Mathematics College

if the surface area of two smilar spheres is 256 feet and 576 feet, what is the ratio of the volume of the smaller sphere to the volume of the largee sphere

Answers

Answer 1
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt{256}}{\sqrt{576}}\implies \cfrac{s}{s}=\cfrac{16}{24}\implies \cfrac{s}{s}=\stackrel{simplified}{\cfrac{2}{3}}[/tex]
Answer 2

The ratio of the volume of the smaller sphere to the volume of the larger sphere, given their surface areas are 256 ft² and 576 ft², is 8:27.

The student has asked about finding the ratio of the volumes of two similar spheres given their surface areas. The surface areas are 256 ft² and 576 ft². To find the volume ratio, we need to use the fact that the ratio of the surface areas of similar spheres is the square of the ratio of their radii, and thus the ratio of the volumes will be the cube of the ratio of their radii.

Let's denote the surface areas as S₁ and S₂, and the volumes as V₁ and V₂. Then, S₁:S₂ = (radius of smaller sphere)² : (radius of larger sphere)² and V₁:V₂ = (radius of smaller sphere)³ : (radius of larger sphere)³.

First, we find the square root of the surface area ratios: [tex]\sqrt{\frac{256}{576} }[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]. Then, taking the cube of [tex]\frac{2}{3}[/tex] gives us the volume ratio V₁:V₂ = [tex](\frac{2}{3} )^3[/tex] = [tex]\frac{8}{27}[/tex].

Therefore, the ratio of the volume of the smaller sphere to the volume of the larger sphere is 8:27.

Related Questions

Use a net to find the surface area of the prism.

•213 m^2
•426 m^2
•336 m^2
•306 m^2

Answers

The surface area of the prism will be given by:
SA=2(L×W)+2(L×H)+2(H×W)
SA=2(12×5)+2(12×9)+2(5×9)
SA=120+216+90
SA=426m²

Answer: 426m²

Which number produces an irrational number when added to 2/5? A) 0.555... B) -0.4 C) -/`5 D) 2/7

Answers

Answer to this question is pie of 5

The number that produces an irrational number when added to 2/5 is 0.55....

What is a rational number?

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

To produce an irrational number when added to 2/5, the number must be irrational itself.

Therefore, options B, C, and D are eliminated since they are all rational numbers.

Option A, 0.555..., is a repeating decimal and can be expressed as a fraction of 5/9. When added to 2/5, we get:

2/5 + 5/9 = (18/45) + (25/45) = 43/45

Since 43/45 is not a rational number, the answer is A) 0.555...

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Q #5 Solve the system by graphing

Answers

That first one is correct there is no solution since they are parallel.
We have the following system of equations:
 (-1/3) x + y = -1
 y = 4 + (1/3) x
 Let's rewrite the system of equations:
 y = (1/3) x - 1
 y = (1/3) x + 4
 We note that both lines have the same slope:
 m = 1/3
 Therefore, the lines are parallel.
 The first line has a cut point with the y axis of:
 (0, -1)
 The second line has a cut point with the y axis of:
 (0, 4)
 Like the lines are parallel, the system has no solution.
 Answer:
 The system of equations has no solution.

Leon deposited $30000 in a bank which paid 2% interest per year. After 1 year, Leon withdrew all his money including the interest. how much money did Leon withdraw?

Answers

The amount of money Leon had after 1 year will be given by:
A=P(1+r)^n
where:
P=principle
r=rate
n=time
But from the information given:
P=$30,000, r=2%, n=1 year
thus
A=30000(1+2/100)^1
A=30000(1.02)^1
A=$30600
Thus amount after 1 year was $30600

Which answer is the best estimate of the correlation coefficient for the variables in the scatter plot?

Answers

Take the points (1,8) and (8,1). Use rise over run to estimate the slope of the scatter plot.

[tex] \frac{1 - 8}{8 - 1} = \frac{-7}{7} = -1[/tex]

The answer is -0.99, as this is the closest answer to the estimate we found.
Final answer:

Correlation coefficient measures the relationship between two variables in a scatterplot. Its value ranges from -1.0 to 1.0. You can estimate it by observing the direction and the closeness of the data points to a line of best fit.

Explanation:

The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.

To estimate the correlation coefficient from a scatterplot, observe the tightness of the points around a line of best fit and whether the points are mainly increasing or decreasing. For tight points increasing, it's close to 1. For tight points decreasing, it's close to -1. If there's no pattern, it's close to 0.

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Test the claim that mean gpa of a night student is significantly different than 2.1 at the 0.02 significance level

Answers

0.60. Is your answer have a nice day

Calculate the total budget and then fill in the missing percentages. You will use some of the answers given more than once. Total budget = Household Budget Item Percent % Amount $ Donations 1,620 Taxes 1,620 Food 3,510 Clothing 2,700 Housing 1,350 Transportation 675 Insurance 675 Savings 675 Recreation and miscellaneous 675

Answers

Total budget = $13,500

Donations = 12%

Taxes = 12%

Food = 26%

Clothing = 20%

Housing = 10%

and the rest are 5 %

Answer:

Step-by-step explanation:

To calculate the percentage of each expenses we use this formula :

[tex]\frac{amountofbudgetitem}{Totalbudget}[/tex]  × 100

Household Budget Items             Amount ($)            Percentage

Donations                                       1,620                       12%

Taxes                                               1,620                       12%

Food                                                 3,510                       26%

Clothing                                           2,700                       20%

Housing                                           1,350                        10%

Transportation                                   675                         5%

Insurance                                           675                         5%

Savings                                              675                         5%

Recreation and

miscellaneous                                    675                        5%

Total Budget                                     13,500                    100%

A copy machine makes 132 copies in 5 minutes and 30 seconds. How many copies does it make per minute?

Answers

24 copies per minute

what is the value of y /2/4/16/20

Answers

I think it's 4. Could be wrong, probably am. 

Marcus has a pool that can hold a maximum of 4500 gallons of water. The pool already contains 1500 gallons of water. Marcus begins to add more water at a rate of 30 gallons per minute. Write an inequality that shows the number of minutes, m, Marcus can continue to add water to the pool without exceeding the maximum number of gallons.

Answers

First, let's subtract the whole pool by the water currently in to find the water needed to fill it:
4500 - 1500 = 3000
Because we need to represent an inequality:
30m = 3000
Divide both by 30:
m = 100
It will take 100 minutes

Answer:

Inequality is m ≤ 1000

Step-by-step explanation:

Capacity of the pool to hold the maximum water is = 4500 gallons of water.

Pool is already having 1500 gallons of water so remaining volume of the pool that can be filled is = 4500 - 1500 = 3000 gallons

Marcus begins to add 30 gallons water per minute and it takes "m" minutes to  fill the remaining volume.

So amount of water required = 30m gallons

There is a condition that Marcus continues to add water without exceeding the maximum amount of water.

This means remaining amount "3m gallons" will be never cross the limit of "3000 gallons" of remaining volume of water.

Now we can form the inequality as 3m ≤ 3000

or m ≤ 1000

Therefore, answer is m ≤ 1000

Booker own 85 video games. He has 3 shelves to put the games on. Each shelf can hold 40 video games. How many more video games do he have room for

Answers

Booker has room for 35 more video games since his 3 shelves (which can hold 40 games each) holds a total of 120. 120-85 = 35
35. Two shelves hold 80. And then the last five can go on the third. That means the third shelf can hold 35 more games

Show that the sum, over the set of people at a party, of the number of people a person has shaken hands with, is even. assume that no one shake his or her own hand.

Answers

If we assume the total no. of people to be odd then the no. of handshakes

each person will have will be an even number.

What are sets and subsets?

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Assuming the no. of total people to be 'n' and 'n' is an odd no.

Now if each person shakes hands with each other except their own hands each person will have (n - 1) no. of handshakes and (n - 1) or odd - 1 will always be an even no.

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The sum of handshakes is always even at a party as each handshake involves two people.

To show that the sum of handshakes is even:

Consider that each handshake involves two people, adding two handshakes to the total.

Since each person shakes hands with an odd number of people, the total sum of handshakes will be even.

Hence, the sum of the number of people a person has shaken hands with will always be even.

250 tickets are sold at a church fundraiser. if sara buys 15 tickets the probability the probability that she will win the prize quilt is

Answers

the probability the probability that she will win the prize quilt:
= 15/250 
= 0.06
= 6%

Go to lesson page Problem If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

Answers

The probability of any particular sequence of N flips of a fair coin is 2^(-N).

Your probability of the given sequence of 3 coin flips is 
   2^-3 = 1/8

First if all, we know that the coin has two sides- head and tail

P(getting a head of the first flip):

1/2

P(getting a tail on the second flip):

1/2

P(getting a head on the third flip):

1/2

To find the final answer, take:

1/2×1/2×1/2=1/8

As a result, the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip is 1/8. Hope it help!

What is the interquartile range for the data set?

Could you please double check my answer for me?

Answers

To solve this problem you must apply the proccedure shown below:

 1-  By definition, the formula for calculate the interquartile range is

 Interquartile range=Q3-Q1

 Where Q1 is the lower quartile and Q3 is the upper quartile.

 2-Keeping this on mind, you have:

 Interquartile range=Q3-Q1

 Q3=245
 Q1=201

 Interquartile range=245-201
 Interquartile range=44

 Therefore, the answer is: 44

 

What is the scale factor of figure ABCD?

a. 1/3

b. 4/3

c. 3

d. the figure isn't dilated properly

Answers

we know that
measure ABCD=scale factor*[measure A1B1C1D1]

in the axis of the y coordinate
we have
scale factor=measure ABCD/measure A1B1C1D1
scale factor=3/1----->3

in the axis of the x coordinate
we have
scale factor=measure ABCD/measure A1B1C1D1
scale factor=8/6----->4/3

therefore

the answer is the option
d. the figure isn't dilated properly

hey can you please help me posted picture of question

Answers

Hey there :)

Now, we need to find how many solutions the nonlinear system of equations graphed has

The points where these given graphs intersect will be the number of solutions.

We can see on the equations graphed that 3 points are where they intersect

[tex]\boxed {Therefore \ your \ answer \ will \ be \ option \ A }[/tex]

Hey can you please help me posted picture of question

Answers

3 transformations are applied to F(x)

1) Multiplication by -1.
This implies F(x) is flipped over x-axis

2) Multiplication by 1/3
This implies F(x) is compressed vertically

3) Addition of 4 to x.
This implies F(x) is shifted by 4 units to left.

Thus, G(x) is obtained from F(x) by flipping it across x-axes, compressing it vertically and shifting it towards left.

Thus, option C is the correct answer

Logarithmic form x^19 = y

Answers

To solve the problem given in the figure attached, you must apply the proccedure shown below:

 1. You have the following expression given in the problem:

 x^19 = y

 2. By definition, you have:

 logb(x)=y
 b^y=x

 3. Therefore, you have:

 
 x^19 = y
 logx(y)=19

 4. Then, as you can see, the answer is:  logx(y)=19

 
log properties or log transformation is;

b ^ x = a , then to solve for the exponent x, log b a = x or read as log a base b = x.

 x^19 = y

x = b
a = y
x = 19

log x y = 19 or log y base x = 19

Which of these is equal to sin(70°)? A) cos(110°) B) cos(160°) C) cos(20°) D) cos(70°)

Answers

sin β = cos (90-β)
sin (70⁰)= cos (90-70⁰)=cos (20⁰)
sin (70⁰)=cos (20⁰)

Answer:

[tex]sin (70^{\circ})=cos (20^{\circ})[/tex]

Option C is correct.

Step-by-step explanation:

we have to choose the option for which the value is equals to sin(70°)

As in the first quadrant sine and cosine both are positive

[tex]\sin \theta = \cos (90-\theta)\\\\\sin (70^{\circ})= \cos (90-70)=\cos (20^{\circ})\\\\sin (70^{\circ})=cos (20^{\circ})[/tex]

hence, option C is correct.

Two trains leave stations 532 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour while the other travels at 100 miles per hours. How long will it take for the two trains to meet?

Answers

The two trains will meet in 2.4 hours.

What is the distance?

Distance is defined as the product of speed and time.

We have been given that two trains depart from stations 532 miles apart at the same time and head in the opposite direction. The first train runs at 90 miles per hour, while the second at 100 miles per hour.

Let's assume x distance 90 mph train traveled

Then (532 - x) is the distance 100 mph train traveled

Travel time = distance/speed (equal in both directions)

⇒ x/90 = (532 -x)/100

⇒ 100x = 90× 532 - 90x

⇒ 100x + 90x = 47880

⇒ 190x = 47880

⇒ x = 47880/190

⇒ x = 252

So travel time = 252/90 = 2.4 hrs

Therefore, the two trains will meet in 2.4 hours.

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The endpoints of a line segments are at the coordinates (-6,3,4) and (4,-1,2) what is the midpoint of the segment

Answers

Answer:(-1,1,3)

Explanation:

The coordinates of the mid point are calculated by dividing the sum of each pair of corresponding coordinates by 2.

This is how you calculate the mid of each coordinate separately:

1) x-coordinate:

mid x-coordinate = (- 6 + 4) / 2 = -2 / 2 = - 1

2) y-coordinate

mid y-coordinate = (3 - 1) / 2 = 2 / 2 = 1

3) z-coordinate

mid z-coordinate = (4 + 2) / 2 = 6 / 2 = 3

So, the midpoint is (-1, 1 , 3)


Find the final amount of $1000 investment after 9 years at 8% interest compound quarterly

Answers

Here's the equation for one year:
1000 + 0.08(1000)
But because it is 9 years:
1000 + 9(0.08(1000))
1000 + 0.72(1000)
We can make it simpler:
1.72(1000)
Multiply:
1720
You will have $1720

Help with this math question please

Answers

51. The area of the rectangle is lw. The triangle's base and height are both w, so its area is 1/2 (w)^2. The total area will be lw + (1/2)w^2, which is choice A.
52. The best answer is G. This is a circle of diameter 10 in, so 10 in is the longest dimension, and you would not be able to cut a 2-in wide section that is 10 in long since the circle immediately gets smaller when you move away from the diameter.

6.
Valdez Construction signed a note with a payment of $5,200 per quarter for 5 years.
Find the amount they must set aside today to satisfy this capital requirement in an account earning 8% compounded quarterly.


$30,506.32

$126,346.32

$51,054.38

$85,027.44

Answers

[tex]PV = C* \frac{1- (1+r/n)^{-nt} }{r/n} [/tex]

Where, PV = Present vale, C = Quarterly payments =$52,000, r = Annual interest rate = 8% = 0.08, n = Number of  payments per year = 4, t= time of payment in years = 5

Substituting,
[tex]PV = 52000* \frac{1- (1+0.08/4)^{-4*5} }{0.08/4} = $85,027.53[/tex]

The closest answer is $85,027.44

How many milliliters equal 1052 cm3? A. 1052 B. 1.052 C. 105.2 D. 10.52 30 points

Answers

Hello there, and thank you for asking your question here on brainly.

Short answer: A. 1052 ml

Why?

1 cm = 1 ml, so what would that be? 1052 cm = 1052 ml.

Hope this helped you! ♥

Hello!

I believe the answer is A) 1052.

I hope it helps!

In a family with 8 ​children, excluding multiple​ births, what is the probability of having 7 boys and 1​ girl, in any​ order? assume that a boy is as likely as a girl at each birth

Answers

there is a 7/8 chance there will be boys and a 1/8 chance there will be a girl 

Final answer:

The probability of having 7 boys and 1 girl in a family with 8 children is 1/128.

Explanation:

To find the probability of having 7 boys and 1 girl in a family with 8 children, we can use the concept of combinations. There are 8 children in total, and we want to choose 7 boys and 1 girl from them. The probability of having a boy or a girl at each birth is 50%, so we can use the binomial coefficient to calculate the probability. The formula for the binomial coefficient is C(n, k) = n! / (k!(n-k)!), where n is the total number of children and k is the number of boys we want. Plugging in the values, we get C(8, 7) = 8! / (7!(8-7)!) = 8. Therefore, the probability of having 7 boys and 1 girl in any order in a family with 8 children is 8 / 2^8 = 1 / 128.

What percent of data is in quartile 1

Answers

One quarter (25%) of the data is in any quartile. That is the meaning of the term "quartile."

25% of data is in quartile 1

hello can you please help me out on this question posted picture

Answers

There are 3 possible outcomes of each game.

So, the tree will start with 3 leaves, and each leaf will further be divided into 3 leaves. Thus the total number of leaves in the tree diagram will be 3 x 3 = 9 leaves.

Option A correctly represent this situation. 

please help........there are 3 problems

Answers

[tex]1.\ x^2+5x+4=x^2+x+4x+4=x(x+1)+4(x+1)=(x+1)(x+4)\\\\2.\ x^2-10x+21=x^2-7x-3x+21=x(x-7)-3(x-7)=(x-7)(x-3)\\\\3.\ x^2+2x-63=x^2+9x-7x-63=x(x+9)-7(x+9)=(x+9)(x-7)[/tex]
if
[tex]x^2+10x+21[/tex]
then
[tex]=x^2+7x+3x+21=x(x+7)+3(x+7)=(x+7)(x+3)[/tex]
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