1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
STatiana [176]
3 years ago
15

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the

flaps are folded upward to form an open box. If the volume of the box is 2706 incubed​, what were the original dimensions of the piece of​ metal?

Mathematics
1 answer:
Alexandra [31]3 years ago
7 0

Answer:

length=53 in

width= 23 in

Step-by-step explanation:

First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:

h=6 in\\w=x-12\\l=x+30-12\\l=x+18\\\\V: volume of the box\\V=6*(x-12)*(x+18)\\2706=6x^{2}+36x-1296\\0=6x^{2}+36x-4002\\\\

We factorize the 6 and we get:

0=x^{2}+6x-667\\

Finally we solve for x, and we get the initial dimensions of the piece of metal:

x=23l=30+x=30+23=53 in\\w=x= 23 in

You might be interested in
In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a go
jolli1 [7]

Answer:

( a ) 463 " human resource professionals " believe that the appearance of a job applicant is most important for a good first impression

( b )  Percent wise the confidence interval should be from about 86.6% to 93.4%

Step-by-step explanation:

I believe these first two parts here is sufficient enough to get you started!

" In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Part A: Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression?

Part B: Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. "

_____

( a ) We are given that n = 514, and p = 90%. The number of human resource professionals that said that the appearance of a job applicant is most important for a good first impression, should be the following -

514 x \frac{90}{100}

= \frac{46260}{100}

= 462.6

As the count of people can't be expressed as a fraction, the solution should be about 463 " human resource professionals. "

_____

( b ) Here the confidence level is 0.99 percent. Knowing that -

1 - ∝ = 0.99,

∝ = 1 - 0.99... = 0.01

Therefore, a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression should be calculated as directed in the attachment. By that the interval ranges as such -

0.8659 < p < 0.9341

And percent wise the confidence interval should be from about 86.6% to 93.4%

8 0
3 years ago
How can you use estimation to find<br> 92 +91 +92 +91 +9?
Over [174]

Answer:

370

Step-by-step explanation:

Round each answer into easier to add numbers. 92 and 91 round down to 90. 9 rounds up to 10.

5 0
2 years ago
Read 2 more answers
how to Evaluate the expression, given functions f and g: f(x) = 3x - 2, g(x) = 7 – x^2. 3f(1) – 2g(-2)​
omeli [17]
3x that answers end of the yearrr
8 0
2 years ago
Which of the following functions represents a cell phone bill if there is a monthly charge of 20 dollars plus 6 cents for each m
pychu [463]

Answer:

f(x)=20+0.06x

Step-by-step explanation:

3 0
3 years ago
A tortoise is walking in the desert. It walks for 62.5 meters at a speed of 5 meters per minute.for how many minutes does it wal
iren2701 [21]

divide 62.5 by 5

62.5/5 = 12.5 minutes

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the interest is you invest $3500 for 9 years at a rate of 4.5%
    15·1 answer
  • a running tap dispenses 0.15 gallons of water every second. how many pints of water is dispensed after 20 seconds?
    15·2 answers
  • I need to understand proofs
    11·1 answer
  • How many 12-inch rulers will be about the same length as a sheet of paper
    6·2 answers
  • Write five diffrent fractions that each simplify to two-fifths
    9·2 answers
  • Helppppppppppppp 20 points
    15·2 answers
  • Plz help ya girl out :)<br> This is alotta points on both ends so u best not waste them
    5·2 answers
  • Cuantos vertices caras y aristas tiene el prisma pentagonal​
    14·2 answers
  • If sinA=a_1/a+1 find value of tanA​
    6·1 answer
  • The value of an investment portfolio decreased by 8 % in 2010. In 2011, its value increased by 5% of
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!