The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m are equal to .
How to find the height of the box ?Let h is the height of the box.
Given Volume of the box is 216 m³ with no top.
And the cost of the bottom is 40USD/m².
For the sides, it is 30USD/m².
The bottom of the box is square, so l = w.
So Volume
[tex]V=hl^{2}[/tex]
[tex]216=hl^{2}[/tex]
[tex]h=\frac{216}{l^{2} }[/tex]
Now Surface Area of the box without a top is
S = 4hl + l²
So,
cost = 4 × 30hl +40l²
cost = 120 hl + 40 l²
Putting h ,
cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]
cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]
To find minimum cost, derivate the by using the calculator at
[tex]l=3\sqrt[3]{4}[/tex]
l=4.762203 m
[tex]h=\frac{216}{4.762203^{2} }[/tex]
h = 9.5244069354 m
Hence the dimensions of the box are
l=w
=9.52 m
and height ,h=3.17 m
Know more about the volume of the box here:
brainly.com/question/11168779
#SPJ4
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,160) and (6,240) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make each minute = 40
In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.
Also, we have been given two points (4,160) and (6,240)
We need to find the number of soda bottles the machine can make each minute.
i.e., we need to find the slope of line passing through points (4,160) and (6,240)
Using the formula of slope,
m = (240 - 160) / (6 - 4)
m = 80/2
m = 40
Therefore, the number of soda bottles the machine can make each minute = 40
Learn more about the slope here:
https://brainly.com/question/16180119
#SPJ1
under what circumstances would a score that is 10 points below the mean be considered to be an extreme value? select one: a. when the mean is much greater than 10 b. when the mean is much less than 10 c. when the standard deviation is much greater than 10 d. when the standard deviation is much less than 10
The correct option d. when the standard deviation is much less than 10.
Describe the term standard deviation?The term "standard deviation" (or "σ") applies to a measurement of the data's dispersion from the mean. A low standard deviation indicate that the data are grouped around the mean, although a large standard deviation indicates that the data are more dispersed.When a value is 10 points beyond the norm, it is said to be an extreme value or an outlier.
When a point deviates significantly from the mean in comparison to other points, it is referred to as an outlier. Z-scores can be used to establish this. Remember the z-score formula:
z = (x - μ) / σ
μ = mean σ = standard deviationx = point of interestThe outlier should have a very big magnitude z-score. We are aware that the score in this issue is 10 points just below mean, we can say:
A lesser value of would raise the magnitude of a z-score, increasing it to the maximum extent achievable.
Therefore, this point would be an outlier whether its standard deviation was drastically lower than 10.
To know more about the standard deviation, here
https://brainly.com/question/475676
#SPJ4
I need to know the answer
Step-by-step explanation:
The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5. That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f. For example, if x = 2, the point (2, 20) is on the graph of f but the point (2, 16) is on the graph of p (so it lies under the point (2, 20).
The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of f and it is reflected over the x-axis. The negative coefficient -1 is doing that. The values of the function p(x) are opposite sign to values of f(x).
The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of p lie farther away from the x-axis than points on the graph of f(x).
If the taxi company only has $10.50 to spend, what value does this represent?
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Amount to spend by the taxi driver ≤ 10.50.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The taxi company only has $10.50 to spend.
This means that,
The maximum amount to spend is $10.50.
We can also represent as:
Amount to spend by the taxi driver ≤ 10.50.
Thus,
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ2
The graph of a quadratic function with vertex (-3,1) is shown in the figure below. Find the range and the domain
The domain of the given quadratic function is { -3 }
and range is { 1 }
What is a domain and range ?A function's domain is the set of values that can be plugged into it. This set symbolizes the x values in a function like f. (x). Additionally, we can deduce that a function's range refers to the set of values it can accept. There are values in this set that the function returns when we enter an x value.
The domain of the given quadratic function is { -3 }
and range is { 1 }
To know more about domain and range you may visit the link which is mentioned below:
https://brainly.com/question/28135761
#SPJ13
Y+4=2(x-7)
In standard form
Answer:
2x-y=18
Step-by-step explanation:
y + 4 = 2(x - 7) (open brackets)
y + 4 = 2x - 14 (re arrange)
4 + 14 = 2x - y
2x - y = 18
3y - x - (4x - 5y)/10 - 7y+2x/4
According to this rate shown in this graph, after 12 minutes the coffee is about 110 degrees. After one hour (60 minutes), what do you think the temperature would be?
After one hour (60 minutes, the value of the temperature is 550 degrees.
What is temperature?Temperature is the degree of hotness and coldness that a body contains.
In this case, after graph, after 12 minutes the coffee is about 110 degrees. The temperature per minute will be:
= 110 / 12
= 9.167° per minute.
Therefore, the temperature after 1 hour which is 60 minutes will be:
= Time × Rate
= 60 × 9.167°
= 550°
The temperature is 550°.
Learn more about temperature on:
brainly.com/question/24746268
#SPJ1
The state board of education has $5,647 to buy new calculators. each calculator costs $2. after buying as many calculators as it can with its budget, how much money will the state board of education have left over?
By basic arithmetic, the state board of education will have $1 left .
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.
The total amount the state board has = $5647
The cost of calculator = $ 2
The total number of calculators bought = 5647/2
= 2323.5
≈ 2823
So, the cost of 2323 calculators
= 2823 × 2
= 5646
So, the money the state board of education left = $5647 - $5646
= $1
To know more about basic arithmetic, visit:
brainly.com/question/14617992
#SPJ1
Carlos is a receptionist at a law firm. he spends 2 minutes routing each phone call as it comes in. write an equation that shows how the total number of minutes carlos spends routing calls, y, depends on the number of calls, x.
The equation to show the total no. of minutes Carlos spends routing calls is y = 2x
To find the required equation, use the following given data:
Time taken by Carols for routing each call = 2 minutes
Total number of calls = x
Total number of minutes Carol spends routing calls = y
The one-dimensional function takes up a single input value (x) and outputs a single evaluation of the given input (y).
So, by practical application of one-dimensional function,
Total number of minutes Carols spends routing calls (y) = Time taken by Carols for routing each call * Total number of calls (x)
∴ The equation will be y = 2*x
Thus, y = 2x shows the total number of minutes Carlos spends routing the calls.
To learn more about similar time calculations,
brainly.com/question/17961064
#SPJ4
Some doctors recommend that men drink 3 liters of water every day. there are approximately 29.6 milliliters in 1 fluid ounce. which measurement is closest to the number of fluid ounces in 3 liters? responses 89 fl oz 89 fl oz 10 fl oz 10 fl oz 101 fl oz 101 fl oz 33 fl oz 33 fl oz
The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.
29.6 milliliters = 1 fluid ounce
3 liters = 3000 milliliters
3000 milliliters / 29.6 milliliters = 101 fluid ounce
Hence, 3 liters ≈ 101 fluid ounces.
To learn more about conversion: brainly.com/question/97386
#SPJ4
Parallelogram PQRS is shown. m/S=(3x), m/R=120, and m/Q=(2y). Find the value of y.A.
20
B.
30
C.
40
D.
60
Option B. From the parallelogram PQRS the value of y is given to be 30
How to solve for the value of y from the parallelogramIn order to get the value of y we have to use the formula
2y + 120 = 80
where the value 120 is the angle that is stated as 120 from the question
2y = 180 - 120
2y = 60
y = 60 / 2
y = 30
Hence the value of y = 30
We can go ahead to get the value of x as well
3x + 120 = 180
take the like terms
3x = 180 - 120
3x = 60
divide through by 3 to get x
60 / 3 = x
20 = x
Read more on parallelograms here: https://brainly.com/question/24056495
#SPJ1
what is the smallest odd number you can make with 3 4 6 and 8
Answer: You cannot.
Step-by-step explanation:
3 can be multiplied into an odd number
4 cannot be multiplied into an odd number
6 cannot be multiplied into an odd number
8 cannot be multiplied into an odd number
Overall, you will not be able to get an odd number with the numbers provided.
Answer: 4683
Step-by-step explanation:
To have an odd number, and since the only odd number you have in your list is 3, that would be in the one's place. Then, you have to put the smallest number (except for 3) in the front. Now, you have two more places to fill in (4 _ _ 3). Like the 4, put the 6 after the 4 to have the smallest possible hundreds place. Now place the eight. Your final number should be... 4683.
A skydiver fell toward Earth at a steady speed for 10.0 seconds. He fell 593 meters in that
time. What was his speed?
Answer:
59.3 meters/second
Step-by-step explanation:
593 / 10 = 59.3
Calculate the area of the square!
Answer:
The answer is 169
Step-by-step explanation:
Whose limeade has a weaker like flavor?
well, your proportion setup is good, let's simply use that then
[tex]\stackrel{Jaylan}{\cfrac{~~ \frac{ 3}{4 } ~~}{\frac{1}{5}}}\implies \cfrac{3}{4}\cdot \cfrac{5}{1}\implies \cfrac{15}{4}\implies \cfrac{3\frac{3}{4}}{1}~\frac{water}{lime} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Wanchen}{\cfrac{~~ \frac{ 2}{3 } ~~}{\frac{1}{6}}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{12}{3}\implies \cfrac{4}{1}~\frac{water}{lime}[/tex]
well, the one with the lesser lime flavor will be the one that put too much water in the drink, the more water the less the fruit mix, the more waterdowned the drink is, well hell who put more water per lime? well Wanchen, shame on you.
pls hurry and thanks 40 pts
The angle of x in the triangle is 75 degrees.
How to find the angles of triangle?The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Therefore, the base angles are equal.
The third angle of the triangle is 30 degrees(vertically opposite angles)
Hence,
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150 / 2
x = 75 degrees
learn more on angles here: https://brainly.com/question/25950519
#SPJ1
A triangle has sided with lengths of 20 miles, 25 miles, and 30 miles. Is it a right triangle ?
Answer:
No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that
If a is the larger side and b , c are the lengths of the other two sides
Then [tex]a^{2} =b^{2} +c^{2}[/tex]
Here a=30 , Then [tex]a^{2}=30^{2} =900[/tex]
and b=20 , c=25 , Then [tex]b^{2} +c^{2} =20^{2} +25^{2} =1025[/tex]
Since [tex]a^{2} \neq b^{2} +c^{2}[/tex]
Then the Triangle is not Right Triangle
suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 60 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? people (b) how many would you expect to be taller than 167 cm?
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.
μ = 170
σ = 5
n = 60
(a) The probability would you expect to be between 165 and 175 cm tall;
P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )
= P( -1 < z < 1 )
= P( z < 1) - P( z < -1 )
= 0.8413 - 0.1587
= 0.6826
Expected number of people between 165 and 175 = n * p
= 60 * 0.6826
= 40.956
≅ 41
(b) The probability would you expect to be taller than 167 cm;
P( x > 167 ) = P( z > (167 - 170)/5 )
= P( z > -0.6 )
= 0.7257
Expected number of people taller than 168 = n * p
= 60 * 0.7257
= 43.542
≅ 39
Hence,
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn. Can Theo mow the lawn in 2 hours if he continue to mow at the same rate?
Yes, he can mow the lawn in 2 hours.
What is work done?We can define the work done as, a work done in a given period of time.
Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn
In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn
Therefore, in 8/5 hours he is mowing 7/9 part of lawn
In 1 hour = 7/9*5/8 = 35/72
In 2 hours = 35/72*2 = 35/36 ≈ 1
Hence, Yes, he can mow the lawn in 2 hours.
For more references on work done, click;
https://brainly.com/question/13662169
#SPJ2
n a recent survey in a statistics class, it was determined that only 60% of the students attend class on fridays. from past data it was noted that 98% of those who went to class on fridays pass the course, while only 20% of those who did not go to class on fridays passed the course. a. what percentage of students is expected to pass the course?
The percentage of students expected to pass the course is 66.8%
The given data represents;
In a recent survey in a statistics class, it was determined that only 60% of the students attend class on Fridays. from past data, it was noted that 98% of those who went to class on Fridays passed the course, while only 20% of those who did not go to class on Fridays passed the course.
We need to find the percentage of students who are expected to pass the course.
Let 'A' be the event of passing,
'B' be the event of attending on Fridays.
P (A I B) = 0.98 * P (A I B') = 0.2
P (B) = 0.6
Then, P (B') = 1 - 0.6
= 0.4
→ P (A ∩ B) = P (A I B) * P (B)
= 0.98 * 0.6
= 0.588
→ P (A ∩ B') = P (A I B') * P (B)
= 0.2 * 0.4
= 0.08
∴ P(A) = P (A ∩ B) + P (A ∩ B')
= 0.588 + 0.08
= 0.668
Hence, the percentage of students expected to pass the course is 66.8%
To learn more about percentage click here:
brainly.com/question/26080842
#SPJ4
(DUE IN 2 HOURS PLEASE HELP) Find an equation for the line that passes through the points (5, 2) and (-4, 5).
Answer:
Y= -1/3x+11/3
Step-by-step explanation:
A recipe requires 4 1/2 cups of milk for every 2/3 of a cup of flour. What is the ratio of cups of milk to one cup of flour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
PLEASE HELP!!!
A marathon is 26.2 miles long. There is a water station every 1 31/100 miles along the race route. Which expression represents the total number of water stations?
The expression that represents the total number of water stations is 26.2 ÷ 1.31
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It's important to note as an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, the marathon is 26.2 miles long and there is a water station every 1 31/100 miles along the race route. The expression will be:
= 26.2 ÷ 1 31/100
= 26.2 ÷ 1.31
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Find DE, please help me
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
Rachel bought three and fifty-two hundred pounds of apples at the store. How is this written in number form?
3.0052
3.052
3.502
3.52
Answer: 3.52
Step-by-step explanation: fifty-two hundredths as a number would be 0.52, so 3.00 + 0.52 would be 3.52
Divide [tex]4\frac{2}{15}[/tex] by 3.1.
[tex]\fbox{1.333333}[/tex]
[tex]4\frac{2}{15} \div3.1[/tex]
Simplify:
[tex]4\frac{2}{15} \div3.1[/tex]
[tex]=1.333333[/tex]
let's firstly convert the mixed fraction to improper fraction and the decimal one to a fraction.
[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]
the binominal distribution: a. is symmetric irrespective of the value of the probability of success. b. models n independent replications of a bernoulli experiment, each with a probability p of success. c. assumes that the average number of occurrences per unit is a constant and that occurrences are independent. d. is a discrete distribution used to model the number of occurrences in some unit of measure
The correct option is B "Models n independent replications of a Bernoulli experiment each with a probability p of success".
What is binomial distribution?It is a frequency distribution of the number of successful outcomes that could occur in a set number of trials with an equal chance of success. In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
To know more about binomial distribution,
https://brainly.com/question/14565246?referrer=searchResults
#SPJ4
a random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selected from the distribution, what value will 15% of the observations be below?
the 2 values X(19.8,30.2) is value will 15% of the observations be below .
by hypothesis .
What is hypothesis ?
A hypothesis is an assertion, a notion put up for the purpose of debating and then examined to discover if it might be true. Prior to conducting any relevant research, other than a brief background review, the hypothesis is developed using the scientific method.Here, Mean(\mu) and Standard Deviation (\sigma)= 5. You need to find the 2 values of which the smallest has 15% of the values below it i.e (Z<x)= 0.15 and the largest has 15% of the values above it i.e(Z>y)= 0.15.
Now we need to refer to the Z tables and see which value of x corresponds to 0.15, and we see that -1.04 is = 0.149 \sim 0.15
Now we know that the Z value is given by Z = X - μ/σ
Substituting we get
-1.04= (X-25)/5
therefore -5.2= X-25 or X= 19.8
Now let us get the value of X for (Z>y)=0.15`. Since Z tables give values for Z<a only, hence we can write that
Z>y=0.15 is the same as Z<y= 1-0.15= 0.85. We now check the Z tables and see which value of Z corresponds to 0.85, and we get 0.850 = +1.04
Again, substituting Z in the equation Z = X - μ/σ
we get
+1.04= (X-25)/5
Therefore 5.2= X-25, therefore X= 30.2
From the 2 values X(19.8,30.2)
Learn more about hypothesis
brainly.com/question/17173491
#SPJ4
Why are most streets designed in a way that they are perpendicular or parallel to each other? ...
The simple reason why streets are usually designed parallel or perpendicular to each other is because that pattern makes it easy for users to connect people easily.
What is meant by perpendicular and parallel streets?A perpendicular street can simply be defined as a street which intersect another streets. However, on the other end, two streets are said to be parallel to each other when they are in the same distance apart. The same is applicable in mathematics as a perpendicular line intercept another line and parallel lines don't meet.
That being said, when streets are parallel or perpendicularly designed, residents of the environment find it easy to communicate with each other. Business owners use this easy accessibility to easily describe their addresses to customers.
So therefore, it can be deduced from the given explanation above that when streets are designed with good planning, it makes people access it easily.
Read more on perpendicular streets
https://brainly.com/question/23860737
#SPJ1
