x + 2y
L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)
As x –> 0+, L –> +inf.
As x –> +inf, L –> (3x)+.
Sketch and see that there will be a minimum in Quadrant I.
dL/dx = 3 - 3(10^6)x^(-2)
Extrema occur when dL/dx = 0:
3 - 3(10^6)x^(-2) = 0
(10^6)x^(-2) = 1
x^2 = 10^6
x > 0, so x = 1000 feet for shortest length.
Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.
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Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is a. much larger than one b. zero c. infinity d. None of these alternatives is correct.
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is much larger than one.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
Firstly, it is important to clarify that when people say ‘‘The Sun Will Rise Tomorrow’ they are implying only how It only appears to an observer on earth that the sun rises and sets. In reality the sun neither rises nor sets it only appears to do so because the earth takes one day (24 hours to rotate on its axis). It has appeared to do this for as long as the earth has existed (approx. 4.5 billion years). Although for the purpose of this short reflection, the idiom will signify part of the day-night process -being able to see the sun rise from the perspective of a human on earth.
Although the chances might be extremely high, they are not certain. Even thought it may be very improbably unless an infinite amount of days in which the sun has risen has occurred, the probability will not exactly be one. Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic and philosophy of mathematics, said, “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.” Although we may reasonably argue that the earth while rise tomorrow to a 99.99999999% chance, there still is that 0.000000001 which states that it would not in fact rise.
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how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other
There are therefore 609638400 different ways to arrange eight men and five women in a line so that no two women are positioned adjacent to one another.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. It states that there are n*m ways to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that.
Here,
Number of ways men can stand,
=8!
=40320 ways
Number of ways women are standing,
=9P5
As shown in the image,
=15120 ways
For arranging both of them,
=40320*15120
=609638400 ways
So there is 609638400 ways of arranging eight men and five women to stand in a line so that no two women stand right next to each other.
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2x³ - x² - 6x-1/x-1
This is probably the answer =2x4−x3−6x2−x−1/x
sean wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between three store locations: the oak ridge, oak wood, and oak park shopping malls. the most appropriate statistical test/analysis would be the .
The most appropriate statistical test/analysis for Sean who wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between 3 store locations would be the T-test.
What is the T-test?A T-test is a statistical test which compares the means of two samples. It is used in hypothesis testing, with a null hypothesis which the difference in group means is zero and an alternate hypothesis which the difference in group means is different from zero.
The choice of T-test depends on whether we are studying one group or two groups, and whether we care about the direction of the difference in group means.
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PLEASE HURRY ITS TIMED
Identify the form the following equation is in
y − 2 = 58(x + 16)
a.point slope form
b.standered form
c.slope intercept form
Pretty sure this is the answer:
C. slope intercept form
in a natural deduction problem if your conclusion is a conditional statement that does not appear in any of the premises, then the basic strateguy tells you to do what
In a natural deduction problem, if your conclusion is a conditional statement that does not appear in any of the premises, then it is not a valid argument.
Natural deduction is a process/theory that we use to derive the conclusion of any argument from the premises by using the rules of inference. Now, as the definition itself has established, in natural deduction problems we solve arguments from the premise. But in the argument, we have been told that the conclusion isn't from the premises.
Any argument or conclusion becomes valid if the premise is valid as well. This means that if the conclusion is not in the premise, then it is not valid.
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