Calculate the lengt line x

The equation for the number of cells after t-15 minute periods is C = 157 x [tex]2^{t/15}[/tex].

The number of cells after 2 hours is  40,192.

The equation for the number of cells after t-15 minute periods is an exponential equation.

The form of the equation will be:

Future population = present population x [tex]2^{number of minutes / 15}[/tex]

C = 157 x x [tex]2^{t/15}[/tex].

Number of cells after 2 hours :

First convert 2 hours to minutes = 2 x 60 = 120 minutes

C =  157 x [tex]2^{120/15}[/tex]

157 x [tex]2^{8}[/tex]

C = 40,192

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Quantitative data can be discrete or continuous

Gregor scored 65 points on the Stats exam.

We can use the formula for calculating z-score:

z = (x - μ) / σ

Where

We are given that the population mean (μ) is 75 and the population standard deviation (σ) is 5.

We are also given that Gregor's z-score (z) is -2.

We can plug these values into the formula and solve for x:

-2 = (x - 75) / 5

Multiplying both sides by 5, we get:

-10 = x - 75

Adding 75 to both sides, we get:

x = 65

Hence, the score is 65 points

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The percent of American households that watched CSI this week is 17.8%.

The percent is the part or fraction of a quantity taken from the whole quantity which is expressed in percentage. The quantity may be numbers, team, population etc.

Given that the total households are 109600000, of which 19508800 watched the television show CSI during the week of October 2, 2005.

Thus,

The percent of American households that watched CSI this week, N, can be determined as follows;

N = fraction/ whole * 100%

  = 19508800/ 109600000 * 100%

  = 17.8

N = 17.8%

The percent of American households that watched CSI this week is 17.8%.

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Using arithmetic οperatiοns it is οbtained that Brandοn must mοw 15 lawns at $25 per lawn tο break even, meaning his revenue will cοver his cοsts.

A subject οf mathematics knοwn as arithmetic οperatiοns deals with the study and use οf numbers in all οther branches οf mathematics. Basic οperatiοns including additiοn, subtractiοn, multiplicatiοn, and divisiοn are included.

Let x be the number οf lawns Brandοn mοws.

Use the arithmetic οperatiοn οf multiplicatiοn.

His revenue frοm mοwing × lawns at $25 per lawn is -

Revenue = Price per lawn × Number οf lawns

Revenue = $25 × x

Revenue = $25x

Use the arithmetic οperatiοn οf additiοn.

His tοtal cοst includes the equipment cοst οf $300 and the variable cοst οf $5 per lawn, sο his tοtal cοst is -

Cοst = Equipment cοst + Variable cοst

Cοst = $300 + $5x

Tο break even, his revenue must be equal tο his cοst.

Use the arithmetic οperatiοn οf additiοn.

Sο we can set the revenue equal tο the cοst and sοlve fοr x -

Revenue = Cοst

$25x = $300 + $5x

$20x = $300

x = 15

Therefοre, Brandοn must mοw 15 lawns at $25 per lawn.

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[tex]x + (x+1) + (x+2) + (x+3) = -326\\[/tex]

[tex]4x + 6 = -326[/tex]

[tex]4x = - 326-6[/tex]

[tex]4x = -332[/tex]

[tex]x = -332/4 \implies x = - 83[/tex]

the integers are:

[tex]-83 < -82 < -81 < -80[/tex]

the largest integer is: -80

The maximum height of the ball is given as follows:

92 feet.

The quadratic function modelling the height of the ball is given as follows:

h(t) = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 75, h(0) = 4.

Hence the equation is:

h(t) = -16t² + 75t + 4.

The coefficients are given as follows:

a = -16, b = 75, c = 4.

As the quadratic equation is concave down, the maximum height is at the vertex.

The t-coordinate of the vertex is given as follows:

t = -b/2a

b = -75/-32

b = 2.34375s.

Hence the maximum height is of:

h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.

h(2.34375) = 92 feet.

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The image of the quadrilateral is R' = (-2, -1), S' = (-4, -2), T' = (-5, -4) and U' = (-3, -3)

From the question, we have the following parameters that can be used in our computation:

R = (1, -2)

S = (2, -4)

T = (4, -5)

U = (3, -3)

The transformation is given as

90 degrees rotation about the origin

This is represented as

(x, y) = (y, -x)

Using the above as a guide, we have the following:

R' = (-2, -1)

S' = (-4, -2)

T' = (-5, -4)

U' = (-3, -3)

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The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

The coordinates of the quadrilateral RSTU is

R = (1, -2)

S =(2, -4)

T = (4, -5)

U = (3, -3)

When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

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A solution to the given system of linear equations is (2, 6).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x - y = 0     ......equation 1.

5x + 2y = 7  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).

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Therefore, sets (2), (3), and (4) can be used to build a triangle, while set (1) cannot.

Any two sides must add up to more than the third side's length in order to form a triangle. Let's use this principle to compare each pair of side lengths:

5 + 3 = 8 + 10 cm, 3 cm, and 5 cm.

3 + 10 = 13 > 5

5 + 10 = 15 > 3

As the total of the lengths of the two shorter sides is not larger than the length of the longest side, a triangle cannot be constructed with this set of side lengths.

3 measurements: 4 cm, 12 cm, and 9 cm 4 + 12 = 16 > 9 4 + 9 = 13 > 12\s12 + 9 = 21 > 4

Given that the total of any two sides is more than the length of the third side, a triangle can be constructed using this set of side lengths.

3, 2, and 5 centimetres

5 + 2 = 7 > 4

2 + 4 = 6 > 5

5 + 4 = 9 > 2

Given that the total of any two sides is more than the length of the third side, a triangle can be constructed using this set of side lengths.

3, 5, and 8 centimetres

3 + 5 = 8 > 8

3 + 8 = 11 > 5

5 + 8 = 13 > 3

Due to the fact that the sum of any two side lengths is bigger, a triangle can be constructed with this combination of side lengths.

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there are 3 cups of lemonade in each cup

The simplified forms are;

1) 2x[tex]y^2[/tex]

2) [tex]x^2y^3[/tex]

3) [tex]2xy^3z^5[/tex]

4)[tex]5p^2q[/tex]

5) [tex]5a^3b^5c^3/2[/tex]

6)[tex]4x^4y^5/3z^3[/tex]

7)[tex]7a^3b^3/2[/tex]

8) [tex]x^2y^3z^6[/tex]

9)-4a

10) [tex]3xy^5z^13/2[/tex]

To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.

We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.

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Answer: Yes

Step-by-step explanation:

Well, since 6+2, 6+2+3 does equal 8 plus 3 because 6+2+3 is basically saying 8+3, but just broken up.

a) The family's best deal is with Smokey's BBG which charges $780 for 60 guests.

b) Choosing Smokey's BBG over Bennie's BBQ will save (difference) the family $40.

The total cost for each company's catering services is worked out using their cost functions.

Smokey's BBG does not charge a fixed cost, unlike Bennie's BBG.

The difference between the total costs of the companies is obtained by subtraction.

The number of guests = 60

                                  Smokey's BBQ       Bennie's BBQ

Catering Fees                       $0                        $100

Charge per person              $13                          $12

The total charge for 60    $780 ($13 x 60)     $820 ($100 + $12 x 60)

Difference between the charges = $40 ($820 - $780)

However, using a system of equations we can determine the number of guests that makes the total cost the same for each company as 100.

Thus, comparing the total costs for the two companies shows the difference or cost savings to be gained by the family.

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Smokey's BBQ charges $13 per person while Bennie's BBG charges a $100 catering fee and $12 per person.

The Congruency Postulates for each of the given triangle are:

1) SAS Congruency

2) AAS Congruency

3) HL Congruency

4) Not enough Information

5) AAS Congruency

There are different congruency postulates such as;

SSS: Side Side Side Congruency

SAS: Side Angle Side Congruency

ASA: Angle Side Angle Congruency

AAS: Angle Angle Side Congruency

HL: Hypotenuse Leg Congruency

1) We are given two triangles with two congruent sides and the included angle and as such it is congruent by SAS Congruency Postulate.

2) We are given two congruent angles and the included side and as such they are congruent by AAS Congruency Postulate.

3) We are given the hypotenuse and leg as congruent and as such we can say that they are congruent by HL Congruency Postulate.

4) We are given two congruent sides and the non-included angle and as such they are not congruent by any congruency postulate.

5) We are given two congruent angles and the non-included side and as such they are congruent by AAS Congruency Postulate.

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For the given rectangle, the ordered pair that represents the location of point Z is (11,6).

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all precisely 90 degrees. The two sides come together at a straight angle at each corner or vertex. The rectangle differs from a square because its two opposite sides are of equal length. Also, it is known as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. A rectangle's diagonals cut each other in half. It has four right angles and is a parallelogram. The complete distance that the rectangle's outside boundary covers is referred to as its perimeter. The area a two-dimensional form occupies in a plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.

The rectangle should have opposite sides of equal length.

Here,

XY = WZ

XW = YZ

From the graph, we can write the coordinates as:

X = (7,11)

Y = (11,11)

W = (7,6)

Point Z should lie directly below Y so that it is in a straight vertical line.

Then it should have the same x coordinate as Y.

It should also lie in the same horizontal line that passes through W.

So it will have the same y coordinate as W.

Therefore for the given rectangle, the ordered pair that represents the location of point Z is (11,6).

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The bridge needs to be 1.6 miles long. The solution has been obtained by using Pythagoras theorem.

What is Pythagoras theorem?

According to the Pythagorean Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given a right angled triangle with base 3 miles and the hypotenuse 3.4 miles.

The perpendicular is given to be 'x'.

Using Pythagoras theorem, we know that

⇒Hypotenuse² = Perpendicular² + Base²

⇒(3.4)² = x² + 3²

⇒11.56 = x² + 9

⇒x² = 2.56

⇒x = 1.6 miles

Hence, the bridge needs to be 1.6 miles long.

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Given that the ball is white, the probability that it was taken from Jar 3 is 1/5, or 0.2. Given that the ball is white, there is a 20% likelihood that it was selected from Jar 3.

We must apply Bayes' theorem in order to determine the likelihood that the ball was taken from Jar 3 given that it is white. Let J stand for the scenario in which Jar 3 is chosen, and W for the scenario in which a white ball is drawn. Next, we have:

P(W | J) * P(J) / P = P(J | W) (W)

where P(J) is the prior probability of choosing Jar 3 (1/6), P(W) is the probability of drawing a white ball, and P(W | J) is the probability of drawing a white ball provided that Jar 3 is chosen.

We must apply the law of total probability to determine P(W):

P(W) is equal to P(W | J1) * P(J1), P(W | J2) * P(J2), and P(W | J3) * P. (J3)

where P(W | J1) represents the likelihood that a white ball will be drawn if Jar 1 is chosen (which is 1/2), P(W | J2) represents the likelihood that a white ball will be drawn if Jar 2 is chosen (which is 2/3), and P(W | J3) represents the likelihood that a white ball will be drawn if Jar 3 is chosen (which is 1/2).

Now that the values have been inputted, we can calculate:

P(W) = (1/2 * 1/2) + (2/3 * 1/3) + (1/2 * 1/6) = 5/12

P(J | W) = (1/2 * 1/6) / (5/12) = 1/5

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The perimeter of the triangle QSU is 88 cm.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given a circle.

And there are three tangents drawn intersecting the circle at points R, T and V.

We have the circle theorem that the tangents that meet at the same point are equal in length.

Using the theorem,

SR = ST

RQ = VQ

TU = VU

We have, segment RQ measures 15 cm, segment ST measures 4 cm, and segment VU measures 25 cm.

So, SR = ST = 4 cm

TU = VU = 25 cm

VQ = RQ = 15 cm

Perimeter of ΔQSU = (2 × 4) + (2 × 25) + (2 × 15) = 88 cm

Hence the perimeter is 88 cm.

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the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given an algebraic expression:

5 - 3|x + 8| = 20

First, we can begin by adding 3|x+8| to both sides of the equation, giving us:

5-20 = 3|x+8|

Simplifying the left-hand side, we get:

-15 = 3|x+8|

Next, we can divide both sides by 3, giving us:

-5 = |x+8|

Now we have an absolute value equation, which has two possible solutions depending on whether x+8 is positive or negative.

If x+8 is positive, then we have:

-5 = x+8

Solving for x, we get:

x = -13

If x+8 is negative, then we have:

-5 = -(x+8)

Solving for x, we get:

x = -5

Therefore, the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

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Answer:ILL GIVE BRAINLIEST!! Pls answer A

Find the mÁB

104°

126°

B

D

Step-by-step explanation:ILL GIVE BRAINLIEST!! Pls answer A

Find the mÁB

104°

126°

B

D

The correct students are Nico, Aditi, and Erick.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

The correct approaches to solving the equation are those that lead to the correct solution. We can check which students are correct by solving the equation and seeing if their approach leads to the correct answer.

Two-fifths (5 + x) = 8

Multiplying both sides by 5 gives:

5/5 * two-fifths (5 + x) = 5/5 * 8

One-fifth (5 + x) = 8/5

One-fifth (5) + One-fifth x = 8/5

1 + One-fifth x = 8/5

Subtracting 1 from both sides gives:

One-fifth x = 3/5

Multiplying both sides by 5 gives:

x = 3

So the solution is x = 3.

From the given approaches, Nico, Aditi, and Erick are correct. Their approaches are equivalent to the correct approach:

Two-fifths (5 + x) = 8

(5/2) * two-fifths (5 + x) = (5/2) * 8

(5/2) * (5/5 + x/5) = 20/5

5/2 + (5/2)x/5 = 4

5/2 + x/2 = 4

x/2 = 3/2

x = 3

Raj and Sandra's approaches are not correct, as they made errors in their calculations. Therefore, the correct students are Nico, Aditi, and Erick.

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Answer:

$10,000

Step-by-step explanation:

Let

Principal= x

Rate = 12%

Time = 2 years

Interest = (Final amount with interest placed on it) - Principal

Therefore,

Interest = 12,400 - x

Using

I = (P·r·t) / 100

Making P, subject of formula,

P = (100·I) / (R·T)

x = [100·(12,400 - x)] / (12.2)

x = (1,240,000 - 100x) / 24

Cross multiply,

24x = 1,240,000 -100x

24x + 100x = 1,240,000

124x = 1,240,000

x = 1,240,000 / 124

x = 10,000

Therefore, the principal, amount we need to invest is

$10,000

Please mark brainliest.

Thanks.

The sum of the first 30 consecutive whole numbers is 465.

What are consecutive numbers?

Consecutive numbers are numbers that follow each other in order without interruption, with a difference of 1 between each two adjacent numbers. For example, 3, 4, 5, 6, and 7 are consecutive numbers.

The formula n x (n+1)/2 is used to find the sum of the first n consecutive whole numbers because it provides a quick and efficient way to calculate the sum without having to add all the numbers individually.

To understand why the formula works, consider the sum of the first n numbers: 1 + 2 + 3 + ... + (n-1) + n. We can rewrite this sum in reverse order, starting with n and working down to 1: n + (n-1) + (n-2) + ... + 2 + 1.

If we add these two expressions together, we get:

(1 + n) + (2 + n-1) + (3 + n-2) + ... + (n-1 + 2) + (n + 1)

Notice that each pair of terms in parentheses adds up to n+1. There are n/2 pairs of terms, so the sum of the first n numbers is:

n/2 x (n+1)

Simplifying this expression gives the formula:

n x (n+1)/2

So to find the sum of the first 30 consecutive whole numbers, we can substitute n=30 into the formula:

30 x (30+1)/2 = 15 x 31 = 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

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Answer:

y= -2

X= 7

[tex]using \: elimination \: method \\ x + 3y = 1 \\ - 3x - 3y = - 15 \\ add \: the \: two \: equations \\ - 2x = - 14 \\ divide \: both \: sides \: by \: 2 \\ x = 7 \\ replace \: x \: with \: 7 \: to \: find \: value \: of \: y \\ (7) + 3y = 1 \\ y = - 2[/tex]

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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The equation that represents the number of zombies after 4 hours is the exponential function N(4) = 6 * (4)⁴.

What is an exponential function?

The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The exponential curve is influenced by both the exponential function and the value of x. Depending on the exponential function, an exponential curve might increase or decrease. A quantity should have either exponential growth or exponential decay if it regularly increases or decreases by a predetermined percentage.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Throughout time, the rate of change quickens.

With exponential decay, the quantity initially falls very quickly and then gradually. The speed of change slows over time.

The number of zombies in the beginning = 6

It is said that it quadruples in size every hour.

So,

After one hour it becomes = 6 * 4

After two hours it becomes = 6* 4 * 4

The size increases as an exponential function.

If the number of hours passed is x, then the number of zombies can be written as the following exponential function.

N(x) = 6 * (4)ˣ

where the number of zombies is N(x).

Therefore the equation that represents the number of zombies after 4 hours is the exponential function N(4) = 6 * (4)⁴.

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The best represent graph of the function is option a.

What is a function?

It is an expression which contains one independent variable and another is dependent variable.

The given function is

   f(x)= [tex]4^{x[/tex] - 4

As it is an exponential function so it must have a horizontal asymptote. Here the horizontal asymptote is f(x)= -4

For x intercept we need to take f(x)=0 and for y intercept substitute 0 for x and solve for y. [Here y can be treated as f(x).]

Here x intercept(s)= None

y intercept(s) = (0,-3)[ putting x=0 in   f(x) so 1-4= -3]

Hence the graph is given below.

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The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.

Total revenue = Price per vetkoek x Number of vetkoek sold

Total revenue = 10 x 300 = 3000

Total cost = Cost per vetkoek x Number of vetkoek sold

Total cost = 3.80 x 300 = 1140

Profit = Total revenue - Total cost

Profit = 3000 - 1140 = 1860

Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.

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The single equivalent discount rate for Company A is 19.28%, and for Company B is 23.18%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

We are given;

The measures of company A and B= 8/10/14/4 10/6/16/3

Now,

To calculate the single equivalent discount rate for each company, we can use the following formula:

Single equivalent discount rate = [(1 - (Discount % / 100)) ^ (365 / Average payment period) - 1] x 100

For Company A, the average payment period is:

(8 + 10 + 14 + 4) / 4 = 9

Using the formula, we can calculate the single equivalent discount rate for Company A:

Single equivalent discount rate = [(1 - (8/100)) ^ (365 / 9) - 1] x 100 = 19.28%

For Company B, the average payment period is:

(10 + 6 + 16 + 3) / 4 = 8.75

Using the formula, we can calculate the single equivalent discount rate for Company B:

Single equivalent discount rate = [(1 - (10/100)) ^ (365 / 8.75) - 1] x 100 = 23.18%

Therefore, by percentage the answer will be 19.28% and 23.18%.

Learn more about percent here:

https://brainly.com/question/11549320

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