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2 years ago

83 and one third percent as a fraction

1 answer:

6 0

83 1/3% = (83 1/3)/100
 = ((3*83 + 1)/3)/100
 = (250/3)/100 
 = 250/300 
 = (5*50)/(6*50) = (5/6)*(50/50)
83 1/3% = 5/6

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Tema [17]

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8 0

2 years ago

The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

gavmur [86]

Answer:

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

$A_{circle} = \pi r^2$

$\pi r^2 = 46$

$r^2 = \dfrac{46}{\pi}$

$r = \sqrt{\dfrac{46}{\pi}}$

$r = 3.83 ~in.$

surface area of sphere

$SA = 4 \pi r^2$

$SA = 4 \times \pi \times (3.83)^2$

$SA = 184~in.^2$

7 0

3 years ago

Maggie's brother is three years younger than twice her age. The sum of their ages is 24 how old is maggie?

Vanyuwa [196]

The variable for Maggie will be M and 2x-3 be her younger brothers age (Twice her age). We then would turn this into an algebraic problem. (m+2x -3=24).

3x-3=24, we would add 3 to both sides (-3 and 24). 24 + 3 equals 27, we now have to divide -3x and 27 on both sides, which equals 9. (x=9)

6 0

3 years ago

Fill in the missing statement and reason in the proof of the Alternate Exterior Angles Theorem.

ludmilkaskok [199]

Answer:

∠EGB and ∠AGF are congruent;

Transitive Property of Equality

Step-by-step explanation:

The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other

Vertical angles are congruent i.e their measures are equal

Look at the attached graph

Given:

AB // CD

E , G , H , F are col-linear

The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD

∵ AB and EF intersected at point G

∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem

When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)

∵ AB // CD and EF is a transversal

∴ m∠AGF = m∠CHF (corresponding angles theorem)

Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal

Therefore, If a = b and b = c, then a = c

∵ m∠EGB = m∠AGF

∵ m∠AGF = m∠CHF

∴ m∠EGB = m∠CHF (transitive property theorem)

∠EGB and ∠AGF are congruent; Transitive Property of Equality