A spherical balloon has a 16-in diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon
c. What is the radius of the half-inflated balloon?

Answers

Answer 1

Answer:

a. 2144.66 cubic inches

b.1072.33  cubic inches.

c. 16  inches

Step-by-step explanation:

hello, to answer this question we have to calculate the volume of  sphere:

Volume of  sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

16 =2r

16/2=r

r= 8 in

Back with the volume formula:

V = 4/3 π r³

V =4/3 π (8)³

V = 2144.66 cubic inches

The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.

2144.66/2 = 1072.33  cubic inches.

To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=1072.33

1072.33 = 4/3 π r³

Solving for r

1072.33 / (4/3 π)= r³

256= r³

16 = r

r = 16 inches


Related Questions

solve for x !
[tex]x {}^{2} - 36 = 0[/tex]

thankyou ~​

Answers

Answer:

X = 6. Give brainliest

Step-by-step explanation:

Solution:

x² - 36 = 0

or x² = 36

or x² = 6²

Therefore, the value of x is 6.

Answer:

x^2-36=0

x^2-36+36=0+36

x^2=36

x=√(36),x=-√(36)

√(36) → 6

-√(36) → -6

x=6,x=-6


Write an equation in standard form of the hyperbola described.
Vertex (10, 0); focus (-26, 0); center (0,0)

Answers

Check the picture below, so the hyperbola looks more or less like the one below, let's find the conjugate axis or namely the "b" component.

[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ a=10\\ c=26 \end{cases}\implies \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 26^2=10^2+b^2\implies 676=100+b^2\implies \underline{576=b^2} \\\\\\ \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{576}\implies \boxed{\cfrac{x^2}{100}-\cfrac{y^2}{576}}[/tex]

how do i solve this?

Answers

Answer:

33

Step-by-step explanation:

to solve for each triangle remember its 1/2 base times height you have four of those so add those four sides to the area of the square.

key concept: 1/2(Base*Height)

plss help :))))))))))))))))))))))))))))))))))))))))))))))))))0

Answers

Step-by-step explanation:

Diameter is 18

So radius will be d/2 which is 9

As the formula of area is

[tex] \pi{\r}^{2} [/tex]

So put the vales

We get s

254

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

The amplitude of this graph is 3 the maximum is 4 the minimum is -2 the period is 4 and the midline is 1 how would the function be written is all I haven’t figured out

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex] \qquad \sf  \dashrightarrow \:y = a \sin(bx) + k[/tex]

Now, let's find the required values :

period (p) = 4

[distance between any successive Crest or trough]

a = - 3 (flipped)

b = 2π/p = 2π/4 = π/2

k = 1

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 3 \sin( \frac{ \pi}{2}x ) + 1[/tex]

For some particular website, the password must start
with the letter X. Then there must be 4 more charters, and each of those characters may be a
numeric digit or a letter of the alphabet. How many different passwords are possible?

Answers

Answer:

Step-by-step explanation:

I take it you are not allowed to mix cases. There are 26 lower case letters (a b c d e f...) to the alphabet and 0 to 9 (which is 1 of 10 choices). The total number of starting choices is

x 36 * 35*34 * 33  = 1413720 possible passwords.

Find the slope of the line passing through the points (7, -3) and (3, -7)

Answers

Answer

The slope is (2,4) and (1,2)

Step-by-step explanation:

The slope is (2,4) and (1,2) I think

The equation shown below is true for which value of x? 5(x + 2) - 3(x - 6) = 7x

Answers

Answer:

x= 28/5 or 5.6

Step-by-step explanation:

5(x+2)−3(x−6)=7x

5(x+2)−3(x−6)=7x

Simplify both sides of the equation.

5(x+2)−3(x−6)=7x

(5)(x)+(5)(2)+(−3)(x)+(−3)(−6)=7x <--(Distribute)

5x+10+−3x+18=7x

(5x+−3x)+(10+18)=7x  <--(Combine Like Terms)

2x+28=7x

2x+28=7x

Subtract 7x from both sides.

2x+28−7x=7x−7x

−5x+28=0

Subtract 28 from both sides.

−5x+28−28=0−28

−5x=−28

Divide both sides by -5.

[tex]\frac{-5x}{-5} \frac{-28}{-5\\} \\[/tex]      

x= 28/5

Answer:

x= 28/5

or

5.6

hope this helps!

A student wants to interview students about their favorite sport. The students asks 50 people who play a sport for the school. Is this an example of a random sample or a biased sample?


A
Random sample

B
Biased sample

Answers

Answer:

Random

Step-by-step explanation:

100 POINTS AND BRAINLIEST. I need help ASAP.
Screenshots Below.




Consider the table of values for functions f(x) and g(x).

x f(x) g(x)
−2 14 4
−1 12 1
0 1 0
1 2 1
2 4 4
3 8 9
4 16 16
Which statements are most likely true based on the given values?

Select each correct answer.


f(x) is a polynomial function.

f(x) is an exponential function.

g(x) is a polynomial function.

g(x) is an exponential function.

The output values of g(x) will remain greater than those of f(x) as the input values continue to increase.

The output values of f(x) will surpass those of g(x) as the input values continue to increase.

Answers

Answer:

Step-by-step explanation:

First what we must do is rewrite the table to find a solution:

0.25^x −0.75x+1

   64     3.25

   16     2.5

    4      1.75

    1      1

 0.25     0.25

 0.0625 −0.5  

 0.015625  −1.25

We see where the values of the function are the same:

x = 0 (1)

x = 1 (0.25)

answer:

x = 0

x = 1

Answers:

f( x ) is an exponential function.g( x ) is a polynomial function.The output values of f( x ) will surpass those of g( x ) as the input values continue to increase.

Explain how stroke is caused by substance abuse

Answers

Answer:

Cocaine, methamphetamines, and other stimulants can cause stroke in two ways. To begin with, stimulant drugs increase blood pressure. These drugs also have a direct effect on the vessel walls, and the extra pressure can cause them to rupture and leak blood into the brain. This is known as a hemorrhagic stroke.

Step-by-step explanation:

How many ounces are in 4 pounds?

4 ounces
56 ounces
64 ounces
72 ounces

Answers

Answer:

64

Step-by-step explanation:

16 ounces per pound

16 x 4

The answer would be C. 64

The difference between two positive integers is2. If the smaller is added to the square of the larger the sum is 40. Find the integers

Answers

Answer:

4 and 6

Step-by-step explanation:

first you must write your let statements

let x = smaller integer

let y = bigger integer

y - x = 2

x + y^2 = 40

then you use substition to find your anaswer

x = y - 2

y - 2 + y^2 = 40

y^2 + y - 42 = 0

then find the numbers that add up to 1 and multiply to -42

-6 and 7

y^2 + 7y - 6y - 42

y(y + 7) - 6(y + 7)

(y - 6)(y + 7)

set both sides equal to 0

y = 6, -7

y must be positive so it is 6

then plug y into one of the equations to get your answer

6 - x = 2

x = 4

your answer is 4 and 6

If the discriminant of a quadratic equation is equal to Negative 8, which statement describes the roots?

Answers

Answer:

There are two complex roots

Step-by-step explanation:

Answer:

A. There are two complex roots

Step-by-step explanation:

got it right on edg.2022 <3


d. Henrietta Hardworker normally earns $8.50 per hour in a given 40-hour work-
week. If she works overtime, she earns time and a half pay per hour. During the
month of October, she worked 40 hours, 50 hours, 45 hours, and 42 hours for the
four weeks. How much did she earn fotal for October?

Answers

Answer:

1432.25

Step-by-step explanation:

8.50 x 40 = 340

340 x  4 = 1360

half of 8.50 is 4.25

4.25 x 10 = 42.5

4.25 x 5 = 21.25

4.25 x 2 = 8.5

add

1360 + 42.5 + 21.25 + 8.5  = 1432.25

i hope i did my math right, good luck mate

What is the slope of a line parallel to the line with equation 5x−2y=11?


−112

−52

−25

52

Answers

Answer: 52

Step-by-step explanation: Using the slope-intercept form, the slope is 52 . All lines that are parallel to y=5x2−112 y = 5 x 2 - 11 2 have the same slope of 52 .

An amusement park charges an admission fee of 30 dollars for each person. Let c be the cost (in dollars) of admission for p people. Write an equation relating c to p. Then use this equation to find the cost of admission for 15 people.

Answers

Answer:

c=30p

$450

Step-by-step explanation:

Setting up an equation lets us solve this question quickly. It also lets us create a relationship that can be used to find the cost of admission for any number of people.

Writing the Equation

As stated in the question, c will represent the total cost and p will represent the number of people admitted. Additionally, 30 will be the coefficient because it represents the cost per person. The variable p will take on the coefficient because it is the independent variable. Remember that the independent variable is the one that you can control. On the other hand, c is the dependent variable because it depends on the p variable.

This creates the equation C=30p

Solving the Equation

To solve the equation for 15 people, plug 15 in for p.

C=30(15)

Then, multiply out to solve

C=$450

A store pays 6% commission on the first $500 in sales and 8% on sales over $500 find the commission on an $800 sale

Answers

Answer:

Step-by-step explanation:

Multiplying the sales amount of 500$ and the commision rate of 6% results to

500(0.06)
=30.

In an experiment, the probability that event A occurs is 7/8, the probability that event B occurs is 7/9, and the probability that events A and B both occur is ¾ . What is the probability that A occurs given that B occurs?

Question 5 options:

0.829


0.125


0.762


0.964

Answers

Answer:

Here is answer

Step-by-step explanation:

sorry if it is wrong

I think 0.762 in the answer

Hello I need a little here with this

Answers

I may be wrong but I believe that <1=<2

what is difntion of tautology?

Answers

a phrase or expression in which the same thing is said twice in different words.

The following figure shows a cube. Which expression represents the surface area of the cube?

Answers

Answer:

6 ⋅ 16

This is the sum of the areas of the 6 square faces.

The surface area of the cube in the figure given is 96 squared units

What is surface area of a cube?

The surface area of a cube is calculated by finding the total area of all six faces. Since all sides of a cube are equal in length, you can use the formula:

Surface area of a cube = 6 × (side length)²

In other words, you square the length of one side of the cube and then multiply it by 6 to get the total surface area.

Let's say the side length of the cube is "s," then the formula becomes:

Surface area of a cube = 6 × s²

In the question given, we can calculate the surface area of this cube as;

Surface area = 6 * s²

s = 4

Surface area = 6 * 4²

Surface area = 6 * 16 = 96 unit²

Learn more on surface area of cube here;

https://brainly.com/question/410493

#SPJ2

The diagnoal of a tv is 26 inches long . assuming that this diagonal forms a pair of 30 -60 - 90 right triangles , what are the exact length and width of the tv?

Answers


Answer: 13 inches by 13-√3 inches

Let

x-------> the length side of the TV

y-------> the width of the TV

d------> the diagonal of a TV

we know that

in a 30-60-90 right triangle
cos (30°) = √³/2

sin (30°) =1/2

d = 26 in

sin (30°) = ----> y = d * sin(30°)

cos (30°) = ----> x = d * cos (30°)

substitute the values

y = 26* = 13 in

x = 26³ = 13√√3 in

the length side of the TV is 13√3 in the width of the TV is 13 in

Answer: 13 inches by 13-√3 inches

I hope this helps! :)

If F(x) and f-1(x) are inverse functions of each other and f(x) = 2x+5, what is f-1( 8) ?


O -1
O 3/2
O 41/8
O23

Answers

Answer:

the answer is 3/2........

A quadratic equation is shown below. x^2 – 16x + 50 = 0 Which of the following is an equivalent form of the above equation? (x - 1612 114 (x - 5)2 = 14 (x - 82 = 114 o O (r = 16)2 = 14​

Answers

Answer:

Step-by-step explanation:

( a ± b )² = a² ± 2ab + b²

~~~~~~~~~

x² - 16x + 50 = 0

( x² - 2(x)(8) + 64 ) - 64 + 50 = 0

( x - 8 )² - 14 = 0

( x - 8 )² = 14

Answer:

(x-8)^2=14

:)

Step-by-step explanation:

julia help the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red. there are 8 tables in all how many are red?

Answers

The fraction illustrates that there are 6 red tables.

How to calculate the fraction?

Fron the information, Julia helps the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red.

Therefore, the numbers that are red will be:

= Fraction of red × Total number

= 3/4 × 8

= 6

Therefore there are 6 red tables.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

What is 594 minus 236?

Answers

Answer:

358

Step-by-step explanation:

the answer is 358 because

Use the distributive property to write an expression that is equivalent to the expression below. 5(2x+7)

Answers

Answer:

[tex]10x+35[/tex]

Solution:Use the distributive property to simplify.The distributive property states the following:x(y+z)=xy+xz (x times y plus x times z)Now, simplify:[tex]5(2x+7)[/tex][tex]10x+35[/tex]I multiplied 5 times 2x and 5 times 35.Is [tex]10x+35[/tex] the final answer? Yes, we cannot simplify it anymore, because 10x and 35 are not like terms.

Hope it helps.

Do comment if you have any query.

MAX POINTS help me

The amplitude of this graph is 3 the maximum is 4 the minimum is -2 the period is 4 and the midline is 1 how would the function be written?

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex]\qquad \sf  \dashrightarrow \:a \sin(bx) + c[/tex]

Now, let's find the required values :

period (p) = 4

[distance between any successive Crest or trough]

a = - 3 (flipped)

b = 2π/p = 2π/4 = π/2

k = 1

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 3 \sin( \frac{ \pi}{2}x ) + 1[/tex]

General equation:-

Asin(bx)+c

So

Amplitude=A=-3

Min=-2 ,max=4

Hence

b=|(mn)|π/mxb=|-2|π/4b=2π/4b=π/2

midline =c=1

So plugin the values

y=-3sin(π/2x)+1

Find the area of the parallelogram. of 6 m 10 m

Answers

Answer:

60m

Step-by-step explanation:

The formula for the area of a parallelogram is base x height.

b x h

6m x 10m = 60m

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