As per the given statement, the scuba diver's position means the distance he traveled is below 18 feet at the sea level.
Here we have given that a scuba diver starts at sea level and travels to a position that is a little lower than -18 feet.
Now, we need to find the scuba diver's position means the distance he traveled.
While we consider that the scuba driver travelled on -18 feet.
Here the negative term is defined that the the traveler goes on the bottom level.
Therefore, here we said that the person is going to below the sea level.
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Can a triangle be formed with side lengths 5'7 and 10?
It is possible to construct a triangle whose sides are 5 cm 7 cm and 10 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 10 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 5 and 7
5 + 7 > 10
12 > 10
Now we add 10 and 7
10 + 7 > 5
17 > 5
Now we add 5 and 10
5 + 10 > 7
15 > 7
It is possible to construct a triangle whose sides are 5 cm 7 cm and 10 cm because the sum of two sides are greater than third sides.
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The complete qiestion is:
Can a triangle be formed with side lengths 5 cm 7 cm and 10 cm?
Forty people were randomly sampled and surveyed as to the number of pets in their household. The results are listed below.
To find the number of people with different amounts of pets, we need to first count the number of instances each pet number occurs.The survey of forty people revealed that there were three people with four pets, seven people with three pets, nine people with two pets, seventeen people with one pet
2, 0, 3, 1, 0, 0, 4, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3
There are:
* 3 people with 4 pets
* 7 people with 3 pets
* 9 people with 2 pets
* 17 people with 1 pet
* 8 people with 0 pets
To find the number of people with different amounts of pets, we need to first count the number of instances each pet number occurs. To do this, we can go through the list of numbers and count how many times each number appears.
For example, the number "2" appears three times in the list, meaning that there are three people with two pets. If we do this for all the numbers in the list, we get the results listed above.
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What are the techniques used in 3D applications to convert 2D object to 3D?
Techniques for converting 2D images to 3D in image processing are Stereoscopy, Depth from Focus, Volumetric Rendering, 3D Reconstruction, Machine Learning.
1. Stereoscopy: Stereoscopy is the process of combining two 2D images taken from different angles to create a 3D image. This technique is used in medical imaging, aerial photography, 3D movies, and other applications.
2. Depth from Focus: This technique uses an algorithm to calculate the depth of each pixel in an image. It works by analyzing the blurriness of different parts of the image and using that data to determine the depth.
3. Volumetric Rendering: This technique uses a 3D model to generate a 3D image. The model can be a 3D scan of a real-world object or a virtual 3D model created in 3D modeling software.
4. 3D Reconstruction: This technique uses multiple input images taken from different angles to reconstruct a 3D scene. It is often used in computer vision and robotics applications.
5. Machine Learning: This technique uses machine learning algorithms to automatically generate a 3D image from a 2D image. This is a relatively new technique and is still being developed.
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Solving Equations solve for the variable in each of the following equations. Write your final solution as an equation
please tell me the equation for each 4
Answer:
c = 10
w = -6
r = 6
b = 1.5 or 3/2
Step-by-step explanation:
1) 2c + 4 = 7c - 46
2c - 2c + 4 = 7c - 2c - 46
4 + 46 = 5c - 46 + 46
50 = 5c
c = 10
2) -3w + 8 = -6w - 10
-3w + 6w + 8 = -6w + 6w - 10
3w + 8 - 8 = -10 - 8
3w = -18
w = -6
3) (1/6)r + 1 = 3r - 16
(1/6)r - (1/6)r + 1 = 3r - (1/6)r - 16
1 + 16 = (17/6)r - 16 + 16
(17/6)r = 17
r = 17*(6/17)
r = 6
4) -7b - 1 = -5b - 4
-7b + 7b - 1 = -5b + 7b - 4
-1 + 4 = 2b - 4 + 4
2b = 3
b = 3/2 or 1.5
Hope this helps!
These figures are similar.
The angles are equal of △ABC and △XYZ. Thus △ABC ∼ △XYZ.
What are similar triangles?
Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.
Given that in △ABC and △XYZ:
∠C = ∠X
∠A = ∠Z
∠B = ∠Y = 100°.
AAA rule: If the angles of a triangle are congruent to the angles of another triangle, then the triangles are congruent.
According to AAA rule, △ABC is similar to △XYZ.
The symbol of similar triangles is ∼.
Therefore, △ABC ∼ △XYZ.
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Why isn’t x squared subtract 81 the same as x squared plus 81
Answer:
Step-by-step explanation:
0
Solving systems of equations by elimination calculator
x+y=5, x+2y=7
Answer:
x = 3
y = 2
Step-by-step explanation:
x + y = 5
x + 2y = 7
x = 5 - y
( 5 - y ) + 2y = 7
= 5 + 2y - y = 7
= 5 + y = 7
y = 7 - 5
y = 2
x + ( 2 ) = 5
x = 5 - 2 = 3
A company is developing packaging for a new product as shown below. Choose the expression that can be used to find the volume of the packaging. A. ( 2 × 3 × 4 ) + ( 2 × 9 × 2 ) 2 × 3 × 4 + 2 × 9 × 2 B. ( 2 × 4 × 3 ) + ( 2 × 9 × 4 ) 2 × 4 × 3 + 2 × 9 × 4 C. ( 2 × 4 × 3 ) + ( 4 × 9 × 4 ) 2 × 4 × 3 + 4 × 9 × 4 D. ( 3 × 4 × 4 ) + ( 2 × 9 × 2 ) pls help
(2 × 4 × 3) + (4 × 9 × 4) 2 × 4 × 3 + 4 × 9 × 4 this expression is the correct answer.
What is value?Value is a concept that describes the worth of something in relation to its utility, purpose or importance. Value can refer to tangible items like money, or intangible concepts like morality, loyalty, or trust. Value is subjective, as it differs between individuals and cultures. It can also be expressed in terms of time, effort, resources, or any combination of these. Ultimately, value is a personal judgment of what is valuable and important to each individual.
The expression C. (2 × 4 × 3) + (4 × 9 × 4) 2 × 4 × 3 + 4 × 9 × 4 can be used to find the volume of the packaging.
This expression will calculate the volume of the packaging by multiplying the length, width, and height of both sections of the packaging, then adding the two products together.
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A grocery tore ell pear, where 6 pear cot $9. How much will 8 pear cot at thi rate?
As per the unitary method, the cost of 8 pear is at the rate of $12.
The term unitary method is defined as a process of finding the value of a single unit, and based on this value and then we can find the value of the required number of units.
Here we have given that the grocery store the cost of 6 pear is $9.
Let us consider that x be the cost of one pear.
Here we know that the the cost of 6 pear is $9.
Then the cost of one pear is calculated as,
=> x = 9/6
When we simplify this one then we get, the cost of one pear as,
=> x = 1.5
Therefore, the cost of 8 pear is calculated as,
=> 8 x 1.5
=> 12
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What are the three methods to solve a 3 variable linear system of equations?
The three methods to solve a 3 variable linear system of equations are interchanging the order of any two equations, multiplying both sides of an equation by a non-zero constant, add a non-zero multiple of one eqn to another eqn.
In order to solve any system of equations in three variables, known as three-by-three systems, the primary purpose is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables (x,y,z), is known as an ordered triple.
Step 1. Choose any pair of equations and solve for one variable.
Step 2. Choose another pair of equations and determine the same variable.
Step 3. You have developed a system of two equations in two unknowns. Solve the resulting two-by-two system.
Step 4. Back-substitute the known variables into any one of the original equations and solve for the missing variable.
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need some help with the screenshot
Answer:
(1,4)
Step-by-step explanation:
Match the best answer on the right to the item on the left.
Group of answer choices
α [ Choose ]
Continuous variable [ Choose ]
Normal distribution [ Choose ]
q = 1 – p [ Choose ]
N [ Choose ]
x [ Choose ]
σ² [ Choose ]
σ [ Choose ]
Left skewed distribution [ Choose ]
Data is collected by watching the behavior of sample [ Choose ]
Data is collected by imposing a treatment on a sample and examining the results [ Choose ]
Data is collected as a result of computer modeling [ Choose ]
Data is collected by asking a series of questions [ Choose ]
Data is collected that does not fairly represent the population [ Choose ]
A measure of the spread or variability of the data set [ Choose ]
n [ Choose ]
r [ Choose ]
Most frequently occurring value in the date set [ Choose ]
data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling. Left skewed distribution is data collected that does not fairly represent the population.
Mode [ Choose ]
x Continuous variable
n N
σ σ²
r q = 1 – p
Mode Most frequently occurring value in the date set
Left skewed distribution Data is collected that does not fairly represent the population
Normal distribution Data is collected by asking a series of questions
A measure of the spread or variability of the data set Data is collected by watching
Data is collected by imposing a treatment on a sample and examining the results Data is collected as a result of computer modeling
x is a continuous variable, n is N, σ is σ², r is q = 1 – p, mode is the most frequently occurring value in the date set, a left skewed distribution is data collected that does not fairly represent the population, a normal distribution is data collected by asking a series of questions, a measure of the spread or variability of the data set is data collected by watching the behavior of sample, and data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling.
x is a continuous variable, n is N, σ is σ², r is q = 1 – p, mode is the most frequently occurring value in the date set. Data collected by asking a series of questions is a normal distribution, data collected by watching the behavior of sample is a measure of the spread or variability of the data set, and data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling. Left skewed distribution is data collected that does not fairly represent the population.
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The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
Which equation describes g(x)?
A) g(x)=|x-4|
B) g(x)=|x+4|
C) g(x)=|x|-4
D) g(x)=-4|x|
The Function after reflection over x-axis is D) g(x) = -4IxI.
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
Here The graphs of g may be obtained from the graph of f by shifting up c units. The graph moves downward if we take c out of f(x). Let h(x) = f(x)-c shifting downward c units yields this graph of h from the graph of f.
Now given function f(x)= 4IxI.
It is stated that its graph of is obtained by reflecting a graph of f(x)= 4IxI over the x-axis.
When a figure is reflected across the x-axis, the rule for reflection is
(x,y)=>(x,-y)
Then g(x)=-f(x),
=> g(x) = -(4IxI)
=> g(x) = -4IxI
Hence the correct option is D)g(x) = -4IxI.
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PLEASEEE HELP 100 POINTS
A line has a slope of 0 and a y-intercept of –3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = - 3
Step-by-step explanation:
a line with a slope of zero is a horizontal line, parallel to the x- axis with equation
y = c ( where c is the value of the y- coordinates the line passes through )
the line passes through (0, - 3 ) , the y- intercept with c = - 3 , then
y = - 3 ← equation of line
note this equation cannot be expressed in slope- intercept form
A line with a slope of 1 passes through the points (10,c) and (6,4). What is the value of c
We also know that the line passes through the point (6,4), so we can substitute these values into the equation of the line and solve for c:
4 = 1(6) + c
c = -2
What is slope?The slope of a line is a measure of how steep the line is. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is also commonly referred as the "gradient" of a line. A line with a positive slope goes up from left to right, a line with a negative slope goes down from left to right, and a line with a slope of 0 is a horizontal line.
What is the formula to calculate the slope with given two points?The formula to calculate the slope (m) with given two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Since the line has a slope of 1 and passes through the point (10, c), we know that the y-intercept is c.
We also know that the line passes through the point (6,4), so we can substitute these values into the equation of the line and solve for c:
4 = 1(6) + c
c = -2
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A teacher buys a yogurt cup for $2.00 and a textbook for $13.00 for each student in their classroom. The teacher spends a total of $405.00 for all of the yogurt cups and textbooks.
The number of students the teacher bought for is 27.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cost of a yogurt cup = $2.
Cost of a textbook = $13
Cost for one students = 2 + 13 = $15
Total cost = $405
The number of students.
= Total cost / Cost of one student
= 405 / 15
= 27
Thus,
The number of students is 27.
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Is there a triangle whose sides are of length 2cm 3cm and 5cm?
It is not possible to construct a triangle whose sides are 2cm 3cm and 5cm because the sum of two sides(2 cm and 3 cm) are equal to the third sides(5 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 2cm 3cm and 5cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 2 and 3
2 + 3 = 5
5 = 5
Now we add 2 and 5
2 + 5 > 3
7 > 3
Now we add 3 and 5
5 + 3 > 2
8 > 2
It is not possible to construct a triangle whose sides are 2cm 3cm and 5cm because the sum of two sides(2 cm and 3 cm) are equal to the third sides(5 cm).
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A 6-kg bowling ball sits on top of a building that is 120 meters tall.
The potential energy of the bowling ball is equal to 7,056 Joules.
How to calculate the potential energy of the bowling ball?Mathematically, the gravitational potential energy (GPE) possessed by any physical object or body can be calculated by using this mathematical expression:
GPE = mgh
Where:
GPE represents gravitational potential energy.m represents the mass.h represents the height.g represents acceleration due to gravity.Note: Acceleration due to gravity is equal to 9.8 m/s².
Substituting the given parameters into the formula, we have;
GPE = 6 × 9.8 × 120
Gravitational potential energy (GPE) = 7,056 Joules.
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Complete Question:
A 6-kg bowling ball sits on top of a building that is 120 meters tall. What is the potential energy of the bowling ball?
How many solutions does the pair of linear equations y 0 and y =- 5 has?
Pair of linear equations y = 0 and y = -5 has no solutions as the equations represents the parallel lines.
As given in the question,
Given pair of linear equations are as follow:
y = 0
y = -5
Here linear equation y = 0 represent the whole x- axis.
And the linear equation y = -5 represents the line parallel to x -axis below the origin of x- axis.
Both the linear equation y = 0 and y = -5 represents the parallel lines so they don't intersect at any point.
And has no solution.
Therefore, the given pair of linear equations y = 0 and y = -5 represents parallel lines and has no solution.
The above question is incomplete , the complete question is:
How many solutions does the pair of linear equations y = 0 and y = - 5 has?
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Helloooo helppp me please
The remainder of given polynomial is 10 . An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
What distinguishes a polynomial?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. The word "polynomial" is derived from the Greek words "poly" and "nominal," which together translate to "many terms."
Given,
[tex]fx=x^3+2x^2-5x-6[/tex]
By using remainder theorem
[tex]f(2)=2^3+2*2^2-5*2-6\\f(2)=0[/tex]
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According to th given question x³ - 2x² - 5x + 6 is divided by x + 2 it gives remainder zero.
A split fraction is what?The act of dividing a fraction into further equal portions is known as fraction division. For instance, if you cut a slice of pizza in half and had three-fourths of the pizza left, you would have eaten six slices total, or four of the entire pizza. In mathematics, division is the procedure of dividing a sum into equal parts. For illustrate, we may divide a group of 20 individuals into small groups of 4, 5, 6, and so on.
Given that p(x) = x³ - 2x² - 5x + 6 and g(x) = x + 2
We have to track down the rest.
So let's get started!
Remainder theorem is used;
g(x) = x + 2 = 0
g(x) = x = -2
By substituting the value x = -2
x³ - 2x² - 5x + 6
Substituting the values:
(-2)³ - 2(-2)² - 5(-2) + 6
= - 8 + 10 + 6
= -16 + 16
= 0
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A circle has a diameter with endpoints at –3 18i and 7 – 6i. which point is also on the circle? –7 7i 5 12i 12 – i 14 11i
The only point that has the same distance from the center as the others are point (5 + 12i). Therefore, the answer is option b. (5 + 12i).
To find which point is also on the circle, we can use the distance formula to find the distance between each point and the center of the circle. The center of the circle can be found by taking the midpoint of the diameter, which has endpoints at -3+18i and 7-6i. The midpoint can be found by averaging the x-coordinates and the y-coordinates of the two endpoints:
x-coordinate: (-3 + 7)/2 = 2
y-coordinate: (18 - 6)/2 = 6
So the center of the circle is at (2, 6).
Now we can use the distance formula to find the distance between each point and the center of the circle:
Point a: |(-7 - 2) + (7 - 6)| = |-9 + 1| = 10
Point b: |(5 - 2) + (12 - 6)| = |3 + 6| = 9
Point c: |(12 - 2) + (-1 - 6)| = |10 + 7| = 17
Point d: |(14 - 2) + (11 - 6)| = |12 + 5| = 17
The distance from the center of the circle to each point is the radius of the circle, so all points on the circle should have the same distance from the center. So, the only point that has the same distance from the center as the others is point b.
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The complete question is -
A circle has a diameter with endpoints at -3 + 18i and 7 - 6i. Which point is also on the circle?
a. -7 + 7i
b. 5 + 12i
c. 12 - i
d. 14 + 11i
Dante deposited $5,000 into an account with an annual interest rate of
3.5%. He plans to deposit an additional $200 each year, just after the
interest is compounded. How much money will Dante have after 4 years?
(round to the penny)
Dante will have $5872.50 after 4 years, when compounded $5,000 into an account with an annual interest rate of 3.5%.
What is interest rate?Simply put, interest is the cost of borrowing money, whether it be through a student loan, a mortgage, or a credit card. When you borrow money, you typically have to pay it back along with interest that is calculated as a percentage of the loan amount. There are a few exceptions, such as when you pay off your credit card balance in full each month or when you have a promotional 0% interest rate.
You might be eligible for lower interest rates if prospective creditors and lenders view your track record of responsible credit behaviour and view you as a low-risk borrower.
The compound interest formula is given by
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here,
A = to find
P = $5,000
r = 3.5%
n = 1
t = 4
Putting the values in the formula
First year
[tex]$A = 5000+ 200(1 + \frac{0.035}{1})^{1}[/tex]
2nd year
[tex]A = 5207+200(1 + \frac{0.035}{1})^{2}[/tex]
3rd year
[tex]A = 5421.245+200(1 + \frac{0.035}{1})^{3}[/tex]
4th year
[tex]A = 5643+200(1 + \frac{0.035}{1})^{4}[/tex]
A = $5872.50
Thus, Dante will have $5872.50 after 4 years, when compounded $5,000 into an account with an annual interest rate of 3.5%.
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Which statement could be represented by the following 5m - 12?
Responses
The product of five and a number less than twelve
Twelve less than the product of five and a number
The product of five times a number and negative twelve
The sum of five times a number and twelve
The statement that can be represented by the expression, 5m - 12, is B. Twelve less than the product of five and a number.
What statement is represented by the formula ?The expression given is 5 m - 12. In this formula, the value of m is a mystery number that is multiplied by 5 and then the product of these two numbers is reduced by 12.
This means that representing the formula can be done by saying, Twelve less than the product of five and a number. First the product of 5 and the value of m are found, and then twelve is subtracted from the formula.
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Use the distributive property to simplify the following expression: 3(−5+2x)
The simplified expression of 3 (-5 + 2x) is -15 + 4x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3 (-5 + 2x)
The distributive property of multiplication over addition states that,
a x (b + c) = a x b + a x c
Now,
3 x (-5 + 2x)
3 x (-5) + 2 x (2x)
-15 + 4x
Thus,
The simplified expression is -15 + 4x.
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $145,690. Round the final answer to the nearest hundredth.
24.39%
22.00%
19.81%
17.00%
Answer:
The effective tax rate for a taxable income of $145,690 would be 24.39%.
Step-by-step explanation:
To find the effective tax rate, you need to calculate the total amount of tax paid on the taxable income, and then divide that amount by the taxable income, and multiply by 100 to express it as a percentage.
We can see from the marginal tax rate chart that for a taxable income of $145,690, the marginal tax rate is 24%. This means that the last dollar earned falls in the 24% tax bracket.
We can calculate this in the following steps:
Determine the taxable income in each tax bracket:
$10,276 - $41,175: $41,175 - $10,276 = $30,899
$41,176 - $89,075: $89,075 - $41,176 = $47,899
$89,076 - $170,050: $145,690 - $89,076 = $56,614
Calculate the taxes owed in each tax bracket:
$10,276 - $41,175: $30,899 x 12% = $3,707.88
$41,176 - $89,075: $47,899 x 22% = $10,526.78
$89,076 - $170,050: $56,614 x 24% = $13,547.36
Add up the taxes owed in each bracket to find the total taxes: $3,707.88 + $10,526.78 + $13,547.36 = $27,782.02
Divide the total taxes by the taxable income and multiply by 100 to find the effective tax rate: $27,782.02 / $145,690 x 100 = 19.02%
The effective tax rate for a taxable income of $145,690 would be 19.02%.
It's worth to mention that this is a rough estimate and The final tax calculation would be provided by a tax preparer or software and it would take into account many deductions, credits and any other tax benefits that would affect the final calculation.
is 5/5 greater then 1 or less then 1??
Answer:
It's exactly 1 .........
Refer to the accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with five classes. Begin with a lower class limit of 124.8 volts, and use a class width of 0.2 volts. Does the result appear to have a normal distribution? Why or why not
The normal distribution table appears to be slightly biased to the right. Since the values are randomly distributed, a normal distribution cannot be assumed.
what is normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster near the middle of the range and the remaining ones decrease symmetrically toward one of the extremes.
Maximum Value=121.9
Number of classes=5 (say)
Range=121.1-121.9=0.8
Minimum Value= 121.1
width of each class= 0.8 / 5 = 0.16 = 0.2 (approx)
Therefore, we must create classes so that the first class has the minimum value and the last class contains the highest value. The class interval will therefore be 121.1 - 121.3, 121.3 - 121.5, and so on with a class width of 0.2 volt.
Voltage (volts) Frequency
121.1 - 121.3 2
121.3 - 121.5 5
121.5 - 121.7 10
121.7 - 121.9 6
121.9 - 122.1 2
The normal distribution table appears to be slightly biased to the right. Since the values are randomly distributed, a normal distribution cannot be assumed.
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A linear relationship is shown in the table.
Time (hours) 2 4 6 8
Distance (miles) 4 8 12 16
Is the linear relationship also proportional? Explain.
No, the constant of proportionality is 2.
Yes, the constant of proportionality is 2.
No, there is no constant of proportionality.
Yes, there is no constant of proportionality.
Answer:
It's B
"Yes, the constant of proportionality is 2."
Step-by-step explanation:
The time or X shows the same numbers shown in distance or Y
it's just Time x2 for distance
A study indicated that residents of Springtown wasted 7,622 gallons of water this year. That is 85% more than they wasted last year. How many gallons of water did the city's residents waste last year?
Answer: The study indicated that residents of Springtown wasted 7,622 gallons of water this year, which is 85% more than they wasted last year. To find out how many gallons of water the city's residents wasted last year, we need to find out what 85% of 7,622 gallons is and then subtract that amount from the total amount wasted this year.
85% of 7,622 gallons is (85/100) * 7,622 = 6,465.7 gallons
So, if residents of Springtown wasted 7,622 gallons of water this year, which is 85% more than they wasted last year, then they wasted 7,622 - 6,465.7 = 1,156.3 gallons of water last year.
Step-by-step explanation:
Answer:
x = 4120 gallons wasted last year
Step-by-step explanation:
Let x be the amount of water wasted by the residents of Springtown "last year."
They wasted 85% more this year. This would mean that x*(1+ 0.85) = 7622 gallons. [The "(1+0.85)" represents the decimal equivalent to "85% more."
x*(1+ 0.85) = 7622
1.85x = 7622
x = 4120 gallons wasted last year
Check:
Is 7622 85% more than 4120?
(7622-4120)=3502
(3502/42=4120) = 0.85 YES
This table represents a quadratic function with a vertex at (1, 0). What is the
average rate of change for the interval from x = 5 to x = 6?
a) 9
b) 7
c) 5
d) 25
The average rate of change for the interval from x = 5 to x = 6 can be calculated by taking the derivative of the quadratic function and evaluating it at the midpoint of the interval (x = 5.5).
Given that the vertex of the function is at (1, 0), the equation of the quadratic function is in the form of:
f(x) = a(x-1)^2 +0
The derivative of the function is:
f'(x) = 2ax - 2a
We know that the vertex of the function is at (1,0), which means that the value of a is 0.
So the derivative of the function is 0.
Therefore the average rate of change for the interval from x = 5 to x = 6 is 0.