Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each corner, in order to create a box with the largest possible volume?

A. 0.5 inches
B. 1 inch
C. 1.5 inches
D. 2 inches

Answers

Answer 1

1) Dimensiones of the cardboard:

length: 10 inches
width: 8 inches

2) dimensions of the squares cut

length: x
width: x

3) dimensions of the box:

length of the base = 10 - 2x
width of the base = 8 - 2x
height = x

4) Volume of the box

V = (10 - 2x) (8 - 2x) x = x [80 - 20x - 16x + 4x^2] = x [ 80 - 36x + 4x^2 ] =

V = 80x - 36x^2 + 4x^3

5) Maximum volume => derivative of V, V' = 0

V' = 80 - 72x + 12x^2 = 0

6) Solve the equation

Divide by 4 => 3x^2 - 18x + 20 = 0

Use the quadratic formula: x = 1.47 and x = 4.53 (this is not valid)

So, the answer is the option C. 1.5 inches.

Related Questions

Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a fl at fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission. a. What were Taylor's net proceeds?

Answers

Final answer:

Taylor's net proceeds from the stock transaction are $525, after accounting for the initial purchase cost and broker's commissions on both the buying and selling of the stock.

Explanation:

Taylor bought 200 shares of stock at $18.12 per share and paid a flat brokerage fee of $30. To find the initial cost, we multiply the number of shares by the purchase price and then add the fee:

200 shares × $18.12/share + $30 = $3,654

When Taylor sold his shares at $21 per share, his gross proceeds were:

200 shares × $21/share = $4,200

The broker commission of 0.5% on the selling price is calculated as:

$4,200 × 0.005 = $21

To find Taylor's net proceeds, we subtract both the initial cost and the selling commission from the gross proceeds:

$4,200 - $3,654 - $21 = $525

Therefore, Taylor's net proceeds from the stock transaction are $525.

A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?

Answers

if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)

45000 * 3/8 = 135000/8 = 16,875 seats are still available

Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar. Hint: Use the formula, f(x) = P(1 + r)x. (5 points)

Answers

Hello! I can help you with this!

a. The function that would best represent Samantha's account is f(5) = 500(1 + 0.04)^5. This is because $500 is the principal, the interest rate is 4%, and we're looking for the amount in the savings account 5 years later.

b. Okay. 1 = 0.04 is 1.04. 1.04^5 is 1.216652902. It's a long decimal, but don't delete it. Multiply that decimal by 500 and you get 608.32645 and other numbers behind it or 608 when rounded to the nearest dollar. Samantha will have about $608 in her savings account in 5 years.

Note: The formula goes like this: f(x) = P(1 + r)^x. This means, you add 1 and the simple interest rate in decimal form together and raise that up by the exponent. There is no shortcuts for this, so you'll have to use the calculator. There will be a very long decimal, but don't clear it. Instead, multiply it by the principal to get the answer. It seems very complicating, but if you do this right, it gets easier overtime and you'll make less errors. There are more complex problems out there, so this formula is very important, but it was kept simple for this question.

Answer: The answer is y = 500(1.04) x

Step-by-step explanation: The formula is y = P (1 + r) x

So, given that P which is the initial value 500(1+0.4) x

f(x)=500(1.04) x

Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work

Answers

The question is written oddly...If you mean she has 1/2 a gallon left then she has 64 oz left so she has 6.4 10 oz servings left... 64 divided by 10=6.4

Baruka has [tex]$ \frac{32}{64} $[/tex] gallons left. [tex]$ \frac{32}{5} $ servings of $ \frac{5}{64} $[/tex] gallons; she has 6 servings.

To find out how many [tex]$ \frac{5}{64} $[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]$ \frac{5}{64} $[/tex] gallons.

Since [tex]$ 1 $[/tex] gallon is equivalent to [tex]$ \frac{64}{64} $[/tex] gallons, and she has [tex]$ \frac{1}{2} $[/tex] gallon left, she has [tex]$ \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} $[/tex] gallons left.

Now, we can find out how many [tex]$ \frac{5}{64} $[/tex] gallon servings are in [tex]$ \frac{32}{64} $[/tex] gallons:

[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]

Now, we divide [tex]$ 32 $ by $ 5 $[/tex] to find the number of servings:

[tex]\[ \frac{32}{5} = 6.4 \][/tex]

So, Baruka has [tex]$ 6.4 $[/tex] servings of [tex]$ \frac{5}{64} $[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]$ 6 $[/tex] servings left.

James has 875 feet of rope. There are 13 teams of hikers. If James gives an equal amount of rope to each team how much rope will each team receive

Answers

67.307 feet of rope per team

Answer:

67.307 feet of rope per team

Step-by-step explanation:

A car travels down a highway at 45 m/s. An observer stands 200 m from the highway.

How fast is the distance from the observer to the car increasing when the car passes in front of the observer?

How fast is the distance increasing 40 s later?

Answers

check the picture below.

so, the left-side is when the car is right in front of the observer, at that point, notice the y-distance, is pancaked, so is 0, but increasing, we know dy/dt is 45 m/s, and notice the "r" distance, is the same as the "x" distance, keeping in mind that whilst "r" is increasing or moving about, "x" is static, is a constant.

[tex]\bf \stackrel{\textit{pythagorean theorem}}{r^2=x^2+y^2}\implies 2r\cfrac{dr}{dt}=\stackrel{constant}{0}+2y\cfrac{dy}{dt} \\\\\\ 2r\cfrac{dr}{dt}=0+2(0)(45)\implies \cfrac{dr}{dt}=0[/tex]

now, 40 seconds later, since the car is going at 45 m/s, in 40 seconds it has covered 40 * 45 meters, or 1800, so y = 1800, x = 200, what is "r"?

[tex]\bf r^2=x^2+y^2\implies r=\sqrt{200^2+1800^2}\implies r=\sqrt{3280000} \\\\\\ r=\sqrt{200^2\cdot 82}\implies r=200\sqrt{82}\\\\ -------------------------------\\\\ 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad \begin{cases} r=200\sqrt{82}\\ y=1800\\ \frac{dy}{dt}=45 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{1800\cdot 45}{200\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405}{\sqrt{82}}\implies \cfrac{dr}{dt}=\cfrac{405\sqrt{82}}{82}[/tex]

The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick whats the inside diameter

Answers

Sent the solution on the pic.

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current

Answers

What goes in goes out. This means none of the current is lost. So if 0.7amps+0.68amps+0.47amps = 1.85 amps comes in, then 1.85 amps goes out. So far we have 0.8 amps+0.55 amps going out= 1.35 amps. This means we need an additional 1.85-1.35amps going out= 0.5 amps for the third outgoing current. Cheers!

The measure of the third outgoing current will be 0.5 amperes.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.

Then the measure of the third outgoing current will be

We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.

Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have

I₁ + I₂ + I₃ = I₄ + I₅ + I₆

0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆

1.85 = 1.35 + I₆

I₆ = 0.5

Thus, the measure of the third outgoing current will be 0.5 amperes.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ5

What is the simplified form of the expression k^3(K^7/5)^-5

Answers

[tex]\bf k^3\left( \cfrac{k^7}{5} \right)^{-5}\implies k^3\left( \cfrac{5}{k^7} \right)^5\implies k^3\left( \cfrac{5^5}{k^{7\cdot 5}} \right)\implies k^3\cdot \cfrac{5^5}{k^{35}} \\\\\\ k^3\cdot 5^5\cdot k^{-35}\implies 5^5\cdot k^{3-35}\implies 5^5k^{-32}\implies \cfrac{5^5}{k^{32}}\implies \cfrac{3125}{k^{32}}[/tex]

please help im really dumb lol

Answers

Haha I do K12 WAVA too! Sorry, I'm not 100% sure of the answer, though. :)

draw or write to explain why 1 hundred 4 tens and 14 tens name the same amount

Answers

1 hundred=100
4 tens=40
14 tens= 140

When we add them all we get 280 ones or 2.8 hundreds or 28 tens.

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 9, [0, 2]

Answers

[tex] \frac{f(2)-f(1)}{2-1}= \frac{2^3+2-9-(1^3+1-9)}{1}=8+2-9-1-1+9=8 \\ derivative of f(x) =3x^2+1,3x^2+1=8,3x^2=7,x= \sqrt \frac{7}{3} [/tex]
which supports the mean value theorem, you want even better news
if the function is a polynomial it will always follow the mean value theorem

Let n be a natural number such that the remainder of the division of 4294 by n is 10, and the remainder of the division of 3521 by n is 11. what is n?

Answers

4294 - 10 = 4284 and 3521 - 11 = 3510. The common factors of 4284 and 3510 are 18, 9, 6, 3, and 2. The problems that work are 18 because only with 18 do the remainders work out. Therefore n = 18

Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla

Answers

four ounces out of 12 ounces would be 4/12, or simplified form that would be 1/3, and the rest is 8/12, or 2/3.

Answer:

In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...

hope it helps

What percentage is 1022.40 of 1420 and how do i solve

Answers

Divide 1022.40 by 1420. oh and also × 100

mrs. ellis wants to tile a rectangular room that is 16 feet long and 12 feet wide with square tiles. each square floor is 2 feet. the tiles cost $0.84 per tile. what is the cost to tile the room not including labor?

Answers

The room has 16*12= 192 feet

192:2=96 tiles need Mrs Ellis

96*0,84 $=80,64 $ is the cost

Final answer:

Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.

Explanation:

To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.

Learn more about Floor Tiling here:

https://brainly.com/question/351323

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simplify the fraction 48 over 75

Answers

48/75
Reduce by 3
16/25

48/75

both numbers are divisible by 3

so it simplifies to 16/25

Which rows represent when (p ∧ q) ∨ (p ∧ r) is true?\

Answers

the statement is ambiguous, it must be written as (p ∧ q) ∨ r
or p ∧ (q ∨ r).

Answer:

The answer is B. A, B, and C

Step-by-step explanation:

Just took the test on edg

Find a basis for the row space and column space of a matrix and the rank .

Answers

......................

Final answer:

To identify a basis for the row and column spaces of a matrix and determine its rank, one uses row reduction to reach REF or RREF. The non-zero rows of the RREF are the basis for the row space, the corresponding columns in the original matrix form the basis for the column space, and the rank is the number of these basis vectors. In statistics, the degrees of freedom for the Test of Independence is calculated as (number of columns - 1)(number of rows - 1).

Explanation:

To find a basis for the row space and column space of a matrix as well as the rank, you follow specific procedures. First, perform row reduction on the matrix to bring it to row echelon form (REF) or reduced row echelon form (RREF). The non-zero rows of the RREF correspond to a basis for the row space. The columns in the original matrix that correspond to the leading 1s in the RREF form a basis for the column space. The rank of the matrix is equal to the number of leading 1s in the RREF form, which is also the number of basis vectors for either the row space or column space since they have the same dimension.

The Test of Independence in statistics uses a contingency table to determine if two categorical variables are independent. The number of degrees of freedom for the test is given by the formula: (number of columns - 1)(number of rows - 1). This is critical when referencing the chi-squared distribution table to determine the p-value for the hypothesis test.

If p(a) = 0.62, p(b) = 0.47, and p(a or
b.= 0.88, then p(a and
b.= _____

Answers

use the identity:
P(A or B)=P(A)+P(B)-P(A and B)
Substitute given values,
0.88=0.62+0.47-P(A and B)
=>
P(A and B)=0.62+0.47-0.88=0.21

Probabilities are used to determine the chances of an event

The value of P(a and b) is 0.21

The given parameters are:

P(a) = 0.62

P(b) = 0.47

P(a or b) = 0.88

P(a and b) is calculated using the following formula

P(a and b) = P(a) + P(b) - P(a or b)

So, we have:

P(a and b) = 0.62 + 0.47 - 0.88

P(a and b) = 0.21

Hence, the value of P(a and b) is 0.21

Answers

yes, is subtraction, to get their "difference".

first off, let's convert the mixed fractions, to "improper", and then subtract.

[tex]\bf \stackrel{red~yarn}{9\frac{1}{5}}-\stackrel{blue~yarn}{3\frac{11}{25}}[/tex]

[tex]\bf -------------------------------\\\\ \stackrel{mixed}{9\frac{1}{5}}\implies \cfrac{9\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{46}{5}} \\\\\\ \stackrel{mixed}{3\frac{11}{25}}\implies \cfrac{3\cdot 25+11}{25}\implies \stackrel{improper}{\cfrac{86}{25}}\\\\ -------------------------------\\\\ \cfrac{46}{5}-\cfrac{86}{25}\impliedby \textit{our LCD is 25}\implies \cfrac{(5\cdot 46)~~-~~(1\cdot 86)}{25} \\\\\\ \cfrac{230~-~86}{25}\implies \cfrac{144}{25}\implies 5\frac{19}{25}[/tex]

Use the inequality -4t - 8 ≤ 12 to fill in the missing numbers.

a) t ≥ ?
b) t + 4 ≥ ?
c) t - ? ≥ 0
d) t + 10 ≥ ?
e) 3t ≥ ?
f) t/? ≥ -5

Answers

Attached the solution and work. For b,c,d,e,f, I solved by knowing that what you do to one side you do to the other. I showed all the work for you to see.

60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?

Answers

The concept of answer this item is the man-days equation. This means that the man-days of the original plan should be equal to that of the real activity. From the given,

(60)(16) = (5)(60) + (11 + x)(60 - 5)

where x is the number of extra days that the bricklayers will still have to work to complete the job. The value of x from the equation is 1

Answer: 1

you have a standard deck of 52 cards. you pick one card from the deck and then , without putting the first card back , pick a second card . what is the probability that both cards will be 9s??

Answers

there are 4 9's in a deck

so first pick = 4/52 reduces to 1/13

second pick there would be 3 9's left and 51 cards so it would be 3/51 reduces to 1/17

probability of both happening = 1/13 * 1/17 = 1/221 (fraction form)

if you need it in decimal it = 1/221 = 0.00452, rounded to 0.005

you work for a dress maker and your boss sends you to the fabric store to buy blue fabric she tells you to buy the best deal what's is the best deal

20 yards for $30.00
40 yards for $45.00
50 yards for $70.00
65 yards for $85.00

Answers

Given 20 yards for $30.00, unit rate = $30 / 20 yards = $1.5 per yard

Given 40 yards for $45.00, unit rate = $45 / 40 yards = $1.13 per yard

Given 50 yards for $70.00, unit rate = $70 / 50 yards = $1.4 per yard

Given 65 yards for $85.00, unit rate = $85 / 65 yards = $1.31 per yard

The best deal is the cheapest rate which is 40 yard for $45.00

find factors of 5x^3+10x^2+35x

Answers

Hello!

First, let’s take a look at our terms.

5x^3 + 10x^2 + 35x

All of our terms have an x, so we can factor out this expression/trinomial with our variable. Now, let’s find the GCF (Greatest Common Factor) for our coefficients (or our numbers).

5x^3 + 10x^2 + 35x
Each of these have a factor of 5, so divide each term by 5x (since all our terms have an ‘x’). While we do this, write our GCF outside of a parenthesis and divide our terms by the GCF. The quotient will be inside of our parenthesis.

5x^3 + 10x^2 + 35x

5x(x^2 + 2x + 7)

The terms inside of the parenthesis are our simplified factors; x^2 + 2x + 7.

I hope this helps!

Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8

Answers

No he would get back $4.56. Start with $20 -13.59-1.85=4.56

Mr. Yu applies 1/2 ounce of fertilizer to every 5/8 square meter of his lawn. How many ounces of fertilizer does Mr. Yu use per square meter for his lawn? Enter your answer in the box as a fraction in simplest form.

Answers

Divide both by 5/8 because 5/8 divide by 5/8 =1
(1/2)/(5/8)
1/2*8/5
8/10
4/5

Answer:

[tex]\frac{4}{5} [/tex] ounce

Step-by-step explanation:

We can use rule of three to answer this problem.

The data we have is the following:

fertilizer (ounces) area(m^2)

1/2 ⇒ 5/8

x ⇒ 1

the x represents the unknown quantity of fertilizer that is used in one square meter.

Now we multiply the cross quantities and divide by the remaining value.

[tex]x=\frac{1}{2}*1[/tex] ÷ [tex]\frac{5}{8}[/tex]

[tex]x=\frac{1*8}{2*5} =\frac{8}{10} =\frac{4}{5}[/tex]

He will use 4/5 ounces of fertilizer per square meter.

a light bulb consumes 3600 Watts hours per day. how long does it take to consume 12600 Watts hours?

Answers

3.5
because 12600 divided by 3600 is 3.5

it would take 84 hours,or 3.5 days,hope this helps

forty more than twice malia's age is 64

Answers

To solve this multiply 64 times 2 to get 128. Next, add 40 and you will get 168 as your answer.

You subtract 40 from 64 and get 24. Divide 24 by 2 and your answer is 12.

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