The cubic expression of (1 + i) is given as follows:
(1 + i)³ = 0.
How to obtain the cubic expression?The cubic expression is obtained elevating the binomial (1 + i) to the third power, as follows:
(1 + i)³.
Then we expand the expression, applying the rule for the cube of a binomial, hence:
(1 + i)³ = i³ + i² + i + 1.
The basic complex number relation is:
i² = -1.
Hence:
i³ = i² x i = -1 x i = -1.
Then the expression is given as follows:
i³ + i² + i + 1 = -i - 1 + i + 1 = 0.
TranslationThe problem asks for the cubic expression for (1 + i).
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a vehicle factory manufactures cars. the unit cost (the cost in dollars to make each car) depends on the number of cars made. if cars are made, then the unit cost is given by the function . how many cars must be made to minimize the unit cost? c(x)
The number of cars that must be made to minimize the unit cost is 300 cars which is determined by differentiation.
Differentiation is a mathematical process that determines the instantaneous rate of change of a function based on one of its variables. The most common example is velocity, which is the rate of change of displacement with respect to time. Anti-differentiation is the inverse of finding a derivative.
Differentiation is used to calculate the rate of change of quantities in real time.
Since, we have been given the cost function to be function [tex](cx)= 1.1^{2} - 660x+107,357[/tex] then we have to find the first differentiation in order to get the value and this will be:-
[tex](cx)= 1.1^{2} -660x+107,357\\2.2x=660\\x=\frac{660}{2.2} \\x=300[/tex]
Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.
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the reason why estimators like the hatbs.gif have a sampling distribution is that group of answer choices economics is not a precise science. individuals respond differently to incentives. in real life you typically get to sample many times. the values of the y differs across random samples samples.
Estimators like the hatBS.gif have a sampling distribution because of the following reasons, according to the given sources:
Individuals respond differently to incentives, leading to the difference in values of Y across random samples.
In real life, we typically get to sample many times, leading to the difference in values of Y across samples .
Economics not being a precise science is not mentioned as a reason for the sampling distribution of estimators like hatBS.gif.Estimators are statistical methods used to calculate the values of population parameters based on a sample of data. They are a key tool for making inferences about a population from a sample. An estimator is a function that takes the sample data as input and produces an estimate of the population parameter.
There are two types of estimators: point estimators and interval estimators. Point estimators provide a single estimate of the population parameter, while interval estimators provide a range of values that are likely to contain the population parameter.
The quality of an estimator is measured by its accuracy and precision. An accurate estimator is one that produces estimates that are close to the true population parameter, while a precise estimator is one that produces estimates that are consistently close to each other. There are various methods for selecting the best estimator for a given situation, including mean squared error, bias, and confidence intervals.
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ron started a new job which paid him $60 for the first day of training. after the first day, he will be paid $7 per hour. what is the linear equation that models ron's pay? responses y
Answer:
y = 7x + 60
Step-by-step explanation:
Ron gets paid 7 dollars an hour, this is our constant, since we don't know how many hours he works per day, it can be represented as "x":
7x
He starts his job receiving 60 dollars for his first day:
7x + 60
Of course this needs the outcome "y":
[y = 7x + 60]
the sum of two numbers is 23 less than twice the first number. their difference is 19 less than twice the second number. find each number
The first number is 12.5, and the second number is -3.25.
Let x be the first number, and y be the second number.
2x + 23 = 2y
y - 19 = 2x
Subtracting the second equation from the first:
24 = y
Substituting 24 for y in the first equation:
2x + 23 = 48
2x = 25
x = 12.5
Substituting 12.5 for x in the second equation:
12.5 - 19 = 2y
2y = -6.5
y = -3.25
The first number is 12.5, and the second number is -3.25.
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Mr. Hesch has 4 stations set up in his classroom. Each
station is labeled with a color: blue, purple, green, or yellow.
As each student enters the classroom, they spin the
spinner to decide at which station they will start. What is
the probability a student spins purple?
O
O
P
G
3100
8
25%
B
Y
Y B
G
P
The probability a student spins purple will be 25%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that Mr. Hesch has 4 stations set up in his classroom. Each station is labeled with a color: blue, purple, green, or yellow. As each student enters the classroom, they spin the spinner to decide at which station they will start.
The probability will be calculated as:-
Probability = Probability = Number of favorable outcomes / Number of samples
Probability = 1 / 4
Probability = 0.25 or 25%
Hence, the probability will be 25%.
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What is the image point of (-6, 3) after a translation right 5 units and
down 3 units?
The image of a point (-6, 3) after a translation right 5 units and down 3 units is
How to perform the translationThe transformation rule for translation right 5 units and down 3 units is
(x, y) → (x + 5, y - 3)
Applying the rule to the point (-6, 3)
(-6, 3) → (-6 + 5, 3 - 3) → (-1,, 0)
hence the translation results to create an image of (-1, 0)
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solve 2x + 1 = 9 using the change of base formula log base b of y equals log y over log b.
The solution of the equation 2x + 1 = 9 is 4.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 2x + 1 = 9
Two times of x plus one equal to nine
To solve this we have to isolate the x term.
Subtract 1 from both sides
2x=8
Divide both sides by 2
x=4
Hence, the solution of the equation 2x + 1 = 9 is 4.
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The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 2 heads).
0.8125
0.6875
0.4375
0.0625
The probability of obtaining at least 2 heads is 0.6875.
option B.
What is the probability of getting at least 2 heads?
The probability of obtaining at least 2 heads in 4 coin tosses can be calculated by adding the probabilities of getting exactly 2 heads, exactly 3 heads, and exactly 4 heads. This can be done using the binomial distribution formula:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4)
Where;
X is the number of heads in 4 coin tossesEach coin toss has a probability of 0.5 of landing heads.
P(X = 2) = 4C2 x (0.5)^2 x (0.5)^2 = 6 x 0.25 x 0.25 = 0.375
P(X = 3) = 4C3 x (0.5)^3 x (0.5)^1 = 4 x 0.125 x 0.5 = 0.25
P(X = 4) = 4C4 x (0.5)^4 = 1 x 0.0625 = 0.0625
The total probability is calculated as follows;
P(X >= 2) = 0.375 + 0.25 + 0.0625 = 0.6875
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Answer:
The probability of obtaining at least 2 heads is 0.6875.
option B.
Step-by-step explanation:
Solve for x for each triangle. Find the length of each side. perimeter=42 ft
Answer:
10 ft
Step-by-step explanation:
As the triangle is equilateral, perimeter = (x + 4) * 3 = 42 ft
x + 4 = 42/3 = 14
x = 14 - 4 = 10 ft
how many subsets of $\{1,2,3,4,5,6,7\}$ are there that do not contain two consecutive integers? be sure to include the empty set in your count.
There are 127 subsets of {1,2,3,4,5,6,7} that do not contain two consecutive integers, including the empty set.
Each number in the set {1,2,3,4,5,6,7} can either be included or not included in a subset.
So, the number of subsets of this set is:
2^7 = 128.However, we need to exclude the subsets that contain two consecutive numbers, such as {2,3} or {5,6}. This can be achieved by considering each number as the starting point of a subset and appending it with a number of non-consecutive numbers that can follow.
For example, if 1 is the starting point, the next numbers can only be 3, 4, 5, 6, or 7. Hence, the number of subsets starting from 1 is 5.
By repeating this process for each number in the set, we obtain a total of 5555551 = 127 subsets.
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BIG IDEAS MATH
Chapter 3: 3.4-3.6 Quiz > Quiz 3
6
Write an equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12.
The equation of the line is y=x+
helppppp
Equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12 is y=-3x+17.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12.
3y=12+x
y=1/3x+4
slope of given line is 1/3
So the slope of perpendicular line will be -3
Now let us find the y intercept
y=-3x+b
2=-3(5)+b
2=-15+b
b=17
So, equation of the line passing through the point (5, 2) that is perpendicular to the line -x + 3y = 12 is y=-3x+17.
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a student asked classmates how tall they are, in which month they were born, and whether they are in a relationship. how many of these variables are quantitative and how many of these variables are categorical? one is quantitative. two are categorical. three are quantitative. none is categorical. two are quantitative. one is categorical. none is quantitative. three are categorical.
The correct answer is option (B). The answer is one is quantitative and two are categorical.
Given that,
A student quizzed his or her peers about their height, birth month, and relationship status. what proportion of these variables are categorical and what proportion are quantitative.
To find : How many variables are quantitative and categorical ?
A variable where the data indicate the amounts is referred to be a quantitative variable (e.g. height, age). Any variable where the data represent groupings is referred to as categoric variable.
Any trait that cant be quantified is referred to as categorical variable (also known as a qualitative variable). Nominal or ordinal categorical variables are also acceptable.
Therefore, option is the appropriate response (B). One is a quantitative response, and two is a categorical one.
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Are the ratios 5:2 and 7:3 equivalent?
Answer:
no
Step-by-step explanation:
5:2 =35:14
7:3 = 35 :15
Answer: no
Step-by-step explanation:
They are both in the smallest form that they can me at.
What is the ratio of 2/3 to 4?
The ratio of two thirds to four is given as follows:
1 : 6.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is obtained applying a proportion.
A proportion is applied because the ratio is given by the division of the amount a by the amount b.
The parameters for this problem are given as follows:
Amount a: 2/3.Amount b: 4.Hence the ratio of two thirds and four is calculated as follows:
(2/3)/4 = 2/3 x 1/4 = 2/12 = 1/6.
In ratio notation, it is given as follows:
1 : 6.
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The polynomial x^2 + 3x - 1 is a factor of x^4 + 3x^3 - 2x^2 - 3x + 1. Please select the best answer from the choices provided T F
Yes, it is true that [tex]x^{2}[/tex] + 3x - 1 is a factorization of [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.
How to factorize?Let us factorize the equation,
[tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1
=> [tex]x^{4}[/tex] - 2[tex]x^{2}[/tex] + 1 - 3x + 3[tex]x^{3}[/tex]
Let's construct a complete square using the terms provided:
=>[tex](x^{2}) ^{2}[/tex]- 2 × [tex]x^{2}[/tex] × 1 + [tex]1^{2}[/tex] + 3[tex]x^{3}[/tex] - 3
=> [tex](x^{2} - 1)^{2}[/tex] + 3[tex]x^{3}[/tex] - 3x
After completing the above calculation, take the common 3x from 3x^3 - 3x.
=>[tex](x^{2} - 1)^{2}[/tex] + 3x([tex]x^{2}[/tex] - 1)
=>([tex]x^{2}[/tex] - 1) ( ([tex]x^{2}[/tex] - 1)+ 3x )
=>([tex]x^{2}[/tex] - 1) ([tex]x^{2}[/tex] + 3x - 1)
Hence, ([tex]x^{2}[/tex] - 1) and ([tex]x^{2}[/tex] + 3x - 1) are two factors of the
equation [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.
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you and three of your friends have 7 slices left from a pizza that originally was cut into 8 slices. you plan to slice the 7 slices further into equally sized pieces so that you can each have an equal amount of pizza. when you do so, what fraction of the original pizza will each of you get?
If 7 slices of pizza is divided into equally sized pieces for 4 people then the fraction will be [tex]\frac{7}{32}[/tex] of original pizza.
Total number of people to share the pizza = 4
Total number of slices in the pizza =8
number of slices left = 7
so the fraction of pizza now is [tex]\frac{7}{8}[/tex]
the plan is to slice the 7 slices further into equally sized pieces so that everyone can each have an equal amount of pizza.
Therefore [tex]\frac{7}{8}[/tex] would be divided by 4
The fraction each person will get of original pizza
= [tex]\frac{7}{8}[/tex] ×[tex]\frac{1}{4}[/tex]
= [tex]\frac{7}{32}[/tex]
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Which equation has no solution? 1+2x=1 1+2x=2x+1 2x−1=1+2x 2x−1=−1+2x
Answer:
2x − 1 = 1 + 2x
Step-by-step explanation:
A.
1 + 2x = 1
2x = =0
x = 0
1 solution, x = 0.
B.
1 + 2x = 2x + 1
1 = 1
Infinite number of solutions, all real numbers.
C.
2x − 1 = 1 + 2x
0 = 2
No solution
D.
2x − 1 = −1 + 2x
-1 = -1
Infinite number of solutions, all real numbers.
URGENT HELP BRAINLIST INCLUDED
Answer:
figure 2
Step-by-step explanation:
A rhombus is a flat shape with four equal straight sides. All sides have equal length and it looks like a diamond. It is a special type of a parallelogram whose opposite sides are equal.
Answer: figure 2 only but if the third image is a square thenits 2 and 3 cause I can't see the third very well
Step-by-step explanation:
#9. If bacteria colony of current population 1,000
doubles every 13 minutes, how large will the
bacteria colony be in 52 minutes
The population of the bacteria colony in 52 minutes is 16,000.
What will be the population of the bacteria?The bacteria colony grows at an exponential rate. An exponential equation can be described as an equation with exponents. The exponent is usually a variable.
The general form of exponential equation is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe equation that can be used to determine the population in 52 minutes is:
FV = P(2^(t/13)
Where:
FV = future population t= time P = present populationFV = 1,000(2^52/13)
= 1,000 x (2^4)
= 16,000
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7. Find the equation of the line that goes through the point (-2, -2) and has a slope of -4. y = -4x - 2 y = -4x - 10 y = -2x - 2 y = -2x - 4
The required equation of the line that goes through the point (-2, -2) and has a slope of -4 is y = -4x - 10. Option B is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
The equation of a line with slope m and passing through the point (x₁, y₁) can be found using the point-slope formula:
y - y₁ = m (x - x₁)
Plugging in m = -4, x₁ = -2, and y₁ = -2, we get:
y - (-2) = -4 (x - (-2))
Simplifying, we get:
y + 2 = -4 (x + 2)
Expanding the right-hand side:
y + 2 = -4x - 8
Isolating y on one side:
y = -4x - 10
Thus, the equation of the line is y = -4x - 10.
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Let csc(x) = five-thirds, where 0° < x < 90°. which expression has a value of three-fourths? sec(x) cos(x) cot(x) tan(x)
The trigonometric expression that has a value of three-fourths is; tan (x)
How to solve Trigonometric ratio problems?The basic trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
sec x = 1/cos x
csc x = 1/sin x
cot x = 1/tan x
Thus;
If csc x = 5/3, it means that;
sin x = 3/5
By trigonometric ratios, we know that;
cos x = 4/5 and tan x = 3/4
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Factorise y² - 100 pleaseeeee
Step-by-step explanation:
y² - 100
= y² - 10²
Now by using formula:
[tex]a { \\ }^{2} - {b}^{2} = (a - b)(a + b)[/tex]
= (y - 10)(y + 10)
Put the numbers in order from smallest to largest. 54,900, 535,728, 535,740, 536,312.
Answer:
Put the numbers in order from smallest to largest. 54,900, 535,728, 535,740, 536,312.
54,900, 535,728, 535,740, 536,312
Step-by-step explanation:
You're welcome.
Answer:
All numbers in order:54,312,535,535,536,728,740,900
Step-by-step explanation:
Find the numbers that have the least amount of value. Then put the numbers with the greater value towards the end.
a study compares online instruction with a standard lecture for teaching statistics. the proper way to design such a study is:
The proper way to design a study comparing online instruction with a standard lecture for teaching statistics would be to use a randomized controlled trial.
Participants should be randomly assigned to either the online instruction group or the standard lecture group. Both groups should cover the same content and have equivalent opportunities for interaction and assessment. The effectiveness of the two methods should then be compared by measuring the performance of participants on a common set of assessments. It is also important to control for potential confounders such as prior knowledge, motivation, and learning style. By following these steps, the study can accurately determine the effectiveness of online instruction compared to the standard lecture method.
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-5y+9y please help me with this
Answer: answer is 4y
Step-by-step explanation:
Answer: 4y
Step-by-step explanation:
-5y + 9y - Collect like terms by calculating the sum or difference of their coefficients.
(-5 + 9)y - Calculate the sum
Which will leave you with the answer: 4y
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The picture of the Question is at the bottom
Answer:The first two
Step-by-step explanation: To solve the problem you would
5(x+3)=25
x+3=5
-3 -3
x=2
Solve the system by substitution y=-7x+10 3x+2y=9
Answer:
point form (1,3) equation form: x=1, y=3
Step-by-step explanation:
yw!! :)
Answer: x = 1
Step-by-step explanation: we know what y equals so all we have to do is plug that in into the other equation! if confused, look at attached image.
The town of Todsham currently has a population of 300,000.
Each year, the population of Todsham will reduce by 5%.
How many fewer people will live in Todsham in 6 years compared with now?
Give your answer to 3 s.f.
PLEASEEEE HELLPPP BEGG!!!
In 6 years, there will be 90,000 fewer people living in Todsham compared with now.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that town of Todsham currently has a population of 300,000.
Each year, the population of Todsham will reduce by 5%.
We need to find the number of people will live in Todsham in 6 years compared with now
The population reduction in one year will be 5% of 300,000, which is:
300,000 ×0.05 = 15,000
Now in 6 years, the population reduction
15,000×6 = 90,000 people.
Therefore, in 6 years, there will be 90,000 fewer people living in Todsham compared with now.
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when a researcher attempts to estimate the characteristics of an entire population on the basis of sample measures, the technique employed are called
The technique used by a researcher to estimate the characteristics of an entire population based on sample measures is called "sampling."
Sampling is the process of identifying the group from whom you will gather data for your research. For example, if you want to know what students think at your institution, you may poll 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.
Probability Sampling methods are further subdivided into simple random sampling, systematic sampling, stratified sampling, and clustered sampling.
In a research project, sampling is the selection of a subset of the population of interest. In the great majority of research activities, involvement of an entire population of interest is not possible, hence data gathering is reliant on a smaller group.
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a family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. what is the probability that
The probability that no two members of the family are assigned to the same station is 2/9.
From the information given, the probability that all three family members are assigned to the same station will be:
= 3 × (1/3) ³
= 1/9
Now, the probability that at most two family members are allocate to the same station will be:
= 1 - 1/9
= 8/9.
The total number of outcomes for the experiment is 3^3 = 27.
The number of outcomes in which no two members of the family are assigned to the same station is 3! = 6.
Therefore, the probability that no two members of the family are assigned to the same station is 6/27 = 2/9.
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