How would finding the least common multiple help you when you divide items into equal groups?

Lance bought 12 quarts of lemonade so that everyone who came to his party could have exactly 1/3 quart. How many people did Lanc

igor_vitrenko [27]

Lance invited 36 people to his party.

Step-by-step explanation:

It is given that,

Lance bought 12 quarts of lemonade.
Everyone who came to his party could have exactly 1/3 quart.

We know that,

The total quarts of lemonade available for the party = 12

Each person in the party consumes = 1/3 quart.

We need to find out how many people did Lance invited to his party.

To find the number of people :

Let us consider 'x' be the number of people invited to the party.

Total lemonade = number of people × lemonade for each person.

⇒ 12 = x × 1/3

⇒ 12×3 = x

⇒ x = 36 people

Therefore, Lance invited 36 people to his party.

6 0

3 years ago

Help?. . What is the equation of the function y=5/x translated 4 units to the left and 3 units up?. . I don't even know where to

Dahasolnce [82]

Y = 5/x
If you want to shift the function 4 units left, you can add 4 to the x-value in the parent function:
y = 5 / ( x + 4 )
After that, you can add 3 to your function to shift it up 3 units.
y = 5 /( x + 4 ) + 3 ( the final equation )

4 0

3 years ago

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a

belka [17]

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s

4 0

4 years ago

Read 2 more answers

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answ

kondor19780726 [428]

Answer:

One by third

Step-by-step explanation:

According to the figure the right angle triangle that was on left would be 3 times bigger than the right triangle that was on right. So here the dimension of the right triangle is one by third and equivalent to the dimension of the left triangle

the one on the left is 3 times larger than the one on the right. in other words, the right triangle's dimensions times 1/3 is equal to the left triangle's dimensions.

6 0

3 years ago

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneou

artcher [175]

Answer:

Solid Sphere

Step-by-step explanation:

According to the question, the three shapes have equal masses (m), radii (R) (and diameter).

The shape with the least mass moment of inertia will have the highest acceleration

Let IC represents Inertia

According to calculations, the inertia of

Solid Sphere: IC=(2/5)mR²

Solid Cylinder: IC=½mR²

Hollow Pipe: IC=⅔mR²

Where m = mass of the shape

And R is the Radius of the shape

By comparison, the solid sphere has the least mass of inertia and hollow Pipe has the most mass of inertia.

So, solid sphere will get to the bottom first.

3 0

4 years ago