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3 years ago

How many 1/3 cm by 1/3 cm by 1/3 cm cubes will fit in a 1 cm by 1 cm by 1 cm box? Explain how you know.

Mathematics

1 answer:

Tems11 [23]3 years ago

8 0

1/3^3=0.037 recurring. 1^3= 1. 1/0.37=27.027. That rounds to 27 so you can fit 27 cubes into the box.

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Jenna is at a fair with four friends. They all want to ride the roller coaster, but only three people can fit in a car. How many

pav-90 [236]

Answer:

They can make 10 different groups of three.

Step-by-step explanation:

The order in which the people are in the car is not important, so we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

How many different groups of three can the five of them make?

Combinations of 3 from a set of 5. So

$C_{5,3} = \frac{5!}{3!(5-3)!} = 10$

They can make 10 different groups of three.

6 0

2 years ago

Aiden owns a food truck that sells tacos and burritos. He sells each taco for $4.75 and each burrito for $7. Yesterday Aiden mad

nevsk [136]

Number of tacos sold is 65 and number of burritos sold is 40

<h3><u>Solution:</u></h3>

Given that Aiden sells each taco for $4.75 and each burrito for $7

Let the number of tacos sold be "t" and number of burritos sold be "b"

Given that Aiden sold 25 more tacos than burritos

t = b + 25 ---- eqn 1

Also given that yesterday Aiden made a total of $588.75 in revenue

number of tacos sold x cost of each tacos + number of burritos sold x cost of each burritos = 588.75

$t \times 4.75 + b \times 7 = 588.75$

4.75t + 7b = 588.75 ----- eqn 2

Substitute eqn 1 in eqn 2

4.75(b + 25) + 7b = 588.75

4.75b + 118.75 + 7b = 588.75

11.75b = 470

b = 40

Substitute b = 40 in eqn 1

t = 40 + 25

t = 65

Thus the number of tacos sold is 65 and number of burritos sold is 40

5 0

3 years ago

Which system of equations can be used to find the roots of the equation4x^5-12x^4+6x=5x^3-2x?

goblinko [34]

Answer:

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

Step-by-step explanation:

The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

We simply formulate two equations by splitting the left and the right hand sides of the given equation.

The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.

The roots of the given equation will be given by the points where these two equations will intersect.

The graph of these two equations is as shown in the attachment below;

The roots are thus;

x = 0 and x = 0.813

5 0

3 years ago

A right circular cone is undergoing a transformation in such a way that the radius of the cone is increasing at a rate of 1/2 in

Ivenika [448]

Answer:

The volume is decreasing at the rate of 1.396 cubic inches per minute

Step-by-step explanation:

Given

Shape: Cone

$\frac{dr}{dt} =\frac{1}{2}$ --- rate of the radius

$\frac{dh}{dt} =-\frac{1}{3}$ --- rate of the height

$r = 2$

$h = \frac{1}{3}$

Required

Determine the rate of change of the cone volume

The volume of a cone is:

$V = \frac{\pi}{3}r^2h$

Differentiate with respect to time (t)

$\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})$

Substitute values for the known variables

$\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)$

$\frac{dV}{dt} = -\frac{\pi}{3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{7*3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{21}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{88}{63}$

$\frac{dV}{dt} =-1.396in^3/min$

The volume is decreasing at the rate of 1.396 cubic inches per minute

3 0

3 years ago

Which of the following groups cannot represent the side lengths of a triangle.

Rom4ik [11]

Answer:

try B for an answer, hope it helps

7 0

2 years ago