a box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. what is the maximum volume this box could have? (round your answer to two decimal places.)
Maximum volume through the concept of maxima is 564.22 cm3.
What are maxima?
The maxima are discovered using the arithmetic of variations if the domain of the function for which the maxima is sought consists solely of functions (i.e., if the maxima sought of a functional).There are no any minimum or maximum values in unlimited infinite collections, for example the collection of real numbers.Volume of box=(50-2x)(10-2x).x
=4x^3-120x^2+500x
for maximum volume,
dv/dx=0
⇒12x^2-240x+500=0
⇒3x^2-60+14=0
x=17.63,2.36
d2v/dx2=24x-240
at x=2.36
d2v/dx2<0
∴x=2.36
v will be maximum
Maximum volume through the concept of maxima is 564.22 cm3.
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3. Use the equation V = abc where a = 5, b = 10, c = 3 to find the value of V.Show your work here:Choose the correct answersV = 120V = 50V = 150V = 60
Solution
[tex]V=abc[/tex]Where
[tex]\begin{gathered} a=5 \\ b=10 \\ c=3 \end{gathered}[/tex]Now,
[tex]\begin{gathered} V=abc \\ V=(5)(10)(3) \\ V=150 \end{gathered}[/tex]Therefore, V = 150
help me on this one please
Felipe and Gregory are given the arithmetic sequence - 1, 6, 13, ..... Gregory wrote the explicit definition an = - 1 + 7(n - 1) for the sequence. Felipe wrote the definition as an = 7n -8. Which one of them is correct? Explain. Choose the correct answer below. O A. Only Felipe's definition is correct because it is simplified. Gregory's definition is not simplified, so it cannot be correct. O B. Only Gregory's definition is correct. The explicit definition of an arithmetic sequence is an = a, + d(n - 1), and only Gregory's definition is of that form. O C. Both are correct. Gregory's definition can be simplified to get Felipe's definition. O D. Both are correct. Gregory's definition uses n = 1 for the first term whereas Felipe's definition uses n = 0 for the first term, but both definitions describe the given sequence.
Answer: C. Both are correct. Gregory's definition can be simplified to get Felipe's definition.
Step-by-step explanation:
-1, 6, 13
[tex]a_n=a_1+(n-1)d\\\\d=a_2-a_1\\\\d=6-(-1)\\\\d=6+1\\\\d=7[/tex]
Hence,
[tex]a_n=-1+7(n-1)\\\\a_n=-1+7(n)-7(-1)\\\\a_n=-1+7n-7\\\\a_n=7n-8[/tex]
Raul purchased a pair of shoes for $19.25 that normally sell for $55. What percent discount did he recieve?
He got a 61.5% Discount
Multiply (4.12 x 10-9)(8.3 x 1015). Write the final answer in scientific notation.
© 34.196 x 10^134
O 3.4196 x 107
O 3.4196 x 10^135
© 34.196 x 106
Help ASAP please!!!
Answer: 34.196 x 10^6
I need to determine m∠z. Can anybody help with this?
Answer:
z = 134°
Step-by-step explanation:
You want to know the measure of exterior angle z given remote interior angles of the triangle are 77° and 57°.
Exterior angleThe exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle. (It is useful to remember this.)
z = 77° +57°
z = 134°
__
Additional comment
As you know the value of the interior angle at C will be the supplement of the value of z: (180° -z). Then the sum of the interior angles is ...
77° +57° +(180°-z) = 180°
Add (z -180°) to both sides of this equation and you get ...
77° +57° +(180°-z) +(z -180°) = 180° +(z -180°)
77° +57° = z . . . . simplified
quota sampling produces the same advantages for convenience sampling that ____ sampling produces for probability sampling.
The quota sampling produces the same advantages for convenience sampling that stratified random sampling produces for probability sampling.
Sampling:
Sampling is defined as the process in statistical analysis where researchers take a predetermined number of observations from a larger population.
Given,
Here we need to find the type of sampling that produces the same advantages for convenience sampling quota sampling.
Before, move on to the result, first we have to know the details about quota sampling and the probability sampling.
Probability sampling defined as the selection of a sample from a determined number of population, when this selection is based on the principle of randomization, that is, random selection or chance.
In contrast to probability sampling, Quota sampling means a non-probability sampling method in which researchers create a sample involving individuals that represent a population.
Based on these definition we have identified that the method that is best suitable answer for this one is stratified random sampling.
Because the stratified random sampling means, is a probability sampling technique in which the total population is divided into homogenous groups to complete the sampling process.
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if 4 tickets costs$40, how much does 8 tickets cost?
4 tickets----------------------------->$40
8 tickts------------------------------->$x
Using cross multiplication:
[tex]\begin{gathered} \frac{4}{8}=\frac{40}{x} \\ x=\frac{40\times8}{4} \\ x=80 \end{gathered}[/tex]8 tickets cost $80
Which two graphs are increasing on all points of the domain?
Answer:
Step-by-step explanation:
the first one
True or False Animal-like protists get nutrients by creating them inside themselves.
question 2 (10 points)
The slope of the line between the two points defined in the graph is 1/2.
Slope of the line:
The slope of a line is the change in y coordinate with respect to the change in x coordinate.
m = Δy/Δx
Where the net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line
Given,
There is a graph presented here.
Through the graph we have identified two points,
They are (3,0) and (-3, -3).
Now we need to find the slope of the line between these points.
Here we consider the values of (x1,y1) as (3,0) and the value of (x2,y2) as (-3,-3).
Through the values we have to identify the slope of the line.
For that, we have to apply the values on the formula,
Then we get,
m = (-3 - 0)/(-3-3)
m = -3/-6
m = 1/2
Therefore, the slope of the line is 1/2.
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PLSS HELP IM DESPERATE
Terrence walks at a pace of 2mi/hr to the theater, and watches a movie for 2hrs and 15mins. He rides back home, taking the same route, on a bus that travels at a rate of 40mi/hr. The entire trip takes 3.5 hrs. How far along this route is Terrence’s house from the theater. Explain.
If He rides back home, taking the same route, on a bus that travels at a rate of 40mi/hr. The entire trip takes 3.5 hrs. How far along this route is Terrence’s house from the theater is : 50 mile.
DistanceMovie time = 2hrs and 15mins
Let convert the movie time
2hrs and 15mins = 2 15/60 h = 2 1/4 h = 2.25 h
Now let calculate the bus time and the distance
Bus time = Entire time - Walking time
Bus time = 3.5 h - 2. 25 h
Bus time = 1.25 h
Now let calculate the distance
Distance = Speed × Time
Distance = 40mi/hr × 1.25 h
Distance = 50 mile
Therefore the distance is 50 mile.
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NEED ASAP PLEASEE
Explain why the number 8,000 is a perfect cube.
The number 8,000 is a perfect cube because it is the square of the number 20.
The number 8,000 is a perfect cube because its cube root is an integer.
The number 8,000 is a perfect cube because it is the square root of 64,000,000.
The number 8,000 is a perfect cube because its square root is an integer.
The most appropriate choice for cube and cube root of a number will be given by-
8000 is a perfect cube number because cube root of 8000 is an integer.
Second option is correct.
What is cube and cube root of a number?
Let the number be p. If we multiply p three times with itself ([tex]p \times p \times p[/tex]), then we get the cube of p.
If we take [tex]\frac{1}{3}[/tex] power of p ([tex]p^{\frac{1}{3}}[/tex]), we will get the cube root of p.
[tex]8000 = 2^6 \times 5^3[/tex]
On taking the cube root of 8000, we get
[tex]\sqrt[3]{8000} = 2^2 \times 5[/tex]
[tex]= 20[/tex]
which is an integer.
So 8000 is a perfect cube number.
so, 8000 is a perfect cube number because cube root of 8000 is an integer.
Second option is correct.
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Mr. Arnold drives 130 miles round trip to work 5 days a week. Write and solve an equation to find how many miles he drives in 60 work days.
Answer:
1,560 miles
Step-by-step explanation:
[tex]\frac{130}{5} = \frac{x}{60}[/tex]
Solve for x. Multiply both sides by 60 to get 1,560.
if "f" varies directly with "m" and f = -19 when m=14, what is "f" when m=2? enter the number that belongs in the green box. reduce to the simplest form. f= - ?/?
solution
For this case we can use the following proportion rule:
[tex]\frac{-19}{14}=\frac{f}{2}[/tex]Then we can solve for f on this way and we got:
[tex]f=2\cdot(\frac{-19}{14})=-\frac{19}{7}[/tex]i need help with this
Answer:
32 feet
Step-by-step explanation:
See attached worksheet
Toronto FC have lost 5 of the 20 games
they have played. What percentage of
games have they lost?
Answer:
25%
Step-by-step explanation:
5/20 = 1/4
1/4 x 100 = 100/4 = 25
(1 x 25)/(4x100) = 25/100
25%
Answer:
25%
Step-by-step explanation
5/20 = 1/4
1/4 x 100 = 100/4 = 25
(1 x 25)/(4x100) = 25/100
25% Therefore They have lost 25% of there games
In February, Robbins and Myers, Inc. executed a 2-for-1 split. Janine had 470 shares before the split. Each share was worth $69.48.
a. How many shares did she hold after the split?
b. What was the post-split price per share?
c. Show that the split was a monetary non-event for Janine.
In February, Robbins and Myers, Inc. executed a 2-for-1 split, then the
(a) . The shares did she hold after the split is 940 shares.
(b) . The post-split price per share is $34.74
(c) . Janine didn't gain or lose any money during the event.
Based on the given conditions,
In February, Robbins and Myers, Inc. executed a 2-for-1 split.
That means,
2 - for - 1 stock split.
= 2 / 1
= 2
(a) . How many shares did she hold after the split?
Then,
Janine had 470 shares before the split.
Each share was worth $69.48.
= 470 shares * 2
= 940 shares
Hence,
The shares did she hold after the split is 940 shares.
(b) . What was the post-split price per share?
Each share was worth $69.48.
Then,
= $69.48/2
= $34.74
Hence,
The post-split price per share is $34.74
(c) . Show that the split was a monetary non-event for Janine
We can write,
After the split, Janine had 940 share worth $34.74.
Since they doubled the amount of share, but decrease the amount of each share.
So,
Janine didn't gain or lose any money during the event.
Therefore,
Robbins and Myers, Inc. executed a 2-for-1 split,
(a) . The shares did she hold after the split is 940 shares.
(b) . The post-split price per share is $34.74
(c) . Janine didn't gain or lose any money during the event.
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What is the slope of the line created by this equation?
y = -6.3x+0
Answer:
-6.3 is your slope.
Step-by-step explanation:
Hello, there! Nice to meet you.
This is a pretty easy question, as it's written in y = mx + b form.
When it's written like this, the m in replacement is your slope value.
So, in this case, -6.3 is your slope.
If I had y = 3x + 6, then 3 would be the slope, but that's just an example.
Once more, the m value is your slope.
Hope this helped, and best of luck with the rest of your assignment! (:
pls help need to anwser this question
Answer: y = -3x + 1
Step-by-step explanation:
Find the slope, rise/run:
-5 - (-17) / 2 - 6
-12/4 or -3
Find the y-intercept by substitution:
y = mx + b
-5 = -3(2) + b (Using the first coordinate)
1 = b
If you shift the linear parent function, f(x) = x, up 6 units, what is the equation
of the new function?
OA. g(x)= x+6
OB. g(x) = x-6
O C. g(x)=x
OD. g(x) = 6x
The required equation is g(x)=x+6
What is an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. A polynomial equation is the most common sort of equation. A mathematical equation is akin to a weighted scale. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal. To keep the scale in balance, if grain is withdrawn from one pan of the balance, an equal amount of grain must be removed from the other pan. In general, if the identical operation is done on both sides of an equation, it stays balanced.
The required equation is g(x)=x+6, when the parent function is 6 units up
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What is the answer to 6/3x=30?
Answer:
6/3x=30 = x= 15
Step-by-step explanation:
2x=30
(divide) ^
simplify, x=15
The Pencil Shop sells 20 pencils for $2.50 or single pencils for $0.13 each. Which option has the lesser price per pencil?
Answer:
20 pencils for $2.50 has the lesser price per pencil.
Step-by-step explanation:
$0.13 compared to $2.50 ÷ 20 = $0.125
$0.13 > $0.125
A shot-putter throws a shot and its height is noted every 20 feet, the data is in the table below:
Feet Traveled Feet Above Ground
20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64
Please find the quadratic function of best fit for these data and, to the hundredths place, say how many feet the shot travels before striking the ground.
Best fit quadratic equation is: y = 77x + 140
Define quadratic equation.ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. An example of a quadratic equation is x² + 2x + 1. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as bx+c=0. As a result, we cannot refer to this equation as a quadratic equation.
Given,
A shot-putter throws a shot and its height is noted every 20 feet
Best fit quadratic equation is:
y = 77x + 140
As after this equation, feet above ground is decreasing.
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what is the place value of the 5 in 836.15?
Answer:
The place value of 5 is HUNDREDTH
Explanation:
From the right-hand side, the place value of:
8 is Hundred
2 is Ten
6 is Unit
1 is Tenth
and finally, what we are required to tell,
5 is Hundredth.
How can the square-root property be used to solve y2=6
Given the expression:
[tex]y^2=6[/tex]The first step to solve it using the square root property, is moving the coefficient on the right side of the equation to the left side, changing it's sign:
[tex]\begin{gathered} y^2=6 \\ \Rightarrow y^2-6=0 \end{gathered}[/tex]Now, remember the rule for conjugates:
[tex](a+b)(a-b)=a^2-b^2[/tex]in this case we have the following:
[tex]\begin{gathered} y^2=a^2 \\ \Rightarrow y=a \\ b^2=6 \\ \Rightarrow b=\sqrt[]{6} \end{gathered}[/tex]therefore, we can factor the expression like this:
[tex]\begin{gathered} y^2-6=0 \\ \Rightarrow(y-\sqrt[]{6})(y+\sqrt[]{6})=0 \end{gathered}[/tex]Finally, we have that the only values that make true the expression are:
[tex]\begin{gathered} y_1=\sqrt[]{6} \\ y_2=-\sqrt[]{6} \end{gathered}[/tex]Can someone please solve this
Answer:
f ( 5, 2 )
h ( 4, -2 )
a ( 1,0 )
d ( -3, 5 )
Step-by-step explanation:
Assuming every point is one space.
We can find this by counting how far away it is form the origin for example f is 5 place right of the origin so x=5 and is above the origin two places so y=2. So (5,2) is the answer.
The figure MNP will be reflect across the line x = -2. If point M starts at (1, 2), what is the coordinate of M´?
The coordinates of the point M' is (-6,2) when the point M was reflected across x =-2.
Here, assume that there is a point A(a, b). This point is reflected across the line x = -2. When reflected across this line, the value of the y coordinate of this point A will not change, only the value of the x coordinates of the point A will change.
Here, the point M(1,2) is reflected across the line x = -2.
The coordinates of the reflected point M' are (a, b).
The value of will b will remains same as that of the point M.
Now, the location of a,
the distance between the line x = -2 and a will be same as that of the distance between 2 and x =-2 which is 4 units,
So, the location of a will be fours units away from x =-2 and in the opposite direction so, a = -6
So, the Point M' is (-6,2)
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what is the quotient
will mark as brainliest
The quotient is [tex]x-1+\frac{9}{x+6}[/tex]
What is the formula of division?The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. Here, The dividend is the number, which is being divided. The divisor is the number, which divides the number (dividend) into equal parts.
Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.
In the above question we simply have to divide the dividend that is [tex]x^2+5x+3[/tex] with x + 6
and then we will get the quotient as x - 1 and remainder 9 .
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