What is the quotient of -8(^6)/4x(^-3)

Let's pretend the base price is $100

If the shopper brings enough money to cover 25% of the base price then they are bringing $25

The bargain promises 25% off of the base price of $100, meaning that the bargain price will be $75

The shopper cannot purchase the item because they only brought $25 when they should have brought $75

The shopper went home disappointed because combining a 25% off coupon and paying 25% of the base price results in a net discount of 0%, not the expected 50%.

The shopper went home disappointed because they assumed that by combining a 25% off coupon with paying 25% of the base price, they would get a 50% discount on the item. However, these discounts are applied sequentially, so the actual discount is less than 50%. In this case, the final discount would be 25% off the base price minus 25% of the base price, resulting in a net discount of 0%. The shopper didn't get the expected bargain they were hoping for because the discounts do not add up linearly but are applied to the remaining amount after the previous discount.

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Answer:

4

Step-by-step explanation:

The sum of the measures of all interior angles in triangle is always equal to 180°. So,

∠A+∠B+∠C=180°

∠B=180°-63°-49°=68°

Now use the sine rule:

[tex]\dfrac{c}{\sin \angle C}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{3}{\sin 49^{\circ}}=\dfrac{b}{\sin 68^{\circ}}\\ \\b=\dfrac{3\sin 68^{\circ}}{\sin 49^{\circ}}\approx 3.685\approx 4[/tex]

Answer:

Option C. 1,493

Step-by-step explanation:

If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.

From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.

If the population in 2010 was 1,578. Then, the population in 2060 is going to be:

Using the rule of three:

If 1578 ----------------> Represents 100%

    X       <-----------------       5.5%

X = (5.5%x1578)/100% = 86.79 ≈ 87

Then the total population in 2060 is: 1578 - 87 = 1491

None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!

Answer:

The population would be 1,493.

Step-by-step explanation:

Given,

The initial population, P = 1,578, (  In 2010 )

Also, the decline rate per 10 years, r = 1.1 %,

And, the number of the periods of 10 years since, 2010 to 2060, n = 5,

Hence, the population in 2060 would be,

[tex]A=P(1-\frac{r}{100})^n[/tex]

[tex]=1578(1-\frac{1.1}{100})^5[/tex]

[tex]=1493.09849208\approx 1493[/tex]

Option third is correct.

Answer:

The table in the attached figure N 1

The graph in the attached figure n 2

Step-by-step explanation:

we have

x+2=y

we know that

To graph a linear equation the best way is plot the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0+2=y

y=2

The y-intercept is the point (0,2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x+2=0

x=-2  

The x-intercept is the point (-2,0)

Find additional points to create a table (is not necessary for plot the line)

For x=1

1+2=y

y=3

For x=2

2+2=y

y=4

The table in the attached figure N 1

Graph the linear equation ------> plot the intercepts a joined the points

see the attached figure N 2

Creating a table of values for the equation \( x + 2 = y \):
To create a table of values, we can choose arbitrary values for \( x \), and then calculate the corresponding \( y \) values using the equation. Let's pick a few values for \( x \) and solve for \( y \).
Here's the table:
\[
\begin{array}{cc}
\textbf{x} & \textbf{y (= x + 2)} \\
\hline
-3 & -1 \\
-2 & 0 \\
-1 & 1 \\
0 & 2 \\
1 & 3 \\
2 & 4 \\
3 & 5 \\
\end{array}
\]
For each value of \( x \), taking the equation \( x + 2 = y \) we just add 2 to \( x \) to find \( y \).
Now, let's graph these points on a coordinate plane:
1. Draw a horizontal line for the \( x \)-axis and a vertical line for the \( y \)-axis, ensuring they intersect at the origin (0,0).
2. Mark the scale on both axes. For simplicity, we can choose each grid unit to represent 1.
3. Plot the points from the table onto the graph:
  - (-3, -1)
  - (-2, 0)
  - (-1, 1)
  - (0, 2)
  - (1, 3)
  - (2, 4)
  - (3, 5)
4. Once all the points are plotted, draw a straight line through the points, extending the line as far as the graph allows on both ends since the equation represents a linear relationship without bounds.
5. Label the line with the equation \( x + 2 = y \).
The graphical representation would show a straight line with a slope of 1 (since for every unit increase in \( x \), \( y \) increases by 1) and a \( y \)-intercept at \( y = 2 \) (since when \( x = 0 \), \( y = 2 \)).

Gradient= -3/2 Equation: Y=mx+c Y=2 , X=8

So you substitute the numbers in

2=(-3/2) x 2 + c (then you backtrack to solve for c which is the y intercept)

2=-3+c

5=c So the equation should be Y=-3/2x+5

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = - [tex]\frac{3}{2}[/tex] x + 14 ← equation in point- slope form

Answer:

D. (0,5)

Step-by-step explanation:

Any points on the dashed line is not a solution. In this case, any points in the shade or above the dashed line is a solution.

For this case we must locate each of the points in the graph and see if they are in the region.

The border of the region is dotted, therefore equality is not included. That is, the points (-3,1) and (3,3) do not belong to the region.

On the other hand, we observe that the point (0,0) does not enter the region either.

Finally, it is observed that the point (0,5) if it is located within the region.

Answer:

(0,5)

since the cone's diameter is 6, its radius must be 3 then.

[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi rs+\pi r^2~~ \begin{cases} r=&radius\\ s=&slant~height\\ \cline{1-2} r=&3\\ s=&5 \end{cases}\implies SA=\pi (3)(5)+\pi (3)^2 \\\\\\ SA=15\pi +9\pi \implies SA=24\pi \implies SA\approx 75.398[/tex]

Answer:

24π or 75.4

Step-by-step explanation:

The equation for the surface area is SA=πr²+πrl

Since the diameter is 6, then the radius will be 3

Plug the values in:

π3²+π×3×5

9π+15π

24π =75.39822

Answer:

[tex]\large\boxed{x=\dfrac{4a^2+3a}{9-2a}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x-a}{x+2a}=\dfrac{2a}{3}\qquad\text{cross multiply}\\\\(3)(3x-a)=(2a)(x+2a)\qquad\text{use the distributive property}\\\\(3)(3x)+(3)(-a)=(2a)(x)+(2a)(2a)\\\\9x-3a=2ax+4a^2\qquad\text{add}\ 3a\ \text{to both sides}\\\\9x=2ax+4a^2+3a\qquad\text{subtract}\ 2ax\ \text{from both sides}\\\\9x-2ax=4a^2+3a\qquad\text{distributive}\\\\(9-2a)x=4a^2+3a\qquad\text{divide both sides by}\ (9-2a)\neq0\\\\x=\dfrac{4a^2+3a}{9-2a}[/tex]

Answer:

Range :  {1, 3, 4, 7}

Step-by-step explanation:

Given function is defined as  f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Now we need to find about  what is the range of the given function f.

we know that y-value corresponds to the range.

since each point is written in (x,y) form so we just need to collect y-values of

f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Hence required range is {3, 7, 3, 4, 1}

But we need to remove repeated values

so correct choice is  {1, 3, 4, 7}

Answer:

Is an equilateral triangle

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles measures 60 degrees each

so

In this problem the triangle formed by the route has three equal sides (10 miles)

therefore

Is an equilateral triangle

Answer:

the inter-quartile range will increase

Step-by-step explanation:

The initial data-set was;

20,32,32,45,50

Adding a new value 78 will have several effects;

The mean of the new set of values will increase since 78 is mostly likely to be an outlier.

The median of the new data set will increase. The median of the old data set is 32 while that of the new data set will be 38.5

The mode is the most frequent observation. Both the new and the old sets of values will have a mode of 32. The mode will therefore remain the same.

The inter-quartile range just like the range will increase

Answer:

[tex]64^\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{64}[/tex]

has the meaning of [tex]64^\frac{1}{4}[/tex]

That means that what you have is

[tex]64^\frac{1}{4}*^\frac{1}{3}[/tex]

which means that your final answer is

[tex]64^\frac{1}{12}[/tex]

That would be the answer that I try first. In fact the question is set up in such a way that I would ignore the fact that 64^(1/3) = 4

Answer:

22.9m

Step-by-step explanation:

Using Pythagorean theorem, we can get two equations using the angles.

From Point A:

∠A = 20°

AB = 20m

From Point B:

∠B = 29°

BD = x

What we are looking for is the opposite side of each right triangle, each person makes because we have one adjacent side. We also know that both opposite sides will be equal.

So we use this formula for both point of views:

[tex]Tan\theta=\dfrac{Opposite}{adjacent}[/tex]

Where:

Opposite = height of the building

Adjacent = distance from the building

We are looking for the opposite side so we can tweak our formula to get an equation for the height

[tex]height=(Tan\theta)(distance)[/tex]

Using our given, we can solve for the distance of point B to D:

[tex](Tan20)(20+x) = (Tan29)(x)\\\\(0.3640)(20+x) = (0.5543)(x)\\\\\dfrac{(7.28+0.3640x)}{0.5543}=x\\\\13.1337 + 0.6567x = x\\\\13.1337 = x - 0.6567x\\\\13.1337 = 0.3433x\\\\\dfrac{13.1337}{0.3433}=x\\\\38.2572 = x[/tex]

The distance of point B to D is 38.2572 m.

Now that we know the distance of BD we can solve for the height of the building using only the given from point B.

[tex]height=(Tan\theta)(distance)[/tex]

[tex]height=(Tan29)(38.2572m)[/tex]

[tex]height=(0.5543)(38.2572m)[/tex]

[tex]height=21.21m[/tex]

But this is only the height from the line of sight. To get the height of the building from the ground, we just add the height of the viewer, which is 1.7m.

21.21m + 1.7m = 22.91m

The closest answer is: 22.91 m

Answer:

[tex]\frac{35}{2}[/tex]

Step-by-step explanation:

To solve this problem we need to write the mixed fraction as a fractional number, as follows:

[tex]3 1/3 = 3 + \frac{1}{3} = \frac{9+1}{3} = \frac{10}{3}[/tex]

[tex]5 1/4 = 5 + \frac{1}{4} = \frac{20+1}{4} = \frac{21}{4}[/tex]

Then, evaluating the expression:

[tex]\frac{10}{3}[/tex]×[tex]\frac{21}{4}[/tex] = [tex]\frac{210}{12}[/tex]

→ [tex]\frac{35}{2}[/tex]

Answer:

35 over 2

Step-by-step explanation:

Answer: Light waves

Step-by-step explanation:

Used in the usual sense, radiant energy is just light. When you turn on your electric stove unit, it heats up and emits radio waves, infrared waves, and visible light waves. All of these waves are just light with different frequencies.

Answer:

light waves

Step-by-step explanation:

Answer:

The sum of the first twenty-seven terms is 1,188

Step-by-step explanation:

we know that

The formula of the sum in arithmetic sequence is equal to

[tex]S=\frac{n}{2}[2a1+(n-1)d][/tex]

where

n is the number of terms

a1 is the first term

d is the common difference (constant)

step 1

Find the common difference d

we have

n=7

a1=-8

S=28

substitute and solve for d

[tex]28=\frac{7}{2}[2(-8)+(7-1)d][/tex]

[tex]28=\frac{7}{2}[-16+(6)d][/tex]

[tex]8=[-16+(6)d][/tex]

[tex]8+16=(6)d[/tex]

[tex]d=24/(6)=4[/tex]

step 2

Find the sum of the first twenty-seven terms

we have

n=27

a1=-8

d=4

substitute

[tex]S=\frac{27}{2}[2(-8)+(27-1)(4)][/tex]

[tex]S=\frac{27}{2}[(-16)+(104)][/tex]

[tex]S=\frac{27}{2}88][/tex]

[tex]S=1,188[/tex]

Answer:

[tex]\large\boxed{x=-\sqrt2,\ x=0,\ x=\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^3-2x=0\qquad\text{distributive}\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x^2-2=0\qquad\text{add 2 to both sides}\\\\x^2=2\to x=\pm\sqrt2[/tex]

You can factor out an x:

x ( [tex]x^{2}[/tex] - 2)

Now set x equal to zero and the expression in the parentheses equal to zero

x = 0

[tex]x^{2}  - 2 = 0[/tex]

We don't need to do anything to x = 0 because x is already isolated, but you can further isolate x in the equation:

x^2 - 2 = 0

To do this add 2 to both sides

x^2 = 2

Take the square root of both sides to completely isolate x

x = ± √2

The zeros are:

0 and ±√2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

204,160,000

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%... or 0.638

So, if we assume that the US population is of 320 million, how many people does that make wearing glasses.... we just have to multiply 320M by 0.638

G = 320,000,000 * 0.638 = 204,160,000

Answer:

39.68 million[

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 124 of these people wear contact lenses.

The probability that a randomly selected person will wear contact lenses is:

[tex]P = \frac{124}{1000}\\\\P = 0.124[/tex]

Then, the expected number of people who wear contact lenses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.124[/tex]

[tex]N = 39.68\ million[/tex]

Answer:

Step-by-step explanation:

[tex]\text{The sum of cubes:}\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\text{Therefore}\\\\\text{for}\ a=6\ \text{and}\ b=s:\\\\6^3+s^3=(6+s)(6^2-6s+s^2)=(6+s)(36-6s+s^2)[/tex]

Answer: (6 + s)(s^2 – 6s + 36)

Step-by-step explanation:

Answer:

26 2/3

Step-by-step explanation:

if you walked that distance 4 times last week then you walked 6 2/3 x 4

and that = 26 2/3

Answer:277.50

Step-by-step explanation:you do this than u do that

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

On 1st June, amount in piggy bank = $2.00

On 2nd June, amount in piggy bank = $2.50

On 3rd June, amount in piggy bank = $3.00

So, it forms an arithmetic sequence:

Here, a = $2

d = 0.50

n = 30 days

So, Sum of 30 terms would be

[tex]S_{30}=\dfrac{30}{2}(2\times 2+(30-1)0.5)\\\\S_{30}=15(4+29\times 0.50)\\\\S_{30}=15(4+14.5)\\\\S_{30}=15(18.5)\\\\S_{30}=\$277.50[/tex]

Hence, Option 'D' is correct.

Answer:   173.20 ft

Step-by-step explanation:

Observe the attached image. To know how long the shadow is, we must find the length of the adjacent side in the triangle shown. Where the opposite side represents the height of the building

By definition, the function [tex]tan (x)[/tex] is defined as

[tex]tan(x) = \frac{opposite}{adjacent}[/tex]

So

[tex]opposite = 100\ feet\\x=30\°[/tex]

[tex]adjacent = l[/tex]

Then

[tex]tan(30\°) = \frac{100}{l}[/tex]

[tex]l = \frac{100}{tan(30\°)}[/tex]

[tex]l = 173.20\ ft[/tex]

The answer is:

The shadow is 173.20 feet

To solve the problem, we need to calculate the projection of the building's shadow over the ground.

We already know the height of the building (100 feet), also, we know the angle of elevation (30°), so, we can use the following formula to calculate it:

[tex]Tan(\alpha)=\frac{y}{x}=\frac{height}{x}\\\\x=\frac{height}{Tan(\alpha) }[/tex]

Now, substituting the given information and calculating, we have:

[tex]x=\frac{height}{Tan(\alpha) }[/tex]

[tex]x=\frac{100feet}{Tan(30\°) }=173.20feet[/tex]

Have a nice day!

The specific heat capacity of the alloy is 0.423 cal/g°C: Option A is correct.

The formula for calculating the quantity of heat absorbed by the alloy is expressed as:

[tex]Q=mc\triangle \theta[/tex]

m is the mass of the substance = 45g

c is the specific heat capacity

Q is the quantity of heat required = 956J

[tex]\triangle \theta[/tex] = 37 - 25 = 12°C

Substitute the given parameters to get the specific heat capacity:

[tex]c=\frac{Q}{m \triangle \theta}\\c =\frac{956}{45 \times 12}\\c =\frac{956}{540}\\c = 1.77J/g^oC[/tex]

Convert J/g°C to  cal/g°C

c = 1.77/4.184

c = 0.423 cal/g°C

Hence the specific heat capacity of the alloy is 0.423 cal/g°C

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The specific heat of the alloy is 0.423 cal/g°C, which is calculated using the formula q = mcΔT and converting joules to calories. The final answer corresponds to option A.

The question involves finding the specific heat of an alloy using the concept of heat transfer. To calculate the specific heat, we use the formula q = mcΔT, where q is the amount of heat absorbed, m is the mass of the substance, and ΔT is the change in temperature. The specific heat c can be rearranged to be c = q/(mΔT). Given that the alloy absorbs 956 J of heat (q), has a mass of 45 g (m), and experiences a temperature increase from 25°C to 37°C (ΔT = 12°C), we plug these values into the formula.

Specific heat c will be: c = 956 J / (45 g × 12°C) = 956 J / 540 g°C = 1.77 J/g°C

To convert from joules to calories, note that 1 calorie = 4.184 joules. Thus, c in cal/g°C is calculated as: 1.77 J/g°C / 4.184 J/cal = 0.423 cal/g°C, which corresponds to option A.

Answer:

If x= 4 then f(x) = 4x -5 is 11.

Step-by-step explanation:

f(x) = 4x -5

We need to find the domain value that corresponds to the output f(x) = 11

In this question, we need to solve the expression for value of x such that the answer is 11.

if  x= 3

f(3) = 4(3) -5

     = 12 -5

    = 7

Since we want the answer 11 so we cannot take x= 3

if x = 4

f(4) = 4(4)-5

    = 16 - 5

    = 11

So, if x= 4 then f(x) = 4x -5 is 11.

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

The required polynomial would be y = x² + 38x + 311.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Given that least degree with rational coefficients and with (-19-5√2)

We know that if a polynomial has both rational and irrational roots, the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Apply the distributive property,

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

Thus, the required polynomial would be y = x² + 38x + 311.

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Answer:

Square

Step-by-step explanation:

Well, the options they have given you to choose from are a pentagon, a quadrilateral and a square. Let's first take a look at these options and eliminate which ones can't be possible. The first option, a pentagon, can be eliminated from the possibilities because a pentagon has five sides and figure ABCD has only four sides. The second option, quadrilateral, is true because a quadrilateral has four sides and so does figure ABCD. But, if you look at the third option, a square, this is the best way out of all the options to classify this figure because there are three things ALL squares must have:

- four sides

- all right angles

- all the sides MUST be equal

Knowing this, taking a look at the picture, you will see that there are indeed four right angles, four sides AND all congruent sides, proven by the four triangles inside the square. The answer isn't quadrilateral because, although that may be true, there are MANY types of quadrilaterals, trapezoids, rectangles, rhombuses and so on, each having different properties and characteristics. Therefore, the third option, SQUARE is the right answer.

HOPE THIS HELPED! Please contact me if you have any further questions about this topic and feel free to ask any more questions you need! :)

I could be wrong but

area=172.1

Area of the pentagon after rounding to the nearest tenth is 172.5 cm²

Given: a regular pentagon with sides measuring 10 cm and apothem measuring 6.9 cm

To find: area of the pentagon

We know that the area of a regular pentagon can be found by the formula:

[tex]\text{area}= \frac{1}{2} \times \text{perimeter of pentagon} \times \text{apothem}[/tex]

Before putting the values in the formula, we need to find the perimeter of the pentagon. It can be found by fining the sum of all of its side as follows:

[tex]\text{perimeter} = 10+10+10+10+10 = 5 \times 10 = 50[/tex] cm

Now we can put the values in the formula for area as follows:

[tex]\text{area}= \frac{1}{2} \times 50 \times 6.9\\[/tex]

[tex]\text{area}= 172.5[/tex] cm²

As the area is already rounded off to the nearest tenth we do not need to perform any additional calculations

So, area of the given pentagon is 172.5 cm².

Answer:

Step-by-step explanation:

y=5+2(3+4x) - Multiply parenthesis by 2

0=5+6+8x - Add the numbers

0=11+8x - Move variable to left

-8x=11 - Divide both sides by -8

x=-1.375

Answer:

(i) 16 cm.

(ii) 37 pieces in total.

Step-by-step explanation:

Through determining each lengths factors, it can be determined that every ribbon can be equally divided into 16 cm. long ribbons, so we already have our first answer. A 160 cm. long ribbon divided into 16 cm. long pieces will create 10 ribbons from that one piece; the 192 cm. long ribbon cut into the same 16 cm. lengths will equal 12 pieces of equal length; and the 240 cm. long ribbon will divide its 16 cm. lengths into 15 pieces of equal length. So the 10 pieces, plus the 12 pieces, plus the 15 pieces, will equal 37 total pieces, each 16 cm. in length.  

Final answer:

This answer explains how to find the largest length of pieces and total number of pieces cut from different ribbon lengths. Therefore, the largest piece length is 16 cm. and  Total number of pieces of ribbons cut  is 37.

Explanation:

(i) Largest possible length of each piece of ribbons: To find the largest piece length, we need to determine the greatest common divisor (GCD) of the ribbon lengths. The GCD of 160, 192, and 240 is 16. Therefore, the largest piece length is 16 cm.

(ii) Total number of pieces of ribbons cut: To find the total number of pieces, divide each ribbon length by the largest piece length. For 160 cm, it gives 10 pieces. For 192 cm, it gives 12 pieces, and for 240 cm, it gives 15 pieces. Adding these, the total number of pieces is 37.