What is the period of the function y = 3 csc x?

Answers

Answer 1

since csc(x) is the reciprocal identity of sin(x), they both have the same period, and since sin(x) has a period of 2π, so does csc(x).

Answer 2

The period of the function is 2π.

What is period of the function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.

Given:

y = 3 csc x

As, csc(x) carry the reciprocal identity of sin(x).

So, they both have the same period

The period of sin(x) is 2π.

Hence, the period of csc(x) is 2π.

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Related Questions

what is the probability of obtaining six tails in a row when flipping a coin?

Answers

tossing the coin it will either be heads or tails, so the chances of getting tails is 1/2, sample space is just 2 possible outcomes.

now, what is the probability of getting Tails AND Tails AND Tails AND Tails AND Tails AND Tails?

well, keep in mind that AND means "times" or the product, so, since the probability of getting tails once is 1/2, the probability of getting tails 6 times in a row is

[tex]\bf \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\implies \cfrac{1}{64}\implies 0.015625\implies 1.5625\%[/tex]

a copper alloy that is 40% copper is to be combined with a copper alloy that is 80% copper to produce 120 kilograms of an alloy that is 70% copper. how many kilograms of each alloy must be used? please work it out

Answers

Try this way:
1. note, that in such tasks mass of pure copper before merging and after merging is the same (this is the base);
2. If the mass of pure copper in alloy with 40% solution is 'x' and the mass of pure copper in alloy with 80% solution is 'y', then It means before merging was x/0.4 and y/0.8, after merging was (x+y)/0.7. It is one equation of the future system.
3. Using 120 kg. of 70% solution, it is possible to define mass of pure copper after merging, 120*0.7(=84 kg.). And before merging it was 'x+y' kg. of pure copper. It is the second equation of the future system.
4. according to the items no.2&3 (to make up the system of two equations and solve it). All the details are in the attached picture.
5. pure copper in 40% solution is 12 kg., pure copper in 80% solution is 72 kg. It means, that the copper alloy with 40% solution is x:0.4=12/0.4=30 kg., and the copper alloy with 80% solution is y:0.8=72/0.8=90 kg.

After setting up and correcting a system of equations, the student needs to use 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy to create 120 kg of a 70% copper alloy.

To solve this problem, we need to set up a system of equations. Let x be the amount of 40% copper alloy needed, and y be the amount of 80% copper alloy needed.

First, we have the total weight equation:

x + y = 120 kg (the final alloy's total weight)

Next, we have the copper content equation:

0.40x + 0.80y = 0.70 × 120 kg (the final alloy's copper content)

Now, let's solve this system of equations:

Address the second equation: 40x + 80y = 8400

Express x in terms of y: 40x = 8400 - 80y

Divide by 40: x = 210 - 2y

Substitute x in the first equation: (210 - 2y) + y = 120

Solve: 210 - y = 120, y = 90 kg

Finally, substitute the value of y back into x = 210 - 2y: x = 210 - 2 imes 90 = 210 - 180 = 30 kg

So, we need 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy.

what is the missing reason in the proof?

Answers

perpendicular bisector theorem

Answer:

Perpendicular bisector theorem

Step-by-step explanation:

Perpendicular bisector theorem: if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

So, if segment ST is the perpendicular bisector of segment RV, then, by perpendicular bisector theorem, any point in segment ST (like S) is equidistant from points R and V, in consequence, segments RS and SV are equal.

What is the distance between (-6,8) and (-3,9)

Answers

[tex]d= \sqrt{(-3-(-6))^2+(9-8)^2}= \sqrt{9+1}= \sqrt{10} [/tex]

Answer:10

Step-by-step explanation:I seen the answer

find the area of an equilateral triangle (regular 3-gon) with the given measurement

Answers

you do length x width x height x width divided by 2

Determine the distance between point (x1, y1) and point (x2, y2), and assign the result to pointsdistance. the calculation is: distance=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√distance=(x2−x1)2+(y2−y1)2 you may declare additional variables. ex: for points (1.0, 2.0) and (1.0, 5.0), pointsdistance is 3.0.

Answers

For this case what you should know is that the distance between two points can be thought of as a line. To find the length of this line, you can use the formula:
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]
Example,
for points (1.0, 2.0) and (1.0, 5.0):
d: √ [(1 - 1) ^ 2 + (5 - 2) ^ 2]
d: 3.0
Answer:
the distance between point (x1, y1) and point (x2, y2) is:
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]

What is the period of y = 3cot(4x - 3pi)

Answers

4x = 2π when x = π/2

The period is π/2.

The period of y = 3cot(4x - 3pi) is π/2 units.

The period of the function y = 3cot(4x - 3π) is calculated as the reciprocal of the absolute value of the parameter in front of x.

To find the period, identify the coefficient of x, which is 4 in this case. The period is then given by 2π/|4| = π/2.

Therefore, the period of the given function y = 3cot(4x - 3π) is π/2 units.

Solve the equation on the interval (0,2pi )

2 Sin Θ cos Θ = -1

Answers

To solve the trigonometric equation 2sin(θ)cos(θ) = -1 on the interval (0,2π), use the double angle identity and find the solutions to be θ = π/4 and θ = 3π/4.

Solve the trigonometric equation:

2sin(θ)cos(θ) = -1

Use the double angle identity: sin(2θ) = 2sin(θ)cos(θ)

Substitute and solve to get sin(2θ) = -1

Find the solutions within the given interval (0,2π) which are θ = π/4 and θ = 3π/4.

Prove that the angle bisector of the angle opposite to the base of an isosceles triangle is also the altitude to the base

Answers

Given:
.. apex angle is divided into 2 equal parts
.. base angles are equal
.. side lengths are equal
1. The triangles are congruent by ASA
2. The angles where the bisector meets the base add to 180°. (They are linear angles formed by the bisector and the base.)
3. The angles where the bisector meets the base are congruent. (The are corresponding angles of congruent triangles.
4. The angles where the bisector meets the base are 90°. (Congruent angles that add to 180° must be 90°.)
5. The bisector is a line from the apex meets the base at a right angle, so is an altitude. (Definition of altitude.)

Suppose that m∠A = m∠D. Which other fact would guarantee that the triangles are SIMILAR? A) AB DE = CB FE B) m∠C = m∠F C) m∠A + m∠B + m∠C = 180° D) 180° - m∠D = m∠E + m∠F

Answers

Given that m∠A=m∠D. The facts that would guarantee similarity of triangle ABC and triangle FDE is :
The ratio of corresponding sides are similar, that it:
AB/DE=CB/FE=CA/FD
also the corresponding angles should be equal.
hence the answer is:
A] AB/DE=CB/FE and m∠C=m∠F

a rectangular prism has a volume of 144 cm3. the base is a square with a length of 4 cm. what is the height of the prism

Answers

Answer:

9 cm

Step-by-step explanation:

The volume is given by the formula ...

V = LWH

Filling in the given numbers, you have ...

144 cm^3 = (4 cm)(4 cm)H

H = (144 cm^3)/(16 cm^2) = 9 cm

The height of the prism is 9 cm.

Write an equation in slope- intercept form of the line through points S(-7,-6) and T(10,8)

Answers

Final answer:

The slope-intercept form of the line passing through points S(-7,-6) and T(10,8) is calculated by first determining the slope or 'rise over run' which is 14/17. Subsequently, the slope and point T(10,8) are used to find the y-intercept which is -8/17. Hence, the equation of the line is y = 14/17x - 8/17.

Explanation:

To create an equation in the slope-intercept form we first need to find the slope or rise over run given our two points S(-7,-6) and T(10,8). The formula to find the slope (m) = (y2 - y1) / (x2 - x1). By substituting the values into the formula we get (8-(-6)) / (10-(-7)) = 14/17, which is our slope (m).

Next, we use the slope (m) and one point, let's take T(10,8), in the equation y = mx + b to find the y-intercept (b). Substituting the known values into the equation gives us 8 = 14/17*10 + b. Solving for b gives us b = -8/17.

Therefore, the slope-intercept form of the line passing through the given points S(-7,-6) and T(10,8) is y = 14/17x - 8/17.

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Final answer:

To write the equation of a line in slope-intercept form, find the slope and y-intercept. For the points S(-7,-6) and T(10,8), the equation is y = (14/17)x + 70/17.

Explanation:

To write the equation of a line in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The slope can be found using the formula:

m = (y2 - y1) / (x2 - x1)

After finding the slope, we can substitute it along with one of the given points into the slope-intercept form equation: y = mx + b, where y and x are the coordinates of any point on the line. Solving the equation will give us the value of the y-intercept.

So, for the given points S(-7,-6) and T(10,8),

Find the slope: m = (8 - (-6)) / (10 - (-7)) = 14/17Substitute the slope and one point into the slope-intercept form equation: Solve for b: -6 = -98/17 + b, b = -6 + 98/17, b = 70/17Therefore, the equation in slope-intercept form is: y = (14/17)x + 70/17

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Latifah makes $12 per hour. She works 18 hours per week. She calculates that in 4 weeks, she will earn $864. If her hourly rate and weekly hours are rounded to the nearest ten, which amount represents an estimate of the amount she will make over 4 weeks? Is her original calculation reasonable?

Answers

here is the steps to figure it out with the answer:
she makes $216 per week. If her hourly rate and weekly hours are rounded to the nearest tenth then it would make her weekly pay $200. Her hourly pay is now $10 and her weekly hours are 20. Now multiply the 20 (weekly hours) by 4 (which would be 4 weeks) 20x4= 80. So 80 hours in 4 weeks. Now her hourly pay is $12 rounded to the nearest tenth = $10 per hour. SOOO the $10 multiplied with the 80= $800 in 4 weeks.

Answer and step-by-step explanation:

Rounding her hourly rate to the nearest ten, we get $10.

Rounding her number of hours to the nearest ten, we get 20.

This gives us an estimate of 10(20)(4) = $800

Her original calculation is reasonable; it is higher because the actual hourly rate is larger than the estimate, so her amount of pay should be higher than the estimate.

Which pair of expressions is equivalent using the Associative Property of Multiplication? (3 points) 5(3a ⋅ 4) = 15a ⋅ 20 5(3a ⋅ 4) = (3a ⋅ 4) ⋅ 5 5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4 5(3a ⋅ 4) = 5 ⋅ 3a ⋅ 4 6

Answers

Answer:

5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4

Step-by-step explanation:

The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.

In this sense, the associative property for the sum is mathematically given by:

[tex](x+y)+z=x+(y+z)[/tex]

and for the multiplication by:

[tex](xy)z=x(yz)[/tex]

Now, let:

[tex]x=5\\y=3a\\z=4[/tex]

Using the Associative Property of Multiplication:

[tex](xy)z=x(yz)\\\\Replacing\hspace{3}the\hspace{3}values\\\\(5\cdot 3a)\cdot4=5(3a\cdot 4)[/tex]

Therefore the equivalent expressions are:

5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4

Answer: C

Step-by-step explanation: Sorry If I am wrong, ty!!

-☈⊙⌘☿

Three golfers, Vijay, Ernie, and Phil , during five years had a total of 221 top-10 finishes. Ernie had 13 more top-10 finishes than Phil. Vijay had 16 more top-10 finishes than Phil. Determine the number of top-10 finishes for each golfer.

Answers

For this case what you must do first is to define the following variables:
x: number of top-10 finishes for Vijay.
y: number of top-10 finishes for Ernie.
z: number of top-10 finishes for Phil.
We write the following system of equations:
x + y + z = 221
y = 13 + z
x = 16 + z
Solving the system we have:
Step 1:
x + y + z = 221
(13 + z) + (16 + z) + z = 221
3z + 29 = 221
z = (221-29) / (3)
z = 64
Step 2:
y = 13 + z
y = 13 + 64
y = 77
Step 3:
x = 16 + z
x = 16 + 64
x = 80
Answer:
the number of top-10 finishes for each golfer is:
Vijay: 80
Ernie: 77
Phil 64

For which of these does correlation most likely imply causation?

Answers

Hello!

Correlation most likely implies causation in the following case: As rainfall increases, the number of umbrellas sold increases.

"Correlation doesn't always imply causation" is a common saying in statistics. Sometimes when there's a high correlation coefficient between two variables, that doesn't always mean that one is the cause for the other.

When rainfall increases, people are in need of umbrellas and often buy new ones, so for this pair of variables, the correlation most likely implies causation.

Have a nice day!

Answer:

As the use of a condition that increases the electricity bill increases as well

Step-by-step explanation:

The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. between what two values do the middle 95% of the lengths of all pregnancies fall?

Answers

218, 314 are the two values do the middle 95% of the lengths of all pregnancies fall.

are the fractions 1/2 and 1/8 equivalent fractions

Answers

Hello there,

1/2 and 1/8 are not equivalent, meaning they are not valued as the same.

1/2 is larger than 1/8 because 1/2 is pretty much half of 1 whole, while 1/8 is smaller than half of 1 whole.

Hope this helps you.
Have a great day! (:

The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

The fraction numbers are given below.

1/2 and 1/8

In the fraction numbers, the numerator is the same. If the denominator is the same, then the numbers will be equal.

The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.

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A retired couple invested $6000 in bonds at a simple interest rate of 5.1%. At the end of one year, how much interest did they receive on their investment? Please show your work.

Answers

if the interest rate is being paid yearly the:
[tex] \frac{5.1}{100} \times 6000 \\ = 0.051 \times 6000 \\ = 306 \\ 306 + 6000 = 6306[/tex]
they have received $306

The retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

To find the simple interest earned by the retired couple on their investment of $6000 at a rate of 5.1% for one year

we can use the formula: I = P × r × t

where I is the simple interest,

P is the principal (the amount invested),

r is the interest rate (as a decimal), and

t is the time period (in years).

Plugging in the given values, we get:

I = 6000 × 0.051 × 1

I = 306

Therefore, the retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.

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Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <1, -2>, v = <-4, 8>

A) Orthogonal
B) Neither
C) Parallel

Answers

u dot v = <1,-2> dot <-4,8>
u dot v = 1*(-4) + (-2)*8
u dot v = -4 - 16
u dot v = -20
The nonzero dot product tells us that u and v are not orthogonal

u = k*v
<1,-2> = k*<-4,8>
<1,-2> = <-4k, 8k>
1 = -4k implies that k = -0.25
-2 = 8k implies that k = -0.25
The fact we get the same k value each time tells us the two vectors are parallel (they point in the same direction on the compass). One vector is a scaled version of the other.

Answer: C) Parallel

Find the angles of a rhombus in which a diagonal length is equal to the length of a side.

Answers

We can draw the figure as shown in attachment.

Then you can see an equilateral triangle ABD.

So here angle A, B and D all will be 60 degrees.

So one of the angles of rhombus becomes 60°.

Rhombus is a parallelogram.Hence the adjacent angle becomes 120°.

Finally,angles of rhombus are 60 ,120,60,120.

The diagram represents the floor of a museum. The figure is made up of a rectangle and a triangle.

What is the area of the floor?

Enter your answer in the box.

______ ft2 I'll but the link for the pic

Answers

I don't see the pic. :(

The figure is formed of a rectangle and a triangle

The rectangle has dimensions:length=38ft and width=20ft

The triangle has dimensions:base=33ft and height=9ft

Area of rectangle=length*width of rectangle

Area of triangle=[tex] \frac{1}{2} [/tex]*base*height

Area of figure= area of rectangle + area of triangle

Area=length*width+[tex] \frac{1}{2} [/tex]*base*height

Area=38*20 + [tex] \frac{1}{2} [/tex]*33*9

Area=760+[tex] \frac{1}{2} [/tex]*297

So we have, Area=760+[tex] \frac{297}{2} [/tex]

Or, Area=760+148.5

Area=908.5

Area of the floor=908.5[tex] ft^{2} [/tex]

A rectangular park is 5/6 miles wide and 1 5/7 miles long. What is the area of the park?

Please hepl me can't find answer from others!!!!

Answers

Wouldn't it just be:
5 x 12
6 x 7
60/42
or
10/7
or
1 3/7

Find the complete factorization of the expression. 32xy − 56xyz

Answers

xy(32 - 56z)
8xy(4 - 7z)

solve and write multiplication equations

72=0.6r

Answers

The answer is 120 instead of 12 because 12 equals 7.2

72=0.6r
72/0.6 = 0.6r/0.6
r = 120

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered?

Answers

The area of one watered circle will be
.. A = π*r^2 = π*(25 ft)^2 = 625π ft^2

The area of 3 such circles will be
.. 3A = 3*625π ft^2 = 1875π ft^2
.. ≈ 5890 ft^2

Keith had 694 green, yellow and blue marbles altogether. he had 3 times as many blue marbles as yellow marbles. there were 90 fewer green than blue marbles. how many blue marbles did Keith have?

Answers

let the number of blue marbles be x

number of yellow marbles = x/3

number of green = x- 90

ATQ

x + x/3 + x - 90 = 694

2x + x/3 = 784

(6x + x)/3 = 784

7x/3 = 784

x = 784 x 3/7

x = 112 x 3

x = 336

number of blue marbles = 336

Let [tex]g[/tex] the number of green, [tex]y[/tex] the number of yellow and [tex]b[/tex] the number of blue marbles respectively.

We have

[tex]g + y + b = 694[/tex] (we will call this equation 1)

Also, [tex]b = 3*y[/tex] (yellow marbles are three times as many as blue marbles), so equation 1 becomes

[tex]g + y + 3y = 694[/tex]

But, [tex]g = b - 90[/tex] (green marbles are as many as blue marbles - 90)
and because [tex]b = 3*y[/tex], we have that [tex]g = 3*y - 90[/tex]

So, equation 1 is now

[tex]3y - 90 + y + 3y = 694[/tex]
[tex]7y - 90 = 694[/tex]

We add 90 to both sides so

[tex]7y = 694 + 90 = 784[/tex]

We divide each side by 7, so finally

[tex]y = 112[/tex]

and we have

[tex]b = 3*y = 3*112 = 336[/tex]
and
[tex]g = b - 90 = 336 - 90 = 246[/tex]

To check if our results are correct, we can see that

[tex]g + b + y = 246 + 336 + 112 = 694[/tex],

so we are indeed correct.

Write2/3and3/4 as a pair of fractions with a common denominator

Answers

The least common multiple of 3 and 4 is 12.

[tex] \dfrac{2}{3} \times \dfrac{4}{4} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12} [/tex]

[tex] \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12} [/tex]

Answer: 8/12 and 9/12, respectively.

Find the area of a parallelogram with base b and height h. B= 74cm H=14.8 cm

Answers

the area is1,095.2cm

General Idea:

The formula to find the area of parallelogram is given below:

[tex] Area \; of\; the\; parallelogram=BASE \times HEIGHT\\ \\ [/tex]

Applying the concept:

Given, [tex] BASE\; (B)= \; 74\; cm\\ HEIGHT \;(H)=14.8 \;cm\\\\ Area \; of \; the \; Parallelogram = 74 \; cm \times 14.8 \; cm = 1095.2 \; cm^{2} [/tex]

Marianne has been collecting donations for her biscuit stall at the school summer fayre. There are some luxury gift tins of biscuits to be sold at £5 each, normal packets at £1 each, and mini- packs of 2 biscuits at 10p each. She tells Amy that she has received exactly 100 donations in total, with a collective value of £100, and that her stock of £1 packets is very low compared with the other items. Amy wants to work out how many of each item Marianne has. Show how she can do it.

Answers

Answer:

Number of luxury gift tins of biscuits sold at £5 each: 18
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80

Solution:

Number of luxury gift tins of biscuits sold at £5 each: x
Amount received by the number of luxury gift tins of biscuits sold: £5 x Number of normal packets sold at £1 each: y
Amount received by the number of normal packets sold: £1 y
Number of mini- packs of 2 biscuits sold at 10p each: z
Amount received by the number of 2 biscuists sold: 10p z =£0.1z

She tells Amy that she has received exactly 100 donations in total:
(1) x+y+z=100

A collective value of £100:
Total amount receibed: £5 x + £1 y+ £0.1z= £100 → £ (5x+1y+0.1z)= £100 → 5x+y+0.1z=100 (2)

Her stock of £1 packets is very low compared with the other items:
y<<x
y<<z
Then we can despice the value of "y" and solve for "x" and "z":
y=0:
(1) x+y+z=100→x+0+z=100→x+z=100 (3)
(2) 5x+y+0.1z=100→5x+0+0.1z=100→5x+0.1z=100 (4)

Solving the system of equations (3) and (4) using the substitution method:
Isolating z in equation (3): Subtrating x from both sides of the equation:
(3) x+z-z=100-x→z=100-x

Replacing z by 100-x in the equation (4):
(4) 5x+0.1z=100→5x+0.1(100-x)=100
Eliminating the parentheses:
5x+0.1(100)-0.1x=100→5x+10-0.1x=100
Adding similar terms on the left side of the equation:
4.9x+10=100
Solving for x: Subtrating 10 from both sides of the equation:
4.9x+10-10=100-10→4.9x=90
Dividing both sides of the equation by 4.9:
4.9x/4.9=90/4.9→x=18.36734693

Replacing x=18.36734693 in the equation:
z=100-x→z=100-18.36734693→z=81.63265306

We can round x and z: x=18 and z=81 and solve for y in equations (1) and (2):
(1) x+y+z=100→18+y+81=100
Adding similar terms on the left side of the equation:
99+y=100
Subtracting 99 from both sides of the equation:
99+y-99=100-99→y=1

(2) 5x+y+0.1z=100→5(18)+y+0.1(81)=100→90+y+8.1=100→98.1+y=100→98.1+y-98.1=100-98.1→y=1.9→y=2 different to 1

Suppose y=1. Replacing y=2 in equations (1) and (2):
(1) x+y+z=100→x+1+z=100→x+1+z-1=100-1→x+z=99
(2) 5x+y+0.1z=100→5x+1+0.1z=100→5x+1+0.1z-1=100-1→5x+0.1z=99

Repeating the process:
z=99-x
5x+0.1z=99→5x+0.1(99-x)=99→5x+9.9-0.1x=99→4.9x+9.9=99→4.9x+9.9-9.9=99-9.9→4.9x=89.1→4.9x/4.9=89.1/4.9→x=18.18367346
z=99-18.18367346→z=80.81632653
x=18 and z=80
(1) x+y+z=100→18+y+80=100→y+98=100→y+98-98=100-98→y=2
(2) 5x+y+0.1z=100→5(18)+y+0.1(80)=100→90+y+8=100→y+98=100→y+98-98=100-98→y=2

Answer:
Number of luxury gift tins of biscuits sold at £5 each: 18
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80

Answer:

Number of luxury gift tins of biscuits L sold is 18.

Number of mini- packs of 2 biscuits M sold is 80.

Number of normal packets N sold is 2.

Step-by-step explanation:

Let L, M, N represent the number of Luxury, Mini, and Normal packets sold.

Total earned by selling luxury gift tins of biscuits = 5L

Total earned by selling normal packets = £1N

Total earned by selling 2 biscuits at 10p = 0.1M

Marianne tells Amy that she has received exactly 100 donations in total:

Equation becomes:

[tex]L+N+M=100[/tex] .... (1)

total earning is £100, so another equation becomes:

[tex]5L+N+0.1M=100[/tex] .......(2)

Given is that stock of £1 packets is very low compared with the other items:

so, N<L and N<M

Putting y = 0 in equation 1 and 2

[tex]L+M=100[/tex] or [tex]L=100-M[/tex] .....(3)

[tex]5L+0.1M=100[/tex] ......(4)

Replacing L by 100-M in the equation 4

[tex]5(100-M)+0.1M=100[/tex]

[tex]500-5M+0.1M=100[/tex]

4.9M=400

M=81.63

As, L=100-M

[tex]L=100-81.63=18.37[/tex]

L=18.37

We can round L and M to 18 and 81 respectively and solve for N from 1 and 2 equations.

[tex]L+M+N=100[/tex]

=>[tex]18+N+81=100[/tex]

=>[tex]N=1[/tex]

[tex]5(18)+N+0.1(81)=100[/tex]

[tex]90+N+8.1=100[/tex]

=> N=1.9

We will repeat the same process with N = 2 and get the following result.

Number of luxury gift tins of biscuits L sold is 18

Number of mini- packs of 2 biscuits M sold is 80

Number of normal packets N sold is 2

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