Mathematics High School

If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?

Answers

Answer 1

Answer:  The required ratio of the volumes of two spheres is 125 : 512.

Step-by-step explanation:  Given that the ratio between the radii of the two spheres is 5 : 8.

We are to find the ratio of the volumes of the two spheres.

Let, 'r' and 'R' represents the radii of the two spheres, so

r : R = 5 : 8.

The volume of a sphere  with radius 'r' units is given by the formula:

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

Let, V and V' be the volumes of the spheres with radius r and R units respectively.

Then, the ratio of the volumes of the two spheres will be

[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]

Thus, the required ratio of the volumes of two spheres is 125 : 512.

Answer 2

Answer: 125:512

Step-by-step explanation:

a p e x

Related Questions

for which of the following numbers does 5 appear in the tens place ?
*check all that applies*
a. 125.634
b. 56.89
c. 1250
d. 3.5
e. 92.57



Answers

5 appear in the tens place

answer:
b. 56.89 
c. 1250
The answers are b and c. It's talking about the "tens" place, not the "tenths" place, so neither d or e are correct. 

Rewrite the rational exponent as a radical.

5 to the 3 over 4 power, to the 2 over 3 power

A.the cube root of 5 squared
B. the twelfth root of 5
C. the square root of 5
D.the cube root of 5 the fourth power

Answers

[tex]\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5} [/tex]

C. the square root of 5

P(A)=25,P(B|A)=920,P(A∩B)=?

Answers

Final answer:

We use the product rule in probability to find P(A∩B) = P(B|A) * P(A). Substituting given values, P(A∩B) = (9/20) * 25, which equals 11.25.

Explanation:

The subject area of this question is probability, a topic within mathematics. Here, we are asked to find the intersection of Events A and B given the probabilities of A and the conditional probability of B given A. The rule of product in probability states that P(A∩B) = P(B|A) * P(A).

Let's calculate: P(B|A) is given as 9/20 while P(A) is 25. Thus,

P(A∩B) = P(B|A) * P(A) = (9/20) * 25 = 11.25

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Please check my work!

Answers

That is correct! The graph shows that the students their are 40 students that have both a part-time job and a cell phone. B) Is correct.

20 POINTS PLUS BRAINLIEST!!!

Which function is represented in the table of values?

x 0 -1 -2 -3
y 2 4 8 16

A.
y=2^x
B.
y=2(1/2)
C.
y=-2^x
D.
y=(1/2)^x

Answers

The correct answer is D.
y = (1/2)^x

y = (1/2)^-1 = 2
y = (1/2)^-2 = 4
y = (1/2)^-3 = 8

Hope it helped!

decimal fundamentals
add 729.3 + 3.4006

Answers

732.7006 is the answer to this question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2-3x-3=0

Answers

x^2 - 3x = 3
(x - 1.5)^2 - 2.25 = 3
(x - 1.5) = +/- sqrt 5.25

x = 1.5 +/- sqrt5.25

x  = -0.79, 3.79  to nearest hundredth
This is the answer I wrote it all out

Find the value of the variable and DF if D is between C and F if CD 4y -9, DF 2y-7, and CF 14.

Answers

CF = CD + DF (since D is simply a point on the line, and C to that point added onto F to that point is CF), so 4y-9+2y-7=14. Adding it up, we get 6y-16=14 and adding by 16 we get 30=6y. Dividing both sides by 6, we get y=5. Plugging that into DF, we get 10-7=DF=3

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Answers

check the picture below.

so, the left-part of the picture is the focus point and the directrix... .so.. notice, the focus is above the directrix, meaning is a vertical parabola and is opening upwards.

now, looking at the right-part of the picture, bear in mind that, the vertex is "p" units away from the directrix and the focus, so, the vertex is half-way between those fellows, notice in the picture what "p" is, keep in mind that, because the parabola is opening upwards, "p" is a positive unit, thus is 3.

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=-5\\ k=2\\ p=3 \end{cases}\implies [x-(-5)]^2=4(3)(y-2) \\\\\\ (x+5)^2=12(y-2)\implies \cfrac{(x+5)^2}{12}=y-2\implies \cfrac{(x+5)^2}{12}+2=y \\\\\\ \cfrac{1}{12}(x+5)^2+2=y[/tex]

Answer:  D

Step-by-step explanation: took the test

Factor the following.

Answers

This trinomial is also a perfect square trinomial so it can be solved using perfect squares.

(x-10)^2

Answer: B

Hope this helps :)
Please give brainliest
x² - 20x + 100

Once again, I'll just go through all of the answer choices :)

a)  (x - 5)(x - 4)

Simplify.

x² - 4x - 5x + 20

Add like terms.

x² - 9x + 20

So, A is incorrect.

b)  (x - 10)(x - 10)

Simplify.

x² - 10x - 10x + 100

Add like terms.

x² - 20x + 100

So, B is correct.

c) (x + 10)²

(x + 10)(x + 10)

Simplify.

x² + 10x + 10x + 100

Add like terms.

x² + 20x + 100

So, C is incorrect.

d)  (x + 10)(x - 10)

Simplify.

x² - 10x + 10x - 100

Add like terms.

x² - 100

So, D is incorrect.

Therefore, B is correct.

~Hope I helped!~

PLEASE HELP ME!!!!

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.

Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answers

Part A:

The equation in standard form is given Ax+By+C = 0
where x is the gradient of a straight line (or the rate of change)

The rate of change = (113-43) / (8-3) = 70/5 = 14
This value means there's an increase of $14 for every hour rented.

We also need to work out the value of C, which is the fixed value (happen at x=0)

We know that Amir paid $43 for 3 hours. 
Amir would have paid $29 for 2 hours
Amir would have paid $15 for 1 hour
Since the hourly rate is $14, the fixed fee is 15 - 14 = $1

The equation that represents the total cost of renting a scooter is

y = 14x + 1

Rearranging this equation to get the standard form
14x - y + 1 = 0

Part B:

Writing the equation as function ⇒ f(x) = 14x + 1

Part C:

To graph the equation, we can start by choosing the x-intervals, say we have the value of x between 0 and 10

x   0   1     2    3    4    5    6     7    8     9     10
y   1   15  29  43  57  71   85   99  113  127  141

Each pair of x-value and y-value is then plotted on a graph then each plot is joined to draw a straight line.


Answer:

Step-by-step explanation:

Part A: The two points that represent this situation are (3,43) and (8,113). To put this in standard form, I will first find the slope-intercept form. I did this in the image below.

Now, to find the standard form I will rearrange, 14x -y +1 = 0.

Part B: To put this in function notation I simply take my slope-intercept equation of y=14x+1, and replace y with f(x) so,   f(x)=14x+1

​

Part C: To graph this, put the y, intercept at 1, and give the line a slope of 14/1. Label the x-axis with hours, from 0 -  8, and the y-axis with dollars, from 0-150.

Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°. Approximately how tall is the tree?

Answers

This is the concept of trigonometry, the height of the tree will be given by:
tan theta=[opposite]/[adjacent]
theta=80
height=h
adjacent=5 m
hence;
tan80=h/5
hence;
h=5tan80
h=28.36 m

10 POINTS!!! TO ANSWER CORRECTLY AND BRAINLIEST!!!!

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.

Answers

1/5 = 3/15
2/3 = 10/15
3/15 + 10/15 = 13/15

The LCD is 15, so multiply the numerator and denominator of 1/5 by 3, this leaves us with 3/15. Now, multiply the numerator and denominator of 2/3 by 5,
this leaves us with 10/15. Now, if we add 3/15 and 10/15, we get 13/15. This cannot be simplified because 13 is a prime number, thus it is only divisible by itself and 1.

If F(theta)=tan theta=3, find F(theta+pi)

Answers

Given:
f(θ) = tan(θ) = 3

Note that
[tex]tan(x+y) = \frac{tanx + tany}{1-tanx \, tany} [/tex]

Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
            = (tanθ + tan π)/(1 -tanθ tan π)
            = 3/1 = 3

Answer: 3
As given 
[tex]f(\theta) = tan( \theta) = 3[/tex]

So [tex]f(\theta + \pi) = tan (\theta + \pi)[/tex]

And we know [tex]tan(\theta + \pi) = -tan(\theta)[/tex] because it is in second quadrant and tan is negative in second quadrant.

So [tex]f(\theta + \pi) = -tan(\theta) = -3[/tex]

So answer is -3.

Convert 48°36'12" to the nearest thousandth of a degree

Answers

48 degrees remains

divide minutes by 60

36/60 = 0.6

then divide seconds by 3600

12/3600=0.003 ( to nearest thousandth)

now add them all up

48 +0.6 + 0.003 = 48.603 degrees

Determine whether the sequence converges or diverges. If it converges, give the limit.

11, 44, 176, 704, ...

Answers

The term to term rule is multiplying by 4 and if we continue doing this, we will move towards very large positive numbers.

This sequence, therefore, diverges to infinity

how to solve 46.2 x 10 with a negative 2 exponent

Answers

The answer is 0.462 because you have to move the decimal point 2 spaces to the left
hope this helps:)
46.2 x 10^-2  = 46.2 / 10^2  =  46.2 / 100 = 0.462

Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building. If he places the ladder at a 60° angle with the ground, about how long is the ladder?

Answers

Check the picture.

Let BC represent the wall, AC the ladder and AB the distance of the feet of the ladder to the wall.

ABC form a right triangle, with m(B)=90°, m(A)=60° and m(C)=30°.

AB is the side opposite the angle 30°, so the length of AB is half of the length of the hypotenuse AC.

Thus, let |AC|=2x, and |AB|=x.

By the Pythagorean theorem:

[tex] (2x)^{2}= x^{2} +30^{2} [/tex]

[tex] 4x^{2}= x^{2} +30^{2} [/tex]

[tex] 3x^{2}=30^{2}=900 [/tex]

[tex] x^{2}=300 [/tex]


thus [tex]x= 10\sqrt{3} [/tex]

the length of the ladder is [tex]2x= 20\sqrt{3}=34.64 [/tex] feet


Answer: [tex]20\sqrt{3}=34.64 [/tex] feet

The height of the ladder will be;

⇒ 20√3 feet

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building.

And, He places the ladder at a 60° angle with the ground.

Now,

Let the height of the ladder = h

So, We can formulate;

⇒ sin 60° = 30/h

⇒ √3/2 = 30/h

⇒ h = 30 × 2/√3

⇒ h = 20√3

Thus, The height of the ladder = 20√3 feet

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PLZ HEEEEEEEELPPPPPPPP!!!!!!!!!

Answers

y= ∛(-x) - 3
for x = -8 → y = ∛-(-8) - 3 ↔ y = 2-3 ↔y = -1
for x= 8 → y= ∛(-8) - 3 ↔ y = -2 -3 ↔ y = -5
Then  - 5≤ y≤ - 1
hence the range of y is {y|-5≤y≤-1}

Find two consecutive positive integers such that thw sqaure of the first decreased by 25 equa;s three times the second

Answers

consecutive integers are 1 apart

so

square of the first decreased by 25 equals 3 time the 2nd
the 2 integers are x and x+1

x²-25=3(x+1)
distribute
x²-25=3x+3
minus (3x+3) from both sides
x²-3x-28=0
factor
what 2 numbers muliply to get -28 and add to get -3
-7 and 4
(x-7)(x+4)=0

set to zero

x-7=0
x=7

x+4=0
x=-4
false, we want positive integers

x=7
x+1=8

the inegers are 7 and 8

The question is "Find the number of elements in the following sets"
I sort of get it but it docks me points every time I get it wrong so I don't want to risk it

Answers

I hope this helps you


U=66+17+53+82=218


A' = 53+82=135


A'∩B=53


(A∩B)'=66+53+82=201


(A∪B)'=82


A' ∩ B' = 82

what is the least common multiple of X and Y? X=2*2*2*2 Y=2*2*2*3

Answers

[tex]\text{lcm}(x,y)=2^4\cdot3=48[/tex]
The least common multiple is the product of the highest occurring primes of the numbers prime factorizations, in this case:

2*2*2*2*3=48

Help please..........,.,,,

Answers

A, the cost of 6 show tickets is $30, the blue dot is where 30 and 6 intersect. Hope this helps.
A is your answer its  30 dollars for 6 tickets 


If a line contains the point (0, -1) and has a slope of 2, then which of the following points also lies on the line?

A. (2, 1)
B. (1, 1)
C. (0, 1)

Answers

The answer is B because y=2x-1
Answer:

                The point that lie on the line is:

                        B.  (1,1)

Step-by-step explanation:

We are given that a line passes through the point (0,-1) and has a slope of 2.

We know that the equation of a line passing through (a,b) and having slope m is given by:

           [tex]y-b=m(x-a)[/tex]

Here we have:  (a,b)=(0,-1) and m=2

This means that the equation of line is:

[tex]y-(-1)=2(x-0)\\\\y+1=2x\\\\y=2x-1[/tex]

Now we will check which option is true.

A)

                (2,1)

when x=2

we have:

[tex]y=2\times 2-1\\\\\\y=4-1\\\\\\y=3\neq 1[/tex]

Hence, option: A is incorrect.

B)

                     (1,1)

when x=1

we have:

[tex]y=2\times 1-1\\\\\\y=2-1\\\\\\y=1[/tex]

                Hence, option: B is correct.

C)

                      (0,1)

when x=0

we have:

[tex]y=2\times 0-1\\\\\\y=0-1\\\\\\y=-1\neq 1[/tex]

Hence, option: C is incorrect.

Find the missing factor n(n-3)+2(n-3)=() (n-3)

Answers

Greetings!

Solve for the missing factor: [tex](x)[/tex]
[tex]n(n-3)+2(n-3)=x(n-3)[/tex]

Divide both sides by [tex](n-3)[/tex]:
[tex] \frac{n(n-3)}{(n-3)} + \frac{2(n-3)}{(n-3)}= \frac{x(n-3)}{(n-3)} [/tex]

Cancel Common Factors:
[tex]n+2=x[/tex]

The Missing Factor is:
[tex]\boxed{n+2}[/tex]

I hope this helped!
-Benjamin

Help!!!!! Identify KPN

Answers

m<KPN = 1/2(90+50) = 140/2=70

answer D. 70 (last choice)

Answer:

it is 70

Step-by-step explanation:

I guessed and got it right, lol

If 3a2 – 5ab – 2b2 is factored, one of the factors might be:

Answers

We want to factor 3a² - 5ab - 2b².

Note that 
(3a)*(-2b) + a*b = -6ab + ab = -5ab
(3a)*a = 3a²
b*(-2b) = -2b²

Therefore
3a² - 5ab - 2b² = (3a + b)(a - 2b)

The factors are (3a + b) and (a - 2b).

Answer:
One of the factors is (3a + b).
Another factor is (a - 2b).

D: y> -1/3 x+1 helpppp

Answers

The answer is A. It is less than or equal to because the line is solid instead of dashed. It is less than because the shaded portion is below the line.

if <6 = <10 and <5 = <7, which describes all the lines that must be parallel?

Answers

second: Only lines t and u must be parallel

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.

h=1+13t-5t^2

Find all values of t for which the ball's height is 8 meters.

Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answers

Here the answer is: 0.76 and 1.84

I hope I don't have to explain it again.






For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].

What is equation?

An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.

How to solve equation?

We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.

So,

1+13t-[tex]5t^{2}[/tex]=8

[tex]-5t^{2}[/tex]+13t+1-8=0

[tex]-5t^{2}[/tex]+13t-7=0

Removing negative signs.

[tex]5t^{2}[/tex]-13t+7=0

We cannot solve through factorization so e use the following formula:

x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]

t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5

t=(13+-[tex]\sqrt{169-140}[/tex])/10

t=(13+5.38)/10, (13-5.38)/10

t=1.838, 0.762

By rounding off to nearest hundred t=1.84, 0.76.

Hence value of t for which h=8 meters are 1.84 and 0.76.

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