Lara found the volume of a sphere with a diameter of 10.

v = 4
3
π(103)

1. v = 4
3
π(1000)

2. v = 4000
3
πunits3

analyze lara’s work. is she correct? if not, what was her mistake?
yes, she is correct.
no, she used the diameter instead of the radius measure.
no, she should have multiplied 4 and 10 first before applying the exponent.
no, her units should be squared for volume.

No, she used the diameter instead of the radius measure.

Step-by-step explanation:

we know that

The volume of the sphere is equal to

we have

----> the radius is half the diameter

substitute

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0

the homeowners insurance cost for a 115,000 wood frame house is 80,500.

step-by-step explanation:

it is given that the coverage rate for wood frame house is 0.7.

the value of wood frame house is 115,000.

.

homeowners insurance cost for a 115,000 wood frame house is

therefore the homeowners insurance cost for a 115,000 wood frame house is 80,500.