Mathematics College

The volume of a triangular prism is increased by a factor of 8.

By what factor is the surface area of the figure increased?

Answers

Answer 1

we  know that

[tex]larger\ volume=original\ volume*(scale\ factor)^{3}[/tex]

and

[tex]larger\ surface\ area=original\ surface\ area*(scale\ factor)^{2}[/tex]

so

Find the scale factor

we know that

[tex](scale\ factor)^{3}=8 \\ scale\ factor=\sqrt[3]{8}=2[/tex]

Find the factor of the surface area increased

[tex](scale\ factor)^{2}=2^{2} =4[/tex]

therefore

the answer is

the surface area increased by a factor of [tex]4[/tex]

Answer 2

The need to cut the plastic by finding the measures of the angles (scale factor) is 4.

We have given,

Marcel is designing a circular necklace that will consist of 4 sections, each with a different color of plastic.

We  know that

What is the formula of larger volume?

larger volume=original volume×(scaler factor )^3

larger surface area =original surface area× (scaler factor)^2

To find the scale factor

we know that

(scalar factor)^3=8

Taking cube root on both sides

scale factor=2

Find the factor of the surface area increased

(scale factor)^2=2^2=4

Therefore, The surface area increased by a factor of 4.

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Related Questions

Surface area of a right cone.
Solve for P S=2b+ph

Answers

s = 2b + ph

Lets subtract both sides by 2b

s - 2b = ph

Now, divide both sides by h

(s-2b)/h = p

Hope this helps!

Answer:

P=S-2b/h

Step-by-step explanation:

To solve this equation the first thing we do is subtract 2B from both sides of the equation. S-2b=ph+2b-2b which would give us S-2B=PH. next, we divide H from both sides of the equation which would give us the answer: S-2B/h=p

60÷5(7-5)=24 is that correct ? Thanks

Answers

Absolutely, it is correct.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]

Further explanation

In the 1500s the specific rules of the order of operation were promptly issued. The order of these workings states which processes take precedence (as a key priority) before which other operations.

Operation priorities are as follows.

Brackets (simplify in it)ExponentMultiplication or Division (from left to right)Addition or Subtraction (from left to right)

Let's implement the rule.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = \ ? \ }[/tex]

Subtract 7 by 5 in parentheses.

[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]

Properly apply rule number 3 from the priority operation above. Initially, we have to divide 60 by 5.

[tex]\boxed{ \ 12(2) = \ ? \ }[/tex]

Continuing with multiplication 12 by 2 proves the exact result.

[tex]\boxed{ \ 12 \times 2 = 24 \ }[/tex]

Thus, this equation is correct.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]

Note:

What is the result if we don't follow operation priorities? Let's see.

At this crucial point.

[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]

We decide to multiply 5 by 2, even though there are no parentheses from them, only parentheses for 2.

[tex]\boxed{ \ 60 \div 5 \times 2 = \ ? \ }[/tex]

[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 6 \ }[/tex]

That's what happens if we don't follow operating priorities.

Unless the problem like this:

[tex]\boxed{ \ 60 \div (5 (7 - 5)) = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div (5 (2)) = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]

Thus, the difference must be considered. Consequently, follow the priority of the operation and look at the problem in detail.

Learn moreThe simplified form of 5(14 - 2)^2 ÷ 2 https://brainly.com/question/1602237Determine 3 digits are in the units period of 4,083,817 https://brainly.com/question/5586929 ten thousands divided by 10 in unit form https://brainly.com/question/4786449

Keywords: the order of operation, operation priorities are as follows, parentheses, brackets, simplify, exponent, multiplication, division, from left to right, add, subtract

Need help with math problem
The temperature of a lake drops by the same amount each day for 10 days. The temperature drops by a total of 5 degrees.

Drag the numbers to form the equation that represents the change in the lake's temperature each day.

( ? ) ( ? ) = ( ? )

5, -5, 10, -10, 1/2, -1/2, 1/10, -1/10
Thanks

Answers

(10)(-½) = (-5)
Hope it helps you.
Let the temperature be initially be t.

Let [tex]\displaystyle{ d_n[/tex] be the temperature after day 1 of the period where the teperature decreases.

For example,

[tex]\displaystyle{ d_1[/tex] is the temperature after the first day

[tex]\displaystyle{ d_2[/tex] is the temperature after the second day

and so on...

The temperatures during these 10 days are:

[tex]d_0=t\\\\d_1=t-5\\\\d_2=(t-5)-5=t-2\cdot5\\\\d_3=(t-2\cdot5)-5=t-3\cdot5\\\\.\\\\.\\\\d_{10}=t-10\cdot5 [/tex]

The change of the temperature each day, is given by the difference of the temperature in 2 consecutive days, for example day 4 and day 5:

[tex]d_5-d_4=(t-5\cdot 5)-(t-4\cdot5)=t-25-t+20=-5[/tex]


In general, the equation can be given as :

[tex]d_n-d_{n-1}=-5[/tex]


Remark: we cannot see the letters to "drag", so adopt them according to the variables that we defined in the solution.



One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 500, find the numbers

Answers

Let the first number be x.
Then the second number is 3x.
Then the third number is (x+100).
Sum of the numbers=500

x+3x+(x+100)=500
4x+(x+100)-500=0
5x=400
x=80
The first number is 80.
The second number is 240.
The third number is 180.

We can check by adding all three of those numbers together: 80+240+180 = 500

Hope this helps! If you have any questions just ask!

What's 39,230 rounded to the nearest ten thousabd

Answers

40,000 is the correct answer

The correct answer is 40 000

39230 correct to 10 000 would have been 39 000, but there is 9 after 3, so we must add 1 to the 9 giving a result of 40 000.


Hope it helped!

Find the domain of the function. (enter your answer using interval notation.) f(x) = 5 x 3 − 1 x2 + 2x − 24

Answers

The function is [tex]f(x)=5x^2-x^2+2x-24[/tex], 

this function is a polynomial function, because all the powers of the x-es are non-negative integers.

The domain of polynomial functions is always all the real numbers.


Answer: all the Real numbers

A tee-ball team for 5 year-olds has half as many girls as boys. If there are 15 children on the team, how many are boys and how many are girls?

Answers

there are 10 boys because half of 10 is 5 5+5 equals 10

As the has half as many females as males, the number of males in the team is 10, and the number of females in the team is 5.

What is the number of males and females in the team?

Given the parameter:

A team for 5-year-olds has half as many females as males.

There are 15 children on the team.

There are half as many females as males, this can be expressed as:

Let G represents females and B represents males.

G = 0.5B

Also, there are 15 children on the team, so we can write an equation based on the total number of children:

B + G  = 15

Now, we solve the system of equations:

G  = 0.5B

B + G  = 15

First, substitute the expression for females from the first equation into the second equation:

B + 0.5B  = 15

1.5B = 15

B = 15/1.5

B = 10

Plug B = 10 into the first equation and solve for females:

B + G = 15

10 + G  = 15

G = 15 - 10

G = 5

So, there are 10 males and 5 females on the team.

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Suppose that 10 of the 30 freshmen, 40 of the 60 sophomores, 5 of the 20 juniors and 40 of the 50 seniors were in favor of multiple choice exams. what is the overall estimate of the proportion of students in favor of multiple choice exams?

Answers

I believe it would be 59%? Or does it have to be in ratio form?

Jim walks 3.5km every day. How far does he walk in 5 days?

Answers

3. 5 times
5=
17. 5km

Hope it helps :)

Why -4 x (-4) = 16 not -16? Simple...

Answers

The reason why it is a positive 16 and not a negative 16, is because when you multiply a negative number with another negative number  you will always get a positive number. But, if you multiple a negative number with a positive number, you will get a negative. So, in order for you to get a -16, the equation would have to be -4*4=-16.

A retired woman has $60,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in her CD?

Answers

Let x be the amount the woman invests in the 15% bond, then the amount she invested in her CD is given by $60,000 - x.

The interest she receives from the 15% bond is given by 0.15x while the interest she receives from the 7% CD is given by 0.07(60,000 - x) = 4,200 - 0.07x

Giving that her total annual interest is $6,000, then

[tex]0.15x+4,200-0.07x=6,000 \\ \\ \Rightarrow0.08x=6,000-4,800=1,200 \\ \\ \Rightarrow x= \frac{1,200}{0.08} =$15,000[/tex]

Therefore, the amount of dollars she will be able to invest in her CD is $60,000 - $15,000 = $45,000

Charles can type 675675675 words in 999 minutes.
How many words can Charles type in 131313 minutes?

Answers

I think, 8.881381373*10^10

A completely filled 20 gallon tank originally contains 10 pounds of salt dissolved in water. pure water enters the tank at the rate of 5 gallons/minute, and the well-stirred mixture leaves the tank at the same rate. find the amount of salt in the tank at any time t .

Answers

Final answer:

To find the amount of salt in the tank at any time t, we can use the equation S(t) = 10 - 10(W(t)/20), where W(t) represents the amount of water in the tank at time t. Substituting the given values, we can calculate the amount of salt in the tank.

Explanation:

To find the amount of salt in the tank at any time t, we need to consider the rate at which pure water enters and leaves the tank. Since water enters the tank at a rate of 5 gallons/minute, the amount of water in the tank at any time t can be represented by the equation: W(t) = 5t, where t represents time in minutes. The concentration of salt in the tank remains constant, so the amount of salt in the tank at any time t can be represented by the equation: S(t) = 10 - 10(W(t)/20), where S(t) represents the amount of salt in pounds and W(t) represents the amount of water in gallons.

Let's solve for S(t) when t = 10 minutes:
S(10) = 10 - 10(5/20) = 10 - 10(1/4) = 10 - 10/4 = 10 - 2.5 = 7.5 pounds of salt.

Choose the word phrase (greater than, less than, or equal to) to make the statements true.

Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.

Three pencils are worth [less than, greater than, or equal to] seventeen paper clips.

which one pls

Answers

Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips which can be traded for (6 x 3 = 18) eighteen matches.

Two pencils and two paper clips are worth (2 x 18 + 2 x 3 = 36 + 6 = 42) which is greater than thirty-eight matches.

Therefore, Two pencils and two paper clips are worth thirty-eight matches.

Answer:

Three pencils are worth greater than seventeen paper clips.

Step-by-step explanation:

Each paper clip can be traded for three matches.

Each pencil can be traded for six paper clips.

Three pencils are worth [tex]3\times6=18[/tex] paper clips.

So, the correct statement is - Three pencils are worth greater than seventeen paper clips.

What is the probability that a randomly chosen rod will fit into a randomly chosen ring?

Answers

the probability would be 50 and 50

What is the size of the largest and smallest numbers of vertices of degree 1 possible in an n-vertex tree, for n > 2?

Answers

Following the formula: Pn on n+1 vertices {v0, v1, v2, …, vn} With n>2 edges as vertices we know that the component is not a tree. At the same time we know it must contain a cycle. Therefore the size of the vertices is not possible to exceed 2n, and the degree of any vertex in any sub-graph has a minimal value of vn. Therefore the maxim is 2n and the minimum is vn.

A mural inspired by photo graph measures 107 inches by 180 inches.the scale factor is 12.what are the dimensions of the photograph

Answers

[tex]\bf \cfrac{mural}{photo}\qquad \cfrac{12}{1}\implies \stackrel{mural}{12}:\stackrel{photo}{1}\qquad \qquad \cfrac{\stackrel{width}{107}}{w}=\cfrac{12}{1}\implies \cfrac{107\cdot 1}{12}=w \\\\\\ \cfrac{\stackrel{height}{180}}{h}=\cfrac{12}{1}\implies \cfrac{180\cdot 1}{12}=h[/tex]

Since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as:

Answers

[tex]20*20*20*20.....= 20^{n} [/tex]

Since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as [tex]20^n[/tex].

What are Amino acids?

Amino acids may be defined as compounds that significantly contain carbon, hydrogen, oxygen, and nitrogen. These compounds serve as the monomers or the building blocks of proteins that are composed of an amino group, a carboxyl group, a hydrogen atom, and a specific side chain.

Two amino acids are held together by a linkage known as peptide linkage. When a number of peptide linkages are present in the structure of the protein, it is known as polypeptides.

If any polypeptide chain is derived from 20 amino acids. So, the possibility of a combination for any polypeptide chain will be [tex]20^n[/tex], where n = the number of amino acid residues in the polypeptide chain.

Therefore, since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as [tex]20^n[/tex].

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alvin is 13 years older than elga. the sum of their ages is 107. what is elga's age

Answers

alvin is 94 years old!
a = e + 13
a + e = 107

e + 13 + e = 107
2e + 13 = 107
2e = 107 - 13
2e = 94
e = 94/2
e = 47 <=== elga's age

a = e + 13
a = 47 + 13
a = 60....alvin's age

You ate 2⁄3 of the pizza. How many twelfths is that?

Answers

You would multiply 2x4 and 3x4 and it would be 8/12 so that leaves you with 4 twelths left.

Ratio Conversion Table mile : yard 1 : 1,760 yard : foot 1 : 3 foot : inch 1 : 12 Using the conversion table, match the equivalent measurements. Tiles 29 feet 352 yards 372 feet 124 yards 2 miles 0.2 miles 1,016 yards 10,560 feet 348 inches Pairs What would all the pairs be HELP 52 points

Answers

 29 feet = 348 inches

352 yards = 0.2 miles

372 feet = 124 yards

2 miles = 10560 feet 


 you can actually just google for the answers lol

29 feet = 348 inches

352 yards = 0.2 miles

372 feet = 124 yards

2 miles = 10560 feet  


-2 1/2 = t/10 what is t?

Answers

-2 1/2 = - 5/2 = -25/10

-25/10 = t/10

t = -25

hope this helps

Answer:

4

Step-by-step explanation:

In the number 514,482,441, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s? How is it different?

Answers

Notice that the number  514,482,441 can be written as:

500,000,000+10,000,000+4,000,000+400,000+80,000+2,000+400+40+1


starting from the left:

the value of the first 4 is 4,000,000

the value of the second 4 is 400,000

thus the first 4 is 10 times the second 4


the value of the third 4 is 400

the value of the fourth 4 is 40

thus the third 4 is 10 times the fourth 4


The similarity is that both pairs of fours differ by a factor of 10

the difference is that the first pair of fours are larger than the second pair of fours, as described above.

Maria has 3/4 pound of cheese to use making sandwiches. she's used about 1/32 pound of cheese on each sandwich. how many sandwiches can she make

Answers

(3/4)/(1/32)= 24 sandwiches.

Write word form for number 7.351

Answers

Answer:

seven point three five one thousandths


Step-by-step explanation:


Music may help people relax. John got two groups of people together. He took everybody's pulse of blood pressure. The one group to listen to soothing music while other group sat in silence. After the song was over, he measured everyone's pulse and blood pressure.

What is the independent variable?
What is the dependent variable?
What are the constants or control variables?

Answers

Independent: Music or silence

Dependent: Pulse and blood pressure

Constants: Similar rooms, similar temperature, similar heart health, same time in areas, same kind of environment, etc.
Final answer:

In John's experiment, the independent variable is the condition of the groups (listening to music or sitting in silence), the dependent variables are pulse and blood pressure, and the control variables could include room temperature, the timing, the duration of the experiment, and the use of consistent measurement devices.

Explanation:

In this experiment conducted by John, the independent variable is the condition under which each group is placed—which is, one group listening to soothing music and the other group sitting in silence. This is the independent variable because it's the factor that John changes or manipulates during the experiment.

The dependent variables here would be the pulse and blood pressure of the individuals in both groups. These variables are considered dependent because their values may change based on the effect of the independent variable (i.e., the type of noise the group is subjected to).

The constants, or control variables, in this experiment could include the room temperature, the timing of the experiment, the duration for which the conditions are applied (the length of the song), and the same pulse and blood pressure checking device, among others. These are the factors that remain the same throughout the experiment to ensure that the results are only influenced by the independent variable and not by any other factors.

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A square field has an area of 479 ft what is the approximate length of a size of the field

Answers

Answer:

21.9 ft

Step-by-step explanation:

The area of a square is the square of the side length, so the side length is the square root of the area:

... s = √(479 ft²) ≈ 21.886 ft

This is approximately 21.9 ft.

Is 3/47 a rational number?

Answers

Yes 3/47 is a rational number because a rational number is any number that gives the results when divided one integer by another except ZERO.

3/47= 0.06383 so it is RATIONAL

Answer:

Rational.

Step-by-step explanation:

We have been given a fraction [tex]\frac{3}{47}[/tex]. We are asked to determine whether our given number is rational or not.

We know that a number is rational number, when it can be represented as a fraction of form [tex]\frac{p}{q}[/tex], where q must be a non-zero number.

Upon looking at our given number, we can see that it is a fraction and numerator is equal to 47 that is a non-zero number.

Therefore, our given number is a rational number.

Solve for v
8v-4v=8
Answer:2

Answers

Solve for v:4 v = 8
Divide both sides of 4 v = 8 by 4:(4 v)/4 = 8/4
4/4 = 1:v = 8/4
The gcd of 8 and 4 is 4, so 8/4 = (4×2)/(4×1) = 4/4×2 = 2:Answer: v = 2

Solve for x: u= kx + yx

Answers

u = kx + yx
u = kx + yx
u = (k+y)x
u / (k+y) = (k+y)x / (k+y)
u / (k+y) = x
x = u / (k+y)

Answer:

The value of the equation for x is [tex]x=\frac{u}{k+y}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]u= kx + yx[/tex]  

We need to solve the equation for x.

Take x common from right side as shown below:

[tex]u= x(k + y)[/tex]

Divide both the sides by k+y.

[tex]\frac{u}{k+y}=\frac{x(k + y)}{k+y}[/tex]

[tex]x=\frac{u}{k+y}[/tex]

Hence, the value of the equation for x is [tex]x=\frac{u}{k+y}[/tex].

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