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3 years ago

How many cubic inches of storage space are in Leo’s cabinet ? Please help :)

Mathematics

1 answer:

Paha777 [63]3 years ago

4 0

Answer:

the amount of space present is 15,120 cubic inches

Step-by-step explanation:

To get the amount of space, we simply calculate the volume of the space

This is the area of the base multiplied by the length

Mathematically, we have this as;

Area of the triangle multiplied by the length of the cabinet

We have this as;

(1/2 * 20 * 21) * 72

= 210 * 72

= 15,120 cubic inches

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

erma4kov [3.2K]

Answer:

$\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

Step-by-step explanation:

Given

5 tuples implies that:

$n = 5$

$(h,i,j,k,m)$ implies that:

$r = 5$

Required

How many 5-tuples of integers $(h, i, j, k,m)$ are there such that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

$^{n}C_r => ^{n + 4}C_5$

$^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}$

$^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}$

Expand the numerator

$^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

<u><em>Solved</em></u>

6 0

2 years ago

What is the area of a rectangle with side lenghts 3x+2 and x-4

melamori03 [73]

For a rectangle, A = LW.

A = (3x + 2)(x - 4)

A = 3x^2 - 12x + 2x - 8

A = 3x^2 -10x - 8

6 0

3 years ago

Need help with a,b,c! D: helpzzz

nlexa [21]

A: 11ft B: 45 C: 556

3 0

2 years ago

*GEOMETRY*please help me find the surface area of the solid along with the volume of it step by step!

Serjik [45]

Surface area of the solid = 7.1781 in²

Volume of the solid = 0.804 in³

Explanation:

Surface area of the solid = surface area of the square prism - 2(base of the cylinder) + lateral surface of cylinder

surface area of a square prism = 2(lw + lh + wh)

l = length = 1 in

w = length = 1 in

h = height = 1 in

$\begin{gathered} \text{Surface area = 2(1}\times1\text{ + 1}\times1\text{ + 1}\times1) \\ \text{Surface area = 2(1 + 1 + 1) = 2(3)} \\ \text{Surface area = 6 in }^2 \end{gathered}$

using the value π as it is on the calculator

Base area of a cylinder = πr²

2(Base area of cylinder) = 2πr² = 2π(0.25)² = 0.3927

Lateral surface area = 2πrh = 2π(0.25)(1) = 1.5708

Surface area of the solid = 6 - 0.3927 + 1.5708

Surface area of the solid = 7.178 in²

Volume of the solid = Volume of the square prism - volume of the cylinder

Volume of square prism = length × width × height

length = 1 in, width = 1 in, height = 1 in

Volume of the solid = 1 in × 1 in × 1 in = 1 in³

Volume of a cylinder = πr²h

Volume of the cylinder = π × 0.25 × 0.25 × 1 = 0.196

Volume of the solid = 1 - 0.196

Volume of the solid = 0.804 in³

4 0

1 year ago

Which function has a minimum of -4?

icang [17]

I think it is c but I’m not sure

7 0

11 months ago