PART 2: TABLE 1: Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes. This helps him to be sure that he has enough petrol when driving certain distances - due to the nature of his work. The table below represents the car's petrol consumption. The extreme petrol price per litre of R22,50 also impacts Mr. Flynn's travelling. Study the table and answer the questions that follow. 2.1 2.2 2.3 4 2.4 PETROL CONSUMPTION VERSUS TRAVEL DISTANCE (OBSERVABLE PATTERN) DISTANCE TRAVELLED PER LITRE PETROL CONSUMED Litres of Petrol 0 1 2 3 B 5 6 7 8 Distance to Travel (km) A 12,5 25,0 37,5 50,0 62,5 C 87,5 100 Describe the general relationship between distance travelled and litres ​

The future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84

what is compound interest ?

Compound interest is the interest earned on an initial deposit or investment, plus all the interest that has accumulated on it over time. It is interest calculated on both the principal amount and any interest earned from previous periods, which is added to the principal amount at the end of each compounding period.
[tex]FV = P * (1 + r/n)^{n*t}[/tex]

Where:

FV = Future Value

P = Principal or initial investment

r = Annual interest rate

n = Number of times interest is compounded per year

t = Time in years

According to the question:
In this case:

P = $1200

r = 7% = 0.07

n = 12 (compounded monthly)

t = 10

Plugging these values into the formula, we get:

[tex]FV = P * (1 + r/n)^{n*t}[/tex]

[tex]FV = 1200 * (1 + 0.07/12)^{12*10}[/tex]

[tex]FV = 1200 * (1.00583333)^{120}[/tex]

[tex]FV = 1200 * 1.97236812[/tex]

[tex]FV = 2366.84[/tex]

Therefore, the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84 (rounded to the nearest cent).

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The area of the triangle is 3 cm^2.

Area is the measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, or circle. It is usually measured in square units, such as square centimeters, square inches, or square meters.

Two-dimensional shapes are flat shapes that exist in only two dimensions - length and width. They are also known as 2D shapes. Some common examples of two-dimensional shapes include:

In the given question,

To find the area of a triangle, we need the length of two sides and the angle between them. We are given that the length of two sides of the triangle are 3 cm and 4 cm, and the angle between them is 30°.

We can use the formula for the area of a triangle, which is:

Area = (1/2) x base x height

We can take the side of length 3 cm as the base of the triangle, and the side of length 4 cm as the height, as it forms a right angle with the base. To find the height, we can use trigonometry.

sin(30°) = opposite/hypotenuse

sin(30°) = height/4

height = 4 x sin(30°)

height = 2 cm

Now, we can substitute the values in the formula for the area of the triangle:

Area = (1/2) x base x height

Area = (1/2) x 3 x 2

Area = 3 cm^2

Therefore, the area of the triangle is 3 cm^2.

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The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25.

Exponential growth is a pattern of growth that occurs when a base number is multiplied by a consistent number over a period of time. This type of growth is often seen in population growth, inflation, the money supply and other areas of mathematics. The growth rate of an exponential function increases over time, making it an important concept in mathematics, economics, and other fields.

This equation utilizes the concept of exponential growth, which is when a quantity increases at a rate which is proportional to its current value. In this case, the quantity is the value of the collection, and the rate of growth is 2% per year.

The equation can be broken down into its components in order to better understand what it is saying. The base value of the collection, 320, is represented by the first part of the equation, V = 320. The second part, (1.02)^5, represents the growth rate over 5 years. The 1.02 is the growth rate of 2% per year, and the 5 indicates that the growth rate will be compounded for 5 years. In other words, the rate of growth is applied to the original value, and then the resulting value is used as the new base for the growth rate to be applied again, and so on for 5 years.

The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25. This means that in 5 years, the collection would have appreciated to a total value of 413.25.

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Answer:

Translation

Step-by-step explanation:

Translation

Answer:

35$ - 17% gives you 29.05$

while 32$ - 12% gives you 28.16$

so 35$ - 17% would be your answer

The best option to find a reasonable estimate for the amount of time it takes to run the obstacle course among 200 contestants is to option D: Time 20 contestants and average their times.

A reasonable estimate is an approximation that is based on logical reasoning and information available, and it is within a reasonable margin of error. It is not expected to be precise, but it is expected to provide a fair idea of the value being estimated.

For example, estimating the cost of a renovation project within 5% of the actual cost would be considered a reasonable estimate.

By timing only one contestant, the time might not be representative of the entire group since individual performances can vary significantly. Timing the race official himself also won't give an accurate estimate since the official might not be a typical contestant in terms of speed and agility.

On the other hand, timing 2 contestants and averaging their times might not provide a big enough sample size to get a good estimate.By timing 20 contestants, there is a higher chance that the sample size will be representative of the entire group, and the average time will provide a more accurate estimate of the typical performance on the obstacle course.

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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The number of problems assigned initially to each student by Lin’s teacher is 4.

Equations are mathematical statements that have two algebraic expressions on either side of equals (=) sign. The phrases written on the left and right sides are equal, as shown by this example.

Equations can be resolved in order to ascertain the value of a variable that represents an unknowable quantity. In the absence of the "equal to" symbol, a statement is not an equation. That will be taken into consideration as a phrase.

Lin’s teacher assigned each of them the same number of problems to complete.

Total number of problems assigned by Lin's teacher  to students = 30

Let the  total number of problems assigned  to each student initially  be x

So, the number of problems assigned   to  all the  students  initially = 5x

Also it is given that  Lin's teacher assigns 2 more problems to each student

which means he gives 10 more problems to solve

5x+10 = 30

5x = 20

x = 4

Hence, The number of problems assigned initially to each student by Lin’s teacher is 4.

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Answer:

The correct answer here is B

Step-by-step explanation:

You already did the first 2 rows and it got a COP of 3. The last few rows do not.

Answer:

Answer is C

Step-by-step explanation:

Yes, the person who said B is half correct but tables CAN show proportions, however this one doesn't since you aren't multiplying by 3 in every row. Only the top 3 rows do the rest don't. That's why C is correct not B.

The value of function f(x) at x =1 will be 4.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function f(x) = -3x + 7

To calculate the value of the function at x = 1,

We need to substitute the value of x = 1 in the function,

thus,

f(1) = -3 * 1 + 7

f(1) = -3+ 7

f(1) = 4

This represents the point (1, 4) on function f(x) = -3x +7.

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Answer:

The statement that is sometimes true is C: A rectangle is a parallelogram.

Step-by-step explanation:

A parallelogram is a four-sided shape with opposite sides parallel. A rectangle is a specific type of parallelogram where all angles are right angles, and opposite sides have equal lengths. Therefore, a rectangle is considered a parallelogram. However, not all parallelograms are rectangles because other parallelograms may have angles that are not right angles.

Answer: :)

n

_

8

I used n as the unknown number

Step-by-step explanation:

The quotient is the result of division between two numbers.

The quotient of a number (I used n) and 8 would be n 8

Answer:

Step-by-step explanation:

sorry I don’t know

Answer:

-8

Step-by-step explanation:

4x - 9 + 3x = 8x - 1

7x - 9 = 8x - 1

7x = 8x + 8

x = -8

Therefore, the solution to the equation 4x - (9 - 3x) = 8x - 1 is x = -8.

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:B

Step-by-step explanation:

Answer: D : 7cm

Step-by-step explanation:

The distance between the twο y-intercepts is 7 - 19 = -12.

Value is the impοrtance, wοrth, οr usefulness οf sοmething. It is a measure οf the relative wοrth οf sοmething and can be expressed in variοus ways, such as mοnetary, sοcial, οr practical. Value can be determined by cοnsidering factοrs such as quality, utility, and scarcity. Values are subjective and can be influenced by persοnal, cultural, and sοcietal factοrs. They οften reflect a persοn's beliefs, attitudes, οr preferences. Value is an impοrtant cοncept in ecοnοmics, finance, and sοcial science.

The y-intercept οf f(x) is 7, while the y-intercept οf g(x) is calculated by subtracting the x-value οf the first rοw frοm the g(x) value, which is 20 - 1 = 19.

Therefοre, the distance between the twο y-intercepts is 7 - 19 = -12.

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The surface area of the figure is 549.5 square ft

Given that

The composite figure comprises of a cone and a cylinder of the following dimensions

Cone: Radius = 5 ft and Height = 12 ft

Cylinder: Radius = 5 ft and Height = 6 ft

The surface area of the figure is calculated as

Surface area = Cone + Cylinder -  Circle

So, we have

Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²

Substitute the known values in the above equation, so, we have the following representation

Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²

Evaluate

Surface area = 549.5

Hence, the surface area is 549.5

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Answer:

40?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The answer is 21 because the pattern is multiplying by 3!

The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U

13. A ⋃ B  = {1, 2, 3, 4, 5, }   14. A ⋃ C  = { 1, 2, 3, 4, 5, 6}

15. A ⋂ C  = { 4 }                   16. B ⋂ C = { }

17. [tex]A^{c}[/tex]  =  {6, 7, 8, 9, 10}         18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}  

In mathematics, a set is a collection of distinct objects, which are called its elements or members. These objects can be anything - numbers, letters, people, animals, or other sets.

Sets are typically denoted using curly braces, and the elements of the set are listed inside the braces, separated by commas.

Here we have

A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6}  and U = {numbers from 0 to 10}

=> U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

i. Indicate if each statement is true or false.

7. 3 ∈ B which means 3 belongs to set B

Since, set B = {1, 3, 5}

=> ∴ 3 ∈ B is true

8. 5 ∈ C which means 5 belongs to set C

The set C = {4, 6}

=> 5 ∈ C is false

9. B ⊂ A which means B is a subset of A and elements of B are belongs to set A.  

Since elements of B are lies in set A

=> B ⊂ A is true

10. C ⊂ A which means C is a subset of A

Since all the elements of C are not lie in set A

=> C ⊂ A is false

11. C ⊂ B which means C is a subset of B

Since all the elements of C are not lie in set B

=> C ⊂ B is false

12. C ⊂ U which means C is a subset of U

Since all the elements of C are lies in U

=> C ⊂ U is true  

13. A ⋃ B = {1, 2, 3, 4, 5} ∪ {1, 3, 5} = {1, 2, 3, 4, 5, }  

14. A ⋃ C = {1, 2, 3, 4, 5} ∪ {4, 6} = { 1, 2, 3, 4, 5, 6}

15. A ⋂ C  = {1, 2, 3, 4, 5} ⋂ {4, 6} = { 4 }

16. B ⋂ C =  {1, 3, 5} ⋂ {4, 6} = { }

17. [tex]A^{c}[/tex]  = The elements in the universal set but not in A = {6, 7, 8, 9, 10}

18. [tex]B^{c}[/tex] = The elements in universal set but not in B = {0, 2, 4, 6, 7, 8, 9, 10}  

Therefore,

The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U

13. A ⋃ B  = {1, 2, 3, 4, 5, }   14. A ⋃ C  = { 1, 2, 3, 4, 5, 6}

15. A ⋂ C  = { 4 }                   16. B ⋂ C = { }

17. [tex]A^{c}[/tex]  =  {6, 7, 8, 9, 10}         18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}  

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If to help pay for culinary school, Keiko borrowed money from her credit union:

a. Keiko's monthly payment is  $542.63.

b. The  total amount to repay the loan is $65,115.60

c. The total amount of interest she will pay is $15,115.60

(a) To find Keiko's monthly payment, we can use the formula for calculating the monthly payment for an amortized loan:

P = (r * A) / (1 - (1 + r)^(-n))

Where:

P =Monthly payment

A=  loan amount

r = Monthly interest rate

n = Total number of payment

Plugging in the values for Keiko's loan, we get:

P = $50,000

r = 0.055 / 12 = 0.00458

n = 10 * 12 = 120

P = (0.055/12 * $50,000) / (1 - (1 + 0.055/12)^(-120)) = $542.63

(b) If Keiko pays the monthly payment each month for the full term, the total amount she will repay the loan will be:

Total amount = Monthly payment * Total number of payments

= $542.63* 120 = $65,115.60

(c) If Keiko pays the monthly payment each month for the full term, the total amount of interest she will pay will be:

Total interest = Total amount - Loan amount

=$65,115.60 - $50,000 = $15,115.60

So, Keiko will pay a total of $15,115.60 in interest over the 10-year term of the loan.

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Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.

The sum of money that a borrower must give a lender as interest is compensation for the use of borrowed funds. It is typically computed as a percentage of the principal, which is the amount borrowed, and is repaid alongside the principal over a predetermined amount of time. The cost of the lender, the likelihood of a default, and the desire for credit in the economy are just a few of the variables that affect the interest rate, or the percentage charged for borrowing the money.

given

We can use the following method to determine the total interest paid:

Principal x Interest Rate x Duration equals total interest.

where Principal denotes the sum borrowed, Interest Rate denotes the annual interest rate (in decimal form), and Time denotes the number of years over which interest will accrue.

Assume Britta took out a $50,000 loan to pay for her schooling.

Therefore, the amount of her loan at the conclusion of that time frame would be:

$50,000 x 1.06^2 = $56,420

The interest that will be charged on this balance for the remaining 10 years and 6 months of the loan period needs to be calculated now. Using the above method, we obtain:

$56,420 multiplied by 0.06 times 10.5 equals the total interest, or $33,782.

Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.

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The amount of time it would take the water to cool to 150°F is: C. About 8 min.

In this scenario, the time would be plotted on the x-axis of the scatter plot while the temperature would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the time and temperature, an exponential equation for the line of best fit is given by:

[tex]y = 192e^{-0.028x}[/tex]

When temperature y = 150°F, the value of x (in minutes) can be calculated as follows:

[tex]150 = 192e^{-0.028x}[/tex]

ln(150/192) = -0.028x

x = -0.24686007793/0.028

x = 8 mins.

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Answer:

23

Step-by-step explanation:

(16-12)×4+7

(4)×4+7

16+7

=23 I think

a. The x-intercepts are 1/4 and 4. b. The vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.

The object's form is symmetrical because of the axis of symmetry, which is a straight line. On each of its sides, the axis of symmetry produces a perfect reflection. It could be lateral, vertical, or horizontal. The two sides of an object are the same if we fold and unfold it along the axis of symmetry. Various forms have various symmetry lines. There are four lines of symmetry in a square, two lines in a rectangle, infinite lines in a circle, and no lines of symmetry in a parallelogram. There are n axes of symmetry in a regular polygon with n sides.

We know that,

To find the x-intercepts, we set f(x) equal to 0 and solve for x:

-16x² + 60x + 16 = 0

4x² - 15x - 4 = 0

4x² - 16x + x - 4 = 0

4x (x - 4) - 1(x - 4) = 0

(4x - 1) (x - 4) = 0

x = 1/4

x = 4

The x-intercepts are 1/4 and 4.

The vertex of the graph of f(x) can be found using the formula x = -b/2a

x = -60 / (2(-16)) = 1.875

To establish whether the vertex is a maximum or minimum, we examine the shape of the coefficient of the x square term, which is negative (-16). This signifies that the graph expands down and the vertex is a maximum.

Hence, the vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.

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Answer:

t ≤ -3

Step-by-step explanation:

4t + 5 ≤ -7

4t ≤ -12

t ≤ -3

Answer:

the answer is A

hope it helps u

mark brainlist

Answer: D

As x Values-Decrease, the function increases toward positive infinity.

As the x values decreases, the function decreases towards y=-2

Step-by-step explanation:

It's a basic function that follows within the 2^x format. Where x-> infinity would mean that y-> infinity as well. However, since there was a translation within the y unit (hence the -2) the asymptote decreased by two.

So as the x unit increases, so does the y.

However, as the x unit decreases, the y decreases to -2.

The population in thousands of a town in the year 2007 is 16.56 thousand.

In an exponential function, the base value controls how quickly the function increases or decreases. The function expands exponentially if the base value is more than 1, whereas it degrades exponentially if the base value is between 0 and 1. Faster growth or decay is indicated by a bigger base value.

Given that,

y = 8.5(1.1)ˣ

The value of x is calculated as:

x = 2007 - 2000 = 7 years.

Substitute the value of x in the given function:

y = 8.5(1.1)⁷

y = 16.56

Hence, the population in thousands of a town in the year 2007 is 16.56 thousand.

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The side x of the similar triangle is 12.7 units.

The triangles are similar triangle.

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.

Therefore, using the proportion

37- 5 / x = x / 5

Evaluate the difference of 37 and 5

32 / x = x / 5

Cross multiply the equation

x × x = 32 × 5

So, we have

x² = 160

Take the square root of both sides

x = √160

Evaluate the square roots

x = 12.6491106407

Hence, the value of x is x = 12.7 units (when approximated)

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