Two cubes have surface areas of 72 square feet and 98 square feet. what is the ratio of the volume of the small cube to the volume of the large cube?

Answers

Answer 1

Let's denote the sides of the small and bigger cubes a and b respectively. Then, we can write that 6[tex] a^{2} [/tex]=72, a=[tex] 2\sqrt{3} [/tex] and 6[tex] b^{2}=98, b=[tex] \frac{7}{sqrt{3}} [/tex]. The volume of the smaller cube is [tex] 2 sqrt{3} ^{3} [/tex] = [tex] 24 sqrt{3} [/tex]. The volume of the bigger cube is [tex] \frac{7}{sqrt{3}}^{3} [/tex] = [tex] \frac{343}{3sqrt{3}}{[/tex]. We have to find [tex] \frac{24 sqrt{3}}{frac{343}{3sqrt{3}} [/tex] = 216/343

Answer 2

Answer:

Ratio of the volumes of the cubes = 216 : 343

Step-by-step explanation:

Since surface area of a cube is represented as 6a² where a is the side of a cube.

Let a is one side of large cube and b is the side of smaller one.

Ratio of their surface area = [tex]\frac{6a^{2} }{6b^{2}}=\frac{72}{98}[/tex]

[tex](\frac{a}{b})^{2}=\frac{36}{49}[/tex]

[tex]\frac{a}{b}=\sqrt{\frac{36}{49}}[/tex]

[tex]\frac{a}{b}=\frac{6}{7}[/tex]

Now ratio of the volumes = [tex]\frac{a^{3} }{b^{3}}=(\frac{1}{b})^{3}[/tex]

Ratio = [tex](\frac{6}{7})^{3}=\frac{216}{343}[/tex]

Therefore, ratio of the volumes of the cubes = 216 : 343

Related Questions

put the following equation in slope intercept form: 3x - 2y = 14

Answers

y = 2/3x - 7

Subtract the x term from both sides and then divide by -3.

(-6-8i) + (-6-i)
study island question please help

Answers

You can treat "i" as though it were a variable and combine like terms in the usual way.
= (-6+(-6)) +(-8 +(-1))i
= -12 -9i

Or, you can let your calculator do it.

What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.

To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
Question 1 options:
The formula for the surface area of a sphere is 4 x pi x radius^2
The formula for the volume of a sphere is 4/3 x pi x radius^3.

Answers

we know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere

if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere

if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere

examples
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area

2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area

3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area

Bernice estimated that 69% of 242 is 168. Is her estimate reasonable?

Answers

Her estimate is not reasonable.

Since she estimated 69%, you could do either of these options. You could...
A. Divide 242 (or .5) to show how much half off would be, then compare her estimate with half of 242 (121). OR...
B. Simply divide 242 by 69% (.69) and compaor her estimate to the exact amount (166.98).

I hope this helps!

Answer:

D Yes, because her calculation should be 70% of 240.

Step-by-step explanation:

Use a calculator to find the approximate value of sin-1( 0.655).

Answers

arcsin(0.655) ≈ 40.9196° ≈ 0.714183 radians

Answer:

Radian = 0.7142

Degree = 40.92°

Step-by-step explanation:

Given: [tex]\sin^{-1}(0.655)[/tex]

Let, [tex]y=\sin^{-1}(0.655)[/tex]

It is inverse trigonometry function. We have to use calculator to find angle of trigonometry.

The value of y in two form radian or degree

Using calculator to find the value of y

In radian,

[tex]y=0.7142[/tex]

In degree,

[tex]y=40.92^\circ[/tex]

Hence, The value of [tex]\sin^{-1}(0.655)[/tex] in radian 0.7142 and in degree 40.92°

The graph of which function has a minimum located at (4, –3)?

f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35

Answers

[tex]f(x)=ax^2+bx+c[/tex]

The graph of this function has minimum if a > 0.

Minimum is in point (h; k) where:

[tex]h=\dfrac{-b}{2a};\ k=f(h)[/tex]

[tex]minimum(4;-3)\to h=4;\ k=-3[/tex]

[tex]f(x)=x^2+4x-11;\ a=1 > 0;\ b = 4\\\\h=\dfrac{-4}{2\cdot1}=-2\neq4[/tex]

[tex]f(x)=-2x2+16x-35;\ a=-2 < 0[/tex]

[tex]f(x)=x^2-4x+5;\ a=1 > 0;\ b=-4\\\\h=\dfrac{-(-4)}{2\cdot1}=\dfrac{4}{2}=2\neq4[/tex]

[tex]f(x)=2x^2-16x+35;\ a=2 > 0;\ b=-16\\\\h=\dfrac{-(-16)}{2\cdot2}=\dfrac{16}{4}=4\\\\k=f(4)=2\cdot4^2-16\cdot4+35=2\cdot16-64+35=32-64+35=3\neq-3[/tex]

Answer: Any graph of this functions hasn't a minimum located at (4; -3).

If the coordinates of minimum are (4; 3),
then your answer is f(x) = 2x² - 16x + 35

Answer:

f(x) = 1/2x^2 – 4x + 5 (the third option)

Step-by-step explanation:

On ed :)

The length of a rectangular field is represented by the expression 14x-3x^2+2yThe width of the field is represented by the expression 5x-7x^2+7y How much greater is the length of the field than the width?

Answers

[tex](14x-3x^2+2y)-(5x-7x^2+7y)\\\\=14x-3x^2+2y-5x+7x^2-7y\\\\=-3x^2+7x^2+14x-5x+2y-7y\\\\=4x^2+9x-5y[/tex]

Please help me with my question

Answers

Television
A=w *l=w* 5w=5w²
w=x+7, x- width of tablet
A=5(x+7)²=5(x²+14x+49)= 5x²+70x+245
A(television)=5x²+70x+245
"at least" means more or equal,so
5x²+70x+245≥1,050 - the answer

If tablet has width 8, x=8,
then
5*8²+70*8+245≥1050
1125≥1050 True,
so we can say
Yes, 8 in is a reasonable size for Adrew's tablet.

If f(x)=2x+1 and g(x)=x^2-7, find (f+g)(x)

A. x^2=2x-6
B. 2x^2-15
C. x^2+2x+8
D. 2x^3-6

Answers

f(x)=2x+1 and g(x)=x^2-7
(f+g)(x) = 2x + 1 + x^2 - 7
(f+g)(x) = x^2 + 2x - 6

answer
x^2 + 2x - 6

Answer: The correct option is (A) [tex]x^2+2x-6.[/tex]

Step-by-step explanation: We are given the following two functions :

[tex]f(x)=2x+1,\\\\g(x)=x^2-7.[/tex]

We are to find the value of [tex](f+g)(x).[/tex]

We know that

for any two functions p(x) and q(x), we have

[tex](p+q)(x)=p(x)+q(x).[/tex]

Therefore, we get

[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(2x+1)+(x^2-7)\\\\=2x+1+x^2-7\\\\=x^2+2x-6.[/tex]

Thus, option (A) is CORRECT.

( Please help me, the year is ending and I'm almost at a failing grade): ) An athlete is running along a circular path that has a diameter of 250 yards. The arc traveled by the athlete is 120 degrees. Using 3.14 for (symbol that looks like two Ts that are connected), how many yards did the athlete run? Round the answer to the nearest yard.

Answers

For this case the arc length is given by:
S = R * theta
Where,
R: radius of the circle
Theta: central angle
Substituting values we have:
S = (250/2) * (120) * (3.14 / 180)
S = 261.6666667 yards
Round to the nearest yard:
S = 262 yards
Answer:
the athlete ran:
S = 262 yards

To find the distance an athlete ran on a circular path with a diameter of 250 yards and an arc length of 120 degrees, calculate the arc length using the radius and angle in radians. The athlete ran approximately 262 yards.

To find the distance the athlete ran around a circular path with a given arc length of 120 degrees and a diameter of 250 yards, first, determine the radius of the circle:

Radius (r) = Diameter / 2 = 250 yards / 2 = 125 yards

Convert 120 degrees to radians: 120 degrees × π / 180 = 2π / 3 radians

Calculate the arc length using the formula: Arc Length = Radius × Angle in radians = 125 yards × 2π / 3 = 250π / 3 ≈ 261.8 yards

Therefore, the athlete ran approximately 262 yards.

The width of a rectangle is 5 inches less than twice the length. The area of the rectangle is 700 square inches. What is the length of the rectangle?

Answers

To calculate the length of the rectangle we let the length be x in, let width be
(2x-5) inches
The area will be given by:
A=length×width
A=x(2x-5)
but
A=700 in²
thus
700=x(2x-5)
700=2x²-5x
this can be written in quadratic form as:
2x²-5x-700=0
solving the quadratic we get:
x=20 or x=-35/2
since the length cannot be negative then:
x=20 in
thus the width will be:
2*20-5
=40-5=35 inches

A survey was conducted that asked 1011 people how many books they had read in the past year. results indicated that x overbarequals14.8 books and sequals16.6 books. construct a 90% confidence interval for the mean number of books people read. interpret the interval

Answers

Since we do not know the population standard deviation, we will use the t-distribution to construct the 90% confidence interval of the mean number of books people read. The value of [tex]t_{\frac{\alpha }{2}}[/tex] with 1010 degrees of freedom and with alpha equals to 0.10 is 1.64

First, we need to solve for the margin of error, E.
[tex]E=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}=1.64\cdot \frac{16.6}{\sqrt{1011}}=0.86[/tex]

The lower bound of the confidence interval is
[tex]LB=\overline{x}-E=14.8-0.86=13.94[/tex]

The upper bound of the confidence interval is
[tex]LB=\overline{x}+E=14.8+0.86=15.66[/tex]

Therefore, the 90% confidence interval is (13.94, 15.66).

We are 90% confident that the interval from 13.94 books to 15.66 books does contain the true value of the population mean number of books people read.

Let A = {the whole numbers} and B = {the integers}. Find A ∩ B.
0
the integers
the whole numbers
the real numbers

Answers

The correct answer is THE WHOLE NUMBERS.
Whole numbers refers to numbers starting from zero to any number, but they do not include negative numbers, fractions and decimals. Integers refers to whole numbers but they also include negative number. The intersection between the two refers to the numbers that are common to the the two of them. Thus, in this case the common numbers are the whole numbers, because whole numbers exist in the two groups.

The answer is WHOLE NUMBERS.

Please help!!!!!!!!!!!!!!

Answers

Pay attention here because I'm adding an extra letter to our circle to help keep track of the values in our formula. OUTSIDE of the intercepted arc I'm adding the point E. So the major arc is arc BEG and the minor arc is arc BG. The formula then for us is ∠[tex]BFG= \frac{1}{2}(arcBEG-arcBG) [/tex]. We just don't have values for the arcs yet. If the measure of the central angle is 4x+238, then the measure of arcBG is also 4x+238. Around the outside of the circle is 360°. So we will use it in an expression. ArcBEG=360-(4x+238). Fitting that into our formula we have [tex]2x+146= \frac{1}{2}[(360-4x-238)-(4x+238)] [/tex]. Doing all the simplifying inside there we have [tex]2x+146= \frac{1}{2}(122-4x-4x-238) [/tex] and [tex]2x+146= \frac{1}{2}(-8x-116) [/tex]. Multiply both sides by 2 to get rid of the fraction: 4x+292=-8x-116. Combine like terms to get 12x = -408 and divide to solve for x. x = -34. Fourth choice down from the top.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

T.A.=

Answers

Answer: Total area of the given prism is (104 + 16√13) Square inches.

Step-by-step explanation:

By the given diagram,

In the right triangular prism,

The sides of the base ( right triangle ) are 4 inches and 6 inches,

We have to finds : T.A. ( the total area of the prism )

Thus, the total base area of the prism = 2 × ( Area of triangle having base 4 inches and height 6 inches )

= 2× ( 1/2 × 4 × 6 )

= 4 × 6

= 24 square inches,

Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )

Thus, by the given diagram,

[tex]x^2 =4^2+6^2[/tex]

[tex]x^2 = 16 + 36[/tex]

[tex]x^2 = 52[/tex]

[tex]x=2\sqrt{13}[/tex]

Now, the total lateral area of the prism,

= 8×2√13 + 8×4 + 8×6

= 16√13 + 32 + 48

= (16√13 + 80) square inches,

Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)

= 24 + 16√13 + 80

= (104 + 16√13) Square inches.

Find the x-intercept of the function: f(x) = 6x - 2. Round answer to the nearest hundredth, if necessary. A) (0.39, 0) B) (1.00, 0) C) (2.58, 0) D) (3.00, 0)

Answers

The function f(x) = 6^(x)-2 has an x-intercept at approximately (0.39, 0)
              f(x) = 0 = 6^(x) - 2
                        2 = 6^(x)
       log(2)/log(6)= x
                          x = 0.3868 = 0.39
The answer to this question is A) (0.39, 0).

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!! What is the simplified form of the expression (3x^7/2)^6 (x^2)^6

A. x^33
B. 3x^29
C. 729x^29
D 729x^33

Answers

[tex](3x^ \frac{7}{2} )^6(x^2)^6= (729x^{21})(x^{12}) = 729x^{33}[/tex]

The correct option is: Option (D) 729x^33

Explanation:
Given expression:
[tex](3x^{7/2})^6 (x^2)^6 \\ (3^6x^{42/2})(x^{12}) \\ 729x^{21+12} \\ 729x^{33} \\[/tex]

Which is option (D)

A system of equations consists of two lines. One line passes through (-1, 3) and (0, 1). The other line passes through (1, 4) and (0, 2). Determine of the system has no solution, one solution, or an infinite number of solutions.

Answers

The equation of the line in its generic form is:
y = mx + b
Where,
m = (y2-y1) / (x2-x1)

For (-1, 3) and (0, 1):
We look for the value of m:
m = (1-3) / (0 - (- 1))
m = (- 2) / (0 + 1)
m = -2
We look for the value of b:
1 = m (0) + b
b = 1
The line is:
y = -2x + 1

For (1, 4) and (0, 2):
We look for the value of m:
m = (2-4) / (0-1)
m = (- 2) / (- 1)
m = 2
We look for the value of b:
2 = m (0) + b
b = 2
The line is:
y = 2x + 2

The system of equations is:
y = -2x + 1
y = 2x + 2

Answer:
the system has one solution

Simplify the following expression.

[tex]4a^{-2} b [/tex]

Answers

The first step for solving this expression is to express with a positive exponent using [tex] a^{-n} X \frac{1}{ a^{2}} X b[/tex].
4 × [tex] \frac{1}{ a^{2} } [/tex] × b
Now calculate the product.
[tex] \frac{4X1b}{ a^{2} }[/tex]
Before you get your final answer,, you must remember that any expression multiplied by 1 stays this same. This makes our final answer the following:
[tex] \frac{4b}{ a^{2}}[/tex]
Let me know if you have any further questions.
:)

Answer: C

Step-by-step explanation:

The grid shows a section of the beach in Coast City where each square has sides that are 100 yards long.

On a coordinate plane, the beach front is about 800 yards long. From the south pier to the north pier along harbor drive and park street, the distance is 1200 yards long.

Lisa walked from the South Pier to the North Pier along the beachfront. Deanna walked from the South Pier to the North Pier along Harbor Drive and Park Street. Which statement best describes the distances the two women walked?

a. Lisa walked about 400 yards farther than Deanna.

b. Lisa walked the same distance as Deanna.

c. Lisa walked about 400 yards less than Deanna.

d. Lisa walked about 400 yards.

Britany sends between 10 and 20 text messages per day. Each text message costs $0.80. Suppose Britany's cellular bill spans a period of 8 weeks. Which is a reasonable amount that she would spend on text messages on one cellular bill

Answers

well if its between 10 & 20 take the median which is 15 and multiple it by the about of days which is 56 and you get 840 dollars

Write the equation of the line going through the point (4,6) that is perpendicular to the lie 3x+6y=12

Answers

3x + 6y = 12
6y = - 3x + 12
y = - 1/2x + 2

Since your slope is - 1/2, we take the opposite reciprocal to find the perpendicular slope. Your perpendicular slope is 2.

y = 2x + b

Plug in the point to solve for b and get your final line.

6 = 2(4) + b
6 = 8 + b
6 - 8 = b
- 2 = b

y = 2x - 2 is your perpendicular line

Solve by factoring AKA zero product property method. If the equation has no real solutions, write no real solutions.
3. x^2 − 5 + 4 = 0
4. x^2 + 7 + 12 = 0

Answers

Hello,

[tex]1)\\ x^2-5x+4=0\\ x^2-4x-x+4=0\\ x(x-4)-(x-4)=0\\ (x-4)(x-1)=0\\ Sol=\{1;4\}\\\\ 2)\\ x^2+7x+12=0\\ x^2+3x+4x+12=0\\ x(x+3)+4(x+3)=0\\ (x+3)(x+4)=0\\ Sol=\{-4;-3\} [/tex]

What Is the Measure of Y

41

49

51

61

Answers

The answer is:  " 41 " .
_____________________________________________________
→  " y = 41 " .
_____________________________________________________
Explanation:
______________________________________________________

From the "image attached", note that:

"139" and "y" ; together; form a "straight line" ;

→ that is: "139" and "y" are supplementary ;

and by definition; "supplementary angles" add up to " 180 degrees" ;
______________________________________________________

  → y + 139 = 180 ; Solve for "y" ;

Subtract " 139 " from each side of the equation;
to isolate "y" on one side of the equation; & to solve for "y" ;

→ y + 139 − 139 = 180 − 139 ;

to get:

→ y = 41 degrees:
_____________________________________________________
The answer is: " 41 " .
_____________________________________________________
→ " y = 41 " .
_____________________________________________________

Answer:

ITS A.) 41

Step-by-step explanation:

Hal’s sporting Goods had a 1 day sale. The original price of a mountain bike we 325. In a sale it was 276.25. What is the percent decrease for this sale?

Answers

Well, the decrease of the amount would be $48.75 then you would divide this by how the original price which is $325, so the answer would be about 6% decrease.

Decrease = 325 - 276.25 = $48.75

Percentage decrease = 48.75/325 x 100 = 15%

Answer: 15%

please help with math? will give branliest!!
2. A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds.
howler monkey: {15, 16, 17, 17, 17, 17, 18, 19}
spider monkey: {12, 13, 13, 14, 14, 14, 16, 16}
(a) Calculate the median each type of monkey.
(b) Calculate the mean for each type of monkey.
(c) Calculate the MAD for each type of monkey.
(d) Calculate the means-to-MAD ratio for the two types of monkeys.
(e) What inference can be made about the weight of both types of monkeys? Explain.
Answer:

Answers

howler 17 17 0.75
spider 14 14 1

The median of howler monkey is, 17

And, Median of spider monkey is, 14

The mean for the howler monkeys is 17 and the MAD is 0.8571.

The mean for the spider monkeys is 14 and the MAD is 1.1429.

The means-to-MAD ratio is 2.6249.

This means that on average, the number of mean absolute deviations that separate the means is 2.6. This means they are different.

Find the median of data set as;

For howler monkey;

There are 8 number of howler monkey.

Hence, Median is,

= (8/2 + 1)

= 5 th term

= 17

For spider monkey;

There are 8 number of spider monkey.

Hence, Median is,

= (8/2 + 1)

= 5 th term

= 14

To find the mean of the howler monkeys, add all of the data values and divide by 7:

= (15+16+17+17+17+17+18+19)/7

= 119/7

= 17

To find the MAD, subtract each data point from the mean; take the absolute deviation; then average these together:

= (|15-17|+|16-17|+|17-17|+|17-17|+|17-17|+|17-17|+|18-17|+|19-17|)/7

= (2+1+0+0+0+0+1+2)/7

= 6/7

= 0.8571

And, Repeating these processes for the spider monkeys:

Mean:

(12+13+13+14+14+14+16+16)/7

= 98/7

= 14

And, MAD:

= (|12-14|+|13-14|+|13-14|+|14-14|+|14-14|+|14-14|+|16-14|+|16-14|)/7

=(2+1+1+0+0+0+2+2)/7

= 8/7

= 1.1429

To find the means-to-MAD ratio, find the difference in the means and divide it by the larger MAD:

17-14=3;

Hence, We get;

3/1.1429 = 2.6249

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ2

At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional?

Answers

Michael:
3 books = $6
1 book = $6 ÷ 3 = $2

Darnell:
5 books = $10
1 book = $10 ÷ 5 = $2

Both Michael and Darnell bought their book at $2/book. The rates are proportional.

Answer Yes, the rate of proportional.

3 for $6 = 6/3 = $2/book
-------------↑-----------------
Michael
_____________________________________________________________

5 for $10 = 10/5 = $2/book
---------------↑-------------------
Darnell
_____________________________________________________________

Yes,they can form a proportion because they are equal

Hope this helps :)

Calculus question... I need help understanding thanks.
Calculate Гx^3dx

Answers

Apply the power rule:

[tex]\displaystyle\int x^3\,\mathrm dx=\dfrac{x^4}4+C[/tex]

which holds since

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{x^4}4+C\right]=\dfrac{4x^3}4+0=x^3[/tex]

6x – 2y = 10 2x + 3y = 51 solving the first equation above for y gives:

Answers

The first equation is 6x - 2y = 10. To solve for y, you will use inverse (opposite) operations to undo what is happening to y. Please see the steps below for the work.

6x - 2y = 10
-6x -6x
-2y = (-6x + 10)
-2 -2
y = 3x - 5

4 students ran for class president. In the elction, Mario got 40% of the votes. Jazmyne got 35% of the votes, Arturo got 10%,and Rachel got 60 votes. How many students voted?

Answers

Rachel = 100% - 35% - 40% - 10% = 15%

15% = 60 votes

1% = 60 ÷ 15 = 4 votes

100% = 4 x 100 = 400 votes

Answer: 400 students voted

44 points, please answer this question ASAP!

Answers

add the 5 amounts:

-10 + -23 = -33

-33 + 8 + 7 + 3 = -15 cents
now divide by the number of changes (5)

-15 / 5 = -3 cents
the mean change is -3 cents

Answer:

-3

Step-by-step explanation:

mean = sum of terms/number of terms

mean = (-10-23+8+7+3)/5

mean = -15/5

mean = -3

Other Questions

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