The volume of a sphere whose diameter is 18 centimeters is

Volume of a Sphere Formula:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

Diameter/Radius Relationship:
[tex]\displaystyle r = \frac{d}{2}[/tex]

Let us clearly sort out what information this specific problem gives us:

We can consolidate this into mathematical symbols:

Given what we know, we now need to find the volume of the sphere. With knowledge implied, found under the General Formulas and Concepts section above, we can first solve for the radius [tex]\displaystyle r[/tex]:

[tex]\displaystyle\begin{aligned}r & = \frac{d}{2} \\& = \frac{10 \ \text{in}}{2} \\& = \boxed{5 \ \text{in}} \\\end{aligned}[/tex]

∴ the radius of the sphere is equal to 5 inches.

Now that we have our radius, we can substitute this value into our volume of a sphere formula and evaluate:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \boxed{ \frac{500}{3} \pi \ \text{in}^3 } \\\end{aligned}[/tex]

∴ the volume of the sphere is equal to [tex]\boxed{ \frac{500}{3} \pi \ \text{in}^3 }[/tex].

To estimate our answer, we can simply substitute the value of [tex]\displaystyle \pi[/tex] for 3.14, as defined by the problem, and evaluate once more:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \frac{500}{3} \pi \ \text{in}^3 \\& = \frac{500}{3} (3.14) \ \text{in}^3 \\& \approx \boxed{ 523.333 \ \text{in}^3 }\end{aligned}[/tex]

∴ the volume of the sphere is approximately equal to [tex]\displaystyle \boxed{ 523.333 \ \text{in}^3 }[/tex].

∴ the best answer choice that corresponds to our gathered result is answer choice b. 523.333 cu. in.

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Topic: Geometry

Unit: Volume

Answer:

x = log(5) / log(3)

x=1.46497

Step-by-step explanation:

3^x - 5 =0

Add 5 to each side

3^x = 5

Take the log of each side

log 3^x = log 5

We know log a^b = b log (a)

x log (3) = log (5)

Divide side by log (3)

x = log(5) / log(3)

x=1.46497

Answer:

median

Step-by-step explanation:

the median is literally the middle number--half the numbers are higher, half the numbers are lower.

Answer:

Sin 3A = 1

cos 3A = 0

tan 3 A = undefined

Step-by-step explanation:

[tex]\sin A = \frac{1}{2} \\ \therefore \: \sin A = \sin \: 30 \degree.. \bigg( \because \: \sin \: 30 \degree = \frac{1}{2} \bigg) \\ \therefore \: A = 30 \degree \\ \\ now \\ \sin 3A =\sin (3 \times 30 \degree)= \sin \: 90 \degree = 1 \\ \\ \cos 3A =\cos (3 \times 30 \degree)= \cos \: 90 \degree = 0\\\\ \tan 3A =\tan (3 \times 30 \degree)= \tan \: 90 \degree = \infty [/tex]

Answer:

I will answer in English.

In each group, A and B, we have 24 students.

a) The number of girls in A is twice the number of boys in A.

Then, if G is the number of girls and B the number of boys.

G + B = 24

G = 2B

Now we can replace the second equation into the first one:

2B + B = 24

3B = 24

B = 24/3 = 8

G = 24 - 8 = 16

We have 16 girls in class A.

b) In B we have 4 more girls than boys, then:

G  = B + 4

G + B = 24

we can replace the first equation into the second one:

B + (B + 4) = 24

2*B = 24 - 4 = 20

B= 20/2 = 10

We have 10 boys in class B:

Answer:

XVII

Step-by-step explanation:

VII + X =

V = 5

I = 1

X = 10

5+1+1 + 10 = 17

XVII

Answer:

a. 14

b. 28

Step-by-step explanation:

a. ex: (6+3)2 - 4 = 9(2) - 4

18 - 4 = 14

b. ex: 23 + (14 - 4) / 2

Use PEMDAS

P 1st

10

D over A

5

A

28

Hope this helps!

Answer:

C. 14.75

Step-by-step explanation:

To find mean is fairly easy. All you have to do is add all of the numbers in your data set, and then divide it by the total amount of numbers in the set. So:

12 + 17 + 16 + 10 + 20 + 13 + 14 +14 + 12 + 12 + 19 + 18

Total numbers in the set: 12

All numbers added together: 177

177 / 12 = 14.75

brainliest is always epic :)

Answer:

Step-by-step explanation:

1. First add all the listed numbers which equals to 177

2. Divide 177 by the amount of number given above so there are

12 numbers

So 177÷12= 14.75

Answer is c

Answer:

1.x=(z/4)-y

2.b=(e-cd)/a

Step-by-step explanation:

1.

z=4(x+y)

Divide both sides by 4

z/4=x+y

Subtract y from both sides

(z/4)-y=x

Answer

x=(z/4)-y

2.

ab+cd=e

subtract cd from both sides

ab=e-cd

divide both sides by a

b=(e-cd)/a

Answer

b=(e-cd)/a

Answer:

[tex]1) x = \frac{z}{4} - y[/tex]

[tex]2) b = \frac{e}{a} - \frac{cd}{a}[/tex]

Explanation:

(1) Making x the subject: [tex]4(x + y) = z[/tex]

To make x the subject of original expression, we send the x to the left side of expression and all of the other components to the right side of expression.

The detail procedure is described as following:

    [tex]4(x + y) = z[/tex]

Apply associate property:

<=> [tex]4x + 4y = z[/tex]

Send 4y to the right side (the sign of 4y must be changed from positive to negative):

<=> [tex]4x = z - 4y[/tex]

Divide both sides by 4:

<=> [tex]x = \frac{z}{4} - y[/tex]

(2) Make b the subject: [tex]ab + cd = e[/tex],  applying the similar procedure in part (1):

      [tex]ab + cd = e[/tex]

Send [tex]cd[/tex] to the right side (the sign of

<=> [tex]ab = e - cd[/tex]

Divide both sides by [tex]a[/tex]:

<=> [tex]b = \frac{e}{a} - \frac{cd}{a}[/tex]

Hope this helps!

:)

Answer:

152

Step-by-step explanation:

Why is this still worth 18 points?
because if you math 12+273 it = 8281 or something free point thank

Answer:

Correct option: A -> AA postulate

Step-by-step explanation:

In the figure we can see that in triangle ABC we have:

A = 53°

B = 72°

And we can see in the triangle LMN that:

L = 53°

M = 72°

We have two pairs of angles (A - L  and B - M) that are congruent, and therefore we can use the case AA (angle-angle) to affirm that these triangles are similar.

So the correct option is A: AA postulate.

Answer:

0.18

Step-by-step explanation:

Given that:

P₁ = $10, P₂ = $20

From the tables Q₁ = 900, Q₂ = 800

Using midpoint method:

Percentage change in quantity = [tex]\frac{Q_2-Q_1}{(Q_1+Q_2)/2} *100\%=\frac{800-900}{(900+800)/2}*100\%= -11.76\%\\[/tex]

Percentage change in price =

[tex]\frac{P_2-P_1}{(P_1+P_2)/2} *100\%=\frac{20-10}{(20+10)/2}*100\%= 66.67\%\\[/tex]

Price of elastic demand = Percentage change in quantity/ Percentage change in price = -11.76% / 66.67% = 0.18

The Price of elastic demand is positive because we took the absolute value and elasticity are always positive

Therefore since Price of elastic demand < 1, the demand is inelastic in this interval.

This means that, along the demand curve between $10 to $20, if the price changes by 1%, the quantity demanded will change by 0.18%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 1.8% decrease in quantity demanded and a 10% decrease in the price will result in only a 1.8% increase in the quantity demanded

Answer:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1 , Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5. hope that helps love!

Answer:

i dont know but here is some help

Step-by-step explanation:

Scale Factor. Suppose you have two similar figures , one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 .

Answer:

[tex] {a}^{6} {b}^{2} [/tex]

solution

[tex] {a}^{3} \times b \times {a}^{3} \times b \\ = {a}^{3 + 3} \times {b}^{1 + 1} \\ = {a}^{6} {b}^{2} [/tex]

hope this helps...

Good luck on your assignment..

Answer:

[tex]a^{6}b^{2}[/tex]

Step-by-step explanation:

[tex]a^3 \times b \times a^3 \times b[/tex]

If there are no exponents written, then the exponent is 1.

[tex]a^3 \times b^1 \times a^3 \times b^1[/tex]

When multiplying two powers that have the same base, you can add the exponents.

[tex]a^{3+3} \times b^{1+1}[/tex]

[tex]a^{6} \times b^{2}[/tex]

Answer: Go and do something :)

Step-by-step explanation:

Get off your phone and get the motivation to fo and find something to do for now :)

Answer:

36 units

Step-by-step explanation:

The short leg is 9 units and the long one is 12 units.

Use pythagorean theorem to find the hypotenuse, a² + b² = c²

Plug in the numbers: 9² + 12² = c²

81 + 144 = c²

225 = c²

√225 = c

15 = c

Find perimeter by adding all 3 sides: 9 + 12 + 15 = 36 units.

Answer:

140 units^2

Step-by-step explanation:

Area of a parallelogram is base times height, A = bh. Multiply the height (10) times the base (14) to get your final answer.

A = bh

A=14(10)

A=140units^2

Answer:

[tex]\fbox{\begin{minipage}{4em}36 ways\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Re-state the problem in an easier way to set up a permutation problem

"The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven"

The series above can be represented again, in form of:

7a + 1, 7b - 1, 7c + 1, 7d - 1, 7e + 1, 7f - 1

with a, b, c, d, e, f are non-negative integers.

=> 3 numbers are multiply of 7 plus 1

=> 3 numbers are multiple of 7 minus 1

Step 2: Perform the counting:

For the 1st number, there are 6 ways to select

To satisfy that each pair of numbers creates a multiple of 7, then:

For the 2nd number, there are 3 ways left to select

For the 3rd number, there are 2 ways left to select

For the 4rd number, there are 2 ways left to select

For the 5th number, there are 1 way left to select

For the 6th number, there are 1 way left to select

=> In total, the number of possible ways to select:

N = 6 x 3 x 2 x 2 x 1 x 1 = 72

However, these numbers are located around a circle, each option is counted twice.

=> The final number of possible ways:

N = 72/2 = 36

Hope this helps!

:)

Answer:

The median would be found in the middle of the histogram

Step-by-step explanation:

It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.

Hope this helps.

Answer:

70-79

Step-by-step explanation:

I took the test :)

Answer:

a = √(b+ 6)

a² = b + 6 (Square both sides)

b = a² - 6 (subtract 6 from both sides)

Answer:

b = a^2 - 6

Step-by-step explanation:

a = sqrt(b+6)

Find the square of both sides

a^2 = (b+6). Open brackets

a^2 = b+6

Subtract 6 from both sides

a^2 - 6 = b + 6 -6

b = a^2 - 6

Answer:

Step-by-step explanation:

this graph is probably : 2(x+1)^(2)+5:

it was transformed :

vertically stretched by a factor of 2

left 1 unit

up 5 units

from the graph, we can see that the points are (-1, 5) and (-2, 7)

m=(y2-y1)/(x2-x1)

m=(7-5)/(-2-(-1))

m=2/-1

m=-2

Answer:

hope this helps! pls mark brainliest

Step-by-step explanation:

a = quadrant 1

b = quadrant 1

c = quadrant 3

d = quadrant 2

e = quadrant 4

f = quadrant 3

g = quadrant 2

h = quadrant 4

In parallelogram PQRS, QP is extended to point T and ST is drawn. If ST = SP and m∠R = 130°, what is m∠PST?

Answer: 80°

Step-by-step explanation:

ST = SP and m∠R = 130°

If m∠R = 130°, then,

QPS = 130° ( Opposite angles of a parallelogram are equal)

QPS + SPT = 180° (angle on a staght line)

130° + SPT = 180°

SPT = 180° - 130° = 50°

PTS = SPT = 50° (Base Angle of an isosceles triangle)

m∠PST = 180° - (50° + 50°) (sum of Angle in a triangle)

m∠PST = 80°

Answer:

2 : 5

Step-by-step explanation:

700 g : 1.75 kg

Since ratio should be between same units, so we'll convert either g into kg or kg into g. For convenience, kg will be converted to g

700 g : 1.75 kg × 1000

700 g : 1750 g

÷ 50 ÷50

14 : 35

÷7 ÷7

2 : 5

Answer: Irrational, assuming b is irrational

Step-by-step explanation:

You didnt state what "b" is, but:

Youre dividing "a" by an irrational number. you could do something simple like 4 divided by pi. Youre going to get an irrational number

Answer:

9 feet

Step-by-step explanation:

The height of the ball in feet is given by the polynomial:

[tex]h(t) = -16t^2+50t+3[/tex]

where t is the time in seconds.

After 3 seconds, t = 3:

[tex]h(3) = -16(3)^2 + 50(3) + 3 \\\\h = -144 + 150 + 3 = 9 feet[/tex]

The height of the ball after 3 seconds is 9 feet.

Answer:

C. 5.4

Step-by-step explanation:

Range means highest number minus lowest number.

7.5 - 2.1 = 5.4

[tex]answer =5.4 \\ given \: data = 2.1 , 2.6 , 7.2 , 5.5 ,4.1 , 5.5 ,7.5 , 6.1 \\ range = highest \: score - lowest \: score \\ \: \: \: \: \: \: \: \: = \: 7.5 - 2.1 \\ \: \: \: \: \: = 5.4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer: The second endpoint is  (2,6)

Step-by-step explanation:

[tex]\frac{-6 +x}{2}[/tex] = -2  solve for x  

-6 +x = -4

+6        +6

x= 2

[tex]\frac{-6+y}{2} = 0[/tex]  

-6 + y = 0

+6         +6

 y= 6

Answer:

Step-by-step explanation:

[tex](\sqrt{2}+3)^2=(\sqrt{2})^2 + 6\sqrt{2}+9 = 6\sqrt{2} +9+2=6\sqrt{2}+11[/tex]

hope this helps