Mathematics College

A 200 centimeter-long wire is cut into three pieces. The second piece is 3 times as long as the first. The third piece is 2 times as long as the second. How long is each piece?

Answers

Answer 1
Let x be the length of the first piece, y be the length of the second piece and z be the length of the 3rd piece. We just need to figure out how these lengths (x,y,z) relate to the total length and each other as follows:

x + y + z = 200 since the sum of the lengths equals the total length of the wire

y = 3x since piece two is 3 times longer than piece one
z = 2y = (2)(3)(x) = 6x since piece three is 2 times longer than piece two

Now we have (x,y,z) in terms of x alone, so we can substitute into the first equation:

x + 3x + 6x = 10x = 200 which means x = 20.

Then, substitute this value into all the other equations.

y = 3(20) = 60
z = 6(20) = 120

This can be checked by summing them up like this: 20 + 60 + 120 = 200.
Answer 2
Final answer:

The lengths of the three wire pieces are 20 cm for the first piece, 60 cm for the second piece, and 120 cm for the third piece.

Explanation:

A wire that is 200 cm long is cut into three pieces.

We are told that the second piece is 3 times as long as the first piece and the third piece is 2 times as long as the second piece.

Let's denote the first piece's length as x centimeters.

According to the problem, the second piece will then be 3x centimeters long, and the third piece will be 2 * 3x = 6x centimeters long.

To find the length of each piece, we need to set up the following equation based on the total length of the wire:

x + 3x + 6x = 200

Combining terms, we have:

10x = 200

Dividing both sides by 10, we find:

x = 20

Therefore, the first piece is 20 cm long, the second piece is 3 * 20 cm = 60 cm long, and the third piece is 6 * 20 cm = 120 cm long.

Related Questions

what is the ratio in lowest terms of 14 miles to 84 miles

Answers

the lowest ratio in terms of 14 miles to 84 miles is 1:6

the greatest common factor between 14 and 84 is 14.

14÷14=1. 
84÷14=6.

the ratio is 1:6; or 1 to 6.



I think the answer is 1/6.

A store has a contest to guess the mass of 10,000 peanuts if a peanut has a mass of about 0.45 g what would be a reasonable guess with a mass of 10,000 peanuts

Answers

You can just multiply the 0.45 grams by 10,000. Just keep moving to decimal to the right.

0.45 * 10000 = 4500

The mass of 10,000 peanuts is 4,500 g or 4.5 kg.

The question asks for a reasonable guess for the mass of 10,000 peanuts, given that each peanut has a mass of about 0.45 g. To calculate this, we simply multiply the number of peanuts by the mass of each peanut:

Mass of one peanut = 0.45 g
Number of peanuts = 10,000
Total mass = 0.45 g/peanut x 10,000 peanuts

Now we will carry out the multiplication:

Total mass = 4,500 g

Since we are dealing with a large quantity of peanuts, it is more convenient to express this mass in kilograms:

4,500 g is equivalent to 4.5 kg (since 1 kg = 1,000 g).

raise g
to the 7th power,
then subtract h
from the result

Answers

Final answer:

To carry out the student's request, you would first raise 'g' to the 7th power to obtain g^7, then subtract 'h' from this result to get the final expression 'g^7 - h'.

Explanation:

To solve the expression mentioned by the student, you need to carry out two mathematical operations in sequence. The first operation is raising 'g' to the 7th power, which can be expressed as g^7. The second operation is subtracting 'h' from the result of the first operation. This can be represented mathematically as g^7 - h.

For example, if g equals 2 and h equals 3, then you would first calculate 2^7 which equals 128. Then you would subtract 3 from 128, yielding an answer of 125.

slope=-1 and y-intercept (0,10).
graph the line.

Answers

I dont know how to upload a picture of a graph so I'll just try to explain it. Place a dot on (0, 10) then go to the right one unit and down 1 unit and mark another dot. Continue to do this until you have placed enough dots to make a line.

at the bake sale connie bought 4 chocolate cookies kevin bought 4 brownies and luis bought 6 sugar cookies in simplest form what fraction represents the number of cookies bought

Answers

14 over 14 equals one

Claire picked some apples. She used 2/5 of the apples to make jam, She gave 1/3 of the remainder to her neighbor. What fraction of the apples did she give to her neighbor? Can someone please explain step by step please

Answers

Of course! Let's start!


Lets imagine that you have a circle. That circle represents all of the apples that Claire has.

Now let's imagine this. You take 2/5 of that circle out, you completely wipe it away. These 2/5 are the apples she took out to make the jam.

Ok, so now you are left with 3/5 of the circle, or the apples.

You need to take out 1/3 of those apples to give to your neighbor. So we need to find 1/3 of 3/5.

So, draw 3 small circles on a piece of paper.

Those each represent 1 part of the 3/5.

So what is 1/3 of the three fifths?

1/5 because one circle is 1/3 of 3/5!

So the neighbor recieved 1/5 of the apples!

I hope this helped!

Comment if you have any questions!!
Glad to help!
Step 1:
Find remainder after making jam.
[tex]1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} [/tex]

Step 2:
Find 1/3 of remainder.
The word "of" refers to multiplication.
[tex]\frac{1}{3} * \frac{3}{5} = \frac{3}{15} = \frac{1}{5} [/tex]

Therefore she gave 1/5 of apples to her neighbor.

What is greater 7/12 0.75 or 5/6

Answers

7/12=.58
5/6= .83
soooo
if the numbers are .58, .83 and .75 your order would be 
.58, .75, .83
in other words
7/12, .75, 5/6
if your just looking for the biggest number your answer would be
5/6
hope this helps!




Mountain Ski Corp. was set up to take large risks and is willing to take the greatest risk possible. Lakeway Train Co. is more typical of the average corporation and is risk-averse.

Projects Returns:
Expected Value Standard
Deviation
A $ 527,000 $ 834,000
B 682,000 306,000
C 74,000 135,000
D 140,000 89,000

a-1. Compute the coefficients of variation. (Round your answers to 3 decimal places.)

Coefficient of
Variation
Project A
Project B
Project C
Project D

a-2. Which of the following four projects should Mountain Ski Corp. choose?


Project A
Project B
Project C
Project D

b.

Which one of the four projects should Lakeway Train Co. choose based on the same criteria of using the coefficient of variation?

Project A
Project B
Project C
Project D






Answers

a-2: Project D.

b: Project A.

Not sure about a-1, hope I helped.

Please help me with substitution! I'm terrible at it. :(
-3x+5y=-11
y=2x-5

Answers

-3x+ 5* 2x-5= -11
 -3x+10x-5=-11
(-3x=10x=7)
7x-5=-6
(+5 on each end)
7x=-6
divide by 7

What value of b will cause the system to have an infinite number of solutions?

Answers

Answer:

Step-by-step explanation:

b=6

here is another question 2/5 divided by 1/6

Answers

2/5 divided by 1/6 = 12/5

12/5 = 2 2/5


3-3x6+2=what is correct answer
This is how I did it:
3 - 1(3x6)+2=
-1x3= -3
-1x6= -6
-3x-6= +18
3+18+2= 23
Is it correct 2 add parentheses around 3x6 and then add an "invisible" 1 in front of the parentheses?

Answers

no, because only three is negative when you multiply by six... you could just do 
3-3x6+2
3-18+2
-15+2
-13

Final answer:

The expression 3 - 3×6 + 2, following the order of operations, results in -13. There is no need to add unnecessary parentheses or introduce an "invisible" 1; multiplication inherently takes precedence.

Explanation:

The expression should be evaluated according to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's solve the expression step by step:

3 - 3×6 + 2

Step 1: Perform multiplication first, since it precedes addition and subtraction in the order of operations.
3 - (3×6) + 2 = 3 - 18 + 2

Step 2: Proceed with addition and subtraction from left to right.
3 - 18 results in -15, and then adding 2 gives us -15 + 2 = -13.

Therefore, the correct answer to the expression is -13.

There's no need to introduce an "invisible" 1 or to add parentheses around the multiplication, as the multiplication already has precedence over addition and subtraction.

2500 kilobytes in 5 minutes

Answers

You just divide 5 by 2,500 and the answer you get is 500
divide 5 by 2,500 and the answer you get is 500

find the radian measure of an angle at the center of a circle with radius 67.0 cm that intercepts an arc length of 118 cm

Answers

Arc length = radius* angle
Solving for angle
---> angle = ArcLength/radius

[tex] \theta = \frac{118}{67} [/tex]

write the equation of a line perpendicular to 9x+8y=3 that passes through the point (8,-7). Type an equation using slope- intercept form or using the given point in point- slope form. use integers or simplified fractions for any numbers in the equation.

Answers

9x + 8y = 3
8y = -9x + 3
y = -9/8x + 3/8...slope here is -9/8. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So the perpendicular slope is 8/9 (see how I flipped the slope and changed the sign)

y = mx + b
slope(m) = 8/9
(8,-7)....x = 8 and y = -7
now we sub and find b, the y int
-7 = 8/9(8) + b
-7 = 64/9 + b
-7 - 64/9 = b
-63/9 - 64/9 = b
-127/9 = b

so ur equation is : y = 8/9x - 127/9

A recent survey suggests that 85% of adults know what Twitter is. How many adults should you survey in order to be 90% confident that your estimate is within 5% of the true population proportion?

Answers

an odd number of adults so you have no tie at all, I would recommend to survey at least 75 adults to get a good 90% confident.

A new tire that you need for your bike has a radius of 13 inches. What is the circumference of the tire? Use 3.14 to approximate pi. Round your answer to the nearest tenth.

Answers

the circumference =81.7

Answer:

81.6

Step-by-step explanation:

this question is pretty old but I hope this helps people like me trying to find the actual answer unlike the first one.

What is the compound interest if $410 is invested for 13 years at 8% compounded continuously?

Answers

compounded contiously
[tex]A=Pe^{rt} [/tex]
A=future amount
P=present amount
r=rate in decimal
t=time in years

to find the interest, we do A-P
find A first

given
P=410
t=13
r=0.08

[tex]A=410e^{13*0.08} [/tex]
[tex]A=410e^{1.04} [/tex]
aprox
A=1159.97897
A-P=1159.97897-410=749.9789
the interest is $749.98

If linear correlation between two variable is negative, what can be said about the slope of the regression line

Answers

If one of the two variables is negative the regression line will be negative. 

A rectangle's length and width are in a ratio of 8:3. The area is 384 square millimeters. What are the length and width?

Please I really am desperate 

Answers

Let, the length = 8x
width = 3x
Now, 8x * 3x = 384
24x² = 384
x² = 384/24
x² = 16
x = √16
x = 4

So, length = 8(4) = 32 & Width = 3(4) = 12

It's dimension would be 32 × 12 mm

Hope this helps!

how to calculate z=1.15 and z = 2.37 bell shaped normal distribution

Answers

P(1.15 < z < 2.37) = P(z < 2.37) - P(z < 1.15) = .9911 - .8749 = .1162

Look up 2.37 and 1.15 in table (attached)

2.37 ----> 0.9911
1.15 ----> 0.8749


frieda has 12 red apples and 15 green apples she is going to share equally among8 people and keep any extra apples for herself.how many apples will frieda keep for herself

Answers

12+ 15= 27
27/8 = 3 with a remainder of 3.
she keeps 3 apples for herself.

Frieda will keep 3 apples to herself after sharing

Proportions

From the given question, we are told that frieda has 12 red apples and 15 green apples. The total number of fruit is expressed as:

Total = 12 + 15Total = 27 fruit

If she is going to share equally among 8 people, then the remainder when 27 is divided by 8 will be the remaining fruit

Taking the ratio

Ratio = 27/8

Ratio = 3 remainder 3

Frieda will keep 3 apples to herself after sharing

Learn more on proportion here: https://brainly.com/question/24481042

A car rental cost $80 per day, for the first 250 miles, plus $0.20 for each additional mile. If Sonya's rental cost was $124 for one-day rental, how many miles did she drive?

Answers

i hope this helps you
Well, 80 dollars is the price originally, so that 80 is by its self. Now we see that its 0.2 ever mile after so lets do the math.

The equation would be $80 + $0.2x = 124

Do the math, subtract 80 from both sides

0.2x = 44

No divide by 0.2

x= 220

since the first $80 is 250 miles what would the rest be? well since you did the math and got x = 220 that means after you have 220 addition miles. Add the two up :) 220+250= 470 :D 

This problem involves empirical probability. The table shows the breakdown of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is in the Army.

Answers

The table shows the breakdown of 97 thousand single parents on active duty in the ... of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in ...

The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is [tex]\( \frac{6}{97} \)[/tex], which is approximately 0.0619 or 6.19%.

To find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force, we need to divide the number of women in the Air Force by the total number of single parents in the military.

1. First, find the number of women in the Air Force from the table. This is given as 6 thousand.

2. Next, find the total number of single parents in the military. This is given as 97 thousand.

3. Finally, divide the number of women in the Air Force by the total number of single parents in the military and express the result as a fraction or decimal to represent the probability.

So, the probability P can be calculated as:

[tex]\[ P = \frac{{\text{Number of women in the Air Force}}}{{\text{Total number of single parents}}} \][/tex]

Substituting the values:

[tex]\[ P = \frac{6}{97} \][/tex]

[tex]\[ P ≈ 0.0619 \][/tex]

Therefore, the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is approximately 0.0619 or 6.19%.

Complete question:

This problem involves empirical probability. The table shows the breakdown of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force.

             Army    Navy   Marine Corps  Air Force  Total

Male        27         26            4                      14           71

Female    11            8             1                       6            26

Total        38          34           5                      20          97

The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is?

Find The last two digit of 36^2015

Answers

Answer:

  76

Step-by-step explanation:

The last two digits of powers of 36 repeat in a pattern of length 5:

  36^1 mod 100 = 36

  36^2 mod 100 = 96

  36^3 mod 100 = 56

  36^4 mod 100 = 16

  36^5 mod 100 = 76

  36^6 mod 100 = 36

The last two digits of the power 2015 are the same as those of the 5th power: 76.

resultado de x/12 = 9/x+2

Answers

x=27.874508 or x=−3.874508

the function f(x) varies inversely with x and f(x)=8 when x=3
what is f(x) when x=2
12
14
22
48

Answers

I hope this helps you

Answer:

[tex]12[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

For [tex]x=3[/tex] -----> [tex]f(x)=8[/tex]

so

Find the value of k

[tex]f(x)*x=k[/tex]

substitute the value of x and f(x)

[tex]8*3=k[/tex]

[tex]k=24[/tex]

therefore

the equation is equal to

[tex]f(x)=24/x[/tex]

For [tex]x=2[/tex] -------> substitute in the equation and find the value of f(x)

[tex]f(x)=24/2=12[/tex]

Where's the vertical asymptote?

Answers

at the values x = –4 or x = 2.

what percent of 67.5 is 7.02

Answers

Use the proportion equation. Cross multiply. Answer is 10.4%

7.02 is approximately 10.4 percent of 67.5.

To find what percent 7.02 is of 67.5,

Since we know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We can use a proportion.

Let's call the unknown percent "x."

The proportion would be:

7.02/67.5 = x/100

We can cross-multiply to solve for x:

(7.02 * 100) / 67.5 = x

Simplifying this expression, we get:

x = 10.4

Therefore, 7.02 is approximately 10.4% of 67.5.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ6

what's the answer to this

Answers

it is y^12, hope this helps you
y¹¹.y = y¹²
Whenever, you need to multiply that type of digits then consider y as y¹ & then add the powers.
Here, powers are 11+1 = 12.
Write it on the top. You'll get your answer.

So, your final answer is y¹²

Hope this helps! Happy studying :)
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