Write z in exponential form:
\(z=1-i=\sqrt2 e^{-i\frac\pi4}\)
Then taking the logarithm, we get
\(\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}\)
so a is the correct answer.
the volume of a right cone is 27 π units^3. if its height is 9 units find its circumference in terms of π.
Given:
the volume of a right cone is 27 π units³
And the height of the cone = h = 9 units
First, we will find the radius of the base (r) using the formula of the volume.
\(V=\frac{1}{3}\pi r^2h\)Substitute V = 27π and h = 9
\(27π=\frac{1}{3}πr^2(9)\)Solve the equation to find (r)
\(\begin{gathered} r^2=\frac{3*27}{9}=9 \\ r=\sqrt{9}=3 \end{gathered}\)Now, we will find the circumference using the following formula:
\(circumference=2πr\)substitute r = 3
\(circumference=2π(3)=6π\)So, the answer will be: Circumference = 6π units
Solving quadratics by factoringx2-4x-25=-4x
Answer:
x = ± 5
Step-by-step explanation:
Given
x² - 4x - 25 = - 4x ( add 4x to both sides )
x² - 25 = 0 ( add 25 to both sides )
x² = 25 ( take the square root of both sides )
x = ± \(\sqrt{25}\) = ± 5
What mistake was made in the construction of this angle bisector?
Answer:
Usually, angle bisectors divide a given angle into two separate angles with equal measures, or two equal parts.
Based off of the picture you've given, it seems as if the angle bisector doesn't split the angle into 2 equal measures, since one angle looks like it will be bigger than the other.
If a 6.2% Social Security tax is applied to a maximum wage of $106,800, the maximum amount of Social Security tax that could ever be charged in a single year is: a. $213.60 b. $6,408.00 c. $6,621.60 d. $17,225.81
Answer:
Correct Answer:
C: $6,621.60
(EDGE 2021)
Step-by-step explanation:
The maximum amount of Social Security tax that could ever be charged in a single year exists $6,621.60.
What is Social Security tax?Social Security exists financed through a reliable payroll tax.
Knowing that a 6.2% Social Security tax exists applied to a maximum wage of $106,800, the maximum amount of Social Security tax that could ever be charged in a single year stands at $6,621.60. Social Security offers all but unemployment insurance.
Therefore, the correct answer is option c. $6,621.60
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Cassandra has a rectangular Panto in her backyard the painter is 12.74 m long and 5.45 m wide round the length and width to the nearest whole number then estimate the perimeter of cosines is Pantel write an equation to model your work
The perimeter of the rectangular Panto will be 38 meters.
How to calculate the perimeter?It is important to note that the perimeter of a rectangle is calculated as:
= 2(length + width)
In this case, Cassandra has a rectangular Panto in her backyard the painter is 12.74 m long and 5.45 m wide.
We are told to convert the dimensions to the nearest whole numbers. This will be 13m and 6m. Therefore, the perimeter will be:
= 2 (length + width)
= 2 13 + 6)
= 2(19)
= 38m.
The perimeter is 38m.
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What is the area of the trapezoid shown below?
Answer:
\(180units^{2}\)
Step-by-step explanation:
\(Area = \frac{1}{2} *(a + b )*h\\\\\)
Here,
(a+b) = sum of the parallel sides
h = perpendicular distance between parallel sides
Before find the area we have to find the perpendicular distance between parallel side by using Pythagorean theorem
\(7^{2} + h^{2}= 25^{2}\\49+h^{2} =625 \\h^{2}= 625-49\\h^{2}=576\\h = \sqrt{576} \\h=24\)
Now let's find the area
\(Area = \frac{1}{2} *(a + b )*h\\\\\)
\(=\frac{1}{2}*(11+4)*24\\=\frac{1}{2}*15*24\\ =180units^{2}\)
Hope this helps you.
Let me know if you have any other questions :-)
Is 8.253725372537 a irrational number
Answer:
no
Step-by-step explanation:
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 4/9. What is the probability that it will rain on exactly three of the six days they are there? Round your answer to the nearest thousandth.
The probability that it will rain on exactly three of the six days they are there is 0.242.
The given information can be represented as follows:P(Rain on any given day) = 4/9
The hiking club is camping for 6 days and the probability of rain on any given day is given as 4/9.
We are to find the probability that it will rain exactly three days out of the six days they are camping.
The number of ways that it can rain exactly three days out of the six days is given by:C(6,3) = 6!/(3!3!) = 20The probability of rain for any one of the 20 ways of getting exactly three days of rain is:
P(Rain on three days and no rain on three days) = (4/9)³(5/9)³
The probability of getting exactly three days of rain out of six is given by: P(exactly three days of rain) = 20(4/9)³(5/9)³ = 0.242, rounded to the nearest thousandth.
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Solve n/6= 30/36 for the unknown quantity,n
Answer:
n=5
Step-by-step explanation:
First cross multiply to get:
36n = 180
Divide both sides by 36
36n/36 = 180/36
n=5
28453 dg a t
porfa ayudenme
pipipipi
Answer:
488
Step-by-step explanation:
You divide 28453 by 58.3053278689 and get 488.
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
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The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
PLEASE HELP ME
The function f(x) = -2(4)^x+1 +140
represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
PLEASE SEE PHOTO FOR FUNCTION
The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).
The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.
To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.
For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.
Therefore, the practical domain of the situation is x ≥ 0.
For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.
Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.
Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).
To summarize:
- The practical domain of the situation is x ≥ 0.
- The practical range of the situation is [140, ∞).
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Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
Round the numbers in each expression to the nearest whole number.
Then select the expression that can be estimated to 8.
A.
3
1
5
+
5
7
9
B.
1
5
8
+
5
2
5
C.
15
5
7
−
8
2
9
D.
10
1
4
+
1
11
15
Answer: A, and B
A) 894
B) 728
Step-by-step explanation:
Olivia is growing roses and keeps track of how much fertilizer (in ounces) she adds to the soil and how many blooms each rose
bush has. She finds a linear relationship that can be modeled by the equation y = 1.345x + 4. What does the 1.345 mean in the
context of the problem?
Answer:
i am in middle school but i know it Yx6
Step-by-step explanation:
HELP AS SOON AS POSSIBLE PLEASE
A scatter plot, because it would show the association, or relationship, between the two variables
How to determine the most appropriate to construct for the dataFrom the question, we have the following parameters that can be used in our computation:
The table of values
To show the relationship and association between data values, the data values are best represented on a scatter plot
using the above as a guide, we have the following:
The most appropriate to construct for the data is (b)
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Andy wants to find the distance across a river. In order to find the distance CD, Andy stands at point D , directly across from point C , and walks 200 feet to the left, placing a marker at a point E. Andy continues walking another 300 feet to point A , and then follows the path to the left, walking until the markers at points E and C line up. Andy marks this location B and measures AB. What is CD
Answer:
98
Step-by-step explanation:
200/300 x 147= 98
the volume of a rectangle prism is 8cm height 4 width.
Answer:
Step-by-step explanation:
Which statements are true from the graph ? Check all that apply:
the line is horizontal the line is vertical
The statements that are true from the graph are:
The line is horizontalThe line goes through (4, 4 )The y- values are all 4Calculations and ParametersGiven the graph, we can note some things:
There is a line with a slope of zero.This is a horizontal line parallel to the x-axis.The equation of the line is y = cc is the value of the y- coordinates the line passes through.
The line passes through (0, 4 ) with a y- coordinate of 4
Therefore, the equation of the line of y= 4
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rolling a number greater than 0 but less than 7
Probability of rolling a number greater than 0 but less than 7 is 1.
Define probability?The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, probability has also been introduced in mathematics.The probability formula is as follows:
Probability = Favourable outcomes / Total outcomes
Sample space of rolling a dice:
S = {1, 2, 3, 4, 5, 6}
Total outcomes = 6
Favourable outcomes: number greater than 0 but less than 7
Favourable outcomes: 6
Then, probability of rolling a number greater than 0 but less than 7
Probability = Favourable outcomes / Total outcomes
Probability = 6/6
Probability = 1
Thus, probability of rolling a number greater than 0 but less than 7 is 1.
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The complete question is-
A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7
As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
.......................................................................................................
Answer:
1640
Step-by-step explanation:
Are of the square
a = \(s^{2}\)
a = \(10^{2}\)
a = 100
Area of a trapezoid
a = 1/2(a + b)h
a = 1/2(48 + 40)35
a = 1/2 (48 + 40)35
a = 1/2(88)35
a = 44(35)
a = 1540
100 + 1540 = 1640
Helping in the name of Jesus.
Answer:
The area is 1640 square meters
Step-by-step explanation:
the area of the short block(top right) is
\((10)(10) = 100\\\)
Now, the total length of the top side is(of the bottom portion),
38 + 10 = 48
We can divide the bottom portion into a square and triangular part,
for the square part we get the area,
\((40)(35)=1400\)
For the triangle, we first have to find the length of the base,
which we see from the figure that it will be,
48 - 40 = 8
(and height is 35)
so the area of the triangle is,
\((1/2)(8)(35)=140\)
so the total area of the park is
\(140 + 1400 + 100 = 1640\)
Write a simplified expression that represents the...
a. area of the large rectangle.
b. area of the small rectangle.
c. area of shaded region.
Answer:
See below
Step-by-step explanation:
a.
Area of the large rectangle = (6 + x) (6 - x)->Area of the large rectangle \(=(6)^2-x^2\)-> Area of the large rectangle \(= 36-x^2\)b.
Area of the small rectangle = (2 + x) (2 - x)->Area of the small rectangle \(=(2)^2-x^2\)->Area of the large rectangle \(= 4-x^2\)c.
Area of shaded region = Area of the large rectangle - Area of the small rectangle-> Area of shaded region \(=( 36-x^2)-(4-x^2)\)-> Area of shaded region = \(=36-x^2-4+x^2\)-> Area of shaded region \(=32 \:units^2\)To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm.
a) What percent of possums have heads less than 95.4 mm?
b) What percent of possums have heads more than 85.8 mm?
c) What percent of possums have heads between 85.8 and 95.4 mm?
d) What is the maximum head length of the shortest 10% of possum heads?
a) Approximately 77.94% of possums have heads less than 95.4 mm.
b) Approximately 96.93% of possums have heads more than 85.8 mm.
c) Approximately 74.93% of possums have heads between 85.8 and 95.4 mm.
d) The maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.
a) We can use the normal distribution to answer this question. Let X be the head length of a brushtail possum. Then X has a normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm. We want to find P(X < 95.4 mm).
Using the standard normal distribution table or a calculator, we can find the z-score corresponding to a head length of 95.4 mm:
\(z = \frac{(95.4 - 92.6)}{3.6} = 0.78\)
Then, using the standard normal distribution table, we can find the probability that a standard normal variable is less than 0.78:
P(Z < 0.78) = 0.7794
Therefore, approximately 77.94% of possums have heads less than 95.4 mm.
b) Again, using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find P(X > 85.8 mm).
Finding the corresponding z-score:
\(z = \frac{(85.8 - 92.6)}{3.6} = -1.89\)
Using the standard normal distribution table, we find:
P(Z > -1.89) = P(Z < 1.89) = 0.9693
Therefore, approximately 96.93% of possums have heads more than 85.8 mm.
c) To find the percentage of possums with heads between 85.8 and 95.4 mm, we can subtract the probability of heads less than 85.8 mm from the probability of heads less than 95.4 mm:
P(85.8 < X < 95.4) = P(X < 95.4) - P(X < 85.8)
Using the same calculations as in parts (a) and (b), we get:
P(85.8 < X < 95.4) = 0.7794 - 0.0301 = 0.7493
Therefore, approximately 74.93% of possums have heads between 85.8 and 95.4 mm.
d) We want to find the maximum head length of the shortest 10% of possum heads. This is equivalent to finding the 10th percentile of the distribution. Using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find the head length x such that P(X < x) = 0.1.
Using the standard normal distribution table or a calculator, we can find the z-score corresponding to the 10th percentile:
P(Z < z) = 0.1
z = -1.28
Then, we can find the corresponding head length x:
x = μ + zσ = 92.6 + (-1.28)(3.6) = 87.68
Therefore, the maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.
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What is AOM under what type of equation?
AOM is under zero, as stated in the sequential equation
Factor each polynomial
Odds only
The solution is: Factorization of the polynomial completely is:
2( x+2) (x-1)
Here, we have,
the given polynomial is:
2x^2 +2x-4
now, we have to factorize it completely.
we have,
2x^2 +2x-4
We can factor out a 2
2(x^2 +x-2)
What numbers multiply to -2 and add to 1
=> 2*(-1) = -2
=> 2+ (-1) = 1
=> 2( x+2) (x-1)
Hence, The solution is: Factorization of the polynomial completely is:
2( x+2) (x-1).
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Pls help :)
Find the value of x
Answer:
x = 20
Step-by-step explanation:
You have pointed out the angles are supplementary, so they add to 180.
Add both angles to equal 180.
7x + x + 20 = 180
Combine like terms.
8x + 20 = 180
Subtract 20 from both sides.
8x = 160
Divide out the 8 to get x.
x = 20
PLEASE ANSWER NUMBER 2