A retailer buys merchandise from a supplier with an invoice amount of $12,400. The terms of the sale are 6/20, n/30. What is the net amount due (in $) on the order if the bill is paid by the 20th day?

The height c of the flagpole c is 5.5 metres.

The triangles formed by the two flags are similar.  

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

The distance between flag a is 12 metres.

The distance form the flag c to s is 10 metres.

The height of the flagpole a  is 12.1 metres.

Therefore, let's find the height of the pole c.

Hence, using proportion,

12.1 / c = 22 / 10

cross multiply

121 = 22c

divide both sides by 22

c = 121 / 22

c = 5.5

Therefore,

height of the flagpole c = 5.5 metres

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These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.

When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

The cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

What is a function?

A mathematical statement or rule that establishes the link between an independent variable and a dependent variable is called a function. Relationships called functions provide an output for each input. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Assuming the question is the one given below.

Given a function C which gives the cost of buying the n apples in dollars.

The first expression given is:

1) C(5) = 4.50

The input of the function is 5 and the output is 4.50.

This means that when the number of apples is 5 the total cost is $4.50.

Let us assume the general equation of the function as below:

C(n) = kn

When n = 5

C(5) = 5k = 4.50

k = 4.50/5 = 0.9

Hence the function is C(n) = 0.9n

2) We found the function as C(n) = 0.9n

 C(2) means the cost when the number of apples is 2.

C(2) = 0.9 * 2 = $1.8

Therefore the cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

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By answering the above question, we may state that Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

[tex]x^3[/tex] - 8 ≥ 1

[tex]x^3[/tex] ≥ 9

Taking the cube root of both sides, we get:

x ≥ ∛9

Since ∛9 ≈ 2.08, the solution to the inequality is:

x ≥ 2.08

Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

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Answer: Three equivalent ratios of 8 : 5 are 16 : 10, 24 : 15 and 32 : 20.

Step-by-step explanation:

In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.

Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:

x + y = 28

The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.

The costs and quantities of the two varieties of coffee can be used to create a new equation.

0.9x + 2.4y = $40.60

With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution

28 + y = x - 0.9x + 2.4y = 40.60

0.9x + 2.4(28 - x) = $40.60

0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73

We can apply the first equation to determine y now that we know x: x + y = 28.

17.73 + y = 28 \sy = 10.27

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Answer:

c

Step-by-step explanation:

60>30 since pi is 180 ........

Answer:

See below

Step-by-step explanation:

[tex]7(6+ x)[/tex] = [tex](7)(6) + (7)(x)[/tex]
            = [tex]42 + 6x[/tex]

The measure of ∠M and ∠N = 76

An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides.

Given:- ∠NLM = 28°

The given triangle is an isosceles triangle as sides LM and LN are equal.

Therefore ,∠LMN and ∠LNM will be equal.

Let us assume ∠M as x

Therefore,

∠LMN = ∠LNM = x

Sum of all angles of a triangle =180°

Therefore,

∠NLM + ∠LNM + ∠LMN = 180°

28 + x + x = 180

28 + 2x = 180

2x = 180 – 28

2x = 152

x = 152/2

x = 76

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John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035

By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.

Here we have,

μ = 83,0 = 9, n = 78

Since sample size is large so we can assume normal distribution using CLT.

The z-score for x= μ-0.4 is

z=(μ-0.4-μ)/o/√n

=-0.4/9/√78

= -0.39

The z-score for x= μ +0.4 is

z=(μ+0.4-μ)/σ/√n

= 0.4/9/√78

= 0.39

The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035.

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The triangles are classified as:

4. Acute 5. Obtuse 6. Obtuse 7. Acute 8. Obtuse 9. Acute 10. Obtuse

To classify a triangle as right, obtuse, or acute, we need to apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

If the square of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is obtuse. If the square of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is acute.

4. To check if this is a right triangle, we need to find if 9² is equal to 4² + 6², which is not true, so the triangle is acute.

5. To check if this is a right triangle, we need to find if 16² is equal to 10² + 12², which is not true, so the triangle is obtuse.

6. To check if this is a right triangle, we need to find if (8√6)² is equal to 8² + 16², which is not true, so the triangle is obtuse.

7. To check if this is a right triangle, we need to find if 29² is equal to 20² + 21², which is true, so the triangle is acute.

8. To check if this is a right triangle, we need to find if √73² is equal to 3² + 8², which is not true, so the triangle is obtuse.

9. To check if this is a right triangle, we need to find if 12² is equal to 8² + 10², which is true, so the triangle is acute.

10. To check if this is a right triangle, we need to find if (3√34)² is equal to 9² + 15², which is not true, so the triangle is obtuse.

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The third side of the triangle is 8  

Pythagoras' theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.

It states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Here we have

A right-angled triangle

From the figure

The sides of the triangle are 7 and √15  

As we know from Pythagoras' theorem

=> Hypotenuse² = side² + side²    

Substitute the above values in the condition

=> Hypotenuse² = (7)² + (√15)²    

=> Hypotenuse² = 49 + 15

=> Hypotenuse² = 64

=> Hypotenuse = 8  

Therefore,

The third side of the triangle is 8  

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Complete Question is given picture

The exponential growth equation is P ( t ) = 332 ( 1.0059 )^t , where t is the number of years and P ( t ) is the population after 2020

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be represented as x₀

Now , the value of x₀ = 332 million

And , the exponential growth rate r = 0.59 %

where the population of the U.S. at time/ years after 2020 is of the form equation P( t ) = aekt

On simplifying , we get

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.59% )^t

Now , the value of P ( t ) is

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.0059 )^t

The population of the U.S. at a time P ( t ) = 332 ( 1.0059 )^t

where the growth factor k = 1.0059

Hence , the exponential growth equation is P ( t ) = 332 ( 1.0059 )^t

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Using the graphs, Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

An organised-representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Information and data have different purposes: Data is an unadorned truth; information is the meaning that can be inferred from data.

Challenge 1

Olivia may have, for example, translated 10 units to the right after reflecting over the x axis.

Let's use point C to apply this series of steps.

C = (-2,-4) (-2,-4)

After reversing the x axis, C' becomes (-2,4); the y coordinate changes sign, and C" becomes (8,4) after moving to the right by 10 units. The x coordinate is then increased by 10.

The graphic shows that point C (-2, -4) shifts to C"(8,4). The other four points I'll let you investigate.

Olivia may have also tried shifting 10 units to the right before reflecting across the x axis. The sequence here is irrelevant. Order does important, though, for several other combinations of transformations.

Challenge 2

The point (x,y) will become after reflection across the y axis (-x,y). Here, the sign is reversed, and only the x coordinate changes. The y coordinate remains constant.

With the y axis reflection, a point like C (-2, -4) becomes C'(2, -4). By moving up 8 units, we get at C"(2,4) by adding 8 to the y coordinate, but this is not what the graphic displays. Thus, Angelica's approach is flawed.

The last four points should also contain other contradictions, as well.

Challenge 3

Even Michael's approach is flawed. Instead of using an x axis reflection, he completely relies on translations to change ABCDE into A"B"C"D"E".

Quick inspection suggests that Michael might be right. Yet, if you examine much more closely, you'll notice that things aren't exactly in line.

This time, we'll choose point D rather than point C.

D can be found at (-6, -2). To reach D' if we move up 8 units, we must add 8 to the y coordinate (-6,6). Then, to move 10 units to the right, add 10 to the x coordinate. And brings us to D" (4,6).

The diagram, however, reveals that D" is actually at (4,2)

Let you examine the other points, please. The only points that should go to the right places are C and E; the remaining points should not. Once more, Michael's failure to apply an x axis reflection is to blame. His A"B"C"D"E" figure is reversed from how it should have been.

To sum up, the strategies mentioned in problem 1 are the proper ones to use in order to make ABCDE go to A"B"C"D"E. Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

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Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

Answer:

Yes

Step-by-step explanation:

We just need to (0,6) in the equation to see if it gives a true answer or not!

y = -x + 6

6 = 0 + 6

6 = 6

So, (0,6) is a solution to the equation y = -x + 6

Answer:

It is true that graphs exponential functions either increase or decrease for all x-values.

An exponential function is defined as follows:

y = ab^x.

In which:

An exponential function can either increase or decrease depending on the values of a and b, however the behavior is uniform, meaning that it is true that graphs exponential functions either increase or decrease for all x-values.

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The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.

Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.

To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.

Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.

Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The limit of f(x) as x approaches -6 from the positive side is 6.

When x gets closer to 2 on the positive side, we can see that the function seems to be heading towards a value of -8. As a result, f(x) has a limit of -8 as x approaches 2 from the positive side.

The function seems to be heading towards a value of 6 when x approaches 2 from the negative side. Hence, when x gets closer to 2 from the negative side, the limit of f(x) is 6.

The function seems to be getting closer to a value of 6 when x approaches -6 from the positive side. Hence, as x gets closer to -6 on the positive side, the limit of f(x) is equal to 6.

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The lateral limits of the function g(x) at x = 4 are given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]

A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]

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1. The loan term of the truck is 5 years.

2. The contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. In in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

1. The loan term of the truck in years is calculated as follows:

Number of years = Loan term in months / 12

Number of years = 60 months / 12

Number of years = 5 years

Therefore, the loan term of the truck is 5 years.

2. Monthly repayments = Monthly instalment of the truck + Insurance premium

Monthly repayments = R22,301.67 + R8,500

Monthly repayments = R30,801.67

Therefore, the contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. Number of instalments paid = Loan term in months / 2

Number of instalments paid = 60 months / 2

Number of instalments paid = 30 months

The total amount of money owed to the financer excluding the insurance in June 2022 would be:

Total amount owed = Remaining instalments x Monthly instalment of the truck

Total amount owed = (Loan term in months - Number of instalments paid) x Monthly instalment of the truck

Total amount owed = (60 months - 30 months) x R22,301.67

Total amount owed = 30 months x R22,301.67

Total amount owed = R669,050.10

Therefore, in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

The significance of including an insurance cover when a contractor purchases a water tanker is to protect the asset from unforeseen circumstances such as accidents, theft, or damage. If the contractor did not have insurance, they would have to pay for any repairs or replacements out of pocket, which could be expensive and financially devastating. Insurance also provides peace of mind and allows the contractor to focus on their business operations without worrying about potential risks to their asset.

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Answer:

Step-by-step explanation 0.4 0.8 5 7 10, 10

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.

The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.

In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.

Here we have

Problem 1:

10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.  

The down payment was 10% of the purchase price of the home

=> Down payment = 10% of $110,000

= [10/100] × $110,000 = $11,000

∴ You will be paid $11,000 as your down payment.

Amount borrowed = the purchase price of the home - Down payment

=> Amount borrowed = $110,000 - $11,000 = $99,000

∴ Your mortgage (loan) was for $99,000.    

To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:

P = (A / D) x (r / 12)

Where:

A = amount borrowed

D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)  

r = monthly interest rate,      

n = total number of payments,  

=> P = ($99,000 /124.4) x 0.0075 = $471.15  

∴ The current monthly payment is $471.15.  

The formula for total interest = (P x n) - A  

=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00              

∴ You will pay a total of $169,334.00 in interest over the life of the loan.    

Therefore,

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.      

Problem 2

This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.

i. Amount paid off = Original loan amount - Current loan balance

Original loan amount = $99,000

Current loan balance = $88,536

Amount paid off = $99,000 - $88,536

Amount paid off = $10,464

∴ you have paid off $10,464 of the loan.

ii. Total paid = Monthly payment x Number of payments

P = ($99,000 / 207.483) x 0.0075

P ≈ $471.15

The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.

Total paid = $471.15 x 120

Total paid = $56,538

∴ you have paid $56,538 to the loan company so far.

iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:

Interest paid = Total paid - Amount paid off

Interest paid = $56,538 - $10,464

Interest paid = $46,074

∴ you have paid $46,074 in interest so far.

iv. Equity = Current value of the home - Current loan balance

Equity = $150,000 - $88,536

Equity = $61,464

∴ you have $61,464 of equity in your home.

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The expression that represents the area of the given door is (3w+8)w.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

So, we know that:
width = w

And we also know that:

length = 3w + 8

Now, the area formula is:
l*w

Insert values as follows:

l*w

(3w + 8)w

Therefore, the expression that represents the area of the given door is (3w+8)w.

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