If [tex] 300cm^{2} [/tex]300 cm of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Answers
[tex]\bf \textit{volume of a rectangular prism}\\\\ V=lwh\quad \begin{cases} l = length\\ w=width\\ h=height\\ -----\\ w=l=x \end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\ -------------------------------\\\\ \textit{surface area}\\\\ S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h \\\\\\ \boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\ -------------------------------\\\\ V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3[/tex]
so.. that'd be the V(x) for such box, now, where is the maximum point at?
[tex]\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2 \\\\\\ \cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100 \\\\\\ x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}[/tex]
now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.
so, the volume will then be at [tex]\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3[/tex]
![If [tex] 300cm^{2} [/tex]300 Cm Of Material Is Available To Make A Box With A Square Base And An Open](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/SuY8axodKjSc45xX09ItTsfObk9efghr.jpeg)
![If [tex] 300cm^{2} [/tex]300 Cm Of Material Is Available To Make A Box With A Square Base And An Open](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/rcQ00DjExKuMpqjeQg6QDZbKbUq7vSFU.jpeg)
Related Questions
$14,146,727 is what percent of $117,190,375
Answers
______________________________________________________
" $14,146,727 is 12.016 % of $117,190,375 . "
______________________________________________________
Explanation:
___________________________________________________________
14,146,727 is what percent of: 117,190,375 ?
___________________________________________________________
14,146,727 = (n/100) * 117,190,375 ; Solve for "n" ;
↔ (n/100) * 117,190,375 = 14,146,727 ;
Divide each side of the equation by "(117,190,376)" ;
___________________________________________________________
[ (n/100) * 117,190,375 ] / [ 117,190,375 ] = [ 14,146,727 ] / [ 117,190,375 ] ;
___________________________________________________________
to get:
___________________________________________________________
(n/100) = [ 14,146,727 ] / [ 117,190,375 ] ;
(n/100) = 0.1207157755063076 ;
___________________________________________________________
Multiply EACH SIDE of the equation by 100 ;
to isolate "n" on one side of the equation; and to solve for "n" ;
___________________________________________________________
(n/100) * 100 = ( 0.1207157755063) * 100 ;
______________________________________________________
to get: n = 12.0715775063 .
______________________________________________________
The answer is: " 12.0715775063 % " ; round to: " 12.016 % " .
______________________________________________________
" $14,146,727 is 12.016 % of $117,190,375 . "
______________________________________________________
Determine the number of elements in the Sample Space for each of the following:
1. Tossing a coin three times
2. The order that the top 5 students will receive their diplomas.
3. Tossing a pair of dice.
Answers
1. Tossing a coin three times
There are possible outcomes.
Tossing the coin for the first time it can be a haid (H) or a tail (T). So, we can have this outcomes:
HHH
HHT
HTH
THH
TTH
THT
TTT
total: 6 outcomes
2. The order that the top 5 students will receive their diplomas.
Here we need to find the number of permutations: 5!=5*4*3*2*1=120
3. Tossing a pair of dice
The possible outcomes are the following: (a,b), where a is the first dice and b is the second dice
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) , total 36 possible outcomes.
Guys help me out on this one plizzz
Answers
The term that you want is 5C2*p^2*q^3 representing 2 successes and 3 failures. This term's value is
(5C2)(0.5^5) = 10*0.03125 = 0.3125 = P(2 successes in 5 trials) =31.3%
What is the difference between an image and a pre-image in a transformation? How do you tell them apart?
Answers
To tell them apart, they will usually be defined separately. For example, the square ABCD, when translated four units right becomes square A'B'C'D'.
If you know the transformation performed, you can apply this to differentiate between the preimage and image if they are not labeled. Only one square will be on the right of the other square, and since the translation is "four units right", it has to be the rightmost square that is the image.
The image is the product of a transformation while a pre-image is the original image on which a transformation operation is performed.
What is the image in a transformation?The image is the product of a transformation or it is the figure obtained after a transforms operation is performed.
What is the preimage in transformation?A pre-image is the original image on which a trabsosfiemarion operation is performed.
The pre-image is differentiated from the image by the labelling convention used as well as by studying the transformation performed.
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How many degrees are in the compliment of 54 degree angle? Why?
Answers
A triangle has side lengths 24, 32, and 42. is it a right triangle? explain.
Answers
Answer:
triangle given is not a right triangle
Step-by-step explanation:
Given:-
- The side lengths of a triangle are given as:
24 , 32 , 42
Find:-
is it a right triangle? explain
Solution:-
- Any triangle which conforms to the pythagorean theorem can be classified as a right angle triangle.
- The Pythagorean theorem states that the square of the longest side length known as hypotenuse (H) should be equal to the sum of square of other two side lengths ( Perpendicular / opposite [ P ] and Base / Adjacent [ B] ).
- This can be mathematically expressed as:
H^2 = P^2 + B^2
- From the given side lengths. The largest side length is hypotenuse H = 42. While P and B can be used interchangeably for the other two side lengths. So using the theorem we have:
42^2 = 32^2 + 24^2
1764 : 1024 + 576
1764 ≠ 1600
- We see that the three side lengths of the triangle does not conform to theorem. So we can conclude that the triangle given is not a right triangle.
Since 1764 is not equal to 1600, the triangle is not a right triangle.
To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the sides as follows:
a = 24, b = 32, c = 42
Using the Pythagorean theorem:
c² = a² + b²
Plugging in the values:
42² = 24² + 32²
1764 = 576 + 1024
1764 = 1600
Is 2(x+5) factored?
Answers
A bag contains 10 tiles with the letters A, B, C, D, E, F, G, H, I, and J. Five tiles are chosen, one at a time, and placed in a row. Meghan says that the probability of the five tiles spelling FACED is 1/252 . Her work is shown below.
Answers
For the possible number of arrangement of letter, n(S), the basic principles of counting should be used.
= 10 x 9 x 8 x 7 x 6 = 30,240
This is similar as to what was done in Meghan's work.
For the five tiles to spell out FACED, there is only one (1) possibility.
Therefore, the probability should be equal to 1/30,240 instead of the 1/252 which was presented in the steps above.
Find the area ratio of a cube with volume 125 m to a cube with volume 64 m.
Answers
*Keep in mind that the faces of a cube are squares.
Surface Area of a cube = Area of a side * 6
Area = length * width
Area of a square = length * length
We don't know the length/width of the cube, so we need to solve for it using the values for the volumes of the two cubes.
[tex]Volume = length * width* height\\Volume of a cube = length * length * length\\\\125\ m^{3}=length^{3}\\\\\sqrt[3]{125\ m^{3}}=\sqrt[3]{length^{3}}\\\\5\ m=length\\\\\\64\ m^{3}=length^{3}\\\\\sqrt[3]{64\ m^{3}}=\sqrt[3]{length^{3}}\\\\4\ m=length[/tex]
Now find the area of the sides:
[tex] Area = length *length\\\\Area\ of\ cube\ 1=5\ m*5\ m=25\ m^{2}\\\\Surface\ Area\ of\ cube\ 1=side\ area*6\\\\SA_{cube\ 1}=25\ m^{2}*6=150\ m^{2}\\\\\\Area\ of\ cube\ 2=4\ m*4\ m=16\ m^{2}\\\\Surface\ Area\ of\ cube\ 2=side\ area*6\\\\SA_{cube\ 2}=16\ m^{2}*6=96\ m^{2}[/tex]
Now find the ratio between the Surface areas:
[tex]150\ m^{2}:96\ m^{2}\\\\150\6:96\6\\\\25:16=\frac{25}{16}=1\ \frac{9}{16}=1.5625[/tex]
Thus the answer is 25/16 = 1.5625
The required ratio of area of cubes is 25 : 16.
Volume of cube 1 = 125
Volume of cube 2 = 64
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Volume of cube 1 = 125
a³ = 125
a = 5
Volume of cube 2 = 64
A³ = 64
A = 4
Area of cube 1 = a² x 6
= 5² x 6
= 150
Area of cube 2 = A² x 6
= 4² x 6
= 96
Now ,
The ratio of areas of cube 1 to cube 2 = 150:96.
= 25:16
Thus, the required ratio of area of cubes is 25 : 16.
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Find the length and width of a rectangle that has perimeter 24 meters and a maximum area.
Answers
Let the length of the rectangle = x
since the perimeter is 24m then the width of rectangle is (12-x)m.
the area of
rectangle is:
A=x*(12-x)
A=-x^2+12x
x=-12/-2 =6:
Since the length is 6m the width will be: 12-6=6m
We conclude
that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :
Area = 6^2 =36M^2
Which polynomial can be simplified to a difference of squares? 10a2 + 3a – 3a – 16 16a2 – 4a + 4a – 1 25a2 + 6a – 6a + 36 24a2 – 9a + 9a + 4
Answers
16a² - 4a + 4a - 1 =
16a² - 1 =
(4a)² - 1² =
(4a-1)(4a+1)
Answer:
2.[tex]16a^2-4a+4a-1[/tex]
Step-by-step explanation:
We have to find the polynomial can be simplified to a difference of squares.
1.[tex]10a^2+3a-3a-16[/tex]
Combine like terms
[tex]10a^2-16[/tex]
10 in [tex]10a^2[/tex] is not a perfect square number because when a number end with one zero then the number is not perfect square number.
Therefore, it can not be simplified to a difference of squares.
2.[tex]16a^2-4a+4a-1[/tex]
[tex]16a^2-1[/tex]
Combine like terms
[tex](4a)^2-(1)^2[/tex]
Hence, the polynomial can be simplified as difference of squares.
3.[tex]25a^2+6a-6a+36[/tex]
Combine like terms
[tex]25a^2+36[/tex]
[tex](5a)^2+(6)^2[/tex]
Hence, the polynomial can not be simplified as difference of squares because the polynomial can be simplified as sum of squares.
4.[tex]24a^2-9a+9a+4[/tex]
Combine like terms
[tex]24a^2+4[/tex]
[tex]24a^2+(2)^2[/tex]
[tex]24=2\times 2\times 3\times 2[/tex]
24 is not a perfect square number because when factorize 24 then 2 and 3 are not paired.
Hence, the polynomial can not be simplified as difference of squares.
You drive your car for three hours at an average speed of 130 kilometers per hour how far did you go
Answers
given that speed=130kmph and time=3h
d=130kmph times 3h
d=390km
you went 390 kilometers
Earth has a radius of about 6.4 x 10^6m. Approximate the surface area of Earth using the formula for the surface area of a sphere. S=4*pi*r^2
Answers
know some things
(x^m)(x^n)=x^(m+n)
so
S=4pir^2
S=4pi(6.4*10^6)^2
S=4pi(6.4*10^6)(6.4*10^6)
S=4pi(6.4)(6.4)(10^6)(10^6)
S=4pi(40.96)(10^12)
S=163.84pi(10^12)
aprox
S=514.71854036415172418971949191651 times 10^12 m²
The surface area of the earth using the given formula is 51471.85 m².
What is the surface area of a solid?The surface area of a solid can be defined as the area covered by its surface. There are two types of area for a solid exact and lateral.
The lateral area represents only the visible portion of the surface area while the exact area is the area of the total surface of the solid.
Given that,
The radius of earth r = 6.4 × 10⁶ m.
The area of a sphere is given as S = 4π × r².
Substitute the value of r to obtain,
S = 4π × (6.4 × 10⁶)²
= 51471.85
Hence, the surface area of Earth is approximated as 51471.85 m².
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Kristin opens a savings account with $3500. She deposits $2400 every year into the account that has a 0.65% interest rate, compounded quarterly. If she doesn't withdraw any money, what will the account balance be in 10 years?
1. $28551.51
2. $24776.39
3. $28511.25
4. $24816.65
I don't know what formula to use or how to solve.
Answers
The formula of a compound interest is
A=p (1+r/k)^kt
A future value?
P present value 3500
R interest rate 0.0065
K compounded quarterly 4
T time 10 years
Also the formula of the future value of an annuity ordinary is
Fv=pmt [(1+r/k)^(kt)-1)÷(r/k)]
Fv future value?
PMT since the payment per year is 2400 so you should find the payment per quarter which is 600 (2400÷4) because the interest is quarterly.
R interest rate 0.0065
K compounded quarterly 4
T time 10 years
The sum of those two formulas is the answer.
The balance is
3,500×(1+0.0065÷4)^(4×10)
+600×(((1+0.0065÷4)^(4
×10)−1)÷(0.0065÷4))
=28,511.25.....answer
(05.03)
Karma baked 48 cookies yesterday. Every hour, she bakes another batch of 12 cookies.
What is the rate of change for the scenario described?
4
12
60
48
Answers
what is 0.004% of 6800 round to the nearest hundredth
Answers
Now lets get started working out this problem of yours
[tex]0.004(6800) \\ \frac{0.004}{100} = 0.00004[/tex] [tex]0.00004(6800) \\ Actual Answer: 0.272 \\ Rounded Answer: 0.72[/tex]
Also, remember: [tex]5[/tex] and down is rounded to [tex]0[/tex] | [tex]6[/tex] and up is going closer to [tex]10[/tex]
How many hours are in a year?
Answers
Which table describes the behavior of the graph of f(x) = 2x³ - 26x - 24?
Answers
(-3,0),(-1,0) and (4,0)
therefore the interval will be:
(-∞,-3)-below, (-3,-1)-above,(-1,4)-below,(4,∞)-above
The answer is ]
Answer:
The answer is the table B
Step-by-step explanation:
we have
[tex]f(x)=2x^{3}-26x-24[/tex]
Using a graphing tool
see the attached figure to better understand the problem
Relation of graph to the x-axis
Interval (-∞,-3) -----> below (the function is negative)
Interval (-3,-1) -----> above (the function is positive)
Interval (-1,4) -----> below (the function is negative)
Interval (4,∞) ----->above (the function is positive)
PLEASE HELP!!
f(x)=16x+12
g(x)=4x+3
Find: (fg)(x)
Select one:
a. 4x+4
b. 8
c. 4
d. 12x+9
Answers
(f/g)(x) = [ f(x) ]/[ g(x) ]
(f/g)(x) = (16x + 12)/(4x + 3)
(f/g)(x) = (4(4x+3))/(4x+3)
(f/g)(x) = 4
So the answer is choice C
The gross weight of a package in its contents is 11 lbs. 5 oz. if the packaging weighs 1 lb. 15 oz. what the net weight of the content
Answers
10 pounds 21 ounces then we subtract
1 pound 15 ounces giving us the net weight of
9 pounds 6 ounces.
The function H(t)=-16t+48t+12 shows the height H(t), in feet, of a cannon ball afte t seconds. A second cannon ball moves in the air along a path represented by g(t)=10+15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: create a table using integers 0 through 3 for the 2 functions. Between wat 2 seconds is the solution to H(t)=g(t) located? How do you know?
Part B: Explain what the solution from Part A means in the context of the problem.
Answers
The table is shown in the first picture below
From the tables, we can read that the solution [tex]H(t)=G(t)[/tex] is located between 0 and 2 seconds.
The reason is that in between the interval of 0 and 2, [tex]H(t)[/tex] is turning (the cannon ball is moving toward the ground) whereas the function [tex]G(t)[/tex] increase its height. At one point these two paths will cross, as shown in the graph in the second picture below
Part B:
In the context of the problem, the one point where [tex]H(t) [/tex] and [tex]G(t)[/tex] crosses is the point where the two cannon balls will collide.
Who is known as the "founding father of geometry?"?
Answers
The sum of the reciprocals of two consecutive integers is startfraction 11 over 30 endfraction 11 30. find the two integers.
Answers
It's 5 and 6.
The consecutive integers are 5 and 6.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
The sum of the reciprocals of two consecutive integers is 11/30.
Let the integers be n and n+1.
Then,
1/n + 1/n+1 = 11/30
{n + 1 + n}/n(n+ 1) = 11/30
30(2n+1 ) = 11(n²+n)
60n + 30 = 11n² + 11n
11n² - 49n - 30 = 0
(11n +6) (n-5) = 0
Only taking,
n = 5.
So, 5 and 6.
Therefore, 5 and 6 are the integers.
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Find the number of ways to purchase 5 different kinds of drinks from a selection of 13 drinks.
Answers
12 choices for 2nd drink
11 choices for 3rd drink
10 choices for the 4th drink
9 choices for the 5th drink
13*12*11*10*9=154440 ways to purchase 5 kinds of drinks
In one town, 79% of adults have health insurance. what is the probability that 4 adults selected at random from the town all have health insurance? round to the nearest thousandth if necessary.
Answers
This is becasue the probability of finding each adult having health insurance is independent of others.
When, events are independent, the combined probability is the product of each probability =>
Probailibty of one adult with healt insurance * probability of one adult with healt insurance * probability of one adult with health insurance * probability of one adult with health insurance = 0.79 * 0.79 * 0.79 * 0.79 = (0.79)^4.
Answer: 0.400
Answer:
0.039 on gradpoint
Step-by-step explanation:
I got it right on the test
What are the intercepts of 6x + 8y=24
Answers
x =4
y=0
6x+8y=24
6(0)+8y=24
0+8y=24
8y=24
Divided 8 to both side
8y/8=24/8
y=3, so the x-intercept is (0,3)
Next, find the y-intercept by making y=0, to find the value of x.
6x+8y=24
6x+8(0)=24
6x+0=24
6x=24
Divided both side by 6
6x/6=24/6
x=4, so the y-intercept will equal (4,0). Hope it help!
Johnny's baseball team raised $1456 for next month's tournament. They need a total of $2,000 to play. The team has a total of 11 players. Let x represent how much each player needs to raise in order to play in the tournament.
Answers
Total amount needed = $2,000
Remaining balance = 2000 - 1456 = $544
Let x = amount that each of the 11 players should raise.
Therefore
11x = 544
x = 544/11 = $49.45
Answer: $49.45
help me please!! Anyone??
Answers
put the paranthesis around 4 squared and 2
15)a natural number is always a whole number, however, a whole number is not always a natural
16) 10, because natural numbers can only be positive, also, zero is not a natural number
17) 3, for abc/abc will equal 1, leaving 3 x 1 = 3
18) No, for if it is division or multiplication, it will have completely different results
19) (x times y) times z ; x times (y times z) ; x times y times z
hope this helps :D
mc:radio:(05.05 LC)
A company rents gym equipment for a fixed amount plus a fee based on the number of days for which the equipment is rented. The table shows the total charges, y, in dollars, of renting gym equipment for x number of days:
Gym Equipment Rentals
Number of days
(x)
Total Charges in dollars
(y)
0 25
1 40
2 55
What is the fixed amount charged?
$2 $15 $25 $40
Answers
the first line in the chart has x as 0 and Y as 25
this means the fixed amount would be $25
Answer:
$25
Step-by-step explanation:
because the first number in the chart is $25
hope this helps!
I will give the Brainliest answer! PLEASE HELP! The vertices of a triangle are located at the points A (1,1) , B (2,3), C (5,0). The triangle is translated 4 units down, then reflected across the x-axis to obtain triangle A'B'C'. What are the coordinates of the vertices of triangle A'B'C'?
Answers
To find the coordinates of the vertices A'B'C' of the new triangle after translation and reflection, subtract 4 from the y-coordinate of each vertex and change the sign of the y-coordinate.
Explanation:To find the coordinates of the vertices A'B'C' of the new triangle, we first translate the original triangle 4 units down. This means we subtract 4 from the y-coordinate of each vertex. So, the new coordinates of A', B', and C' are: A' (1, -3), B' (2, -1), and C' (5, -4).
Next, we reflect the translated triangle across the x-axis. To do this, we change the sign of the y-coordinate of each vertex. So, the final coordinates of A'B'C' are: A' (-1, 3), B' (-2, 1), and C' (-5, 4).