Katie approximated the volume and the surface area for a ball she was using for some exercises by assuming the ball is a sphere. She was surprised when the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. What is the radius of the ball?

Answers

Answer 1

Answer:

3

Step-by-step explanation:

Volume of sphere:

4/3 * pi * r^3

Surface Area of Sphere:

4 * pi * r^2

So if V = SA

4/3 * pi * r^3 = 4 * pi * r^2

4/3 * pi * r^3 = 4 * pi * r^2

1/3 * r^3 = r^2

1/3 * r = 1

r = 3

Answer 2

Volume is a three-dimensional scalar quantity. The radius of the ball is equal to 3 units.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the sphere is given by the formula,

V = (4/3)πR³

The surface area of the sphere is given by the formula,

Surface area = 4πR²

Also, it is mentioned that the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. Therefore,

(4/3)πR³ = 4πR²

R³/3 = R²

R = 3

Hence, the radius of the ball is equal to 3 units.

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Related Questions

Jessica is traveling at a speed of 60 miles per hour in her truck. After 4 hours, how far will she have traveled?

Answers

Answer:

240 miles

Step-by-step explanation:

60*4=240

Answer: 240

Step-by-step explanation: If she is traveling 60 miles per hour you can multiply it by 4, which is 240.

How many 3-digit numbers can you write if you cannot use any other digits except 4 and 6?

Answers

Answer:

Step-by-step explanation:

4 4 4

4 4 6

4 6 6

4 6 4

6 6 6

6 6 4

6 4 4

6 4 6

7.2b + 6.5 > 4.8b – 8.1

Answers

Answer:

[tex]7.2b+6.5>4.8b-8.1[/tex]

Multiply both sides by 10

[tex]72b+65>48b-81[/tex]

Subtract both sides by 65

[tex]72b>48b-146[/tex]

Subtract both sides by 48b

[tex]24b>-146[/tex]

Divide both sides by 24

[tex]b>-\frac{73}{12}[/tex]

OAmalOHopeO

In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x

ax – 2 = 12.5

Answers

Answer:

x = 14.5/a

Step-by-step explanation:

ax – 2 = 12.5

Add 2 to each side

ax – 2+2 = 12.5+2

ax = 14.5

Divide by a

ax/a = 14.5/a

x = 14.5/a

f (x) = -x^2 + x + 14 Find f(2)

Answers

f(x) = -x² + x + 14

f(2) = -2² + 2 + 14 = -4 + 16 = 12

f(2) = 12

Answer:

12

Step-by-step explanation:

f (x) = -x^2 + x + 14

Let x= 2

f(2) = - (2)^2 +2+14

     = -4 +2+14

  = -2 +14

  = 12

Suppose there are approximately 220 calories in 3 servings of a particular brand of cereal and 362 calories in 5 servings of the same cereal. Find the rate of change.

Answers

Answer:

.93 calories per serving

Step-by-step explanation:

220 ÷ 3 = 73.3333333 calories per serving

3 ÷ 220 = 0.0136363636

362 ÷ 5 = 72.4

5 ÷ 362 = 0.0138121547

73.3333333 - 72.4 = 0.9333333 = around .93

GIVING BRAINLIEST Graph and solve the inequality y>-|x-5|-1

Answers

Answer:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For:

x

=

0

y

=

0

+

5

y

=

5

Or

(

0

,

5

)

For:

x

=

2

y

=

2

+

5

y

=

3

Or

(

2

,

3

)

We can now plot the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-5)^2-0.125)((x+2)^2+(y-3)^2-0.125)(y-x-5)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

graph{(y-x-5) >= 0 [-20, 20, -10, 10]}

The shape is a parallelogram. CD=10cm, BD=7cm. Find it's area.​

Answers

70

Step-by-step explanation:

here,

area of parallelogram =base ×height

so,

base is given 10 cm and height is given 7 cm

Now

base ×heights

10×7

70

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following statements is true?
A. A data set will always have exactly one mode
B. A data set can have multiple modes
C. A data set will always have at least one mode
D. A data set will never have a mode

Answers

Answer:

B

Step-by-step explanation:

Let's go over each option with the process of elimination!

A. A data set will always have exactly one mode.

Contradiction: 2, 2, 3, 3, 4, 5, 6

in this data set, both 2 and 3 are modes, so it is incorrect.

B. A data set can have multiple means.

True, example as A.

C. A data set will have at least one mode.

Contradiction: 2, 3, 4, 5, 6

There are no modes in here.

D. A data set will never have a mode.

Contradiction: 2, 2, 3, 4, 5

The mode is 2.

The only true statement is answer B.

I hope this helped! :D

Answer:

b

Step-by-step explanation:

if a data set had 1,1,3,4,4 how would you have 2 modes, 1,4. If you had 1,1,2,2,3,3 you would have 1,2,3 as your modes

a is wrong, c is wrong, d is wrong

a:my example has more that one

c:i have no explanation

d:is well already wrong

Please help! For any positive numbers a, b, and, with b≠1, log b(a/d)

Answers

Answer:

B

Step-by-step explanation:

when logarithms of the same base (the base in this case is 'b') are being subtracted, divide the arguments ( 'a' and 'd')


Write a verbal expression for (c-2)d

Answers

Answer:

the sum of c minus 2 multiplied by d ------> (c-2)d

The test statistic of z=2.93 is obtained when testing the claim that p≠0.523. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of α=0.01​, should we reject H0 or should we fail to reject H0​?

Answers

Answer:

Step-by-step explanation:

Confidence Level - "P" values  

99%  2.58

Confidence Interval - "P" values  

(0.5289 , 0.6097 )  

Reference=0.523 Reject H0

3 pizzas cost $22.50,how much does 1 pizza cost?

Answers

Answer:

7.50

Step-by-step explanation:

Take the total cost and divide by the number of pizzas

22.50/ 3 pizzas

7.50 per pizza

[tex] \rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{Cost \: \: of \: \: 3 \: \: pizzas }{Total \: \: pizzas }[/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{22.50 }{3 } \\ [/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \cancel\frac{22.50 }{3 } \: \: ^{7.5} \\ [/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \: 7.5 [/tex]

Hence, the cost of 1 pizza is $7.5

(a + b)2 = 1a2 + 2ab + 1b2
(a + b)3 = 1a3 + 3a2b + 3ab2 + 1b3
How are binomial expansions related to Pascal’s triangle?

Answers

The Pascal triangle terms and binomial are related by the binomial theorem fomrula:

The row of the Pascal triangle is the same as

where n is the same as the row of the Pascal triangle.

For example,

.

is the same as the 2nd row of the Pascal triangle.

.

Also know the leading coefficient and last term degree will be the nth row of the Pascal triangle.

The first term, a will be 1 less than the previous terms and the second term, b will be 1 more than the previous terms. For example, look at

.

Another example is

.

The third row of Pascal Triangle

.

.

Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

Binomial expansions are directly related to Pascal's triangle.

Pascal's triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it. The first and last numbers in each row of Pascal's triangle are always 1.

The coefficients of the terms in a binomial expansion correspond to the numbers in Pascal's triangle. Each row of Pascal's triangle represents the coefficients of the corresponding power of the binomial.

For example, in the expansion of (a + b)², the coefficients are 1, 2, and 1. These coefficients can be found in the third row of Pascal's triangle: 1, 2, 1. Similarly, in the expansion of (a + b)³, the coefficients are 1, 3, 3, and 1, which can be found in the fourth row of Pascal's triangle: 1, 3, 3, 1.

In summary, Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

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2/4+1=1/6 x-7 what is the value of x in this epuation

Answers

X=51
I hope this is correct and is this the answer you’re looking for?

Decide whether the graphs of the given euqations are parallel perpendicular or neither

Answers

Answer: C) perpendicular

Explanation:

Each equation given to you is in y = mx+b form (aka slope intercept form).

The slope m is what we'll focus on.

The first equation has slope of 1, while the second equation has slope -1.

The two slopes multiply to -1. This is a property of any pair of perpendicular lines, as long as neither line is vertical nor horizontal.

Or you could note that -1 is the negative reciprocal of 1, or vice versa.

So there are a few options to see why the lines are perpendicular.

Pls what is the formula for finding the base and the height of a triangular pyramid.

Answers

Answer:

Take the Cubits and multiply

Step-by-step explanation:

This is a problem i had so just fill it in to your numbers etc.

A= 43.3 cubits squared

SA= the base of A +1/2 (p x slant h)

SA= 43.3 cubits squared + 1/2 (30 x 14 cubits)

To sum it up u can message me ur numbers and ill help

Find EF
-----------------------------------------------

Answers

Answer:   6

===========================================================

Work Shown:

(whole length)*(external part) = (whole length)*(external part)

(EG)*(FG) = (SG)*(HG)

(2x+4)*(4) = (x+5)*(5)

8x+16 = 5x+25

8x-5x = 25-16

3x = 9

x = 9/3

x = 3

Use this x value to find EF

EF = 2x

EF = 2*3

EF = 6

For more information, search out "secant secant formula". It's not a typo that I wrote "secant" twice.

Which geometric terms are modeled by the Eiffel Tower

Answers

Point and line are geometric terms for the Eiffel Tower

WILL GIVE BRAINLIEST. Given: SLant Prism, m

Answers

Hi! I ran into a similar problem so i will try, but sorry if i get it wrong, so basically all you do i

What are the factors of the expression below -2x^2+5-3


A -1(2x-3)(x-1)

B -1(2x+3)(x-1)

C -1(2x+3)(x+1)

D -1(2x-3)(x+1)

Answers

d got it right hope you do

Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

In the first quadrant, you start at 2, 6 and move 2units rights and 3 units down what point will you end up on?

Answers

Answer:

[tex]End = (4, 9)[/tex]

Step-by-step explanation:

Given

[tex]Start = (2,6)[/tex]

Transformation: 2 units right and 3 units down

Required

The new point

First, we take the right translation;

When a point is translated right by 2 units, the rule is:

[tex](x,y) \to (x + 2, y)[/tex]

So, we have:

[tex](2,6) \to (2 + 2, 6)[/tex]

[tex](2,6) \to (4, 6)[/tex]

Next, we take the down translation;

When a point is translated down by 3 units, the rule is:

[tex](x,y) \to (x, y + 3)[/tex]

So, we have:

[tex](4,6) \to (4, 6+3)[/tex]

[tex](4,6) \to (4, 9)[/tex]

Hence, the endpoint is:

[tex]End = (4, 9)[/tex]

Name the property: i) (-15) X (-56)
ii) (-72) X 26 = 26 X (-72)
iii) [8 X (-46)] X 32 = 8 X [(-46)] X 32]
iv) (-15) X 105 = [(-15) X (100 +5)] = [(-15) X100] + [(-15) X 5]

Answers

Answer:

Open in answr appOpen_in_app

(i)

15

7

=

30

x

⇒x=

15

7×30

=14

(ii)

3

x

=

18

12

⇒x=

18

12×3

=2

(iii)

x

30

=

24

45

⇒x=

45

30×24

=16

(iv)

16

8

=

x

25

⇒x=

8

25×16

=50

Step-by-step explanation:

yeah

A woman deposits 100 EUR in her daughter's bank account on her first birthday. On every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR.

By the time her daughter is 21 years old, how much money has been deposited in her account?

Answers

Answer:

By the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Step-by-step explanation:

Since a woman deposits 100 EUR in her daughter's bank account on her first birthday, and on every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR, to determine, by the time her daughter is 21 years old, how much money has been deposited in her account, the following calculation must be performed:

100 + (20 x 10) = X

100 + 200 = X

300 = X

Therefore, by the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Pls help me this is due tomorrow

Answers

Step-by-step explanation:

Claim: There's 14 Goats and 9 Chickens!!

Data:

Working with the Provided Information.

Let the Number of goats be x

let the Number of Chickens be y

x + y = 23..... (i)

Since the goat Possesses Two Pair of Legs... Which is a Total of 4 Legs... We say Let its Contribution be 4x.

The Chicken has Only a Pair Of Legs...Which is a total of 2 legs.... We say let its contribution be 2y

4x + 2y = 74 .....(ii)

BRINGING BOTH EQUATIONS TOGETHER.

x + y = 23

4x + 2y = 74

From Eqn i

x= 23 - y

Substitute into eqn ii

4(23 - y ) + 2y = 74

92 - 4y + 2y = 74

92 - 2y = 74

2y = 92 - 74

2y = 18

y= 9.

Substitute y into any of the eqns to get x

x + y = 23

x + 9=23

x = 23 - 9

x = 14

This simply proves that there are 14 Goats and 9 Chickens!!!.

HAVE A GREAT DAY!

Could someone please help me with this

Answers

Answer:

what are the questions

Step-by-step explanation:

arc length of an oval that is 6ft by 5ft. i just want 1/4 of the oval. i want to find out how long i would need a wire to go from the ground to the middle of the "dome".
the picture explains it better.

in the end i want to have a wire frame around the garden and than take some netting and use that to keep out the big bugs and birds. i will of course use zip ties to attach the screen/netting to the frame. unless there is a easier and cheaper way to do this.​

Answers

You can model the ellipse with the equation

(x/6)² + (y/5)² = 1

If you're comfortable with calculus, read on.

Let x = 6 cos(t ) and y = 5 sin(t ), with 0 ≤ t ≤ π/2. Then the curve C parameterized by (x(t), y(t)) traces out one quarter of the ellipse. The arc length of this curve is given by the integral,

[tex]\displaystyle\int_C\mathrm ds = \int_0^{\pi/2}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{36\sin^2(t)+25\cos^2(t)}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{25+11\sin^2(t)}\,\mathrm dt \\\\ = 5\int_0^{\pi/2}\sqrt{1+\frac{11}{25}\sin^2(t)}\,\mathrm dt[/tex]

Unfortunately, you cannot find the exact value of this integral. (Well, you can, but it involves introducing a special kind of function; I'll link it in a comment.)

But you can approximate it, and the integral above comes out to about 8.657.

I'm not sure if there's a simpler, purely geometric way to estimate the arc length. But since the semiaxes (5 ft and 6 ft) are fairly close, you could try a circle with a radius somewhere in between. The arc length would range between 7.854 ft and 9.425 ft. If the material isn't too expensive, you can always overshoot and trim off the excess or repurpose it.

Determine the y-intercept of the quadratic equation Y = x^2 - 4x + 8

Answers

9514 1404 393

Answer:

  (0, 8)

Step-by-step explanation:

The y-value of the y-intercept is the function value when x=0. That is the constant in the equation, since x=0 will make all of the x-terms be zero.

  y-intercept = 8

Jun made a round tablecloth for his kitchen table. The tablecloth is 4.5 feet in diameter. Approximately how much fabric did Jun use for the tablecloth?

Answers

Answer:

the correct answer is 16ft^2

Kraig deposited money into a money market account. It has an interest of 12% and is compounded annually. Kraig thought 3% would be the equivalent quarterly interest rate. Is Kraig correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate. Explain.

Answers

Answer:

If the amount is P, with the interest rate of 12%, the interest over the year is:

P*(1.12) - P = 0.12P

In this case the quarterly interest rate is:

0.12P/4 = 0.03P

With the same amount and 3% quarterly rate, the yearly interest would be:

P*(1.03)^4 - P = 0.1255P

The quarterly interest rate in this case is:

0.1255P/4 = 0.031375P

If the quarterly interest rate is r, it should be little less than 3% to yield a 12% yearly rate.

So Kraig is wrong.

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