The vendor sold 142 sodas and 91 hotdogs.
According to the question:
The vendor sold 233 sodas and hotdogs combined
The number of hot dogs sold was 51 less number of sodas sold
To find:
Number of sodas sold(S)
Number of hotdogs sold(H)
From the question, it is clear that:
S + H = 233 ...(i)
S - H = 51 ...(ii)
These two are simultaneous linear equations.
Adding equations (i) and (ii):
S + H + S - H = 233 + 51
2S = 284
S = 284/2
S = 142
Substitute this value of S in equation (i):
142 + H = 233
H = 233 - 142
H = 91
Therefore, the vendor sold 142 sodas and 91 hotdogs.
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Y varies directly as x, and y=9 when x = 27
If y varies directly as x, when x = 15, the value of y is equal to 5.
If y varies directly as x, we can express this relationship using the formula y = kx, where k is the constant of proportionality.
Given that y = 9 when x = 27, we can substitute these values into the equation:
9 = k x 27
To solve for k, we divide both sides of the equation by 27:
k = 9 / 27
k = 1/3
Now that we know the value of k, we can use it to find y for any other value of x.
Let's find y when x = 15:
y = (1/3) x 15
y = 5
Therefore, when x = 15, y is equal to 5.
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The complete question:
Y varies directly as x, and y=9 when x = 27.
Find the value of y, when x =15.
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
We have to given that;
All expressions are,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
Now, We can simplify all the expressions as;
⇒ 2 + x = 5
⇒ x = 5 - 2
⇒ x = 3
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3
⇒ 9 + x = 6
⇒ x = 6 - 9
⇒ x = - 3
⇒ x + (-4) = 7
⇒ x = 7 + 4
⇒ x = 11
⇒ -5 + x = -2
⇒x = - 2 + 5
⇒ x = 3
Thus, All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
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100 Points! Algebra question. Photo attached. Graph the function. Thank you!
The graph of the function is attached and the amplitude and the period are 5 and 2π
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 5cos(θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 5
Period = 2π/1
Evaluate
A = 5
Period = 2π
Hence, the amplitude is 5 and the period is 2π
The graph of the function is attached
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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?
The expected value of the car 7 years after it was purchased is $47,029.12.
To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:
Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)
In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:
Value after 7 years = 54792 - (54792 × (19/100)×7)
Value after 7 years = 54792 - (54792 × 0.19×7)
Value after 7 years = 54792 - 7762.88
Value after 7 years = $47,029.12
Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.
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Nadeen bought a 91-day T-bill that has an interest rate of
4.30% p.a. and a face value of $5,000.
a) How much did she pay for the T-Bill?
b) After 40 days, Barbara sold the T-bill to her friend when the interest rate for this T-bill in the market increased to 5.30% p.a. What was her selling price?
The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;
a) Nadeen paid about $4,946.24 for the T-bill
b) Barbara's selling price for the T-bill is about $4,962.74
What is a T-bill?A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.
The formula for the price of the T-bill can be calculated with the formula;
Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))
Plugging in the value from the question, we get;
Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24
Therefore, Nadeen paid $4,946.24 for the T-billb) The formula for the selling price can be presented as follows;
Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))
Plugging in the known values, we get;
Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74
Therefore, Barbara sold the T-bill to her friend for $4,962.74
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Mr. Gupta gave his students a quiz with three questions on it. Let
�
XX represent the number of questions that a randomly chosen student answered correctly. Here is the probability distribution of
�
XX along with summary statistics:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.
How to answer the aforementioned questionGiven:
- Each correct question is worth 10 points.
- Every student receives an additional 555 bonus points.
Let's calculate the mean and standard deviation of YY:
Mean of YY:
The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:
μY = μX * 10 + 555
Substituting the value of μX from the given information:
μY = 1.95 * 10 + 555
μY = 19.5 + 555
μY = 574.5
Therefore, the mean score of a random student (YY) is 574.5.
Standard Deviation of YY:
The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:
σY = σX * 10
Substituting the value of σX from the given information:
σY = 0.8 * 10
σY = 8
Therefore, the standard deviation of the random student's score (YY) is 8.
Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
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Given m ∥ n, find the value of x.
given that m is parallel to n,
the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.
using the corresponding angle rule we know that:
2x + 16 = 96
2x = 80
so x = 40
Determine the equation of the circle graphed below.
-12-11-10-9-8-7 -5-4-3-2
11098765432-
hadis
-2
-9
-10
-11
123456
8 9 10 11 12
(8,-2)
Answer:
(x - 3)² + (y + 4)² = 29
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
we have the coordinates of the centre but require to find the radius r
the radius is the distance from the centre to a point on the circle.
using the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle
r = [tex]\sqrt{(8-3)^2+(-2-(-4))^2}[/tex]
= [tex]\sqrt{5^2+(-2+4)^2}[/tex]
= [tex]\sqrt{25+2^2}[/tex]
= [tex]\sqrt{25+4}[/tex]
= [tex]\sqrt{29}[/tex]
then equation with centre (3, - 4 ) and r = [tex]\sqrt{29}[/tex] , is
(x - 3)² + (y - (- 4) )² = ([tex]\sqrt{29}[/tex] )² , that is
(x - 3)² + (y + 4)² = 29
An equilateral triangle has a perimeter of 36 inches. What is the height of the triangle? Express your answer as a simplified radical.
Answer: the height of the equilateral triangle is 6√3 inches.
Step-by-step explanation:
To find the height of an equilateral triangle, we can use the formula:
height = (√3/2) * side
In this case, we are given the perimeter of the triangle, which is 36 inches.
Since an equilateral triangle has three equal sides, each side would be 36 inches divided by 3, which is 12 inches.
Now we can substitute the side length into the formula:
height = (√3/2) * 12
Simplifying:
height = (√3/2) * 12
height = (√3 * 12)/2
height = (12√3)/2
height = 6√3
Therefore, the height of the equilateral triangle is 6√3 inches.
Answer:
RG
Step-by-step explanation:
Test Prep What fraction is represented by the point on the number line?
The fraction represented by the point between 1 and 2 on the number line is 5/3.
If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.
The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.
Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.
2
Thus, the point A corresponds to the mixed fraction 1 -
3
2 5
1 - = (1*3)+2 / 3 = -
3 3
So, the fraction represented by the point between 1 and 2 on the number line is 5/3.
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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?
Answer:
$12270.46----------------------
Use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.Plugging in the values, we get:
A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.
The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .
How to find the probability ?The number of adults with some high school degree or some college would be :
= 3, 561 + 6, 058
= 9, 619 people
The probability that a random adult would have high school degree or some college is therefore :
= Adults with high school degree or some college / Total adults in the town
= 9, 619 / 17, 981
= 53. 50 %
In conclusion, the probability is 53. 50%.
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Find the
approximate height difference between the birdhouse
and the tree house. Is it greater than or less than the
approximate difference in height between the swing
set and the tree house? Round each mixed number to
the nearest whole number.
HELP???
The approximate height difference between the birdhouse and the tree house is 3 ft.
It is less than the approximate difference in height between the swing set and the tree house.
How to find the approximate height difference between the birdhouse and the tree house?A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.
We have:
height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft
height of tree house = 11[tex]\frac{13}{16}[/tex] ft
Thus, the approximate height difference between the birdhouse and the tree house will be:
14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex] = 2[tex]\frac{3}{4}[/tex] ft
= 2.75 ft
= 3 ft
To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:
height of swing set = 8[tex]\frac{1}{4}[/tex] ft
height of tree house = 11[tex]\frac{13}{16}[/tex] ft
difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]
= 3[tex]\frac{1}{2}[/tex]
= 3.5
= 4 ft
Therefore, it is less than the approximate difference in height between the swing set and the tree house
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Need an answer quick!!
What is the volume of the shape on the next page?
Answer:
6 in³
Step-by-step explanation:
volume = width X length X height
= 3 X 1 X 2
= 6 in³
A rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm² What is the side length of its base?
If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.
Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².
We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:
x² * 17.2 cm³ = 24.768 cm³
Simplifying this equation, we get:
x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²
Taking the square root of both sides, we get:
x = 1.2 cm
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8 +[13-(2+1] =
20
18
-3
Answer: false
Step-by-step explanation:
Help Me please!!!!!!!!!!!
The triangles are similar and
Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem
Given data ,
Let the first triangle be ΔPSQ
Let the second triangle be ΔRST
Now , the corresponding sides are
PS / RS = QS / TS
where the corresponding sides of similar triangles are in the same ratio
And , the common angle to both the triangles is m∠S
So , ∠S ≅ ∠S and PS / RS = QS / TS
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are similar
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PLS HELP! In the figure below, m angle SUT=123 and m arc PR= 124 . Find m arc ST.
The measure of the arc of the circle is mST = 122°
Given data ,
Let the circle be represented as C
where the two chords of the circle are RT and PS
And the chords RT and PS intersect at the point U
Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.
On simplifying , we get
m∠SUT = ( 1/2 ) ( mPR + mST )
123° = ( 1/2 ) ( 124° + mST )
On solving for mST , we get
( 124° + mST ) = 246°
Subtracting 124° on both sides , we get
mST = 122°
Hence , the measure of arc mST = 122°
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a) Work out the area of the whole rectangle shown below. b) Use your answer to part a) to help you work out the area of the dotted, purple triangle. 4 cm 7 cm
a) Area of rectangle = 28 cm²
b) Area of triangle = 14 cm²
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Length of rectangle = 4 cm
Width of rectangle = 7 cm
Since, WE know that;
Area of rectangle = Lenght x Width
Hence, We get;
Area of rectangle = 4 x 7
Area of rectangle = 28 cm²
And, By figure,
Heigh of triangle = 4 cm
Base of triangle = 7 cm
Hence,
Area of triangle = 1/2 x 4 x 7
Area of triangle = 14 cm²
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subtract the following measurements 450l 890ml from8700l 750ml
The solution of expression after subtraction is,
⇒ 8249 L 860 ml
We have to given that;
Subtract measurements 450l 890ml from 8700l 750ml
Now, WE can simplify as,
⇒ L ml
8700 750
- 450 890
---------------------------
8249 860
Therefore, After subtraction we get;
⇒ 8249 L 860 ml
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Read instructions and do this on a separate piece of paper and draw all lines with a ruler or any straightedge. I will mark you brainliest.
The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.
What is a parallel line?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.
When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.
When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.
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Please help me :(
What is the measure of p in the following diagram?
PS: Its in a Chapter 11 Go math book! Maybe... can you help me pls?
The measure of p in the diagram is,
m∠P = 45°
We have to given that;
PM is perpendicular to MO.
Now, If m ∠P = m∠2
then it's an isosceles triangle.
And, m ∠M = 90°, therefore it's an isosceles right triangle.
We know that,
the sum of measures of angles in a triangle is equal 180°.
Therefore we have the equation:
m∠P + m∠2 + m∠M = 180°
Substitute m∠M = 90° and m∠P = m∠2 = x:
x + x + 90° = 180°
substract 90° from both sides
2x = 90°
divide both sides by 2
x = 45°
m∠P = 45°
Thus, The measure of p in the diagram is,
m∠P = 45°
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BTS-2 has coordinates (-8,6) and the edge connecting vertices P and Q has the equation y = 4.
(b) Write down the coordinates of BTS-4.
a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4.
b. The coordinates of BTS-4 are (−8,4).
How to explain the informationa. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4. A Voronoi cell is a region of space that is closer to a given point than any other point. In this case, the given point is BTS-4. The Voronoi diagram is a partitioning of the plane into Voronoi cells, one for each point.
b. The edge connecting vertices P and Q has the equation y=4, which means that it is a horizontal line that intersects the y-axis at 4. The coordinates of BTS-2 are (−8,6), which means that it is located 8 units to the left of the origin and 6 units above the origin. Therefore, BTS-4 must be located 8 units to the left of the origin and 4 units above the origin, which gives it the coordinates (−8,4).
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What are the side lengths of triangle Graph shows a triangle plotted on a coordinate plane. The triangle is at A(minus 7, 3), B(minus 3, 6), and C(5, 0). Type the correct answer in each box. If necessary, round any decimal to the nearest tenth. units units units
With the coordinate provided, the lengths of the triangle are Side AB = 5 units, Side BC = 10 units and Side CA = 12.4 units.
How do we find the sides of triangles using coordinates?To find the side lengths of the triangle using the coordinates provided, we use the distance formul.
The distance between two points (x1, y1) and (x2, y2) is given by √((x2-x1)² + (y2-y1)²).
Side AB: Distance between A(-7, 3) and B(-3, 6)
= √((-3 - -7)² + (6 - 3)²)
= √((4)² + (3)²)
= √(16 + 9)
= √25
= 5 units
Side BC: Distance between B(-3, 6) and C(5, 0)
= √((5 - -3)² + (0 - 6)²)
= √((8)² + (-6)²)
= √(64 + 36)
= √100
= 10 units
Side CA: Distance between C(5, 0) and A(-7, 3)
= √((-7 - 5)² + (3 - 0)²)
= √((-12)² + 3²)
= √(144 + 9)
= √153
= 12.4 units
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
6/MN = 8/9
8MN = 54
MN = 6 3/4
The correct answer is B.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The measure,
⇒∠s = 124 degree
In the given figure of kite,
PQRS,
Measure of angle p = 22 degree
And angle R is a right angle
Therefore,
∠R = 90 degree
Now we know that for a kite PQRS
Angle Q and Angle S are equal
Now consider,
Angle s is equal to x degree
Therefore,
∠S = ∠ Q = x degree
We know that,
For a kite the sum of interior angle is equal to 360 degree.
Therefore,
⇒ ∠P + ∠Q + ∠R + ∠S = 360
⇒ 22 + x + 90 + x = 360
⇒ 22 + x + 90 + x = 360
⇒ 2x = 248
⇒ x = 124 degree.
Thus,
Measure of angle s = 124 degree.
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Question 5 Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annua salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. Sh is concerned that the R4000 monthly income tax deduction is too much.
Determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
To assess whether the monthly income tax deduction of R4000 is too much for Joy, we need to calculate her annual income tax liability and compare it to the deduction.
First, let's calculate the amount Joy contributes to her pension fund annually:
Pension fund contribution = 7% of annual salary
Pension fund contribution = 7/100 * R286,500
Pension fund contribution = R20,055
Next, we need to determine Joy's taxable income by subtracting her pension fund contribution from her annual salary:
Taxable income = Annual salary - Pension fund contribution
Taxable income = R286,500 - R20,055
Taxable income = R266,445
Now, we can calculate the income tax liability based on the South African income tax brackets for the 2023 tax year. Please note that tax brackets are subject to change, so it's essential to verify with the latest tax regulations.
According to the current tax brackets, the tax rates for the 2023 tax year are as follows:
18% on the first R216,200 of taxable income
26% on the portion of taxable income between R216,201 and R337,800
31% on the portion of taxable income between R337,801 and R467,500
36% on the portion of taxable income between R467,501 and R613,600
39% on the portion of taxable income above R613,601
Using these tax rates, we can calculate the income tax liability:
Tax liability = (18% * amount within first bracket) + (26% * amount within second bracket) + (31% * amount within third bracket) + (36% * amount within fourth bracket) + (39% * amount within fifth bracket)
First, let's calculate the amounts within each tax bracket:
Amount within first bracket = min(Taxable income, R216,200)
Amount within second bracket = min(max(Taxable income - R216,200, 0), R337,800 - R216,201)
Amount within third bracket = min(max(Taxable income - R337,800, 0), R467,500 - R337,801)
Amount within fourth bracket = min(max(Taxable income - R467,500, 0), R613,600 - R467,501)
Amount within fifth bracket = max(Taxable income - R613,600, 0)
Now, let's substitute the values and calculate the income tax liability:
Tax liability = (18% * min(Taxable income, R216,200)) + (26% * min(max(Taxable income - R216,200, 0), R337,800 - R216,201)) + (31% * min(max(Taxable income - R337,800, 0), R467,500 - R337,801)) + (36% * min(max(Taxable income - R467,500, 0), R613,600 - R467,501)) + (39% * max(Taxable income - R613,600, 0))
By calculating this equation, you can determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
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Question: 4/8
Mr. Oswald, the head of human resources, has
been in the company for 24 years, which
corresponds to three times as many as the
number of years Mrs. Bright, the finance
director, is also employed there.
Considering neither of them leaves their jobs,
how many years will Mr. Oswald have worked for
the company when that corresponds to twice as
many as Mrs. Bright's number of years there?
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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There are approximately as many boys between 167 and 169 as there are between 169 and 170. True False
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
In statistics, understanding and interpreting data is an essential skill. One way to interpret data is by analyzing the distribution of values within a certain range.
To determine whether the statement is true or false, we need to analyze the distribution of boy's heights between the two ranges. Assuming the heights of boys are normally distributed, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of boys within each range.
The empirical rule states that in a normal distribution:
68% of the values fall within one standard deviation of the mean
95% of the values fall within two standard deviations of the mean
99.7% of the values fall within three standard deviations of the mean
We can use this rule to estimate the percentage of boys within each range as follows:
Between 167 and 169: This range is one standard deviation below the mean. Therefore, approximately 68% of boys' heights fall within this range.
Between 169 and 170: This range is between one and two standard deviations below the mean. Therefore, approximately 27% of boys' heights fall within this range.
Based on this analysis, we can see that there are not approximately as many boys between 167 and 169 as there are between 169 and 170. In fact, there are significantly more boys between 167 and 169 than there are between 169 and 170.
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
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Is 34.05 greater than 34.59
No, 34.05 is not greater than 34.59.
When comparing two numbers, we look at their digits from left to right.
In this case, both numbers start with 34, which means they have the same value in the tens place.
However, when we move to the decimal part, 0.05 is smaller than 0.59.
Therefore, 34.05 is smaller than 34.59.
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