Tom's total annual tax for the following year, assuming the tax table remains the same, is R325,287.17.
How much tax will Tom pay per year?To calculate Tom's tax for the following year, we need to first calculate his current monthly PAYE (Pay As You Earn) deduction. We can use the current tax table to do this.
Tom's gross salary is R25,780.25 per month, and he is 45 years old, so according to the 2021/2022 tax table for individuals under 65 years old, his monthly PAYE deduction is:
= R1,458.75 + 25% of the amount over R14,958
= R4,569.96
Tom argues that his PAYE will increase by R593.09 for the following year. This means that his expected monthly PAYE deduction for the following year is:
= R4,569.96 + R593.09
= R5,163.05
Tom's salary for the following year will increase by 8.5%, so his new gross salary will be:
= R25,780.25 + (8.5% x R25,780.25)
= R27,959.83
Tom's pension fund contribution remains the same at 7.5% of his gross salary:
= R27,959.83 x 7.5%
= R2,097.49
His charity organization contribution increases by R50.00 per month:
= R50.00 x 12
= R600.00
Assuming the tax table remains the same as the previous year, Tom's new monthly PAYE deduction is:
= R1,577.98 + 26% of the amount over R17,708
= R5,502.86
To calculate Tom's total annual tax, we need to subtract his annual PAYE deduction from his gross salary and then add back his pension and charity contributions:
Total annual tax = (R27,959.83 x 12) - (R5,502.86 x 12) + R2,097.49 + R600.00
Total annual tax = R325,287.17.
Full question "Tom is 45 years old. He earns a gross salary of R25,780.25 per month.. Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same."
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construct a right angle triangle with one side 4cm and hypotenuse 5cm.
Answer:
See the explanation below.
Step-by-step explanation:
You need to calculate the remaining side.
Pythagorean theorem: c^2 = a^2 + b^2
=> 5^2 = 4^2 + b^2
b^2 = 25 - 16 = 9
b = √9 = 3
Draw a right triangle with the sides of 3cm and 4cm are perpendicular to form 90 degrees angle. Then connect the ends of 2 lines to form the hypotenuse which will be 5 cm long.
Write the linear equation that gives the rule for this table x 0 1 2 3 y 0 2 4 6
The linear equation that gives the rule for the given table x 0 1 2 3 y 0 2 4 6 is y = 2x.
What is linear equation?A linear equation is an equation of a straight line in the form of y = mx + b, where m represents the slope of the line, and b represents the y-intercept.
The slope of the linear equation can be found by calculating the change in y over the change in x:
slope=(y2 - y1) / (x2 - x1)
Taking (x1,y1) = (0,0) and (x2,y2) = (3,6),
slope=(6 - 0) / (3 - 0)
= 2
So slope of the linear equation is 2.
Next, we can use the point-slope form of the linear equation to find the equation of the line:
y - y1 = m(x - x1)
Taking (x1,y1) = (0,0) and m = 2,
y - 0 = 2(x - 0)
Simplifying, we get
y = 2x
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the box and whisker plots below show the average monthly temperature for Mexico City, Mexico, and Shanghai, china, in degrees Fahrenheit
The percentage of temperatures for Shanghai that falls between 46 degrees Fahrenheit and 78 degrees Fahrenheit is A. 50 %.
Where does 50 % of the temperature fall ?The interquartile range (IQR) of a box and whisker plot is defined as the difference between the third quartile (Q3) and the first quartile (Q1). It represents the spread of the middle 50% of the data.
On a box plot, the interquartile range (IQR) is represented by the box itself. The box extends from the first quartile (Q1) to the third quartile (Q3) and contains the middle 50% of the data.
This means that for Shanghai, the temperatures of 46 degrees Fahrenheit and 78 degrees Fahrenheit represent the IQR which means that this is 50 % of the temperature.
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The full question is:
The box-and-whisker plots below show the mean monthly temperatures (°F) for Mexico City, Mexico, and Shanghai, China. What percent of the temperatures for Shanghai fall between 46°F and 78°F? *
{x|x is an even, negative integer and x > - 25}
The number of elements in set A is n = 12 elements of the set A is given by A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the set notation be represented as S
Now , the value of S is
S = {x|x is an even, negative integer and x > - 25}
Now , the value of the set A is given by all the numbers greater than -25 which are negative and even
So , A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
The number of elements in set A = 12 elements
Therefore , the value of n = 12 elements
Hence , the set A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
x = 2 (True)
Step-by-step explanation:
I need help please answer 15 points !!!
The option that describes the correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass is option C
C.
Draw a circle with a radius less than [tex]\overline{DE}[/tex] and center E, and label the points of intersection G and H.Draw a line from point G to point HDraw a circle with radius [tex]\overline{GH}[/tex]and center G and another circle with radius [tex]\overline{GH}[/tex]and center H, and draw an equilateral triangle.Use straightedge to connect E to the rightmost vertex of the equilateral triangle. What is the angle bisector of an angle?An angle bisector is a segment that splits an angle to form two smaller congruent angles.
The steps for construct an angle bisector of the angle ∠DEF, by making use of a compass and a straightedge are;
With point E as the center, draw a circle with a radius less than the segment [tex]\overline{DE}[/tex], to intersect [tex]\overline{DE}[/tex] and [tex]\overline{EF}[/tex] at point G and HWith point G as the center, draw a circle with radius [tex]\overline{GH}[/tex], and with point E as center and with the radius [tex]\overline{GH}[/tex], draw another circleDraw an equilateral triangle to the points G and H from the point of intersection of the two circlesConnect point E to the rightmost vertex of the equilateral triangle, which is the point of intersection of the two circles to draw the angle bisector of ∠DEFLearn more on the geometric constructions here: https://brainly.com/question/29096545
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The diagram shows a triangle. 35* What is the value of x? 11x
The value of the variable x is 10
How to determine the valueFollowing the triangle theorem, we have that the sum of the angles in a triangle is equivalent to 180 degrees.
From the information given, we have the interior angles as;
4x, 9x and 5x
Now, equate the angles to the sum, we have;
4x + 9x + 5x = 180
add the like terms, we have;
18x = 180
Now, let's determine the value of x by dividing both sides by the coefficient of x, we get;
18x/18 = 180/18
divide the values
x = 10
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I need help please ?!!!!??!
Answer:
68
Step-by-step explanation:
x = original number of marbles
x = 104 - 36
x = 68
For what value of k will V= x+ k/x have a relative minimum at x = 3?
The value of k will make V = x + k/x have a relative minimum at x = 3 is k = 9
What is a relative minimum?A relative minimum of a function is the minimum value of the function in a particular interval.
Since we have the function V = x + k/x. We desire to find the value of k that will make V = x + k/x have a relative minimum at x = 3
So, to find the relative minimum of V, we differentiate with respect to x and equate to zero.
So, V = x + k/x
dV/dx = d(x + k/x)/dx
= dx/dx + kd(1/x)/dx
= 1 - k/x²
Equating dV/dx to zero, we have that
dV/dx = 0
⇒ 1 - k/x² = 0
1 = k/x²
k = x²
For a relative minimum at x = 3, substitute x = 3 into the equation. So, we have that
k = x²
= 3²
= 9
So, k = 9
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Select the correct answer from each drop-down menu.
Complete each statement about the key features of function g(x).
What are functions ?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
What are asymptotes ?
An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.
There are three types of asymptotes namely:
1) Vertical Asymptotes
2) Horizontal Asymptotes
3) Oblique Asymptotes
The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity.
What are domain of a function ?
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
What is range of a function ?
The range of a function is the set of values that the function assumes. This set is the values
that the function shoots out after we plug an x value in. They are the y values.
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the number of terms of the sequence 4²,5²,6²....39²,40² that have an even digit in the tens place is
There are 29 terms of the sequence given which is even in tens place.
What are even numbers?A number that is divisible by 2 and generates a remainder of 0 is called an even number.
Examples of even numbers are 2, 4, 6, 8, 10, etc.
Given that, the sequence 4²,5²,6²....39²,40² we need to find the terms that have an even digit in the tens place is.
Finding the squares =
4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13²= 169, 14² = 196, 15² = 225, 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400, 21² = 441, 22² = 484, 23² = 529, 24² = 576, 25² = 625, 26² = 676, 27² = 729, 28² = 784, 29² = 841, 30² = 900, 31² = 961, 32² = 1024, 33² = 1089, 34² = 1156, 35² = 1225, 36² = 1296, 37² = 1369, 38² = 1444, 39² = 1521, 40² = 1600
The terms having even number in tens place,
5, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 10, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 39 and 40
Hence, there are 29 terms of the sequence given which is even in tens place.
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$5 dollars less on dinner than James
An algebraic expression that represents "$5 dollars less on dinner than James" is y = x - 5.
What is algebraic expression?Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression). Let's take the expression 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
We simply combine like terms in an algebraic expression to make it simpler. As a result, similar variables will be combined.
Given:
James Spent = x - $5.00
where x represents the usual amount James spent.
So,
y = x - 5
Thus, An algebraic expression that represents "$5 dollars less on dinner than James" is y = x - 5.
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Complete question:
$5 dollars less on dinner than James spent. Write the phrase an algebraic expression
Question 6 What is the perimeter of the figure shown below, which is not drawn to scale? help
Answer:
C
Step-by-step explanation:
the perimeter means to go along all 4 sides and sum up the distance.
so, we have
x + 12 + x + 12 + 2x + 2x
we combine all similar terms (the ones with a variable and the constants without a variable)
x + x + 2x + 2x + 12 + 12 = 6x + 24
why do you think the sum of x + x + 2x + 2x is 4x ?
and 12 + 12 is 28 ?
do you need any further explanation, or is this now clear ?
What is the total cost of a $707 tablet computer that is on sale at 14% off if the local sales tax rate is 5%?
Answer:
$638.42
Step-by-step explanation:
First, we need to calculate the sale price of the tablet computer after the 14% discount is applied. To do this, we can multiply the original price by 0.86 (1 - 0.14), which gives:
Sale price = $707 x 0.86 = $608.02
Next, we need to add the sales tax to the sale price. To do this, we can multiply the sale price by 0.05 (5%), which gives:
Sales tax = $608.02 x 0.05 = $30.40
Finally, we can find the total cost of the tablet computer by adding the sale price and the sales tax, which gives:
Total cost = $608.02 + $30.40 = $638.42
Therefore, the total cost of the tablet computer with the discount and sales tax included is $638.42.
PLEASEEE HELPPPPPPP
Consider the graphs of the six basic trigonometric functions, and complete the table of key features.
The answer of the given table of key are:
For g(x) =csc(x), Domain: {x|x≠πn}, for any integer n
Range: (−∞,−1]∪[1,∞),{y|y≤−1,y≥1}
What is Domain of a function?The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, whereas the domain of g(x)=1/x is all real numbers other than x=0.
A Function's Range includes all possible values for y. Y = f is the formula to determine a function's range (x). It is only a function in a relationship if each x value has exactly one y value.
For g(x) =csc(x), Domain: {x|x≠πn}, for any integer n
Range: (−∞,−1]∪[1,∞),{y|y≤−1,y≥1}
For f(x) = cos(x), Domain: (−∞,∞),{x|x∈R}
Range : [−1,1],{y|−1≤y≤1}
Amplitude : 1
Midline : y = 0
For f(x) = tan(x), Range: (−∞,∞),{y|y∈R}
Amplitude : None
Midline : Undefined
For g(x) = cot(x), Range : (−∞,∞),{y|y∈R}
Amplitude : None
Midline : Undefined
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56 points! Complete each proof using the most appropriate method.
The triangles given are congruent as shown below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
1) KL = LN [Since L is the midpoint of KN]
ML = LP [ Since L is the midpoint of MP]
∠MLK = ∠MLP [Vertically opposite pair of angles are equal.]
ΔMKL ≅ ΔPNL [Using the SAS Congruence Rule]
2) ∠BAD = ∠BCD [Given]
∠ABD = ∠CBD [Since BD bisects ∠ABC]
BD = BD [Common side]
ΔABD ≅ ΔCBD [Using AAS Congruence rule]
3) QR = ST [Given]
RS = TU [given]
QS = SU [Since S is the midpoint of QU]
ΔQRS ≅ ΔSTU [By SSS Congruence rule]
Hence the triangles are congruent.
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PLS HELPPP THYANK UUU PLS The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=
The Central Angle of each color is:
Red= 100°
Blue= 150°
Green= 50°
Purple = 60°
what is Central Angle?According to the definition of a central angle in geometry, it is the angle that the arc of a circle occupies in its centre. The angle's arms are formed by the two radii. Knowing the ratio of the curve to the circle using the central angle is helpful.
To draw a pie chart we have to find the central angle.
For Red
= 20/72 x 360
= 100 degree
For Blue
= 30/72 x 360
= 150
For Green
= 10/72 x 360
= 50
For Purple
= 12/ 72 x 360
= 60
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Mrs. Foley new rug is 7 feet long and 6 feet wide. What is the area of the rug draw a model to show
The rug covers 42 feet of space. We calculate the area of a rectangle to determine it. A rug is woven fabric or animal skin used as a floor covering.
Why do you use the word rectangle?It is a shape with four straight sides and four right angles that is not square, especially if the sides next to it are uneven.
When a 2-D enclosed shape has four sides, four corners, and four right angles (90°), it is referred to as a rectangle. When opposing sides of a diagram are equal and parallel, the shape is referred to as a rectangle.
Area of rectangle = L × B
So, Area of rug = 7 × 6
= 42 feet
Therefore the required answer is 42 Feet.
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HELP ME please. i dont understand this.
Answer:
Step-by-step explanation:
Perimeter add all the sides.
so let's walk around and combine like terms:
starting on the bottom moving to the left.
3x^2 + x^2= 4x^2 (there are no other squared terms)
back to the bottom moving left again:
-11x-3x+3x+x = -10x (-3x + 3x =0)
so -11x + x = -10x
now add all of the constants
-1 + 2 = 1
so your answer is
4x^2 -10x + 1
Jen has driven 15 miles on her way to the mall. this distance is 3/5 of the total distance. if d represents the total distance in miles, which equation can be used to find d
This can be resolved with d = 25 miles by multiplying equation both sides by
Which equation can be used to find d?If Jen has driven 15 miles, and this is 3/5 of the total distance, we can use the following equation to find the total distance d:
15 = (3/5) * d
To solve for d, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by 3/5, which is the same as multiplying by its reciprocal, 5/3:
15 * (5/3) = d
Simplifying the expression on the left side, we get:
25 = d
Therefore, the total distance Jen needs to travel to get to the mall is 25 miles.
In summary, the equation that can be used to find the total distance d, given that Jen has driven 15 miles and this is 3/5 of the total distance, is:
15 = (3/5) * d
Which can be solved for d by multiplying both sides by 5/3, giving:
d = 25 miles
In conclusion, assuming that Jen has driven 15 miles, which is 3/5 of the entire trip, the equation that can be used to determine the whole distance d is:
15 = (3/5) * d
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24. A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
The most likely distribution of the colors of candies in the bag before it was opened A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange.
What is distribution?Distribution is the process of making a product or service available for use or consumption by a consumer or business. It involves the movement of a product or service from the producer to the customer or end user. Distribution channels can include direct sales, wholesalers, retailers, online stores, or a combination of all of these. Distribution involves the coordination of activities related to the transfer of goods and services, including storage, shipping, return policies, and customer service. Distribution is a key element of the marketing mix, allowing companies to reach their target markets and meet customer needs.
This is the most likely distribution of the colors of candies in the bag before it was opened because it is the closest to the total number of candies that were in the bag to begin with: 1,000. This distribution has a total of 1,000 candies, which is the same as the amount of candies that were in the bag before it was opened.
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PLEASE simplify 2x +24 =64
Answer:
x = 20
Step-by-step explanation:
2x + 24 = 64
2x = 40
x = 20
Let's check
2(20) + 24 = 64
40 + 24 = 64
64 = 64
So, x = 20 is the correct answer.
Answer:
[tex] \sf \: x = 20[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 2x + 24 = 64
Then the value of x will be,
→ 2x + 24 = 64
→ 2x = 64 - 24
→ 2x = 40
→ x = 40 ÷ 2
→ [ x = 20 ]
Hence, the value of x is 20.
Max is finding the perimeter of different-sized equilateral triangles.
The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.
What is constant of proportionality?The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.
For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.
Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.
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Find the value of x.
Leg= 8
Leg=x-4
Hypotenuse=8
The value of x is 10 if Leg= 8 and Leg=x-4.
What is Pythagoras theorem?This states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
In this scenario we were given
Leg= 8
Leg=x-4
Hypotenuse=x
Therefore : x² = 8² + (x-4)²
x² = 64 + x² - 8x + 16
x² - x² = 80 - 8x
8x = 80
x = 80/8 = 10
Therefore hypotenuse is 10 and the length of the other side is (10-4) = 6.
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Diet coke was on sale last week. It cost 10$ for every four packs.
How much will one pack be.
Show step by step
Answer:
$2.5 for one pack
Step-by-step explanation:
let p mean pack
4p=10 (10 dollars)
divide both sides by 4:
4p/4=10/4
p=2.5
One pack of Diet Coke with the sale would cost $2.5 per pack.
please help! ty <3 i appreciate it sm!
Answer: 21
Step-by-step explanation:
A= b x h/2
6 x 7/2= 21
5. The library is installing new
shelves. If the carpenter has
4/5 yard of wood to make
into 2 shelves of equal length,
how long will each shelf be?
Answer:
2/5 yard of wood
Step-by-step explanation:
4/5 for 2 equal shelves.
The shelves are equal, so we need to divide 4/5 by 2.
4/5 divided by 2 is 2/5.
(4/2=2. We then put the denominator of 5. 2/5)
Doreen lives 3/5 mile from the library. Sheila lives 1/3 as far away from the library as Doreen
Select yes or no for each statement
Does Doreen live father from the Library than Sheila
Yes or No
Does Sheila live 1/5 mile from the library
Yes or No
Does Sheila live twice as far from the library as Doreen
Determine the 3-day SMA for the ten consecutive day closing prices for Procter & Gamble Co listed below.
$66.21, $65.90, $67.05, $67.03, $66.80, $66.65, $66.65, $65.80, $65.92, $65.21
Therefore , the solution of the given problem of unitary method comes out to be 66.05, 66.33, 66.96, 66.83, 66.70, 66.03, 66.12, 65.64 for the closing values provided.
What is a unitary method?By utilizing what is explicitly learned thus far, taking variable of this global accessibility, and incorporating all crucial elements from previous expression research that utilized a particular approach, the goal can be achieved. It will be possible to get in touch with the entity again if the expected claim outcome actually happens; otherwise, both crucial processes will surely miss the statement.
Here,
We must take the average of the most recent three closing prices and repeat the procedure for the remaining prices in order to determine the 3-day SMA (Simple Moving Average).
Here's a step-by-step procedure:
=> Day 1: (66.21 + 65.90 + 67.05) / 3 = 66.05
=> Day 2: (65.90 + 67.05 + 67.03) / 3 = 66.33
=> Day 3: (67.05 + 67.03 + 66.80) / 3 = 66.96
=> Day 4: (67.03 + 66.80 + 66.65) / 3 = 66.83
=> Day 5: (66.80 + 66.65 + 66.65) / 3 = 66.70
=> Day 6: (66.65 + 66.65 + 65.80) / 3 = 66.03
=> Day 7: (66.65 + 65.80 + 65.92) / 3 = 66.12
=> Day 8: (65.80 + 65.92 + 65.21) / 3 = 65.64
The 3-day SMA is therefore 66.05, 66.33, 66.96, 66.83, 66.70, 66.03, 66.12, 65.64 for the closing values provided.
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Nevaeh has a bag that contains pineapple chews, lemon chews, and peach chews. She performs an experiment. Nevaeh randomly removes a chew from the bag, records the result, and returns the chew to the bag. Nevaeh performs the experiment 54 times. The results are shown below: A pineapple chew was selected 21 times. A lemon chew was selected 10 times. A peach chew was selected 23 times. Based on these results, express the probability that the next chew Nevaeh removes from the bag will be pineapple or peach as a decimal to the nearest hundredth.
Answer: It is 0.81
Step-by-step explanation:
I wont give an explanation this time sorry I don't feel like it but just so you know I got this answer right so trust me.