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2 years ago

A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.

1 answer:

8 0

The hemisphere is half the volume of a sphere. Since we are given the circumference, we can solve for the radius of the sphere. That is
$C=2\pi r$

$116\:cm=2\pi r$

$r=\frac{116}{2\pi }=18.462\:cm$

Part A
We can now compute for the volume of the hemisphere.
$V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3$

Part B
We just need to convert the volume into its corresponding gallons
$13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons$

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What is the greatest common factor of 16x4y3 and 12x2y7?

Marta_Voda [28]

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two expression

1. List the prime factors of each number.

2. Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

16x^4y^3 = ( 4*4)(x*x*x*x)(y*y*y)

12x^2y^7 = (4*3)(x*x)(y*y*y*y*y*y*y)

So common to them is 4x^2y^3

4 0

2 years ago

Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for $25 off his entire purchase at checkout

KATRIN_1 [288]

Answer:

$60 per ticket

Step-by-step explanation:

$215 is what it costs after the discount, so add the amount taken off, back on.

215+25

240

Then, divide by 4 to find the cost of each individual ticket.

240/4

Hope it helps!

6 0

2 years ago

(-2x²y)³ / (xy²z)² * (-yz)² Hello guys, im having trouble with this babe...

Masja [62]

$\frac{(-2x^2y)^3}{(xy^2z)^2(-yz)^2}$

On top: (-2)³ = -2 × -2 × -2 = -8
(x²)³ = x^6 (the exponents multiply)
and of course, (y)³ = y³

On the bottom: (xy²z)² = x² y^4 z²
(-yz)² = y²z²
Multiplying these together, the exponents add and we get x² y^6 z^4.

$\frac{-8x^6y^3}{x^2y^6z^4}$

So, your reasoning is correct for what you have so far.

Your next step would be cancelling shared factors from the top and bottom.
Just like with regular fractions, if the numerator and denominator are divisible by the same number, you can divide them by it to simplify. (ex: 4/6 = 2/3)

Well, x^6 and x^2 are both divisible by x^2, right?
We can also cancel the y^3.

It might help to visualise the factors like this:

$\frac{-8xxxxxxyyy}{xxyyyyyyzzzz}$

Once you've cancelled out x² and y³ from each, you're left with

$\boxed{\frac{-8x^4}{y^3z^4}}$

7 0

2 years ago

Susan charges $8 per hour walking her neighbor’s dog. She charges $12 per hour babysitting. Part A: Define the variables. Part B

IgorC [24]

Answer:

Part A: The variables are the amount charged per hour dog walking and the amount charged per hour babysitting.

Part B: y=8d+12b

Step-by-step explanation:

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2 years ago

1 2 3 4 5 6 7 8 9 10 David has $90 to spend on sneakers. The sales tax in his state is 6%. Vincent has $95 to spend on sneakers.

Alika [10]

Answer:

Step-by-step explanation:

vincent will be able to buy the shoes

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2 years ago