Given the volume of Figure A is 512cm ^3and Figure B is 343cm^3, find the ratio of the perimeter from Figure A to Figure B.

Answers

Answer 1

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{\textit{figure A}}{\textit{figure B}}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{512}}{\sqrt[3]{343}}\qquad \begin{cases} 512=&2^9\\ &2^{3\cdot 3}\\ &(2^3)^3\\ 343=&7^3 \end{cases}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{(2^3)^3}}{\sqrt[3]{7^3}} \\\\\\ \cfrac{s}{s}=\cfrac{2^3}{7}\implies \cfrac{s}{s}=\cfrac{8}{7}\implies s:s = 8:7\impliedby \textit{ratio of the }\stackrel{sides~and}{perimeters}[/tex]


Related Questions

25 POINTS


I need help in calculating the total cost of packaging for both shapes, the image below:

Answers

Multiply your surface area by your cost/ square in. for your current cereal box to find the total cost of packaging. Then do the same with the new measurements for the new container.

Answer:

1. $21.60     2. 64.80

Step-by-step explanation:

I hope this helps :)

What is the answer to number 2.

Answers

Answer: The correct answer would be B.

Step-by-step explanation:

Because....

24 gets the variable because in total that's number of bottles that Marjorie bought. And each day she would open and drink 2 bottles of juice, which is the reason why you are subtracting 24d with 2.

* Hopefully this helps:) Mark me the brainliest:)!!

∞ 234483279c20∞

The answer is To number two is b

Based on the tree diagram below, what is the probability that a student doesn't have lice, given that the student tested negative? Round your answer to the nearest tenth of a percent.
A. 97.6%
B. 99.4%
C. 96.4%
D. 98.6%

Answers

Answer:

Option D (APEX)

Step-by-step explanation:

L= Student has lice

NL= Student has no lice

PT=Test Shows positive

NT=Test Shows negative

P([tex]\frac{NT}{NL}[/tex]) =0.7708 (Probability that a student has no lice and the test shows negative)

P([tex]\frac{NT}{L}[/tex]) = 0.0108 ( Probability that a student has lice and the test shows negative)

[tex]P\frac{NT}{NL}[/tex] = [tex]\frac{P\frac{NT}{NL} }{P\frac{NT}{NL} +P\frac{NT}{L} }[/tex][tex]\frac{0.7708}{0.7708+00108}[/tex][tex]\frac{0.7708}{0.7816}[/tex]0.98618219 (Simplify)

Terms Of Percentages

0.98618219 × 100

=98.6

Therefore your answer is 98.6% (Option D)

APEX

The probability that the student doesn't have lice, given that the student tested negative is P ( A ) = 98.6 %

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the student doesn't have lice, given that the student tested negative be P ( A )

Now , the equation will be

The probability that a student has no lice and the test shows negative is given by P ( NL ) = 0.7708

The probability that a student has lice and the test shows negative is given by P ( L ) = 0.0108

And , The probability that the student doesn't have lice, given that the student tested negative P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]

On simplifying , we get

P ( A ) = P ( NL ) / [ P ( NL ) + P ( L ) ]

P ( A ) = ( 0.7708 ) / [ 0.7708 + 0.0108 ]

P ( A ) = 0.98618

P ( A ) = 98.6 %

Hence , the probability is 98.6 %

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darr has written 60% or 12 pages of his history report their wants to figure out how many pages he needs to write their work is shown below​

Answers

The answer is 20 pages.

Hope this helps!

For this case we must make a rule of three to determine the number of pages to finish your work.

12 --------------> 60%

x ----------------> 40%

Where "x" represents the number of pages needed to complete the job:

[tex]x = \frac {40 * 12} {60}\\x = 8[/tex]

So, there are 8 pages left to finish their work. The total number of pages of the work is 20.

Answer:

You need to finish 8 pages out of a total of 20

Write and simplify a rational expression for the ratio of the perimeter to the area of rectangle if the width is 4x and the length is x+6

Answers

Answer:

5x + 6 : 2x² + 12x

Step-by-step explanation:

Width = 4x

Length = x + 6

Perimeter

= 2(4x + x + 6)

= 2(5x + 6)

Area

= 4x(x + 6)

Ratio of perimeter to area:

= 2(5x + 6) : 4x(x + 6)

= (5x + 6) : 2x(x + 6)

= 5x + 6 : 2x² + 12x

Answer:

(5x + 6) : (2x² + 12x)

Step-by-step explanation:

Perimeter = 2(length + width)

= 2[4x + x + 6]

= 2(5x + 6)

Area = length × width

4x × (x + 6)

4x(x + 6)

Perimeter : Area

2(5x + 6) : 4x(x + 6)

(5x + 6) : (2x² + 12x)

Express 18^1/2 in simplest radical form

Answers

The simplified form of 18^1/2 is 3√2

Radical expressions and indices

Given the exponential expression

18^1/2

According to power law of Indices:

a½ = \sqrt{a}

Applying this law to the given expression;

This can also be written as:

[tex]18^{1/2} =\sqrt{18}[/tex]

Simplify the radical to have:

[tex]\sqrt{18} = \sqrt{9 \times 2} \\\sqrt{18} = 3\sqrt{2}[/tex]

Hence the simplified form of 18^1/2 is 3√2

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Consider the diagram below.
What is the measure of arc PD?
A. 35°
B. 90°
C. 110°
D. 180°

Answers

Answer:

(C) [tex]110^{\circ}[/tex].

Step-by-step explanation:

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle, therefore

[tex]{\angle}FED=90^{\circ}[/tex].

Now, it is given from the figure that [tex]{\angle}FEP=35^{\circ}[/tex], therefore

[tex]{\angle}FED={\angle}FEP+{\angle}DEP[/tex]

[tex]90^{\circ}=35^{\circ}+{\angle}DEP[/tex]

[tex]{\angle}DEP=55^{\circ}[/tex]

Now, we know that The angle subtended at the center of a circle is double the size of the angle subtended at the edge from the same two points, therefore

[tex]{\angle}PCD=2{\angle}PED[/tex]

[tex]{\angle}PCD=2(55^{\circ})[/tex]

[tex]{\angle}PCD=110^{\circ}[/tex]

Thus, the measure of arc PD is [tex]110^{\circ}[/tex].

Hence, option (C) is correct.

The measure of arc PD is 110. So, The correct option is option C.

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle, therefore

90° = 135° + ∠DEP

∠DEP = 50°

Now, here is given,

∠FEP = 35°

∠FED = ∠FEP + ∠DEP....(1)

Plug the value of ∠FEP = 35° in equation (1),

∠FED = 90

90 = 35 + ∠DEP

∠DEP = 55

∠PCD = 2∠PED

∠PCD = 2 (55)

∠PCD = 110

Therefore, the measure of arc angle PCD is 110.

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Find the output, y, when the input, x, is -1.

Y = ?

Answers

When the input is -1, the output is 3

The answer is 3

In the given graph, the value of y at x = - 1 is 7.

This means that when the input x is - 1, the corresponding output y is 7. The graph visually represents the relationship between x and y, where each point on the graph corresponds to a specific x - y pair. When x takes the value - 1, the graph intersects the y-axis at the point (- 1, 7), indicating that the output y is 7.

In summary, for x = - 1, the associated output value y is 7, as shown by the graph's plotted point.

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Jenna bought 6 pounds of apples for $7.38. What is the unit price per pound of apples?

Answers

Answer:

$ 1.23

Step-by-step explanation:

We are given that Jenna bought 6 pounds of apples for $7.38 and we are to find the unit price per pound of apples.

To find that out, we will simply divide the total price of apples by the number of pounds she bought.

Unit price per pound of apples = [tex] \frac { 7 . 3 8 } { 6 } [/tex] = $1.23

Michael starts with $45 in his savings account and adds $5 to the account each week .write an expression for the number of dollars in Michael's savings account after a week's (w is the variable). Assume no money is added or removed from the account.pls need help asap

Answers

Expression: 45+(5 x w)

Hope this helps man.

The expression for the number of dollars in Michael's savings account after w week's will be;

⇒ y = $5w + $45

Where, y is total amount and w is number of weeks.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Michael starts with $45 in his savings account and adds $5 to the account each week .

Now,

Since, Michael starts with $45 in his savings account and adds $5 to the account each week .

Hence, After w weeks the total amount (y) is,

⇒ y = $45 + $5w

Thus, The expression for the number of dollars in Michael's savings account after w week's will be;

⇒ y = $5w + $45

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URGENT PLEASE HELP!!!!!
A plant is 13 inches tall and grows 2 inches a week. How many weeks will it take for the plant to be 23 inches tall?

Answers

Answer:

5 weeks

Step-by-step explanation:

So if the plant is 13 inches tall in the beginning every week adds 2 inches.

0 weeks = 13 inch

1st week = 15 inch

2nd week = 17 inch

3rd week = 19 inch

4th week = 21 inch

5th week = 23 inch

So it would take 5 weeks to grow 23 inches

Answer:

5 weeks for the plant to be 23 inches long

Step-by-step explanation:

You could take the size the plant is supposed to be, which is 23 inches long then subtract how tall the plant is which is 13 inches long then divide by 2 because the plant grows 2 inches each week. Or you could use a chart to help you, until you get to 23 inches. please give me the brainliest answer?

1weeks= 13 inches + 2 inches = 15 inches

2weeks= 15 inches + 2 inches = 17 inches

3weeks= 17 inches + 2 inches = 19 inches

4weeks= 19 inches + 2 inches = 21 inches

5weeks= 21 inches + 2 inches = 23 inches

:) Hope this helped!!! Have a good day!!! <3

Solve for y: 6x-3y=24​

Answers

Answer:

[tex]y=2x-8[/tex]

Step-by-step explanation:

Isolate the variable and divide by the coefficient to solve for a variable.

[tex]6x-3y=24 \\ \\ -3y=-6x+24 \\ \\ y=2x-8[/tex]

Answer:

y = 2x - 8

Step-by-step explanation:

=> 6x - 3y = 24

=> -3y = 24 - 6x

=> 3y = 6x - 24

=> y = 2x - 8

Vanessa practices the piano for 60 minutes each day. So far, she has practiced 42 minutes today. What percent of her practice time does she have left to complete?


Answers

Answer:

30%

Step-by-step explanation:

1) Find the amount of time left to complete

60 minutes total - 42 minutes already played = 18 minutes left

2) Divide the amount of minutes left by the total minutes

18 minutes left ÷ 60 minutes total = 0.3

3) Multiply that value by 100 to turn the decimal into a percent

0.3 * 100 = 30%

Answer:

30%

Step-by-step explanation:

The answer is thirty percent. One way to solve this problem is to start by finding what percent of Vanessa’s practice time forty-two minutes represents.

Let p represent the unknown percent, and set up a proportion that compares the like ratios of parts to wholes.

Divide out the like minutes and cross multiply.

Divide both sides by sixty to solve for the percent of time Vanessa has already practiced.

Subtract seventy percent from one hundred percent to determine the percent of time she has left to practice.

Vanessa still has thirty percent of her practice time to complete.

What is the answer to this equation? - (-5a^3)(2ab^3)

Answers

The answer is 10a^4b^3

The mean for the set of numbers 12 10 7 8 m is 25 what is the value of m

Answers

Answer:

m = 88

Step-by-step explanation:

The mean of a set of data is calculated using the formula

mean = [tex]\frac{sumofdata}{count}[/tex]

hence

[tex]\frac{12+10+7+8+m}{5}[/tex] = 25 ( multiply both sides by 5 )

37 + m = 125 ( subtract 37 from both sides )

m = 88

need answer... PLZ PLZ

Answers

Answer:

Option A is correct.

Step-by-step explanation:

The credit limit is $6000

New balance after the transactions = $ 3604.50

Available credit on Nikki's card = credit limit - New balance after the transactions

Available credit on Nikki's card = $6000 - $ 3604.50

Available credit on Nikki's card = $ 2395.50

So, Option A is correct.

                                                 

jose went jogging with sam. jose jogged 5/8 miles before resting. sam jogged 1/4 mile more before stopping. after resting, they continued jogging. each of them jogged a total distance of 2 1/5 miles. how far did sam job before stopping? what was the distance jose jogged after resting?

Answers

Answer:

7/8 miles63/40 or 1 23/40

Step-by-step explanation:

1/4 = 2/8

5/8 + 2/8 = 7/8

    2. 2 1/5 = 11/5

11/5 = 88/40

5/8 = 25/40

88/40 - 25/40 = 63/40

For this case we have to, if Sam ran [tex]\frac {1} {4}[/tex]of a mile more than Jose, then, before stopping he ran:

[tex]\frac {5} {8} + \frac {1} {4} = \frac {20 + 8} {32} = \frac {28} {32} = \frac {14} {16} = \frac { 7} {8}[/tex]

I ran [tex]\frac {7} {8}[/tex]miles before stopping.

Now, Jose after resting ran ([tex]2 \frac {1} {5} = \frac {10 + 1} {5} = \frac {11} {5}[/tex]):

[tex]\frac {11} {5} - \frac {5} {8} = \frac {88-25} {40} = \frac {63} {40}[/tex]

Jose ran [tex]\frac {63} {40}[/tex]miles

ANswer:

[tex]\frac {7} {8}\\\frac {63} {40}[/tex]

Use angle ABD shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangles ABC and DBA?

Answers

Answer:

They have the same measure.

Step-by-step explanation:

M<ABD and M<DBA have the same measure.

Answer:

segment BC is a hypotenuse

Step-by-step explanation:

the longest side of a right triangle, opposite the right angle.

What type of triangle has exactly two acute angles?

right
obtuse
equilateral
acute

Answers

Answer:

right and obtuse

Step-by-step explanation:

a right triangle has one right angle and two acute angles, and an obtuse triangle has one obtuse angle and two acute ones

i hope that this helps :)

PLEASE HELP ME FAST!

Answers

Answer:

50% chance

Step-by-step explanation:

There is a 50% chance because there in a 3/6 chance he will pick a number above 2

solve log8 12=x-2. Round your answer to four decimal places.

Answers

Answer:

[tex]\large\boxed{x\approx3.1950}[/tex]

Step-by-step explanation:

[tex]\log_ab=c\iff a^c=b\\\\\log_812=x-2\iff8^{x-2}=12\\\\(2^3)^{x-2}=4\cdot3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(x-2)}=2^2\cdot3\qquad\text{use the distributive property}\\\\2^{3x-6}=2^2\cdot3\qquad\text{divide both sides by}\ 2^2\\\\\dfrac{2^{3x-6}}{2^2}=3\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\2^{3x-6-2}=3\\\\2^{3x-8}=3\qquad\text{logarithm of both sides}\\\\\log_22^{3x-8}=\log_23\qquad\text{use}\ \log_aa^n=n\\\\3x-8=\log_23\qquad\text{add 8 to both sides}[/tex]

[tex]3x=\log_23+8\qquad\text{divide both sides by 3}\\\\x=\dfrac{\log_23+8}{3}\\\\\log_23\approx1.5849625\\\\x\approx\dfrac{1.5849625+8}{3}\approx3.1950[/tex]

Answer:

B

Step-by-step explanation:

edge 2020

One cube is 3 yards by 4 yards by 2 yards. Another cube is 3 feet by 4 feet by 2 feet. What is the ratio of the volume of the first cube to the volume of the second?
(there are 3 feet in a yard)

Answers

Answer:

9ft*12ft*6ft=648

3*4*2=24

648:24

Can someone please help me ASAP?

Answers

Answer:

b. 3

Step-by-step explanation:

Box J has surface area 2(4.5 ft * 2 ft) + 2(3 ft * 2 ft) + 2(4.5 ft * 3 ft) =  57

Box F has surface area 6(3^2 ft) = 54 ft^2

The difference between the surface areas is: 57 - 54 = 3

b. diff = 3

[tex]

S_j=2\cdot(3\cdot2)+2\cdot(4.5\cdot2)+2\cdot(4.5\cdot3) \\ S_j=12+18+27=\underline{57} \\ \\

S_f=6\cdot(3\cdot3)=6\cdot9=\underline{54} \\ \\

S_j-S_f=57-54=\boxed{3}

[/tex]

The answer is 3.

4y+3y+8-5 simplify Plz help meh!

Answers

7y+3

combine like terms.

Hey there!


4y + 3y + 8 - 5

COMBINE the LIKE TERMS

= (4y + 3y) + (8 - 5)

= 4y + 3y + 8 - 5


= 7y + 3


Therefore, your answer is: 7y + 3


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

How many families have at least 4 pets?

Answers

Answer:

6 families have at least 4 pets

Step-by-step explanation:

Hope it helped you!

area of circle
area
inscribed polygon
polygon
perimeter
equilateral
length
octagon
trapezoid
apothem
legs
hexagon
circle
composite figure
regular polygon

Answers

Answer:

1. area

2. circle

3. equilateral

4. length

5. perimeter

6. polygon

7. regular polygon

8. trapezoid

9. legs

10. area of a circle

11. hexagon

12. octagon

13. inscribed polygon

14. apothem

15. composite figure

Step-by-step explanation:

The circle below is centered at the point (-3,4) and has a radius of length 3.
What is its equation?
A. (x+ 3)^2 + (x-4)^2 = 9
B. (x-3)^2 + (x+4)^2=9.
c. (x+4)^2 + (x-3)2 =3^2
D. (x-4)^2 + (x+3)^2 =3^2

Answers

Answer:

(x + 3)^2 + (y - 4)^2 = 3^2 = 9    This matches Answer A.

Step-by-step explanation:

Start with the standard equation of a circle with center at (h, k) and radius r:

(x - h)^2 + (y - k)^2 = r^2

Here the given point (h, k) is (-3, 4) and the radius is 3.

Substituting these values into the above equation, we get:

(x + 3)^2 + (y - 4)^2 = 3^2 = 9    This matches Answer A.

Answer: (x-3)2 + (y+4)2 =9

Step-by-step explanation:

an officer administrator earns 16$ an hour ,and she works 32 hours a week . what is her weekly wage

Answers

Answer: She makes $1632 a week.

Step-by-step explanation:

You multiply 16 times 32 and get your answer.

If a 40 foot tree cast a 12 foot shadow find the length of the shadow cast by a 27 foot tree

Answers

Answer:

8.1 ft

Step-by-step explanation:

We can use proportions to solve.  Put the height over the shadow

40 ft          27 ft

---------- = -----------

12 ft           x ft

Using cross products

40x = 12*27

40x =324

Divide each side by 40

40x/40 = 327/40

x = 8.1

The shadow is 8.1 ft

please help me! this question is worth 30 points!

Answers

Answer:

1/k^4

Step-by-step explanation:

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