How to find volume of sphere explain step by step

Problem 1

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Explanation:

Arc BC is 58 degrees. The arc AB combines with it to form semicircle ABC, which is basically arc ABC with measure 180

This must mean arc AB is 180-58 = 122 degrees

When in doubt, chances are the number 180 might be involved (in some way) when it comes to geometry problems. Of course, this isn't always a guarantee. The number does show up a lot though.

Once we determine what arc AB is equal to, we cut it in half to get the inscribed angle ADB. Refer to the inscribed angle theorem. Notice how angle ADB subtends the arc AB.

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Problem 2

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Explanation:

x = length of AE

Since AC = 13, this makes EC = 13-x

We'll use the intersecting chords theorem to find x.

(AE)*(EC) = (BE)*(DE)

x*(13-x) = 6*6

13x-x^2 = 36

-x^2 + 13x - 36 = 0

x^2 - 13x + 36 = 0

(x-9)(x-4) = 0

x-9 = 0 or x-4 = 0

x = 9 or x = 4

This means AE could be 9 units long or 4 units long.

Usually the diagram isn't drawn to scale so we don't really use it all too much (other than initial set up). However, if the diagram was drawn to scale, then notice that AE is over the halfway point of AC. This means we would be able to rule out x = 4 since 4 is not over the halfway point of 13. I have a feeling this is what your teacher might be going for.

In short, only AE = 9 is possible.

Answer:

  4

Step-by-step explanation:

The number each friend will get is the total number divided by the number of friends:

  (20xy -10x²)/5x = (4y -2x) = 2(2y -x)

__

For x=6 and y=4, the number each friend will get is ...

  2(2×4 -6) = 2(2) = 4

Mary will give 4 sweets to each friend.

Answer:

[tex]a{}^{2} - {b}^{2} = {c}^{2} [/tex]

[tex]12 {}^{2} - (3 \sqrt{7})^{2} [/tex]

[tex]144 - 63 = 81[/tex]

[tex] \sqrt{80 } = 9[/tex]

Answer:

sorry for dirty handwriting

The initial value and base value are 12 and 4/3. The function is a growing function. The domain and the range of the function are real numbers.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

The exponential function is given below.

f(x) = 12(4/3)ˣ

Then the initial value of the exponential function is 12.

Then the base value of the exponential function is 4/3.

If the base value if greater than 1 then the function is a growing function.

The domain and range of the function are real numbers.

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Answer:

length=0.65 mi

length in yr= 0.65x1760=1144

The length of the jogging track is 0.65 miles.

To convert the length of the jogging track from yards (yd) to miles (mi), use the ratio between yards and miles.

1 mile = 1760 yards

Now, set up the equation to convert the length:

Length in miles (mi) = Length in yards (yd) / Conversion ratio

Length in miles (mi) = 1144 yd / 1760 yd/mi

Now, perform the calculation:

Length in miles (mi) = 1144 / 1760 ≈ 0.65 miles (rounded to the nearest hundredth)

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At first glance, you'll notice that the line is going from left to right which tells us that the slope will be negative therefore the bottom option can be eliminated.

Knowing that the formula for slope is rise over run, you'll notice that the lines rises by -8 and runs by 3 which means that the slope would be -8/3.

This leaves us a final answer of  [tex]y=-\frac{8}{3}x-4[/tex]

Answer:

40 feet

Step-by-step explanation:

d = 1/2 at^2      sub in d = ?      a =  5      t =  4

d = 1/2 * (5)(4)^2

d = 40 feet

Answer:

11.1%

Step-by-step explanation:

buy 100 shirts at 2700

each shirt = 2700/100 = $27

sell at $30 each

mark up = (30-27)/27 = 3/27 = 1/9 = 11.1%

Answer:

300 profit

Step-by-step explanation:

The different mathematical operations that have as a result 54 are 9x6,  8x9 - 18, 5x5 + 29, and 27x2.

This refers to calculating values using addition, multiplication, division, etc.

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Answer:

x = 50° y = 130°

Step-by-step explanation:

x and 50° are vertically opposite angles and are congruent , then

x = 50°

y and 50° are adjacent angles and sum to 180° , then

y + 50° = 180° ( subtract 50° from both sides )

y = 130°

The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion is false.

A harmonic motion of constant amplitude in which the acceleration is proportional and oppositely directed to the displacement of the body from a position of equilibrium

The statement "The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion. " is false.

As, motion of simple pendulum is an example of simple harmonic motion.

But the equilibrium should not varies, then it would be simple harmonic with damped oscillations.

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Answer:

Each sandwich costs $5.12

Step-by-step explanation:

Six sandwiches is $30.72

Divide 30.72 by 6 and you get 5.12

That means that each sandwich costs $5.12

The volume of the right pyramid with the given properties is 80√3 cubic volume

The given parameters are:

Start by calculating the base area using:

Base area = 6 * Area of equilateral triangle

So, we have:

Base area = 6 * 4√3

Evaluate

Base area = 24√3

The volume of the pyramid is:

Volume = 1/3 * Base area * Height

So, we have:

Volume = 1/3 * 24√3 * 10

Evaluate

Volume = 80√3

Hence, the volume of the right pyramid is 80√3 cubic volume

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Answer:

WY represents the height.

If the area of an equilateral triangle with sides of 4 ft is 4StartRoot 3 EndRoot square feet, then the area of the regular hexagon base is 24 StartRoot 3 EndRoot square feet.

The volume is 80 StartRoot 3 cubic feet. :D

Answer:

a. What is the probability of the number being between 2-7?

Step-by-step explanation:

i just have a feeling

The probability of the events are given as 0.6 and 0.2 respectively.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

(a) The total number of elements in sample space are 10.

Then, the probability of getting numbers from 2 - 7 is given as,

P(numbers 2-7) =  Number of favorable outcomes ÷ Total outcomes

⇒ 6 ÷ 10 = 0.6

(b) The multiples of 5 are given as 5 and 10

Then, P (Multiple of 5) = Number of favorable outcomes ÷ Total outcomes

⇒  P (Multiple of 5) = 2/10 = 0.2

(c) The complement of selecting one element represents the selection of all remaining elements in the sample space.

Thus, complement of 9 represents selection of all the remaining numbers  from 1 to 10.

(d) For the probability of 3/10, the question can be asked as to find the probability of selecting numbers from 1 to 3.

Hence, the probabilities of the given events can be found by taking the ratio of favorable outcomes to the total outcomes.

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Answer:-30

Step-by-step explanation:kinda hard to tell a little shaky so sorry if it is wrong.

Step-by-step explanation:

that's it b is for brings

b compliment is for doesn't bring

Answer:

2000 kg.

Step-by-step explanation:

Density = mass / volume

-->  mass = density * volume

-->  mass =  40 * 50

-->  mass = 2000 kg.

Answer:

y = 1.25r

Step-by-step explanation:

1.25 x r(the pounds brought) = y(the money spent)

Answer: 20%

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

7.5

[tex] \sqrt{30} [/tex]

- 28

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20

- 20

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0

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(Not a square root! I just used it to show how its being divided. And also on the left of the '30' is a 4, so 30 divided by 4 and so on.)

Sorry if the answer looks messy!

Answer:

15/2

Step-by-step explanation:

If you need to simplify it/it can't be a decimal then 15/2 would be your answer.

Work:

30/4 = 7.5 (decimal)

15 times 2 = 30 (15 goes into 30 twice evenly)

15/2 is the simplest you can make it without it being uneven.

15/2

Answer:

See below

Step-by-step explanation:

For a circle:

   Area = pi r^2   =   3.14 * 1.6^2 = 8.04 units^2

   Circumf = pi * d   = pi * 2r = 3.14 * (2 * 1.6) = 10.05 units

Answer:

A(-2,2),. B(−1, −2), and C(-6, 1). Graph the triangle. Then graph the triangle after a translation 7 units right and. 3 units up.

Step-by-step explanation:

After translation 7units left and 17unit up ΔXYZ become ΔX'Y'Z' with new coordinates X'(-14,4) , Y'(-10,8) an Z'(-14,12).

" Translation is defined as the moving a geometrical shape by certain distance."

According to the question,

In ΔXYZ,

Coordinates of X =(-7,-13)

Coordinates of Y = (-3 ,-9)

Coordinates of Z = ( -7, -5)

After translation 7units left and 17units up and rotation 270° counterclockwise around the origin

New coordinates as shown in the drawn graph of ΔX'Y'Z'

Coordinates of X' = (-14, 4)

Coordinates of Y' = (-10, 8)

Coordinates of Z' = (-14,12)

Hence, translation 7units left and 17unit up ΔXYZ gives ΔX'Y'Z' with new coordinates X'(-14,4) , Y'(-10,8) an Z'(-14,12).

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The composite function for the price a loyalty member would pay based on the original price x is  C(L(x)) = 0.7803x.

We have been given that

Sales price: S(x) = 0.85%

Loyalty member discount L(S) = 0.85S

Final cost: C(L) = 1.08L

Find out- which is the composite function for the price a loyalty

member would pay based on the original price x?

Sales price: S(x) = 0.85%

Loyalty member discount L(S) = 0.85S

Put the value of S then -

L(S) = 0.85× 0.85x

L(S) = 0.7225x

Final cost: C(L) = 1.08L

Now put the value of L

C(L) = 1.08L

C(L) = 1.08 × 0.7225x

C(L(x)) = 0.7803x

Hence , C(L(x)) = 0.7803x is the composite function for the price a loyalty member will pay given the initial price x.

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Answer:

x = -2, -8.

Step-by-step explanation:

x =[(-b +/- √(b^2 - 4ac)] / 2a

x^2 + 10x + 16 = 0

Here a = 1, b = 10 and c = 16, so substituting in the formula:

x = [-10 +/- √(10^2 - 4*1*16)] / 2

= (-10 +/- √36)/2

= (-10 +/- 6)/2

= -4/2, -16/2

= -2, -8.

Answer:

x = - 8 , x = - 2

Step-by-step explanation:

x² + 10x + 16 = 0

with a = 1, b = 10 , c = 16

then using the given quadratic formula

x = [tex]\frac{-10+/-\sqrt{10^2-(4(1)(16)} }{2}[/tex]

  = [tex]\frac{-10+/-\sqrt{100-64} }{2}[/tex]

  = [tex]\frac{-10+/-\sqrt{36} }{2}[/tex]

  = [tex]\frac{-10+/- 6}{2}[/tex]

then

x = [tex]\frac{-10-6}{2}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8

x = [tex]\frac{-10+6}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

If the lines area parallel: x = 69 degrees

Step-by-step explanation:

Answer:

x equals 49°.

outside exterior angle

Answer:

Can't read it.