The trigonometric form of complex number -6√3 + 6i will be option a. 12(cos150 + isin150)
We are given z = -6√3 + 6i
Now the polar form of a complex number is given by r(cosx + isiny)
We first need the modulus which for a complex number a + bi
r = √(a² + b²)
Hence r = √(108+36)
= √(144)
= 12
Now we need to find the angle x such that
tan x' = |b/a|
or, tan x' = |-1/√3|
or, tan x' = 1/√3
or, tan x' = tan(π/6)
or, x' = π/6
Now since a < 0 and b > 0 x will lie in Quadrant 2
Hence x = π - π/6
= 5π/6 =
Hence we get the trigonometric form to be
12(cos5π/6 + isin5π/6)
= 12(cos150 + isin150)
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Please help me with this!!
Answer:
0.084
Step-by-step explanation:
Decimal form:[tex]\sf Thousandth = \dfrac{1}{1000}\\\\\\[/tex]
[tex]\sf Eighty \ four \ thousandth = 84 * \dfrac{1}{1000}=\dfrac{84}{1000}\\[/tex]
= 0.084
The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by overbar(C)(x), is found by dividing C(x) by x. Find (x→9000) is under (lim)overbar(C)(x).
The average cost per tape is 10.
What is average cost?The average cost is the ratio of the total of cost of all the products to the total number of products. We can calculate the average cost by dividing the total cost by the total output quantity.
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. lim x →9000 C (x)
C (x) = 9000 + 9x
x
= 9000 + 9
x
Lim n→ 9000 C (x) = 9000 +9
9000
= 1 + 9
= 10
So, the average cost per tape is 10
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Suppose you have 6 homework assignments to complete one night.
In how many different orders can you complete all of the assignments
There are a total of 6 homework assignments that need to be completed one night. The number of ways to arrange n items in a specific order is n! (n factorial).
How many different orders can you complete all of the assignments?Therefore, for 6 homework assignments, the number of different orders in which they can be completed is 6! = 720.
This means that there are 720 different ways in which you can complete these 6 assignments on one night. Each permutation represents a unique order in which the assignments can be completed, such as starting with assignment 1, then 2, then 3, and so on, or starting with assignment 4, then 5, then 6, and then 1, and so on.
It is worth noting that this formula is only applicable when the order of the assignments matters. If the order of the assignments does not matter, then we would use the formula for combinations, which is n! / (r!(n-r)!).
Multiplying all of these options together results in 6 x 5 x 4 x 3 x 2 x 1 = 720 possible ways to complete the assignments in a different order. This is known as the permutation formula, which states that the number of ways to arrange n items in a specific order is n! (n factorial).
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review the select balance sheet and income statement for apple, inc. (found in the 10-k). for the account assigned to you (see below on assignments), identify assertions that you think are relevant for the assigned accounts.
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Account Assigned: Trade and other receivables
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Existence assertion means that the receivables must exist and they must be recorded in the books of Apple Inc. Rights and obligations assertion means that the receivables must be legally enforceable, and Apple Inc. must have the right to receive the payment from its customers. Completeness assertion means that all the receivables must be recorded in the books of Apple Inc. Valuation assertion means that the receivables must be recorded in Apple Inc.’s financial statements at the correct amount. Valuation can be measured by calculating the amount of receivables as a percentage of total revenue. For example, if the total revenue is $100 million and the total receivables are $20 million, then the receivables are 20% of total revenue.
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Find the answer for "X"
Answer:
(x, y) = (2, 5)
Step-by-step explanation:
You want to solve the system of equations ...
y = 2x +1x = 12 -2ySolutionSubstituting for y, we have ...
x = 12 -2(2x +1)
x = 12 -4x -2 . . . . . eliminate parentheses
5x = 10 . . . . . . add 4x
x = 2 . . . . . . divide by 5
Then the value of y is ...
y = 2(2) +1 = 5
The solution is ...
x = 2y = 5<95141404393>
How to Use a Graphing Calculator to Solve a Word Problem Involving a Local Extremum of a Polynomial Function.
The graphing calculator was used to identify the coordinates of the local extremum point of the polynomial function. This allowed us to find the solution to the word problem by finding the x and y coordinates of the extremum point.
Using a Graphing Calculator to Find the Local Extremum of a Polynomial FunctionBegin by entering the polynomial function into your graphing calculator.Set the calculator to graph the function by pressing the appropriate keys.Observe the graph and locate any local extremum points.Using the calculator’s zoom feature to better view the graph, identify the x-coordinate of the local extremum point.Enter the x-coordinate of the local extremum point into your calculator and press the “Evaluate” key.The calculator will display the y-coordinate of the local extremum point. This is the solution to the word problem.Learn more about Graphing Calculator: https://brainly.com/question/28969437
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1 to 11 for 100 points (serious answers or report and 1 star)
Based on isosceles trapezoid base angle theorem the sides AD and BC demonstrated that corresponding parts are congruent.
What is isosceles trapezoid base angle theorem?It is a 2-dimensional geometry defined as a quadrilateral with four sides, two of which are parallel to each other.
We provided a trapezoid in which:
BA ≅ CD
It is necessary to demonstrate BD ≅ CD
We can demonstrate this by doing the following:
ABCD is a trapezoidal shape (given)
BA ≅ CD (given) (given)
ABCD is a trapezoid with isosceles angles (definition of isosceles trapezoid)
AD ≅ AD (by using reflexive property) (by using reflexive property)
Angle BAD is congruent to Angle CDA = 5) theorem of base angles
BAD angle CDA angle (base angle theorem)
BD ≅ CA (corresponding parts of congruent triangles are congruent) (corresponding parts of congruent triangles are congruent)
As a result, AD ≅ BC has demonstrated that corresponding parts of congruent triangles are congruent.
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Jasmine has a bucket of $600 to spend on home renovations. She will spend $175 on a new sink and the remainder on countertops. The countertops cost 35 per square foot. What is the maximum number of square feet Jasmine can purchase ?
Answer: 12 square feet
600 - 175 = 425
425 / 35 per square foot = 12.14
The maximum number of square feet Jasmine can purchase is 12, because you can not purchase 0.14 of a square foot.
dont ignore please :( i need help
Answer:5
Step-by-step explanation:
Find the length of midsegment of the trapezoid.
MN=?
The length of midsegment of the trapezoid is MN = 66.5 units
How to find the length of midsegment of the trapezoid?
The midsegment of a trapezoid is a line segment that connects the midpoints of the legs of the trapezoid.
The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
In this case, length of midsegment of the trapezoid will be:
MN = 1/2 × (76 + 57)
MN = 1/2 × (133)
MN = 66.5 units
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The questions are in the image
The sampling method used was random sampling.
What was the sampling method used?This sample may not be representative of the entire class as it does not consider the individual characteristics of the students and only takes into account the row that they are seated on.
Additionally, there is a potential for bias as the sample size is quite small and may not accurately reflect the overall population. Therefore, it would be beneficial to use a larger sample size or use a stratified random sampling method to ensure a representative sample.
The sampling method used was random sampling.
This sample is likely to be representative, as it was chosen randomly and evenly from the seating chart. However, there could be potential issues if the student's Exam 1 scores are not evenly distributed among the rows.
For example, if all the higher scores are concentrated in one row, then the sample may not be representative of the entire class. To ensure an accurate estimation of the average Exam 1 score for the entire class, it may be better to use stratified sampling, where each row is given equal weight and students are selected from each row with the same probability.
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Consider a pool of six I/O buffers. Assume that any buffer is just as likely to be available or occupied as any other. Compute the probabilities associated with the following events:
A = At least two but no more than five buffers occupied.
B = At least three but no more than five buffers occupied.
C = All buffers available or an even number of buffers occupied.
D = At least one of the events A, B, and C occurs.
The associated probabilities are A = At least two but no more than five buffers occupied.
There are a total of 2^6 = 64 possible outcomes when rolling 6 dice.
To find the probability of event A, we need to find the number of outcomes where at least two but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where two, three, four, or five buffers are occupied and subtracting the probabilities where six or zero buffers are occupied.
The probability of two buffers being occupied is (6 choose 2)(1/64) = 15/64
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)(1/64) = 6/64
So the probability of event A is (15/64) + (20/64) + (15/64) + (6/64) = 56/64.
B = At least three but no more than five buffers occupied.
To find the probability of event B, we need to find the number of outcomes where at least three but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where three, four, or five buffers are occupied and subtracting the probability where six buffers are occupied.
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)*(1/64) = 6/64
So the probability of event B is (20/64) + (15/64
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three girls shared a piece of land. One got x/3y of the land. Another got x/6y of the land. What fraction of the land will the third girl get.
The third girl will recieve a land area equals to the fraction (2y-x)/2y.
What is fraction ?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.
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 correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
The fractions are x/3y, x/6y and z(say)
so sum of all the fraction must be 1 so
x/3y + x/6y + z = 1
⇒z = (2y-x)/2y
The third girl recieve a land area equals to (2y-x)/2y.
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Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Hannah makes 5 out of 8 attempted free-throws
Now,
The average waiting time of hannah to make her first basket=5/8
The probability of hannah making basket at her last attempt=1/8
The probability of hannah making basket before her last attempt= 2/8
Therefore, the probabilty will be 1/8 and 2/8.
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$40$ is $120\%$ of what number?
Marcus bought 4 packets of baseball cards and 4 packets of animals cards.Write an algebraic expression for the total number of cards Marcus bought.
Answer: How many cards are in a packet?
Step-by-step explanation:
−3/5×8/6= helpplease
Answer:
-4/5 OR -0.8
Step-by-step explanation:
This problem is very simple but it can be broken down
First we do -3 times 8 and get -24
Then we do 5 times 6 and get 30
We put the first answer over the second which equals
-24/30
This can then be simplified further if we divide both sides by 6
-4/5 as a fraction
-0.8 as a decimal
-80% as a percent
A student's course grade is based on one midem that counts as 10% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 15% of his final grade. His midterm score is 68, his project score is 95, his homework score is 93, and his final exam score 62. What his overall final score? What letter grade did he eam (A, C, D, or F) Assume that mean of 50 or above is an A, a mean least 80 but less than 90 is a B, and so on.
The overall final score of the student is 86.35 and he got B grade in the exam.
What is Percentage?
Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole.
Let the final score to be 'f'
According to the question :
midterm score = 10% 68 = 6.8
class project score = 25% 95 = 23.75
homework assignment = 50% 93 =46.5
final exam = 15% 62 = 9.3
So, the Overall final score = midterm score + class project score + homework assignment + final exam
= 6.8 + 23.75 + 46.5 + 9.3
= 86.35.
Hence, he got grade 'B' .
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given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). output each floating-point value with two digits after the decimal point, which can be achieved as follows: print(f'{your value1:.2f} {your value2:.2f} {your value3:.2f} {your value4:.2f}')
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
Given three floating-point numbers x, y, and z, the output would be x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). The formula for each output is as follows:
x to the power of z: x^z
x to the power of (y to the power of z): x^(y^z)
The absolute value of (x minus y): |x-y|
The square root of (x to the power of z): √(x^z)
For example, if x = 2.00, y = 4.00, and z = 3.00, then the output would be: 8.00 4096.00 2.00 4.00
The calculation for each output is as follows:
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
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help me white this for brainliested
Answer:
please take a better picture
Step-by-step explanation:
Is y = 1 over 4 x 0.5 a power function? Explain your reasoning.
The function y = 1 over 4 x 0.5 is not a power function
What is a function?A function can be described as a rule, equation or expression that tends to explain the relationship between two variables.
These variables are;
The independent variableThe dependent variableThe types of functions are;
Into – functionPolynomial functionLinear FunctionIdentical FunctionQuadratic FunctionPower functionA power function is a function single that has a term that is product of a real number, a coefficient, and a variable raised to an exponent.
Hence, y = 1/4 × 0.5 is not a power function.
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2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer
Answer: x= -3 and x= -1
Step-by-step explanation:
We can see from table that when x= -3, the f(x) have the same y with g(x). Also when x= -1, the f(x) have the same y with g(x).
what is the y intercept
x y
34 -52
51 -65
68 -78
Answer:
y- intercept = - 26
Step-by-step explanation:
to find the y- intercept, obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (34, - 52) and (x₂, y₂ ) = (68, - 78) ← 2 ordered pairs from the table
m = [tex]\frac{-78-(-52)}{68-34}[/tex] = [tex]\frac{-78+52}{34}[/tex] = [tex]\frac{-26}{34}[/tex] = - [tex]\frac{13}{17}[/tex] , then
y = - [tex]\frac{13}{17}[/tex] x + c
to find c substitute any of the ordered pairs into the equation and solve for c
using (51, - 65 ) , then
- 65 = - [tex]\frac{13}{17}[/tex] (51) + c = - 39 + c ( add 39 to both sides )
- 26 = c
then y- intercept = - 26
subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after 6 months, the numbers of respiratory tract infections each group had were compared.
Comparison of two randomly assigned groups is given by :
a. Given study is classified in experimental based.
b. Treatment group is represented by herb.
c. The independent variable is given by Placebo
d. The dependent variable represented by the Infection on respiratory tract .
e. Goal of the study is the comparison of two groups herb and the placebo.
Number of randomly assigned group = 2
One group is herb.
Second group is placebo.
a. Two different types of groups given so the study is experimental based.
b. Treatment group is represented by the group one herb.
c. Independent variable is represented by the group two placebo it does not dependent on herb treatment.
d. Dependent variable is represented by the infection on respiratory tract.
e. Goal of the study is given by the comparison of number of respiratory tract infection in each group.
Therefore, the answer of the following question based on the randomly assigned two groups is given by :
a. Study is experimental based.
b. Herb treatment.
c. Placebo represents the independent variable.
d. Infection represents the dependent variable.
e. Goal of the study is doing the comparison of two groups.
The above question is incomplete, the complete question is :
Subjects were randomly assigned to two groups. One group was given an herb and the other group a placebo. After 6 months the numbers of respiratory tract infections each group had were compared
a) Classify this study (circle the answer): experimental OR observational
b) Identify the treatment group:
c) Identify the independent variable_
d) Identify the dependent variable
e) What is the goal of this study?
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What does x equal???
here is ur answer seeee now
an object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. the objects travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
The acceleration of this object is equal to: d) 9.33 m/s^2.
How to calculate the acceleration of this object?In order to calculate the acceleration of the object, we would apply the second equation of motion. Mathematically, the second equation of motion is given by this mathematical expression:
S = ut + ½at²
Where:
S represents the distance travelled or covered.t represents the time.u represents the initial velocity.a represents the acceleration.At time, t = 1.00 seconds, the position is given by:
x₁ = 0 + 1/2(1²)a
x₁ = ¹/₂(a)
At time, t = 2.00 seconds, the position is given by:
x₂ = 0 + 1/2(2²)a
x₂ = 0 + 4a/2
x₂ = 2a
Therefore, the change in position is given by;
Change in position, Δx = x₂ - x₁
Change in position, Δx = 14
From the second equation of motion, the acceleration of this object is given by:
14 = 2a - 1/2(a)
14 = 3a/2
3a = 28
a = 9.33 m/s².
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Complete Question:
An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
a) 5.20 m/s^2 b) 10.4 m/s^2 c) 8.67 m/s^2 d) 9.33 m/s^2 e) 12.1 m/s^2
HELP MATH THIGNY PLSSS
Answer:
Step-by-step explanation:
Your slope would be -1/4 because it is rise over run meaning your y-axis over your x-axis. I am not sure exactly what your question is needing but I hope that helps in some way.
Please help me, I need this.
Answer:
Slope = 4/3
Step-by-step explanation:
The coordinates are,
→ x1 = 6, y1 = 0
→ x2 = 0, y2 = -8
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-8 - 0)/(0 - 6)
→ m = (-8)/(-6)
→ m = 8/6
→ [ m = 4/3 ]
Hence, the slope is 4/3.
2. fill in the exclusive and inclusive ranges for the following items. be sure to show your work below. high score low score inclusive range exclusive range 7 6 89 45 34 17 15 2 1 1
The inclusive range includes all numbers from 2 to 89, while the exclusive range includes all numbers from 3 to 88, excluding the two endpoints.
Inclusive Range: Low Score (2) = Low Score (7) + 1 = 7 + 1 = 8
High Score (89) = High Score (45) + 44 = 45 + 44 = 89
Exclusive Range: Low Score (3) = Low Score (7) + 1 = 7 + 1 = 8
High Score (88) = High Score (45) + 44 = 45 + 44 = 89
The inclusive range includes all values within a given set of numbers, including the endpoints. In this case, the low score is 7 and the high score is 45. Adding 1 to the low score gives us a low score of 8, and adding 44 to the high score gives us a high score of 89. This gives us an inclusive range of 8 to 89.
The exclusive range excludes the endpoints, so we add 1 to the low score and subtract 1 from the high score. This gives us a low score of 8 and a high score of 88, giving us an exclusive range of 8 to 88. This means that the range excludes the values of 7 and 89 from the set.
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Let us choose some number t and consider a point A(2t+3,24t+1).Prove that all such points make a line.What is the slope and the y intercept of this line?
The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.
How to analyze and interpret parametric functions
Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:
y = f(x)
The rectangular form of the function is a line if and only if the resulting expression is of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableFirst, write the components of the parametric functions:
x = 2 · t + 3
y = 24 · t + 1
Second, clear variable t in each parametric expression:
t = (x - 3) / 2
t = (y - 1) / 24
Third, eliminate parameter t by transitive property:
(x - 3) / 2 = (y - 1) / 24
Fourth, obtain the equation of the line:
24 · (x - 3) = 2 · (y - 1)
24 · x - 72 = 2 · y - 2
24 · x - 70 = 2 · y
y = 12 · x - 35
Fifth, determine the slope and intercept of the equation of the line:
m = 12, b = - 35
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