Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with same size variable cut from each corner.
Answers
Arnold creates an open box by cutting squares of size x from each corner of a 6x6 feet cardboard sheet and folding up the flaps, resulting in a box with a base of (6 - 2x) by (6 - 2x) feet and height x feet.
Explanation:To create an open box from a 6 foot by 6 foot sheet of cardboard, Arnold needs to cut squares of equal size from each corner. To represent this action, consider a square of x feet being cut out from each corner. The new dimensions of the cardboard, once the squares are removed, will measure (6 - 2x) feet by (6 - 2x) feet, with x representing the length of each side of the square cut-outs.
When Arnold folds the flaps up to form the sides of the box, the dimensions of the base will be (6 - 2x) feet by (6 - 2x) feet, and the height of the box will be x feet. The largest size for x is 3 feet, but that would result in no base for the box at all, so x must be less than 3 feet. The volume of the box can be calculated as V = x(6 - 2x)2. To maximize the volume, Arnold could use calculus to find the maximum value for V based on x within the range of 0 to 3 feet.
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Related Questions
What is the volume of an aquarium that is 2 yards wide, 1.5 yards deep, and 1 1/3 yard long?
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I did 2 x 1.5 x 1 1/3
I made them fractions, multiplied, and then simplified
The area of a parallelogram is 60 feet the height 5 feet how long is the base
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We have to use a certain formula to find the area of a parallelogram. The formula is:
A = bh
Since we already have the area and the base of the parallelogram, we will be able to find the height!
Notice how we multiply the base by the height to find the area? Well, we'll have to do the opposite to find one of its dimensions.
What's the opposite of multiplication? Division!
Formula for base:
B = A ÷ h
Substitute:
B = 60 ÷ 5
B = 12
ANSWER:
The base is 12 feet long.
Good Day!
the solution for which of the following requires use of absolute value?
a: At a school fundraiser, students washed twenty cars for 5$ per vehicle. Each driver donated and additional $3-$5. How much money was raised.
b: A local merchant donates 10% of her sales on the first day of each month to a local cause. if her annual donations total $1500 what is her average daily sales?
c: If gas cost $3.50 per gallon, how much did Celia pay to fill her tank with 8.2 gallons?
d: Marissa ran a half marathon (about 13.1 miles) in 2 hours and 4 minutes. what was her speed?
Answers
we know that
raised money=total vehicle*[$5+absolute value($3-$5)]
raised money=20*[$5+absolute value(-2)]
raised money=20*[$7]
raised money=$140
the answer Part a) is $140
Part b)A local merchant donates 10% of her sales on the first day of each month to a local cause. if her annual donations total $1500 what is her average daily sales?
step 1
divide $1500 by 12
1500/12=$125/month
if $125 is ------------> 10%
x------------------> 100%
x=100*125/10-----> x=$1250
the answer Part b) is $1250
Part c)If gas cost $3.50 per gallon, how much did Celia pay to fill her tank with 8.2 gallons?
multiply $3.50 by 8.2 gallons
3.5*8.2=$28.7
the answer Part c) is $28.7
Part d) Marissa ran a half marathon (about 13.1 miles) in 2 hours and 4 minutes. what was her speed?
we know that
speed=distance /time
distance=13.1 miles
time=2 hours and 4 minutes----> 2+(4/60)---> 2.07 hour
time=2 hours and 4 minutes----> 2*60+(4)---> 124 minutes
speed=13.1/2.07----> 6.33 miles/hour
speed=13.1/124----> 0.106 miles/minutes
the answer part d) is 6.33 miles/hour or 0.106 miles/minutes
The solution to problem a) requires the use of absolute value
a). Minimum =$160
Maximum =$200
b). $410.96
c). $28.7
d). 0.105645161 miles per minute.
Explanation a.
For the first statements (a) there would be no absolute value. It is a range.
There are 20 vehicles, each washed at $5.
$5×20=$100
If there are 20 vehicles then there are 20 drivers.
$3×20=$60 or $5×20=#100
Total amount of money raised
(60+100) to (100+100)
Minimum =$160
Maximum =$200
Explanation b
Let x be her daily sales. There are 365 days in one year.
Donation for one day = 10% of x = 0.01x
Donation for 1 year =0.01x×365=3.65x
3.65x=1500
x=410.96
Donation for 1 day = $410.96
Explanation c.
Cost of 1 gallon = $3.50
Cost of 8.2 gallon = $3.50×8.2=$28.7
Explanation d.
Marissa runs 13.1 miles in 2 hours and 4 minutes
That is to say that she runs 13.1 miles in ((2×60)+4) minutes.
((2×60)+4)=124 minutes.
speed=distance/(time taken)
speed=13.1/124=0.105645161 miles per minute.
The price of a t-shirt is $50. If you buy 4 shirts, you will get 10% discount. How much do you have to pay if you buy 8 shirts?
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Tamara need tiles to make a border for her bathroom wall.The border will be 9 feet long and 1/3 foot wide.Each tile measures 1/3 foot by 1/3 foot.Each box of tiles contains 6 tiles.How many boxes of tiles doe Tamara need?Write two equations that can be used to solve the problem.
Answers
Answer:
e
Step-by-step explanation:
Final answer:
Tamara needs 5 boxes of tiles to complete her bathroom wall border. The calculations involve finding the total area of the border, the area covered by one tile, and then determining the total number of tiles and boxes required.
Explanation:
To determine how many boxes of tiles Tamara needs for her bathroom wall border, we first calculate the total area of the border and then divide that by the area of an individual tile. The area of the border is obtained by multiplying its length by its width. Then, knowing that each box contains 6 tiles, we calculate how many boxes she needs.
The area needed = Length of border × Width of border = 9 feet × \(1/3\) foot.Each tile covers an area = \(1/3\) foot × \(1/3\) foot.Therefore, the number of tiles needed = Total area needed / Area covered by one tile.Finally, the number of boxes needed = Number of tiles needed / 6 (since each box contains 6 tiles).First Equation
Area of border = 9 × \(1/3\) = 3 square feet.
Second Equation
Number of tiles = 3 / (\(1/3\) × \(1/3\)) = 3 / \(1/9\) = 27 tiles.
Therefore, the number of boxes needed = 27 / 6 = 4.5.
Since Tamara cannot purchase half a box, she would need to round up to 5 boxes in total to complete the border.
solve on the interval [0, 2pi) : 3 sec x -2 = 1
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3sec (x) -2 = 1
3 (1 / cos (x)) -2 = 1
3 (1 / cos (x)) = 1 + 2
3 (1 / cos (x)) = 3
(1 / cos (x)) = 3/3
cos (x) = 1
x = 2 * pi * n
on the interval [0, 2pi):
x = 0
Answer:
x = 0 on the interval [0, 2pi)
The equation 3sec (x) -2 = 1 solved on the interval is x = 0
How to solve the equation on the intervalFrom the question, we have the following parameters that can be used in our computation:
3sec (x) -2 = 1
Express sec(x) as 1/cos(x)
So, we have
3 * (1 / cos (x)) - 2 = 1
Add 2 to both sides
3 * (1 / cos (x)) = 1 + 2
Evaluate the like terms
3 (1 / cos (x)) = 3
Divide through by 3
(1 / cos (x)) = 3/3
So, we have
cos (x) = 1
Take the arc cos of both sides
x = 2nπ
On the interval [0, 2π), we have x = 0
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If two parallel lines are cute by a transversal, then pairs of corresponding angles are _____?
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In other words, the two angles are the same measure (eg: both are 30 degrees each).
simplify 2d(3) expression
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Final answer:
The expression 2d(3) is simplified by multiplying 2 by 3, yielding 6, and then by d, resulting in 6d.
Explanation:
To simplify the expression 2d(3), you simply need to multiply the variable d by the number 2 and then multiply the result by the number inside the parentheses, which is 3. This is straightforward multiplication, similar to the distributive property used in algebra to simplify expressions.
The simplified form of the expression is found by multiplying 2 by 3, giving us 6, and then multiplying that result by d. Hence, 2d(3) simplifies to 6d.
which number is greater than -24
(A) -42
(B) -27
(C) -16 (my answer **)
(D) -30
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You are correct! -16 is the right answer! Good job!
Hope this helps!
Always remember, you are a Work Of Art!
- Nicole :) <3
Therefore, your answer, -16, is correct.
q^2 + 11qr + 18t^2
x^2 - 14xy - 15y^2
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The first one cannot be factored as written. A different expression can be.
.. q^2 +11qt +18t^2 = (q^2 +9qt) +(2qt +18t^2) = q(q +9t) +2t(q +9t)
.. = (q +2t)*(q +9t)
x^2 -14xy -15y^2 = (x -15y)*(x +y) . . . . . . . -15 and 1 are factors of -15 that add to -14
Mia soccer practice started at 3:15 p.m. and ended at 4:10 p.m. how long was Mia soccer practice.
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what is 6.7086 rounded to the nearest tenth
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Decimals used to confuse me a lot! :D
When a question asks to round the decimal to the "nearest tenth", it simply means to round it to one decimal place.
6.7086 would be rounded to 6.7 if we round it to the nearest tenth. See, the 7 is in one place after the decimal point.
The best way to understand decimal places, in my opinion, is to search up a tenths, hundredths, thousandths, etc. chart. Hope this gave you a better understanding of decimal places!
Angle Q measures 30 degrees. If angle Q is rotated 15 degrees, what is the measure of angle Q'? 30 degrees 45 degrees 150 degrees 180 degrees
Answers
After rotating angle Q, which initially measures 30 degrees, by 15 degrees, the new angle Q' measures 45 degrees.
When we talk about rotating an angle, we are referring to moving the angle around its vertex through a specified measure. If we have angle Q which measures 30 degrees and we rotate it by 15 degrees, we are effectively adding 15 degrees to the original angle. Thus, the measure of angle Q' will be 30 degrees plus 15 degrees which equals 45 degrees. Rotations do not change the original angle but instead give us a new angle based on the original position plus the rotation.
Seventy-five bottles of water are randomly tested from the large inventory in a warehouse. Which term refers to the large inventory of water bottles in the warehouse? A) outlier B) parameter C) population D) sample
Answers
This figure is made up of a rectangle and parallelogram.
What is the area of this figure?
Enter your answer in the box. Do not round any side lengths.
Answers
Total Area= 51
Length=3/13
Width= /13
Area of Parallelogram= 12
This figure is made up of a rectangle BDFE and parallelogram ABCD.
The area of this figure= Area of BDFE+Area of ABCD
Area of parallelogram=base*height and Are of rectangle= length*Width
So, Area of ABCD= CD*BH
And, Area of BDFE=BD*DF
area of this figure= BD*DF+CD*BH
From the figure CD=4 and BH=3
To find BD, Let us apply Pythagorean theorem, [tex] hypotenuse^{2} =adjacent^{2}+ opposite^{2} [/tex], to ΔBHD
[tex] BD^{2} =HD^{2}+ BH^{2} [/tex]
HD=2 and BH=3
[tex] BD^{2} =2^{2}+ 3^{2} [/tex]
[tex] BD^{2} =4+ 9=13 [/tex]
[tex] BD=\sqrt{13} [/tex]
To find DF, Let us apply Pythagorean theorem, [tex] hypotenuse^{2} =adjacent^{2}+ opposite^{2} [/tex], to ΔBHD
[tex] DF^{2} =DG^{2}+ GF^{2} [/tex]
DG=6 and GF=9
[tex] DF^{2} =6^{2}+ 9^{2} [/tex]
[tex] DF^{2} =36+ 81=117 [/tex]
[tex] BD=\sqrt{117}=3\sqrt{13} [/tex]
[tex] BD=\sqrt{13} and DF=3\sqrt{13} [/tex]
area of this figure= BD*DF+CD*BH
area of this figure= [tex] \sqrt{13} [/tex]*3[tex] \sqrt{13} [/tex]+4*3
area of this figure=13*3+12
area of this figure=39+12=51
Area of this figure=51 square units
Evaluate
12P3
and
10C4
Answers
10C4 = 210
The value of the expression ¹²P₃ and ¹⁰C₄ will be 1,320 and 210, respectively.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
The value of the expression ¹²P₃ is given as,
¹²P₃ = 12! / (12 - 3)!
¹²P₃ = 12 x 11 x 10 x 9! / 9!
¹²P₃ = 1,320
The value of the expression ¹⁰C₄ is given as,
¹⁰C₄ = 10! / [(10 - 4)! x 4!]
¹⁰C₄ = 10 x 9 x 8 x 7 x 6! / (6! x 4 x 3 x 2 x 1)
¹⁰C₄ = 10 x 3 x 7
¹⁰C₄ = 210
The value of the expression ¹²P₃ and ¹⁰C₄ will be 1,320 and 210, respectively.
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Which point is the solution to the following system of equations
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Estimating square roots
Answers
Search "Square root of ANY number instantly - shortcut math." on youtube. It will teach you everything you need to know.
Write a real world problem using mixed numbers whose sum is 1 3/5
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(50/100 + 40/100 + 70/100 = 160/100 -> 1 60/100 / 20/20 = 1 3/5.)
Final answer:
Sarah has 1 1/5 cups of nuts and must add 2/5 cup of dried fruit to make a total of 1 3/5 cups of trail mix.
Explanation:
Imagine Sarah is making a trail mix for a hiking trip. She already has 1 1/5 cups of nuts and wants to add more dried fruit to reach a total of 1 3/5 cups of trail mix. To find out how much dried fruit she should add, we can set up the equation:
1 1/5 + x = 1 3/5
Converting mixed numbers to improper fractions gives us:
6/5 + x = 8/5
Subtracting 6/5 from both sides, we find that x (the amount of dried fruit to be added) is:
x = 8/5 - 6/5
x = 2/5
Therefore, Sarah needs to add 2/5 cup of dried fruit to the nuts to make 1 3/5 cups of trail mix.
Please help. Find the value of each variable. If your answer is not an integer, express it in simplest radical form.
Answers
cos 45= sin 45
cos 45=√2/2-------> equation 1
in the problem
cos 45=y/11√2----> equation 2
equate 1 and 2
√2/2=y/11√2---------> y=11√2*(√2/2)---->y=11
the legs of the triangle are
11 units
11 units
the hypotenuse
11√2
A CD usually sells for $14 if the CD is 30% off and still taxes 8% what is the total price of the CD including tax
Answers
The 0.004 will likely round up to $10.59
30% of price = 30% * $14 = 0.30 * $14 = $4.20
Sale price: $14 - $4.20 = $9.80
Tax on $9.80: 8% of $9.80 = 0.08 * $9.80 = $0.784 round to $0.78.
Add tax to sale price: $9.80 + $0.78 = $10.58
Answer: The final price is $10.58
solve for f
d=16ef^2
Answers
Here are a bunch of CORRECT answers. Your answer is in the first pic. I got number 3 wrong, but it still showed the correct answer.
-2x+6y=12 in graph ???
Answers
Hope this helps!
rewrite to y = mx + b
m is slope and b is y-intercept
-2x + 6y = 12
add 2x to both sides
6y = 2x + 12
divide both sides by 6
y = 1/3x + 2
Slope, rise 1 over 3
y-intercept at (0, 2)
View attachment
Maria invested $2000 in an account that earns 4.5% interest , compounded annually. The formula for compound interest is A(t) =P(1+l)×
How much did Maria have in the account after 5 years ?
A. $10,450.00
B. $2492.36
C. $2450.00
D. $12,819.47
Answers
Answer:
B. $2492.36
Step-by-step explanation:
We are given the formula for compound interest,
[tex]A(t)=p(1+i)^x[/tex] where p is the amount of principal, i is the interest rate and x is the number of years.
In our problem, p is 2000, i = 4.5% = 4.5/100 = 0.045, and x is 5:
[tex]A(t)=2000(1+0.045)^x\\\\A(5)=2000(1.045)^5\approx 2492.36[/tex]
Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.
What is compound interest ?Compound interest is the interest which is received on the principal and the previous interest.
Amount [tex]=P(1+\frac{R}{100})^t[/tex]
We have,
Invested principal [tex]=\$2000[/tex]
Compound interest Rate [tex]=4.5\%[/tex]
Time of investment [tex]=5[/tex] years
So,
Using the above mentioned formula;
Amount [tex]=P(1+\frac{R}{100})^t[/tex]
[tex]=2000(1+\frac{4.5}{100})^5[/tex]
[tex]=2000(1+\frac{9}{200})^5[/tex]
[tex]=2000\ *\ (\frac{209}{200})^5[/tex]
Amount [tex]=\$\ 2492.36[/tex]
So, Amount in Maria's account is [tex]\$\ 2492.36[/tex].
Hence, we can say that Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.
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Can someone help me with number 5
Answers
Area of the semicircle = pi*r^2/2 = 3.14 * 13^2 / 2 = 3.14 * 169/2 = 265.33
Total area = 676 + 265.33 = 941.33
Answer 941.33 square inches.
How do I fill this table in?what are the answers?
its to plot a graph.
plz show working!
Answers
So, instead of -2.5x -> -2.5(-6).
-2.5(-6)/6 = 15/6 = 2.5
-2.5(-3)/6 = 7.5/6 = 1.25
-2.5(0)/6 = 0/6 = 0
-2.5(3)/6 = -7.5/6 = -1.25
-2.5(6)/6 = -15/6 = -2.5
Hope this helps!
If you use your office computer 40 hours per week, and do not unplug the computer when it is not in use, how much carbon dioxide is produced from the “vampire energy” used by the computer in one year?
Answers
A laptop that is plugged up and turned off uses 0.001kw/hr of energy. Each kwh of energy produces, on average, 1.39 lbs of CO2. There are 24*7=168 hours in the week; subtract the 40 hour work week from this and we have 128 hours a week for 52 weeks a year:
0.001*128*52=6.656*1.39=9.25.
A desktop that is plugged up and turned off uses 0.004kw/hr of energy. A CRT monitor uses 0.002 kw/hr when turned off. This means we have:
(0.004*128*52*1.39)+(0.002*128*52*1.39)=55.51.
For a desktop and an LCD monitor, which uses 0.001 kw/hr of energy, we have:
(0.004*128*52*139)+(0.001*128*52*1.39)=46.26.
Final answer:
A computer that uses 4W of power during 'vampire' mode over weekends throughout a year produces approximately 4.992 kg of CO2 annually. This is calculated by multiplying the total hours in vampire mode by the power consumption and then by the CO2 emission factor for electricity.
Explanation:
To calculate the amount of carbon dioxide produced from the vampire energy used by a computer that is not unplugged, we first have to establish the power consumption while in 'vampire' mode. The power consumed by the computer's LED when it is turned off but not unplugged is stated to be about 4 watts (W).
A year has 52 weeks, and each weekend amounts to 60 hours of the computer being in 'vampire' mode. To find the total number of hours in a year this mode occurs, we multiply 60 hours by 52, which gives us 3,120 hours of energy consumption annually when the computer is in 'standby' mode.
Next, to convert the total power consumed in watts to kilowatt-hours (kWh), we divide the power in watts by 1,000 (since 1 kW = 1,000 W), and then multiply by the total hours per year.
The carbon dioxide emissions can be estimated using an average emission factor for electricity production. For example, if we assume that the emission factor is about 0.4 kilograms of CO2 per kWh (which varies based on local energy sources), we can calculate the total emissions for the computer's vampire energy consumption.
Calculations: 4 W ÷ 1,000 = 0.004 kW
0.004 kW × 3,120 hours/year = 12.48 kWh/year
12.48 kWh/year × 0.4 kg CO2/kWh = 4.992 kg CO2/year
Therefore, the computer produces approximately 4.992 kg of CO2 annually from vampire energy when not unplugged over weekends.
Please show me the work thank you
Answers
Remember: when multiplying or dividing negatives, flip the inequality sign.
3(x + 3) > 4(x - 4) Distributive Property
3x + 9 > 4x - 16 Subtract 4x from both sides
-x + 9 > -16 Subtract 9 from both sides
-x > -25 Divide by -1 to both sides and flip the sign
x < 25 Answer!
To solve this problem, first, we distribute.
3x + 9 > 4x - 16
Then, we can simplify this inequality.
9 > x - 16
0 > x - 25
x < 25
The answer is B.
Hope this helped!
On a piece of paper, use a protractor to construct a triangle with angle measures of 60° and 80°.
A triangle with angle measures of 60° and 80° is_____triangle.
Answers
Work:
180-80=100-60=40. So the triangle would be acute. Since they're all less the 90.
Solve the system by using substitution
6x+y=12
4x+6y=(-8)