The given text presents a map of South Africa with various locations marked. However, important information such as the scale of the map and the number of provinces is missing. Without the scale, we cannot accurately determine distances or calculate probabilities. Similarly, the absence of information regarding the provinces prevents us from calculating the probability of selecting a specific province. Therefore, based on the given text, we can only answer the first two questions, which involve the type of scale and the general direction between two locations.
1. The type of scale given in the diagram is a ratio scale, specifically a linear scale. It represents the relationship between map distance and actual distance in a straight line.
Interpretation of the given scale:
The scale on the map is not clearly visible in the provided text. However, it is typically written as a fraction or ratio, where the numerator represents the map distance and the denominator represents the corresponding actual distance on the ground. For example, a scale of 1:1,000,000 means that 1 unit on the map represents 1,000,000 units in the real world.
2. The general direction of Badplaas from Colesburg is to the northeast.
3. To determine the actual straight-line distance between East London and Bloemfontein, we would need the scale from the map. However, the scale is not provided in the given text, making it impossible to calculate the distance accurately.
4. Stellenbosch is located in the Western Cape province on the map.
5. To calculate the probability of randomly selecting the Western Cape province in South Africa, we would need the total number of provinces in South Africa and the number of provinces that belong to the Western Cape. However, this information is not provided in the given text, so it is not possible to calculate the probability.
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1. The Roth Family took out a $215,000 with a 15-year mortgage at an APR of 5.4%. The
monthly payment was $1,850. What will be their total interest charges after 15 years?
The total interest charges to the Roth Family, after 15 years, given the monthly payment would be $ 118, 000
How to find the total interest charges ?First, find the total amount paid over the 15 years by the Roth Family to be :
= Number of years x Monthly payment x Number of months per year
= 15 x 1, 850 x 12
= $ 333, 000
The total interest charges that the Roth Family paid would be :
= Total amount paid after 15 years - Total amount borrowed as mortgage
= 333, 000 - 215, 000
= $ 118, 000
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NEED THIS SOLVED ASAP!!!!!!!!!!!! I AM GIVING 15 POINTS
Arm Span (inches) / Height (inches)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document. (Recommend me this software so I can do this part).
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document.
The scatter plot for the above data and it's line of best fit is attached accordingly. You may achieve this result using Microsoft Excel.
How to plot scatter plot on Microsoft ExcelEnter your data into two columns in an Excel worksheet. For example, in columns A and B, enter the years and corresponding life expectancies from your given data.
Select the data range by clicking and dragging over the cells containing the data.
Go to the "Insert" tab in the Excel ribbon.
In the "Charts" group, click on the "Scatter" chart type. Choose the scatter plot style that suits your preference (e.g., "Scatter with Straight Lines").
A scatter plot will be created on your worksheet.
Right- click on any data point on the scatter plot and choose "Add Trendline" from the context menu.
In the "Format Trendline" pane that appears on the right side of the screen, select the "Linear" trendline option.
Check the box for "Display Equation on Chart" if you want to show the equation of the line of best fit on the chart.
You can further customize the appearance of the scatter plot and the trendline using various chart formatting options in Excel.
Your scatter plot with the line of best fit is now plotted on Excel.
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What is the quotient of the expression
O7a³ + ab + 3
O7a³ + ab - 3
O7a³ + 4ab+
+8
O7a³+4ab-8
28a b+4a²b²-12ab?
4ab
The quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
How to find the quotientBy dividing each term of the numerator by 4ab:
(7a³ + ab + 3) / (7a³ + ab - 3) ÷ 4ab
= (7a³ / 4ab) + (ab / 4ab) + (3 / 4ab)
Simplifying each term individually:
= (7/4a²) + (1/4b) + (3/4ab)
Thus, the quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).
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4. Higher Order Thinking A national TV
news show conducted an online poll to find
the nation's favorite
comedian. The
website showed
the pictures of
5 comedians and
asked visitors of the
site to vote. The news
show inferred that
the comedian with
the most votes was
the funniest comedian
in the nation.
a. Is the inference valid? Explain.
b. How could you improve the poll? Explain.
No, the inference is not necessarily valid. The fact that a comedian received the most votes in an online poll does not guarantee that they are the funniest comedian in the nation.
Is the inference valid? Explain.The poll's results are influenced by various factors such as the sample size, the demographics of the voters and potential biases in the voting process.
Also, humor is subjective and what one person finds funny may not be the same for someone else. Therefore, determining the funniest comedian based solely on the number of votes in an online poll is an oversimplified and flawed approach.
To improve the poll, several steps can be taken which are:
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Help me please! Thanks
The identification of the polygon that are given in the diagram above would be =
Polygon 1 = Isosceles trapezoid
polygon 2 = parallelogram
polygon 3 = Rectangle
polygon 4 = Rhombus
polygon 5 = Square
polygon 6 = trapezoid
What are the properties of the polynomials given above?Isosceles trapezoid : This is the type that of polygon in which the the top and base are not equal in length, but they are parallel to each other.
Parallelogram : This is defined as the type of polygon that has two pairs of parallel sides.
Rectangle : This has two pairs of sides that are equal and opposite.
Rhombus: All the sides are equal in length with its opposite angles equal .
Square: All sides are equal in length but and all angles are equal to 90°.
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A paint machine dispenses dye into paint cans to create different shades of paint. The
amount of dye dispensed into a can is known to have a normal distribution with a mean of 5
milliliters and a standard deviation of 0.4 milliliters. Find the dye amount that represents the
99th percentile of the distribution.
Select one:
O a. 4.1 milliliters
O b. 5.9 milliliters.
O c. 4.9 milliliters
O d. 5.1 milliliters
Answer:
b. 5.9 mL
Step-by-step explanation:
You want the value that represents the 99th percentile of a normal distribution with a mean of 5 mL and a standard deviation of 0.4 mL.
Inverse normalThe inverse of the normal CDF function is used to find the X value for a given area. Here, we want X such that P(x < X) = 0.99 for μ = 5 and σ = 0.4.
The attached calculator output shows that is about X = 5.9305. Rounded to 1 decimal place, the volume is ...
5.9 mL
<95141404393>
17. Find m2NSR=
Segment AB is tangent to circle C. Find r.
18. r=
176
40°
35
25
Need help. Please show work and answer 17 and 18
1. The value of angle NSR is 110°
2. The value of r 12
What is arc angle relationships?If two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Therefore;
S = 1/2( 170+40)
S = 1/2 ( 210)
S = 110
Therefore the value of angle NSR is 110°
2. There is a theorem that states that the angle between a radius and tangent is 90°
Using Pythagorean theorem
(25+r)² = r² +35²
= 625 + 50r + r² = r² +35²
625 +50r = r² - r² +35²
50r = 1125-625
50r = 600
r = 600/50
r = 12
therefore the value of r is 12
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Need Help ASAP. Thank you in advance :)
The value of x, considering the vertical angles in this problem, is given as follows:
x = 11.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles for this problem are given as follows:
(x + 7)º.(2x - 4)º.As the vertical angles are congruent, the value of x is obtained as follows:
2x - 4 = x + 7
x = 11.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
It would take 21 weeks for the population to surpass 16,000.
The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.
For the population to surpass 16,000, we can set up the following equation:
15,000 + 2500 sin(πt/52) = 16,000
Subtracting 15,000 from both sides, we get:
2500 sin(πt/52) = 1000
Dividing both sides by 2500, we get:
sin(πt/52) = 0.4
We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:
πt/52 = sin⁻¹(0.4)
Multiplying both sides by 52/π, we get:
t = (52/π) sin⁻¹(0.4)
Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.
t = (52/π) (0.4115)
t = 21.02
Therefore, it would take 21 weeks for the population to surpass 16,000.
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The exponential model A=433.4e^0.032t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 796 million.
The population of the country will be 796 million in
(Round to the nearest year as needed.)
The population of the country will be 796 million approximately in the year 2022.
To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:
[tex]A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}[/tex]
Divide both sides by 433.4:
[tex]e^{(0.032t)} = 1.836[/tex]
Take the natural logarithm of both sides:
[tex]ln(e^{(0.032t)}) = ln(1.836)[/tex]
0.032t = 0.605
Divide both sides by 0.032:
t = 18.91
Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:
2003 + 19 = 2022
Therefore, the population of the country will be 796 million approximately in the year 2022.
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Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points. Which of the following equations can be used to determine how many points Patrick earned?
5 + 6 = 14 + y
6y + 5 = 14
5y + 6 = 14
5 + 6 + y = 14
The equation can be used to determine how many points Patrick earned is ;5 + 6 + y = 14.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points.
We can determine the direct answer by taking Billy and Kip's points and subtracting it from the total combined points.
That will give us 11, which means Patrick earned 3 points.
The equation we can use to represent this is ;5 + 6 + y = 14.
On Saturday, a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
78
Step-by-step explanation:
Let the number of hamburgers sold = x.
Then, the number of cheeseburgers sold = 2x.
Total number of sales: x + 2x = 3x
Total number of sales: 234
3x = 234
x = 78
Answer: 78
Ms. Edwards is redecorating her office. She has a choice of 8 colors of paint, 5 kinds of curtains, and 6 colors of carpet. How many different ways are there to redecorate?
240 ways
297 ways
357 ways
19 ways
Answer:
To determine the total number of different ways Ms. Edwards can redecorate her office, we need to multiply the number of choices for each item:
Number of paint color choices = 8
Number of curtain choices = 5
Number of carpet color choices = 6
To calculate the total number of ways, we multiply these choices together:
Total number of ways = Number of paint color choices × Number of curtain choices × Number of carpet color choices
= 8 × 5 × 6
= 240
Therefore, there are 240 different ways for Ms. Edwards to redecorate her office. So, the answer is 240 ways.
For the matrix D shown below, determine the value of the element d12. If the element is not defined, click the undefined button. D = [-3 -8 6 -4] Answer:
The calculated value of the element d₁₂ is -8
How to determine the value of the element d₁₂From the question, we have the following parameters that can be used in our computation:
The matrix D given as
D = [-3 -8 6 -4]
The element d₁₂ represents the element located at the first row and the second column
In this case, the element located at the first row and the second column is -8
Using the above as a guide, we have the following:
d₁₂ = -8
Hence, the value of the element d₁₂ is -8
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Use the graph to answer the question.
Graph of polygon ABCD with vertices at negative 2 comma negative 1, 0 comma negative 4, 4 comma negative 4, 2 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 5 comma negative 1, 7 comma negative 4, 11 comma negative 4, 9 comma negative 1.
Determine the translation used to create the image.
7 units to the right
3 units to the right
7 units to the left
3 units to the left
The translation used to create the image of the second polygon is A, 7 units to the right.
How to determine translation?To determine the translation used to create the image of the second polygon (A' B' C' D') from the original polygon (ABCD), compare the corresponding vertices.
Original polygon (ABCD):
A (-2, -1)
B (0, -4)
C (4, -4)
D (2, -1)
Image polygon (A' B' C' D'):
A' (5, -1)
B' (7, -4)
C' (11, -4)
D' (9, -1)
To find the translation, calculate the horizontal and vertical differences between the corresponding vertices.
Horizontal difference:
For point A: A'x - Ax = 5 - (-2) = 7
For point B: B'x - Bx = 7 - 0 = 7
For point C: C'x - Cx = 11 - 4 = 7
For point D: D'x - Dx = 9 - 2 = 7
Vertical difference:
For point A: A'y - Ay = -1 - (-1) = 0
For point B: B'y - By = -4 - (-4) = 0
For point C: C'y - Cy = -4 - (-4) = 0
For point D: D'y - Dy = -1 - (-1) = 0
From the calculations, see that the horizontal difference is 7 units for all the corresponding vertices, while the vertical difference is 0 units for all the corresponding vertices.
Therefore, the translation used to create the image of the second polygon is 7 units to the right.
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Mathematical form of the question:
Use the graph to answer the question.
Graph of polygon ABCD with vertices at A (-2, -1), B (0, -4), C (4, -4), D (2, -1). A second polygon A' (5, -1), B' (7, -4), C' (11, -4), D' (9, -1).
Determine the translation used to create the image.
7 units to the right
3 units to the right
7 units to the left
3 units to the left
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
(2x^2-9x-5) \div(x-5)
Answer:2x+1
Step-by-step explanation:
1/5 ( x - 10 ) = 4/5
The value of x is 14
What are fractions?Fractions are described as expression that shows the part of a whole number, a whole variable. a whole element.
The different types of fractions are listed as;
Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractionsFrom the information given, we have that;
1/5 ( x - 10 ) = 4/5
This is written as;
(x -10)/5 = 4/5
cross multiply the values, we have;
5(x-10) = 20
expand the bracket
5x - 50 = 20
Collect like terms
5x = 70
Divide the values
x =14
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Expand & simplify.
23p - 3( 2k + 14p ) + 5( 6k - p )
Answer:
23p -6k - 42p + 30k - 5p
23p - 42p - 5p + 30k - 6k
23p - 47p + 24k
-24p + 24k
24(- p + k)
24( k - p)
Answer:
The answer is
60p + 24k
Step-by-step explanation:
1: Expand
=23p - 6k + 42p + 30k - 5p
step2: collect like terms
=42p + 23p - 5p - 6k + 30k
step 3: add/subtract them to get your answer
=60p + 24k
your answer☝
A right circular cylinder has a surface area of 112 π. If the height of the cylinder is 10, find the diameter of the base.
If the height of the cylinder is 10, the diameter of the base of the cylinder is 8 units.
A right circular cylinder has two congruent circular bases and a curved surface area. To find the diameter of the base, we need to first find the radius of the base.
Let's begin by using the given information to write an equation. The surface area of a cylinder is given by the formula:
Surface Area = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
We are given that the surface area of the cylinder is 112π and the height is 10. Substituting these values, we get:
112π = 2πr² + 2πr(10)
Simplifying the equation by dividing both sides by 2π, we get:
56 = r² + 10r
Now we have a quadratic equation in terms of r. We can solve this equation by using factoring, completing the square, or the quadratic formula. Let's use factoring:
r² + 10r - 56 = 0
(r + 14)(r - 4) = 0
The solutions are r = -14 and r = 4. Since the radius cannot be negative, the radius of the base is 4.
The diameter of the base is twice the radius, so the diameter is 8.
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Copy and complete the pattern in the table
The pattern in the table should be completed as follows;
Number of 1 3 9 27 81
students with pets
Total number 3 9 27 81 243
of students
A ratio that compares the number of blue squares to the total number of squares is 3 : 4.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would find the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/1 = 9/3
Constant of proportionality, k = 3.
y = 3x
81 = 3x
x = 27
x = 9/3
x = 3
y = 3(81)
y = 243
For the ratio of blue squares to total squares, we have:
18/24 = 3/4 = 3 : 4
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least common denominator of -3/a and 1/4a^2
Answer:
-12a-1/4a2
Step-by-step explanation:
PLS HELP MARKING AS BRAINLIST
Answer:
108 sq ft
Step-by-step explanation:
The formulas are given in the bottom right.
For the triangles*, the base = 8 ft. The height = 6 feet.
Area = (bh)/2.
Area = (8*6)/2 = (48)/2 = 24 sq ft.
There are two of those identical triangles. 24+24 = 48.
(*Another way to look at this is to say that the base = 8+8 = 16. Area = (bh)/2 = (16*6)/2 = 96/2 = 48. It doesn't matter, mathematically. I can't tell if they have tried to show this as 2 triangles or one.)
For the bottom rectangle, area = length x width = 6*10 = 60 sq ft.
Add them up! 24 + 24 + 60 = 108 sq ft.
Currently it is estimated that 3 out of every 1000 Californians are infected with
coronavirus. The so-called rapid "antigen" test for coronavirus has a very low false
positive rate of just 0.05, but has a high false negative rate of 0.2. The so-called
PCR test is more reliable: it has an even lower false positive rate than the antigen
test, namely only 0.001, but even more importantly its false negative rate is much
lower at 0.01.
What is the probability that you have a coronavirus infection conditional on your
PCR test has coming back positive?
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
We have,
To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.
Now,
Prevalence of coronavirus in California: 3 out of 1000
False positive rate of the antigen test: 0.05 (5 out of 100)
Let's calculate the probability of a positive test result.
The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):
True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)
The probability of a positive test result can be calculated using Bayes' theorem:
P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)
P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)
P(Positive test) = 0.0024 + 0.04985
P(Positive test) = 0.05225
Therefore,
The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.
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Write and solve an equation to find the value of x.
The value of x for each item is given as follows:
28. x = 5.
29. x = 3.44.
How to obtain the value of x in each item?For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:
16x = 10 x 8
16x = 80
x = 5.
For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:
10(x + 10) = 12(12 + 25)
10x + 100 = 444
10x = 344
x = 3.44.
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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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Lines y and z are parallel.
Parallel lines are cut by transversals s and t. The angles formed by lines s, t, and y, clockwise from top left, are blank, blank, (10 x + 5) degrees, blank, (4 x minus 7) degrees, blank; formed by s and z are 65 degrees, 1, blank, blank; formed by z and t are 2, blank, blank, blank.
What is the measure of angle 2?
6 degrees
11 degrees
28 degrees
37 degrees
The measure of Angle 2 is 17 degrees.
The measure of angle 2, the relationships between the given angles formed by the parallel lines and transversals.
1. The angles formed by lines s, t, and y, clockwise from top left, are:
- Blank
- Blank
- (10x + 5) degrees
- Blank
- (4x - 7) degrees
- Blank
2. The angles formed by s and z are:
- 65 degrees
- 1
- Blank
- Blank
3. The angles formed by z and t are:
- 2
- Blank
- Blank
- Blank
From the given information, we can deduce the following:
- Angle 1 is congruent to the angle formed by z and t (corresponding angles).
- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).
- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).
Therefore, we can set up the following equations:
65 = 10x + 5 (Equation 1)
2 = 4x - 7 (Equation 2)
Solving Equation 1:
65 - 5 = 10x
60 = 10x
x = 6
Substituting x = 6 into Equation 2:
2 = 4(6) - 7
2 = 24 - 7
2 = 17
Hence, the measure of angle 2 is 17 degrees.
Therefore, the correct answer is:Angle 2 = 17 degrees.
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Calculate the unknown length, x, in the shape below.
If your answer is a decimal, give it to 1 d.p.
8
8 cm
area = 55 cm²
area=178.2 cm²
15 cm
The triangles are similar triangles. Then the value of 'x' will be 27 cm.
The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
From the above theorem, the equation is given as,
(x/15)² = 178.2 / 55
Simplify the equation, then we have
(x/15)² = 3.24
x/15 = 1.8
x = 27 cm
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Halle planted mint and basil seeds in her herb garden. She measured the height of each herb plant at the end of each week for six weeks. The results are shown in the line graph below.
What is the difference to the nearest tenth in the mean growth per week for both herbs during the six weeks shown in the graph?
A. 0.7cm/week
B. 0.6cm/week
C. 3.7cm/week
The difference in mean growth per week is 3.7cm/week
From the graph given :
Growth per week for Basil = 2, 6, 9, 10, 14, 16
Growth per week for Mint = 1, 2, 4, 7, 9, 12
Mean growth per week = (2+6+9+10+14+16) / 6 = 9.5 cm/week
Mean growth per week (Mint) = (1+2+4+7+9+12)/6 = 5.83 cm/week
The difference cannbe obtained by subtracting the mean Values thus ;
Difference in average growth = 9.5 - 5.83 = 3.67 cm/week
Therefore, the difference in mean growth per week is 3.7cm/week
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