The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.
How to solve the dimension?
Let x be the side of the square to remove. Then the volume of the box is:
V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³
To find the maximum volume, differentiate and set it to 0:
V'(x) = 324 - 144x + 12x²
0 = x² - 12x + 27
0 = (x - 9)(x - 3)
x = 3 or 9
When x = 3,
V"(x) =-144+24x
V"(3) =-144+72=-72<0
so volume is maximum at x=3
Therefore the box is 12x12x3 and the volume is 432.
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ents
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard
model requires 4 hours to assemble and 2 hours for finishing touches. The artisan model requires 2
hours to assemble and 2 hours for finishing touches. Based on their current staffing, they can
manage a maximum number of assembly hours available is 48 per day, and the maximum number
of finishing hours available is 44 per day.
Let x = the number of standard model bookcases produced per day and y = the number of artisan
model bookcases produced per day.
Write the system of inequalities that represents the maximum number of bookcases that can be
produced in one day.
Answer:
48 ≥ 4x + 2y
44 ≥ 2x + 2y
First, we will look at assembling hours.
"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"
We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.
48 = 4x + 2y
Lastly, they do not need to make that many, but they can so we will use greater than or equal to.
48 ≥ 4x + 2y
Now let us look at finishing hours.
"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."
We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.
44 = 2x + 2y
Again, they do not need to make that many, but they can so we will use greater than or equal to.
44 ≥ 2x + 2y
what is the total interest accured for a loan of $3200 at 6.1% interest
Answer:
6.1÷100×3200
press that you will get your answer
Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?
A. 95
B. 98
C. 80
D. 85
Answer: 98
To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
What is math average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics.
When calculating the average for a set of data, we first sum up all the values and divide the result by the total number of values.
Average = (sum of values) / (number of values)
The total of Laurence's marks on the first four biology exams can be calculated using the following formula
Sum of scores = 87 + 80 + 75 + 85
= 327
We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Next score = (sum of all five scores) - (sum of first four scores)
= (85 x 5) - 327
= 25
Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
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the circumference of the hub cap of a tire is 79.38 cm. Find the area of this hub cap. use 3.14 for pi
Answer:
ans 19785.719
Step-by-step explanation:
formula πr^2
Identify a set of parallel lines
Answer:
D
Step-by-step explanation:
Since EF is perpendicular to both AB and CD, that makes AB and CD parallel.
Answer: D
(WHO WANTS BRAINLIEST! :D)
Sitting in your sailboat looking at the horizon, you see a lighthouse 500 feet away. Looking up at a 20 degrees, you see the light at the top of the lighthouse. How far off the ground is the light in the lighthouse? Round your answer to the nearest tenth.
Answer:
182.0
Step-by-step explanation:
500 tan20
=181.98
=182.0(to nearest tenth)
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Answer:
1 pound of peanuts cost 3 dollars
1 pound of wallnuts costs 2 dollars
Step-by-step explanation:
24/6=4
12/6=2
Old-fashioned oatmeal contains 27 grams of carbohydrates per 1/2 cup of dry oats. How many grams of carbohydrates are available in 2 1/4 cups of dry oats?
There 121.50 grams of carbohydrates are available in 2 1/4 cups of dry oats.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have been given that old-fashioned oatmeal contains 27 grams of carbohydrates per 1/2 cup of dry oats.
We have to determine the number of grams of carbohydrates available in 2 1/4 cups of dry oats.
Let x grams of carbohydrates be available in 2 1/4 cups of dry oats.
As per the given information, we can write the ratio would be as:
27 grams of carbohydrates : 1/2 cup of dry oats = x grams of carbohydrates : 2 1/4 cup of dry oats
⇒ 27/ (1/2) = x/(2 1/4)
⇒ 27/ (1/2) = x/(9/4)
Reciprocal the term in the numerator,
⇒ 27 × 2 = x × 4/9
Apply the cross-multiplication operation,
⇒ x = 54 × 9/4
⇒ x = 121.50
Thus, there are 121.50 grams of carbohydrates are available in 2 1/4 cups of dry oats.
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Find the quotient of 3/5 and 2/3
Give your answer as a fraction in its simplest form.
Help plssssssssssssssssssss I NEED THIS TODAY!! PLS
Answer:
The first 1 is the answer (a)
Step-by-step explanation:
PLEASE HELP ASAP DUE TOMORROW
The area of the shaded part of the given figure is 60 square inches'
How to calculate the area of a composite shape.The given figure is made up of a rectangle and 2 similar triangles
Area of the shaded part = Area of rectangle + area of 2 triangles
From the figure
Area of rectangle = 12 * 4 = 48 square in
Area of one triangle = 0.5(6)(4) = 12 square in
Area of the figure = 48 + 12
Area of the figure = 60 square inches'
Hence the area of the shaded part is 60 square inches.
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Write an equation of the line in slope-intercept form.
y =
Find 1 2/5 divided 2 1/3
Answer:
3/5
Step-by-step explanation:
7/5 / 7/3 = 3/5
Answer:
3/5
Step-by-step explanation:
First we make both fractions into improper fractions/top-heavy fractions:
1 2/5 = 7/5
2 1/3 = 7/3
Now we use the rule of KFC (keep flip change):
Keep the first fraction:
7/5
Change the sign to opposite:
÷ → ×
Flip the second fraction:
7/3 → 3/7
Now we multiply the fractions:
7/5× 3/7 = 7×3/5×7 =
21/35
Now we simplify this fraction to simplest terms:
Both the numerator and denominator can be divided by 7 :
3/5
So this is our final answer
Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answer:
[tex]D)\frac{1}{m^{18} }[/tex]
Step-by-step explanation:
Multiply [tex]m^{-1}[/tex] by [tex]m^{5}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](\frac{m^{-1+5} }{m^{-2} } )^{-3} \\[/tex]
Add -1 and 5.
[tex](\frac{m^{4} }{m^{-2} } )^{-3}[/tex]
Move [tex]m^{-2}[/tex] to the numerator using the negative exponent rule [tex]\frac{1}{b^{-n} } =b^{n}[/tex].
[tex](m^{4} m^{2} )[/tex]
Multiply [tex]m^{4}[/tex] by [tex]m^{2}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](m^{4+2} )^{-3}[/tex]
Add 4 and 2.
[tex](m^{6} )^{-3}[/tex]
Multiply the exponents in [tex](m^6)^{-3}[/tex]
Apply the rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
[tex]m^{6*-3}[/tex]
Multiply 6 by -3.
[tex]m^{-18}[/tex]
Rewrite the expression using the negative exponent rule [tex]b^{-n} =\frac{1}{b^{n} }[/tex].
[tex]\frac{1}{m^{18} }[/tex]
Evaluate the triple integral
Answer:
Wow thats hard
Step-by-step explanation:
though luck
PLEASE HELP ME WILL FOLLOW AND GIVE BRAINLIST!!! ASAP
Answer:
1/10 of the members
Step-by-step explanation:
first, see how much is between [tex]2\frac{1}{4}[/tex] and [tex]3[/tex]. you can only see one. then count the number of x's, that's the number of members, and your denominator.
Please somebody help me. I’m begging.
Answer:
d=1
Step-by-step explanation:
d=2*r
r=(1/2)
d=2*(1/2)=1
5x-2y=42
-3x+2y=-26
which of the following shows the results of the two equation added together?
Answer:
Step-by-step explanation:
When we add the two equaions, y will be cancelled becaue -2y + 2y = 0.
Thus we can find the value of x.
5x - 2y = 42 -----------(I)
-3x + 2y = -26 {Now add}
2x = 16
x = 16/2
x = 8
could i have some quick help factoring trinomials?
Solution 1
6x² + 34x -126x² + 36x -2x -126x(x+6)-2(x+6)(6x-2)(x+6)Solution 2
48c²-160c+10012c² - 40c + 2512c² - 30c -10c + 256c(2c-5) -5(2c-5)(6c-5)(2c-5)Solution 3
-6x-51xy+27xy²3x(-2-17y+9y²)3x(-2-18y+y+9y²)3x(-2(1+9y)+y(1+9y))3x(9y+1)(y-2)#1
6x²+34x-126x²+36x-2x-126x(x+6)-2(x+6)(x+6)(6x-2)#2
48c²-160c+100Cancel by 4
12c²-40c+2512c²-30c-10c+25(2c-5)(6c-5)#3
-6x-51xy+27xy²3x(-2x-17y+9y²)What is the Area of the circle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Area of circle :
[tex]\qquad \sf \dashrightarrow \:\pi r {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \pi\times (3.5) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:12.25 \: \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:38.465 \: \: unit {}^{2} [/tex]
Answer:
38.465 units²
Step-by-step explanation:
The formula to find the area of a circle is πr². Simply substitute the radius in the formula to find the area.
Substituting the radius in the formula:
⇒ πr²
⇒ π(3.5)² [Radius (r) = 3.5 units]
Evaluating the area:
⇒ π x 12.25
⇒ 3.14 x 12.25
⇒ 38.465 units²
What are the zeros of the polynomial p(x) = x3 – 19x - 30?
-
1.
-10, 1, 3
2.
-6, -5, 1
3.
-3, -2,5
4.
-15, 1, 2
Answer:
x= -2
x= -3
x= 5
Step-by-step explanation:
Compare using inequalities <>, or
During February in Du Bois, Pennsylvania the temperature was -23 degrees at 11 am. The temperature was -6 degrees
at 7 pm.
-0)
A)
-23 >-6
B)
-23<-6
O
-6<-23
D)
-6=-23
Answer:
B. - 23 < -6
Step-by-step explanation:
2. Find the probability of throwing a 10 with a pair of dice and choosing a red from a standard deck of cards.
Answer:
Step-by-step explanation:
You can get 10 with a pair of dice with:
4 + 6, 6 + 4, 5 + 5
out of a possibile 36 results
There are 52 cards in a standard deck of cards. Reds make up half of them (hearts and diamonds) , meaning theres a 50/50 chance of pulling red
10/36 * 1/2 = 5/36 chance of throwing 10 + pulling red
A bycycling club has 18 members,of which 11 are males and the rest females. What is the ratio of males to all club members
Answer:
11 : 18
Step-by-step explanation:
to figure out number of female members (not neccessary to solve this problem)
18 members = male + female members
18 members = 11 members + female members
-11 -11
---------------------------------------------------------------------
7 members = female members
ratio of males to all club members
11 : 18
What is the f(3) for:
F (x) = 2x^2 + 5 (x-2)
Simplify this fraction to the lowest terms 14/12
Answer:
1 1/6 or 7/6
Step-by-step explanation:
Divide both 14 and 12 by 2
Find the distance between the two points
(−12, 8) and (−3, 8)
Answer:
9
Step-by-step explanation:
Plug into Distance formula --> √(-3 - (-12))^2 + (8 - 8)^2
---> 9
Solve this system of equations. -2x-4y=-12
Answer:
x = 6 and y = 3
Step-by-step explanation:
Your equation: -2x-4y=-12
__________________________________________________
First, we'll solve for x.
You need to divide -2x on both sides.
**We'll exclude/forget the -4y since we're not dealing with it right now.
-2x = -12
x = 6
When dividing with negatives, if both of the numbers are negatives they shall cancel and become positive.
-12 divided by -2 is 6 positive.
Therefore, x = 6
_______________________________________________________
Next, we'll solve for y
The same thing as last, we'll exclude our -2x since we're not dealing with it anymore.
-4y = -12
-12 divided by -4 is a positive answer since the two negatives cancel out.
-12/ -4 = 3
Therefore, y = 3
________________________________________________________
The proper vocabulary of the "x" and the "y" are x-intercept and y-intercept.
We just solved for both.
help me help me help me
Answer:
read step by step
Step-by-step explanation:
6 is +4.
19, 23, 27, 31
7 is all perfect square numbers
25, 36, 49, 64
8 is x2.
32, 64, 128, 256
9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12
so the next few would be 30, 42, 56, 72
What is the vertex of this quadratic function? y=6(x+1)2-9 Please Help!
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y = 6(x+1)^2-9\implies y = 6[x-(\stackrel{h}{-1})]^2\stackrel{k}{-9}\qquad \qquad \stackrel{vertex}{(-1~~,~~-9)}[/tex]