Thang and his friend ndivhu share a job of cleaning a neighbour's yard and they were paid R400 . Thang worked three hours and ndivhu worked for two hours. Determine the amount thang will receive if they decided to share their money according to hours

We can use factorization method to solve quadratic equation.

And, The value of solution of the quadratic equation is,

⇒ x = 2, 6

We have to given that;

Quadratic equation is,

⇒ x² - 8x = - 12

Now, We can simplify as;

⇒ x² - 8x = - 12

⇒ x² - 8x + 12 = 0

Factorized it as;

⇒ x² - (6 + 2)x + 12 = 0

⇒ x² - 6x - 2x + 12 = 0

⇒ x (x - 6) - 2 (x - 6) = 0

⇒ (x - 2) (x - 6) = 0

⇒ x = 2, 6

Thus, We can use factorization method to solve quadratic equation.

And, The solution is,

⇒ x = 2, 6

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Answer:

10

Step-by-step explanation:

I do not know how to make a possibility tree, but I can explain it in words. the possibilities could be at lost, 10  

At the end, Antonio has 4 cups of milk leftover.

We know that Antonio has 1 gallon of mil, and he needs to use 3 quarts of milk for the recipe.

Then we need to perform a change of units, we know that:

1 gallon = 4 quarts.

Then after he uses 3 quarts, he will have 1 quart remaining, and now we want to know how many cups is that, we know that:

1 quart = 4 cups.

So Antonio has 4 cups leftover.

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Answer: the missing angle has a measure of 90 degrees, which is option (d).

Step-by-step explanation:

20 + 70 + x = 180

We are able include the two known angles and after that subtract the result from 180 to induce the degree of the lost point:

20 + 70 = 90

180 - 90 = 90

Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Answer:

The answer to this question is D

Step-by-step explanation:

i solved it

The speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

To find the speed of the boat in still water and the speed of the current, let's follow these steps:

Step 1: Let x represent the speed of the boat in still water, and y represent the speed of the current. The speed downstream is (x + y) and the speed upstream is (x - y).

Step 2: Use the formula distance = time × speed to write two equations based on the given information.

Downstream: 9(x + y) = 189

Upstream: 63(x - y) = 189

Step 3: Simplify both equations:

Downstream: x + y = 21 (divide both sides by 9)

Upstream: x - y = 3 (divide both sides by 63)

Step 4: Solve the system of equations by adding the two simplified equations:

2x = 24

x = 12

Step 5: Plug the value of x back into either equation to solve for y:

12 + y = 21

y = 9

So, the speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

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Answer:

180,000 (OR 90,000 if the figure is a triangle)

Step-by-step explanation:

3 x 3 x 5 x 5 x 4 x 8 x 5 x 5 = 180,000

Area = 180,000

IF THE FIGURE IS A TRIANGLE THEN DIVIDE 180,000 BY 2 AND YOU WILL GET 90,000 AS THE AREA

A ) ⅔ x + 6 = 16

→ ⅔ × 15 + 6 = 16

→ 10 + 6 = 16

→ 16 = 16

Proved

B ) ⅓ x + 4 = 22

→ ⅓ × 15 + 4 = 22

→ 20 = 2

Not Proved

C) 3x + 15 = 30

→ 3×15+15 = 30

→ 3× 30 =30

→ 90= 30

Not Proved

D) x + 25 = 50

→ 15 + 25 = 50

→ 40 = 50

Not Proved

10r -24 = 7r + 12

→ 10r - 7r = 12+24

→ 3r = 36

→ r = 12

3r -2r-8 = -8r + 10

→ 3r - 2r + 8r = 10+8

→ r + 8r = 18

→ 9r = 18

→ r = 2

m/3-18 = m + 6

→ 54- m/ 3 = m + 6

→ 54- m = m + 6×3

→ 54- m = m + 18

→ 18 - 54

→ -36

Answer:

To find the maximum height of the ball, we need to determine the vertex of the parabolic function f(t) = -16t^2 + 5t + 11. The vertex of a parabola is the point where the function reaches its maximum or minimum value.

The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, a = -16 and b = 5, so the x-coordinate of the vertex is:

t = -b/2a = -5/(2*(-16)) = 0.15625

To find the y-coordinate of the vertex, we can substitute t = 0.15625 into the function f(t):

f(0.15625) = -16(0.15625)^2 + 5(0.15625) + 11 ≈ 11.36

Therefore, the maximum height of the ball is approximately 11.4 (rounded to 1/10th).

By finding the ratio of total volume to lemmon juice, we can see that In 600ml of juice we have 150ml of lemmon juice.

We know that 1000 ml of lemonade contains 250 ml of lemon juice. Then the ratio to total volume to lemon juice is:

R = 250/1000 = 0.25

Then in 600ml of juice, we will have 0.25 times that of lemmon juice, it gives:

0.25*600ml = 150 ml

In 600ml of juice we have 150ml of lemmon juice.

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The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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The true statements are:

p(factor of 24) = 6/8: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the numbers 1, 2, 3, 4, 6, and 8 are on the 8-sided die. So, there are 6 favorable outcomes out of 8 possible outcomes. This statement is true.

p(odd number) = 1/2: There are 4 odd numbers (1, 3, 5, 7) on the 8-sided die, so the probability of rolling an odd number is 4/8 = 1/2. This statement is true.

p(number less than 8) = 1: All numbers on the 8-sided die are less than or equal to 8, but not all are less than 8. There are 7 numbers less than 8 (1, 2, 3, 4, 5, 6, 7), so the probability is 7/8, not 1. This statement is false.

p(multiple of 3) = 1/4: There are 2 multiples of 3 on the 8-sided die (3 and 6), so the probability of rolling a multiple of 3 is 2/8 = 1/4. This statement is true.

p(even number) = 1/8: There are 4 even numbers (2, 4, 6, 8) on the 8-sided die, so the probability of rolling an even number is 4/8 = 1/2, not 1/8. This statement is false.

P(the number 9) = 0: The 8-sided die only has numbers 1 through 8, so it is impossible to roll a 9. The probability of rolling a 9 is indeed 0. This statement is true.

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Answer:

y = 12x - 73

Step-by-step explanation:

We are given the line y=4(3x+2).

We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.

Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).

We can do the distributive property to distribute the 4 to both terms on the right side.

y=4(3x+2) => y=12x + 8

Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.

It is also the slope of line G.

We can replace m in y=mx+c with 12 for line G. We'll get:

y=12x + c

Now, we need to find c.

We can use the point (7,11) to help us find c.

Substitute 7 for x and 11 for y.

11 = 12(7) + c

Multiply.

11 = 84 + c

Subtract 84 from both sides

-73 = c

Substitute -73 as c.

y = 12x - 73

Answer:

a) (2x+9) + (3x-4) + 36 = 180

b) x = 27.8

c) 79.4°

Step-by-step explanation:

a) (2x+9) + (3x-4) + 36 = 180

This is because all 3 angles of a triangle equal to 180 degrees.

b) Firstly add like terms

5x + 41 = 180

Subtract 41 from both sides.

5x = 139

Divide 5 on both sides.

x = 27.8

c) <GTN = 3x-4

Plug in x = 27.8

3(27.8)-4 = 79.4

<GTN is 79.4 degrees

The answer of the given question based on the the sentence into an equation is , 2x - 3 = 4.

In mathematics, equation is statement that asserts equality of the two mathematical expressions. It typically contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, division, exponentiation, and logarithm. An equation usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The values of the variables that satisfy the equation are called its solutions.

The sentence be translated into equation are as  follows:

2x - 3 = 4

where x is the unknown number.

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Answer: 64

Step-by-step explanation:

First you do, 237+192+179 which is 608.

Then you do, 800-608 which is 192.

Lastly, you do 192 divided by 3 which gives you 64 as your final answer. So you have to do 192/3 for the 3 7th grade classes to get an equal amount of the prize money.

                                            [tex]192/3=64 \dollars[/tex]

                                             Hope this helps!

Answer:

Step-by-step explanation:

A

the central angle of the arc is π/3 radians.

What is circumference of a circle?

Circumference or perimeter of a circle refers to the measuring of its limits. Contrarily, a circle's radius influences the amount of space it takes up. If a circle is opened up and represented by a straight line, its circumference is equal to its length. It is usually measured in units like centimetres or metres. While utilising the formula, the radius of the circle is taken into account when calculating the circle's circumference. Therefore, we need to know the radius or diameter value to determine the circle's perimeter.

Central angle (in radians) = arc length / radius

In this case, we are not given the radius of the circle directly, but we know that the circumference of the circle is 6. We can use the formula for circumference to find the radius:

Circumference = 2 * pi * radius

6 = 2 * pi * radius

radius = 3 / pi

Now we can use the formula for the central angle:

Central angle (in radians) = arc length / radius

Central angle = 1 / (3/pi) = pi/3

Therefore, the central angle of the arc is π/3 radians.

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The shape that is a concave hexagon with two pairs of congruent sides is an irregular hexagon.

A hexagon is defined as the type of polygon that is made up of six sides and six angles that sums up to 720° and also have 6 vertices.

A hexagon can be of various irregular shapes such as concave, convex and complex irregular shapes.

The properties of irregular hexagon include the following:

The concave irregular hexagon has two pairs of congruent sides that are equal in measurement.

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Answer:

0.25

Step-by-step explanation:

The cost per ounce of candy can be calculated by dividing the total cost of the box by the number of ounces in the box. Since 1 pound equals 16 ounces, the cost per ounce is $4.00 / 16 ounces = $0.25 per ounce.

So the cost per ounce of candy is $0.25.

Answer: 16/1 16x4 = 64/4

Answer:

The area of a square is given by the formula A = s^2, where s is the side length. If Doug has 8 square pieces of wood, each with a side length of s centimeters, the total area of all the pieces can be expressed as:

8s^2 = 200

To solve for s, we can simplify the equation by dividing both sides by 8:

s^2 = 25

Now we can create a quadratic equation by subtracting 25 from both sides:

s^2 - 25 = 0

This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 0, and the constant term is -25. Doug can use this equation to find the side length of each piece of wood by solving for s using methods such as factoring, completing the square, or using the quadratic formula.

The cross product of (a - b) and (a + b) is: [-8, -8, -2].

Given the vectors a = (3, 4, -7) and b = (4, 5, 8), you want to compute the cross product of (a - b) and (a + b).

First, let's compute the vectors (a - b) and (a + b):

a - b = (3 - 4, 4 - 5, -7 - 8) = (-1, -1, -15)

a + b = (3 + 4, 4 + 5, -7 + 8) = (7, 9, 1)

Now, let's compute the cross product of the two vectors:

(-1, -1, -15) × (7, 9, 1) = [(-1)(9) - (-1)(1), (-15)(1) - (-1)(7), (-1)(7) - (-1)(9)] = [-8, -8, -2]

So, the cross product of (a - b) and (a + b) is: [-8, -8, -2].

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Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  [tex]\frac{2cm}{7 feet} = \frac{x cm }{yfeet}[/tex]

where y is the length of the line in real life. Solving for y, we get:

⇒  [tex]y = \frac{7 feet} {2cm} *x[/tex]  

⇒  [tex]y = 3.5 x feet[/tex]

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer:

A

Step-by-step explanation:

the answer would be a because it is shown more than the others

Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

[tex]A(t)=P(1+r/n)^n^t[/tex], where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

[tex]5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t[/tex]

The payback period for Product A is 2.21 years and the payback period for Product B is 1.85 years, NPV of A = $21,215 and NPV of B = -$50,256. Product A: IRR = 28.28%, Product B: IRR = 29.58%, A: PI = 1.00, B: PI = 0.91, A: SRR = 0.49 or 49%, B: SRR = 0.44 or 44%.

Payback period is a financial metric used to evaluate the time required to recover the initial investment made in a project or investment opportunity.

To calculate the payback period, we need to find out how long it takes for the initial investment to be recovered by the annual cash inflows. We calculate the cumulative cash inflows for each year and determine in which year the cumulative cash inflows exceed the initial investment.

Product A:

Year 1: $380,000 - $170,000 - $68,000 - $86,000 = $56,000

Year 2: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $56,000 = $112,000

Year 3: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $112,000 = $168,000

Year 4: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $168,000 = $224,000

Year 5: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $224,000 = $280,000

The payback period for Product A is 2.21 years (rounded to two decimal places).

Product B:

Year 1: $460,000 - $206,000 - $108,000 - $66,000 = $80,000

Year 2: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $80,000 = $160,000

Year 3: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $160,000 = $240,000

Year 4: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $240,000 = $320,000

Year 5: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $320,000 = $400,000

The payback period for Product B is 1.85 years (rounded to two decimal places).

To calculate the net present value (NPV), we need to discount the cash inflows and outflows using the company’s discount rate of 20% and then subtract the initial investment.

Product A:

[tex]NPV = -$340,000 + ($56,000/(1+0.20)^1) + ($112,000/(1+0.20)^2) + ($168,000/(1+0.20)^3) + ($224,000/(1+0.20)^4) + ($280,000/(1+0.20)^5)[/tex]

NPV = -$340,000 + $38,611 + $64,357 + $79,396 + $81,193 + $77,658

NPV = $21,215

Product B:

[tex]NPV = -$540,000 + ($80,000/(1+0.20)^1) + ($160,000/(1+0.20)^2) + ($240,000/(1+0.20)^3) + ($320,000/(1+0.20)^4) + ($400,000/(1+0.20)^5)[/tex]

NPV = -$540,000 + $66,667 + $111,111 + $114,882 + $99,425 + $97,659

NPV = -$50,256

To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV of the cash inflows and outflows equal to zero. We can use a financial calculator or spreadsheet software to solve for the IRR.

Product A: IRR = 28.28%

Product B: IRR = 29.58%

To calculate the profitability index (PI), we divide the present value of the future cash inflows by the initial investment.

Product A:

PV of future cash inflows = $38,611 + $64,357 + $79,396 + $81,193 + $77,658 = $341,215

PI = $341,215/$340,000

PI = 1.00

Product B:

PV of future cash inflows = $66,667 + $111,111 + $114,882 + $99,425 + $97,659 = $489,744

PI = $489,744/$540,000

PI = 0.91

To calculate the simple rate of return (SRR), we divide the average annual cash inflow by the initial investment.

Product A:

Average annual cash inflow = ($56,000 + $112,000 + $168,000 + $224,000 + $280,000)/5 = $168,000

SRR = $168,000/$340,000

SRR = 0.49 or 49%

Product B:

Average annual cash inflow = ($80,000 + $160,000 + $240,000 + $320,000 + $400,000)/5 = $240,000

SRR = $240,000/$540,000

SRR = 0.44 or 44%

6a.

Based on the payback period, Product B is preferred because it has a shorter payback period of 1.85 years compared to Product A’s payback period of 2.21 years.

Based on the net present value, Product A is preferred because it has a positive NPV of $21,215 compared to Product B’s negative NPV of -$50,256.

Based on the internal rate of return, Product B is preferred because it has a higher IRR of 29.58% compared to Product A’s IRR of 28.28%.

Based on the profitability index, Product A is preferred because it has a PI of 1.00, indicating that for every dollar invested, we receive one dollar in return. Product B has a PI of 0.91, indicating that for every dollar invested, we receive only $0.91 in return.

Based on the simple rate of return, Product A is preferred because it has a higher SRR of 49% compared to Product B’s SRR of 44%.

6b. Based on the simple rate of return, Lou’s division should accept Product A because it has a higher SRR of 49% compared to Product B’s SRR of 44%. However, other measures such as the net present value and internal rate of return suggest that Product A may not be the best choice.

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