Carly spends $5 for n notebooks. Write an algebraic expression to represent the cost of one notebook.

Answer:

The volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]

Step-by-step explanation:

Let r be the radius of each sphere

We are given that distance between their centers is [tex]\frac{r}{2}[/tex]

Let [tex](\frac{-r}{4},0)[/tex] be the center of sphere 1 and [tex](\frac{r}{4},0)[/tex]be the center of sphere 2 .

Using the disk points

a=0 and b =[tex]\frac{3r}{4}[/tex]

[tex](x+(\frac{r}{4}))^2+y^2=r^2\\V=2 \int_{0}^{\frac{3r}{4}} \pi y^2 dx\\V=2 \int_{0}^{\frac{3r}{4}} \pi [r^2-(x+(\frac{r}{4}))^2]dx\\V=\frac{27 \pi r^3}{32}[/tex]

Hence the volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]

In attached diagram, we can see 2 circumferences with radius r, and separated centers by r/2.

The solution is:

V = (11/12)×π×r³

Let´s call circumferences  1 and 2, by symmetry, rotating area A will produce a volume V₁ identical a V₂, Obtained by rotating area B ( both around x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) ×r×x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) ×r×x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) ×r×(r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

Related Link : https://brainly.com/question/14301190

Answer:

the first.option is the right answer

Answer:

3x^2+x-2

Step-by-step explanation:

Answer:

(`1/4)^4

Step-by-step explanation:

Since the probability of landing on a head is theoretically the same as that of landing on tails, and since the four flips are entirely independent of one another, the desired probability is

(1/2)^4 or 1/16

Answer:

b

Step-by-step explanation:

Answer:

The answer is 1 percent because if you add the 5% and 4% you get 9% and all there is left of the average interest 10 and get 1

Step-by-step explanation:

May i please get Brainiest

Answer:

x/7

Step-by-step explanatio

Answer:

-8

Step-by-step explanation:

-4 both sides & 16-4 is 12.. -3/2x equals 12 so to solve for x, you would multiply 2 by both sides. You end w -3x equals 24. You then divide -3 both sides and 24/-3 is -8... hopee that helps? :)

Answer:

[tex]V=1436.03 \ cm^3[/tex]

The second choice provides the correct answer.

Step-by-step explanation:

The Volume of a Sphere

The volume of a sphere of radius r is given by:

[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]

The radius of the sphere is r=7 cm, thus:

[tex]\displaystyle V=\frac{4}{3}\cdot 3.14\cdot 7^3[/tex]

[tex]V=1436.03 \ cm^3[/tex]

Note: We have used an approximated value for pi=3.14.

The volume of the sphere rounded to the nearest hundredth is

[tex]\boxed{V=1436.03 \ cm^3}[/tex]

The second choice provides the correct answer.

Answer:

Where are the answers to choose from?

Answer:

x = 1

Step-by-step explanation:

9x−4=2x+3 Move all terms containing x to the left side of the equation.

7x−4=3 Move all terms not containing x to the right side of the equation.

7x=7 Divide each term by 7 and simplify. x = 1

Answer:

- 14

Step-by-step explanation:

Step 1:

- 0.5x - 3 = 4      Equation

Step 2:

- 0.5x = 7        Add 3 on both sides

Step 3:

x = 7 ÷ - 0.5      Divide

Answer:

x = - 14

Hope This Helps :)

Answer:

Here's the parallel line: y = 5x - 4

Answer:

No

Step-by-step explanation:

Let's break this down...

9.03+10.71 is 19.74 and subtracted by 6.8 it will be 12.94 not 13.94 so it is not correct

So the answer is No

Hope this helps!

Answer:

No, it is 12.94

Step-by-step explanation:

9.03 + 10.71 = 19.74, 19.74 - 6.8 = 12.94

Answer: 20/3 square inches

Step-by-step explanation:

Area = length*width

length = 5 in.

width = 4/3 in.

A = 5 * (4/3) = 20/3 in^2

Answer:

0.3

Step-by-step explanation:

Answer:

3/20

Step-by-step explanation:

1/5=4/20

7/20-4/20=3/20

Hope this helps!

Answer:

b

Step-by-step explanation:

Answer: 60

Step-by-step explanation: multiply 4,7,and 5

She can select the bridesmaids' dress in 140 possible ways.

Permutation represents each of the several possible ways in which a set or number of things can be ordered or arranged.

Given is a bride who is choosing a dress for her bridesmaids which are available in 4 styles, 7 colors, and 5 fabrics.

Now, for every possible style there exist a dress for that color. So, with 4 styles and 7 colors, the total number of possible dresses will be = 7 x 4 = 28. Now, for these 28 dresses, their are 5 different fabric available, so the total number of possible ways or dresses from which she can select the dress are = 28 x 5 = 140

Therefore, she can select the bridesmaids' dress in 140 possible ways.

To solve more questions on Arrangements and selections, visit the link below-

https://brainly.com/question/16721336

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Step-by-step explanation:

12 / x¹⁴ = 12x⁻¹⁴

Integrate using power rule.

-12/13 x⁻¹³

-12 / (13x¹³)

You forgot the negative sign.

Answer:

3 and one third

Step-by-step explanation:

(3 1/3)

Answer:

rffrefr

Step-by-step explanation:

answer:

50

explanation:

Answer: Yes you can but it would be the same as dividing 10 by 3, it would just be a repeating fraction

Answer:

I can’t divide 2 by 9 because the number 9 is greater than 2. In other words, there are no 9s in 2

Step-by-step explanation:

Answer: $49

Step-by-step explanation: if there are 7 days in a week and he is saving for 7 weeks, its 7 x 7= 49

Answer:

64$ if he doinles

Step-by-step explanation:

1,2,4,8,16,32,64