The tank with the smallest surface area has dimensions of 6ft.
s = 12ft and h = 6ft.
A(s) = s² + 4 × (V ÷ s)
The rectangular tank has a capacity of 864 feet.
Let the square base's long sides be.
Let h represent the tank's height.
Let A represent the tank's whole area.
A = (Base Area) + (4 × Lateral Area)
Lateral Area = s × h
Lateral Area = s × (V ÷ s²)
Lateral Area = (V ÷ s)
Base Area = s²
Compared to the objective function,
A(s) = s² + 4 × (V ÷ s)
A(s) = s² + 4 × (864 ÷ s)
The area function's derivative,
A'(s) = 2s - (3456 ÷ s²)
The smallest surface area is now.
A'(s) = 0
2s - (3456 ÷ s²) = 0
2 × [tex]s^{3}[/tex] = 3456
[tex]s^{3}[/tex] = 3456
s = [tex]\sqrt[3]{3456}[/tex]
s = 12ft
The volume is,
V = s² × h
864 = 12² × h
h = 6ft
As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.
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The question is -
A rectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.
easy trig please heeelp me
Answer:
9
Step-by-step explanation:
Pythagorean triples. 3, 4, 5. Multiply by 3 and get 9.
a group contains n men and n women. identify the steps used to find the number of ways to arrange n men and n women in a row if the men and women alternate?
With the help of factorisation we can conclude our answer.
What is factorisation?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number or matrix is known as factorization or factoring in mathematics.A polynomial or integer is simply resolved into components that, when multiplied together, produce the original or starting polynomial or integer. The factorization method allows us to simplify any algebraic or quadratic equation by representing the equations as the product of factors rather than by expanding the brackets. Any equation can have an integer, a variable, or the algebraic expression itself as a factor.acc to our question-
n+1 nP * P = factorial(n+1) *factorialnn nlearn more about factorisation click here:
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you have seven different video games. how many different ways can you arrange the games side by side on a shelf?
The number of different ways to arrange 7 video games is = 7!
The question requests for the number of arrangements; That means we're dealing with permutation
the number of video games is 7;
To arrange 7 games, we make use of the following permutation formula;
[tex]^{n}P_{n} = \frac{n!}{(n-n)!}[/tex]
So, we have
n=7
No. of ways we can arrange is = [tex]\frac{7!}{(7-7)!}[/tex] = 7!
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4 tins of soup have a total weight of 1120 grams
3 tins of soup and 5 packets of soup have a total weight of 1015 grams
work out the total weight of 5 tins of soup and 2 packets of soup
One has a face value of $32.50, and one has a face value of $26.50. He uses a coupon and gets both tickets at One-fourth off. If he pays with a $50 bill, how much change should Tamir receive?
The change that Tamir would have to receive would be: $5.75
How to solve for the changeWe would first have to solve for the total amount of the tickets that Tamir has received
This would be given as
32.5 + 26.5 dollars
= 59 dollars
Given that he has a 1/4 off in both of the tickets the amount that he would have to pay would be
59 - 1/4 * 59
59 - 14.75
= $44.25
This is the amount that he would have to pay for the coupons.
Given that he used a $50 bill, we would have to solve for his change.
This would be solved as $50 - $44.25
= 5.75
Hence his change is going to be $5.75
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slope of the line passing through (3,-4), (-5,2)
Answer:
[tex]\boxed{\sf Slope( m)=-\cfrac{3}{4}}[/tex]
Step-by-step explanation:
To find the slope between two points we'll use the Slope formula:-
[tex]\boxed{\sf \mathrm{Slope(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]
______________
Given:-
(3,-4)(-5,2)Where,
[tex]\mathrm{\left(x_1,\:y_1\right)=\left(3,\:-4\right)}[/tex]
[tex]\mathrm{\left(x_2,\:y_2\right)=\left(-5,\:2\right)}[/tex]
[tex]\mathrm{m=\cfrac{2-\left(-4\right)}{-5-3}}[/tex] ← Subtract
[tex]\sf m=-\cfrac{6}{8}[/tex]
[tex]\sf m=-\cfrac{3}{4}[/tex]
Therefore, the slope of the line is m = - 3/4.
______________________
Hope this helps!
Have a great day!
question 4 while verifying cleaned data, a data analyst encounters a misspelled name. which function can they use to determine if the error is repeated throughout the dataset?
The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".
The given condition needs the following function;
Data Integration Error:
Data from a single source, obtained and entered in the same way across time is unusual to be present in a database of significant size and age. A database frequently comprises data that has been gathered over time from various sources using various ways. As an illustration, consider how the meaning of "affected" is evolving or changing as the crisis progresses and the number of people affected is tracked over time. In addition, many databases evolve in practice by joining together different pre-existing databases. Almost always, the databases involved in this merging effort include discrepancies involving various data units, measurement intervals, formats, etc. Any process that combines data from various sources has the potential to make mistakes. When two or more databases are combined, errors will be found where there are discrepancies between the databases as well as new errors will be produced (i.e. duplicate records). A few potential origins and types of errors in a big assessment are shown in Table 1 below, at three fundamental levels: after completing the survey, when adding information to the database, and when conducting the analysis.
So, we use " COUNTA "
The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".
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TEXT ANSWER
Jason provided the following work when asked to convert 0.105 to its simplest fraction
form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction form.
Jason's Work:
0.105=
105
21
1000 200
Answer:
See below
Step-by-step explanation:
.105 is 105 THOUSANDTHS or 105/1000
Divide top and bottom by '5'
to get 21/100
Meal Deal £5.00
A sandwich
A dessert
A drink
The following choice is available:
5 different sandwiches
4 different desserts
6 different drinks
a) How many different combinations are possible with the Meal Deal?
b) Two of the desserts are sugar-free.
Three of the drinks are sugar-free.
A Meal Deal combination is selected at random.
Work out the probability that both the dessert and the drink are sugar-free
Give your answer as a fraction.
2^(x+3) = ((1)/(8))^(x+2) solve for x
step by step exlanation
I NEED HELP ASAP :
if a volume of an object varies directly with its width and if the volume is 16, while the with is 4 what is k?
The value of k is 4.
What is Proportion ?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Volume= 16
Width = 4
So, we can write the relation as
Volume= k (width)
k = Volume/ width
k= 16/4
k = 4
Hence, the value of k is 4.
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Rewrite the point-slope form equation into slope-intercept form.
y+4= -3(x-5)
The slope-intercept form of the equation is
(Type an equation. Use integers or fractions for any numbers in the equation.
The point slope and the intercept form is y = -3x + 11
What is the slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
This written in the form of y = ax + b
where a is the slope and b is the intercept
We have the equation as
y + 4 = - 3 ( x - 5 )
we would have to open the bracket and then take the like term
this is going to be
y + 4 = -3x + 15
From here we would get the like term
y = -3x + 15 -4
y = -3x + 11
The slope is -3 and the intercept is 11.
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The length of a rectangle is 5 yd longer than its width.
If the perimeter of the rectangle is 70 yd, find its length and width
Answer:
length is 20 yards, width is 15 yards
Step-by-step explanation:
Length = width + 5
2(W + 5) + 2(W) = 70
2W + 10 + 2W = 70
4W + 10 = 70
4W = 60
W = 60 ÷ 4
W = 15 yards
L = 15 + 5
L = 20 yards
I need help like asap !!!
number and decimal points
Answer:
a = 5 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (13)² = a² + (12)²
→ 169 = a² + 144
→ a² = 169 - 144
→ a = √25
→ [ a = 5 cm ]
Hence, value of a is 5 cm.
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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Write an equation for the line parallel to the given line that contains the given point.
Line: 8y=6x+5 Point: (-8,-10)
Please answer quick!!
The linear equation parallel to 8y=6x+5 is:
y = (3/4)*x - 4
How to find the equation of the parallel line?Remember that two linear equations are parallel if and only if both lines have the same slope and different y-intercept.
Here we want to find a line parallel to:
8y = 6x + 5
Rewriting this in slope-intercept form we get:
y = (6x + 5)/8
y = (3/4)*x + 5/8
Then a parallel line to this one will be:
y = (3/4)*x + b
To find the value of b, we use the fact that this line must pass through the point (-8, -10).
-10 = (3/4)*(-8) + b
-10 = -6 + b
-10 + 6 = b
-4 = b
Then the linear equation is:
y = (3/4)*x - 4
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PLEASE HELPPPP!!!
Simplify the imaginary number...
Compare these fractions by filling in the blank with the appropriate sign. 5/11 _____ 4/9
Answer:
5/11 > 4/9
Step-by-step explanation:
5/11 = 0.45454545....
4/9 = 0.44444444....
algebra solution for tiffany had $330 in her account in 1999 and the value has been growing exponentially at a constant rate. the value of the account reached $590 in the 2007. what is the value in 2009?
The value of the account in the year 2009 will be $682.
The acount's balance, in t years after 1999, can be modeled by the following equation.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999This means that $590 in the year 20072007 is 8 years after 1999, so P(8) = 590.We use this to find r.Determine the value of the account, to the nearest dollar, in the year 2009.2009 is 10 years after 1999, so this is A(10).The value of the account in the year 2009 will be $682.learn more about solutions here:
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I need help like asap !!!
only numbers and decimal points
Answer:
24.41
Step-by-step explanation:
a^2+b^2=c^2
14^2+20^2=c^2
196+400=596
14^2+20^2=24.41^2
a question posted on the lycos web site on june 18, 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes. what is the most likely issue with the sample they collected?
The most likely problem with the sample they gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
Defined the term biased survey?This phrase describes the different factors and biases that may affect survey results. Either biased responses are deliberate or unintentional, they make survey results less valuable because they are erroneous.With participant surveys that ask for self-reporting, this might become a specific problem.Any survey's bias response is crucial since it determines the validity of the data, so preventing bias is absolutely necessary if you want insightful survey responses.Among the most prevalent types is leading bias. As an illustration, consider the scenario in which your question concerns customer happiness and the response alternatives are Very Satisfied, Satisfied, and Dissatisfied. Results in this case may be affected by bias.Thus, the most likely problem with the sample lycos web site gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
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How many complete centerpieces can she make? Find the exact answer.
The number of centerpieces that she can make, using proportions, is of:
25.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem, and basic arithmetic operations, especially multiplication or division, to find the desired amounts in the same context of this problem.
In the context of this problem, the number of centerpieces is given by the division of the the total number of flowers by the number of flowers in each centerpiece.
The amounts are given as follows:
Flowers: 430.Flowers per centerpiece: 17.Hence the division giving the number of flowers per centerpiece is:
n = 430/17 = 25.2.
The amount is rounded down to 25, as for 26 centerpieces, more flowers would be needed.
Missing InformationHailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project.
How many complete centerpieces can she make? Find the exact answer.
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a restaurant has special menu that features three choices of salad, six choices of entree, and eight choices of dessert. how many different three course meals could you order
72 three course meals we can order.
Question states that;
A restaurant offers a special menu with three salad options, six meal options, and eight dessert options.
Counting Principle:
The counting rule is another name for the Fundamental Counting Principle. It's a way to figure out how many possible outcomes there are in a probability word problem. Probability is the likelihood that an event will occur. An event's probability is always a number between 0 and 1. The probability of all events added together equals one.
We need to find how many three course meals we can order;
Total number of ways,
P(A) = 3 * 6 * 8
P(A) = 72
72 three course meals we can order.
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Helppppppppppppp Thxs ‼️
Answer:
False
Step-by-step explanation:
If is a real number and m and n are positive integers
A prize is divided in the ratio 1:8.If the larger share is £72 what is the smaller share?
Answer:
£9
Step-by-step explanation:
1:8=9
?:72
72÷9=8
9×1=9
Sophia earned $36 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
A chess board is made using the ratio of square length to king's height, 2.5 inches to 4.5 inches. If a chess board is made with a king's height of 2.25 inches, what is the length of the square? 0.75 inch 1.25 inches 2.25 inches 4.75 inches
The length of the square, given the height of the King, can be found to be 1.25 inch.
How to find the height?The chessboard is made such that its square length as a ratio would be 2 . 5 inches to 4 . 5 inches for the King's height.
If the King's height is 2. 25 inches, the square length of the chess board can be found by the formula:
= ( King's height x Ratio of square length ) / Ratio of King's height
Solving gives us:
= (2 . 25 x 2 . 5 ) / 4.5
= 5.625 / 4. 5
= 1.25 inches
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What’s Question 6 and 7 ?
Step-by-step explanation:
6.
the factors need to be zero for the x-intercepts.
but (-3 - 3) = -6 and not 0.
the same for (-7 - 7) = -14 and not 0.
his mistake was the signs.
what do I need to add to -3 to get 0 ? 3. and 7 to -7.
so, the correct f(x) is
f(x) = (x + 3)(x + 7)
to get x-intercepts at -3 and -7.
7.
in the same way we get the factors here : for a given x the y value has to be 0.
how is y turning 0 for a polynomial in factor form ? well, at least one of the factors has to be 0.
therefore, for (-6, 0) the factor has to be
(x + 6) as -6 + 6 = 0
for (2, 0) the factor has to be
(x - 2) as 2 - 2 = 0
pick one of them as your answer. they are both correct factors for f(x).
poisson distribution is applied for a. continuous random variable b. discrete random variable c. irregular random variable d. uncertain random variable
Poisson Distribution along with Binomial Distribution is applied for Discrete Random variable.
What is discrete variable and example?
Counting is the method used to determine the value of a discrete variable. examples: the number of pupils in attendance. how many red marbles are in the container. number of heads when three coins are flipped. grade level of the pupils.What is discrete and continuous random variable?
The range of possible values for a discrete random variable is finite. Any value could be assigned to a continuous random variable (usually within a certain range). Although it could be a rational fraction, a discrete random variable is normally an integer.Learn more about discrete random variable
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a) 110⁰
b) 70⁰
c) 73⁰
d) 115⁰
Answer:I think is am B
Step-by-step explanation:
Step-by-step explanation:
(5x)°+(3x+4)°=180°
5x+3x+4=180
8x=176
x=22
D=5x
D=110°
