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2 years ago

What is an expression that compares two or more numbers

1 answer:

8 0

A ratio comparing two quantities measures in different units . An equation stating that two ratios or rates are equivalent. Percent proportion . One ratio or function compares part of a quantity to the whole quantity.

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A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

2 years ago

There are 5 comedy, 8 action, and 11 children DVDs on a rack. Susan randomly selects 3 of them. What is the probability that she

ipn [44]

$|\Omega|=24\cdot23\cdot22=12144\\
|A|=5\cdot8\cdot11=440\\\\
P(A)=\dfrac{440}{12144}=\dfrac{5}{138}$

5 0

2 years ago

Use inductive reasoning to write the five square numbers that follow 25

Oduvanchick [21]

If we observe the square numbers series, we can understand a pattern:
1,4,9,16,25.
In other words, we have the following
1+3=4
4+5=9
9+7=16
16+9=25
In this pattern, we added 3,5,7 and 9 respectively to the previous number. In this way, to get the next numbers, we need to add 11,13,15,17 and 19 respectively to get the answer to previous number.
25+11=36
36+13=49
49+15=64
64+17=81
81+19=100
So, the five square numbers that follow 25 are 36, 49, 64, 81, 100.
answer
36, 49, 64, 81, 100.

6 0

2 years ago

Solve and graph each of the following inequalities for x.

Ulleksa [173]

2x + 4 > 8

Step 1: Subtract 4 from both sides.

2x + 4 − 4 > 8 − 4

2x > 4

Step 2: Divide both sides by 2.

2x/2 > 4/2

x > 2

2x − 3 < 5