The length and breadth should be 2 feet each and height should be 3 feet to minimize the cost of the materials.
Let consider the length of the box =x
considering a square bottom ,
length = breadth = x
and let the height =h
The surface area of the box is
SA = x² + 4xh ( box is open from top )
cost of 1sq feet material for bottom =$3
cost of 1sq feet material for sides =$1
The cost functions can be written as
C = 3x² + 1(4xh)
C = 3x² + 4xh
Also the volume equation is
x²h = 12
h = 12/x²
substituting the value of h into the cost function.
C = 3x² + 4x (12/x²)
C = 3x² + 48/x
C = (3x³ + 48)/ x
Take the derivative of C and set it equal to zero. So we get
6x³ - 48 = 0
x³ = 48/6 = 8
x = 2
∴ h = 12/x²
h = 12/4
h = 3
This is the value of x and h that minimizes the cost.
learn more about lagrange method here :
https://brainly.com/question/24208980
#SPJ4
Which expressions simplify to a rational answer?
Select each correct answer.
Options (1), (3), (4), (7) and (8) are rational numbers.
What is the rational number?Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).
1) 1/4 + 1/2 = 1/4 + 2/4
= 3/4
3/4 is the rational number
2) √3 + 4 is an irrational number
3) √4 + 7
2 + 7 = 9
9 is the rational number
4) 2·√9
= 2·3
= 6
6 is the rational number
5) 7·√6 is an irrational number
6) 4·2√3 = 8√3
8√3 is an irrational number
7) 3·7·(1/3) = 7
7 is the rational number
8) 7·√81
=7·9 = 63
63 is the rational number
Therefore, options (1), (3), (4), (7) and (8) are rational numbers.
To learn more about the rational numbers visit:
https://brainly.com/question/19161857.
#SPJ1
Write the equation of the line that passes through the points (7,-6)(7,−6) and (3,8)(3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line is y = -0.35x – 3.55
Given,
The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).
Since the line passes through the points (7,-6) and (3,8),
• (x₁, y₁) = (7,-6) and
• (x₂, y₂) = (3,8).
So, substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/(x₂ - x₁).
m = (8 - (-6))/(3 - 7).
m = (8 + 6)/ -4
m = 14/-4
m = -3.5
The equation of the line passing through the point (x₁, y₁) in point-slope form is given by
y - y₁ = m(x - x₁) where
• m = gradient =- 0.35 and
• (x₁, y₁) = (7, -6)
So, substituting the values of the variables into the equation, we have
y - y₁ = m(x - x₁)
y - (-6) = -0.35(x - 7)
y + 6 =-0.35 (x - 7)
y = (-0.35x + 2.45 – 6)
y = -0.35x – 3.55
So, the equation of the line is y = -0.35x – 3.55
Learn more about equation of line here:
https://brainly.com/question/26941842
#SPJ1
tv sets: according to the nielsen company, the mean number of tv sets in a u.s. household in 2013 was 2.24 assume the standard deviation is 1.3. a sample of 80 households is drawn.
The probability of a random sample of 80 households having a sample means a number of at least 2.55 televisions per household is 0.48173.
Given: Mean(μ) = 2.24, Standard deviation(σ) = 1.38, Sample size(n) = 1.28 and a random variable for X = 2.55
The formula to calculate the z-score from the mean. The standard deviation is:
z = (X - μ) / ( σ / √(n)) where,
z = z-score,
X = random variable,
μ = mean,
σ = standard deviation, and
n = sample size
Let's solve the given question:
We have,
Mean(μ) = 2.24,
Standard deviation(σ) = 1.38,
Sample size(n) = 80, and
a random variable for X = 2.55
As it is given sample means at least 2.55 so we have to find the Z(x ≥ 2.55).
Therefore, Z(x ≥ 2.55) = (2.55 - μ) / ( σ / √(n))
Substituting all values we get:
Z(x ≥ 2.55) = (2.55 - 2.24) / ( 1.38 / √(80))
Z(x ≥ 2.55) = 0.01 / 0.21819
Z(x ≥ 2.55) = 0.48173
Hence the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.
learn more about of “probability distribution” here: brainly.com/question/11234923
#SPJ4
Which shows the expressions in the order they would appear on a number line from least to greatest? (5 points) a 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3 b 3 to the power of 3, square root of 30, square root of 15, square root of 6, 17 over 9 c 3 to the power of 3, square root of 6, square root of 15, 17 over 9, square root of 30 d 17 over 9, square root of 30, square root of 15, 3 to the power of 3, square root of 6
An expression which shows the order the numbers would appear on a number line from least to greatest is: A. 17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.
In Mathematics, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In order to arrange the given numbers in order from least to greatest, we would convert them into a decimal number as follows:
17/9 = 1.8889√6 = 2.4495√15 = 3.8730√30 = 5.47723³ = 9Read more on number line here: brainly.com/question/28032137
#SPJ1
График функции y=-0,5(10-x) Дополнительная информация -2≤x≤12
sam's bowling score is 5 less than twice the score of eva's. The sum of their scores is 235. Write and solve the equation to find the score of each student.
2. Find the volume to the nearest cubic millimeter of the 3-D object in the diagram.
200 mm
300 mm
Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.
What is the volume of the square pyramid?Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.
A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.
The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.
32 = 4² × h/3
32 = 16 × h/3
Multiply both sides by 3
96 = 16 × h
Divide both sides by 16
H = 96/16
H = 6
Therefore, the height is 6 feet.
The complete question is:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.
To learn more about the volume of the square pyramid refer to:
https://brainly.com/question/18994842
#SPJ13
What is the discriminant of the quadratic equation -x^2+6x-4=0?
Answer:
[tex]x = - 3 + - \sqrt{13} [/tex]
Step-by-step explanation:
formula is x=-b+-sqrt b^2-4ac/2a
4 root symbol 84 x 10 to the power of 4
The simplified value for 4 √84 x [tex]10^4[/tex] is 800 √21.
What is exponents?The exponent of a number shows how many times the number is multiplied by itself.
For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, xn means that x is multiplied by itself for n times.
Given:
4 √84 x [tex]10^4[/tex]
Now, first factorize 84 into prime factor
84 = 2 x 2 x 3 x 7
The, we can write it as
4 √84 x [tex]10^4[/tex]
=4 x √(2 x 2 x 3 x 7 x (10²)²)
= 4 x 2 x 10² √( 3 x 7)
= 8 x 10² √21
=800 √21
Hence, the simplified value is 800 √21.
Learn more about exponents and powers here:
https://brainly.com/question/15722035
#SPJ1
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due?
The total amount due will be equal to $6.24.
This question can be solved by converting the situation into form of an equation. An equation may be defined as an expression which consists of numbers, variables related to each other by arithmetic expressions. The solution of equation often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality. The cost of video game is given as $12.98, and tax is equal to $0.78, and he paid an amount of $20. let the change left be x.
Total amount = cost of game + tax + change
$20 = $12.98 + $0.78 + x
$20 = $13.76 + x
=> x = $20 - $13.76
=> x = $6.24 which is the due amount.
Learn more about equation at:
brainly.com/question/10413253
#SPJ1
Complete Question:
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due? Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?
In the figure below, N lies between M and P.
1
Find the location of N so that MN is of MP.
1/2 of MP
Answer:
8
Step-by-step explanation:
See attached image.
find the confidence interval specified. assume that the population is normally distributed. a sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. their mean score is 76.2 and their standard deviation is 21.4. construct the 95% confidence interval for the mean score of all such subjects.
The 95% confidence interval for the mean score of all such subjects. will be ( 67. 7 , 84.7) using mean.
What is mean?
Mathematicians, particularly statisticians, use a variety of means. Every mean serves to condense a certain set of facts, frequently to help grasp the general significance of a particular data set.
sample mean = x' = 76.2
sample S = 21.4
sample size n = 27
Confidence level = a = 0.95
α=1-a=0.05
95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
E = [tex]\frac{tc*s}{\sqrt{n}}[/tex]
E = [tex]\frac{2.056*21.4}{\sqrt{27}}[/tex]} = 8.466
95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
=(76.2-8.466 , 76.2+8.466)
=(67.734 , 84.666)
= ( 67. 7 , 84.7)
Hence The answer will be ( 67. 7 , 84.7).
Learn more about mean by following the link below.
brainly.com/question/24304697
#SPJ4
the population of a town increased by 2.59% per year from the beginning of 2000 to the beginning of 2010. the town's population at the beginning of 2000 was 74,500.
the town's population at the beginning of 2000 was 74,500.Then the population in 2010 will be 96206.97
In 2000, the population of a town = 74500
Every year, it increase by 2.59%
To find the equation P(t) which represents the population of this town t years from 2000 to 2010.
Formula
If a be the original population of a town and it increases by r% every year, after t year the population will be
A = P ( 1+r/100)^t
Now,
Taking, P =74500, r = 2.59% we get,
A = 74500( 1+0.0259)^10
A= 74500(1.0259)^10
A= 96206.97
learn more about of percentage here
https://brainly.com/question/15892381
#SPJ4
What percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water? (1 point)
69%
30%
1%
71%
The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.
We need to find the percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Over 69 percent of the fresh water on Earth is found in icecaps and glaciers, and just over 30 percent is found in ground water. Only about 0.3 percent of our fresh water is found in the surface water of lakes, rivers, and swamps.
The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ1
adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, write an equation that represents how far they will travel, d, in h hours
If adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, The equation that represents how far they will travel, d, in h hours is: r = d / t, D = r × t.
Speed and distanceGiven data;
Travels time : 2 hours in 90.5 miles
Formula for speed is:
r = d / t
Where,
r = Speed
d = Distance
t = Time
Hence,
Speed = 90.5 / 2
Speed =45.25miles per hour
Since they travels d distance in h hour with the same speed let find the distance
D = r × t
Distance = Speed × Time
Distance = 45.25 × h
Distance = 45.25h miles
Therefore r = d / t, D = r × t is the equation that represent the distance they travel.
Learn more about speed and distance here: https://brainly.com/question/26046491
#SPJ1
Helen needs 6 pints of water to make lemonade. How many gallons does she need?
Which symbol correctly compares these fractions? −4/5 −8/9
Answer:
-4/5 > -8/
-4/5 greater than -8/
Answer:
" > "
Step-by-step explanation:
-4/5=4x9 5×9
-4/5 = - 36/ 45
-8/9=8×5 9×5
-8/9 =-40/45
-36/ 45 > -40/45
-4/5 > -8/9
in this case - 4/5 is closer to 0
Julie is using a 1/2
1
2
-cup measuring cup to fill a gallon jug with water. Julie will need Response area scoops of the 12
1
2
-cup measuring cup to completely fill the jug.
16 cups of water using 1/2 cup of measuring cup will fill a gallon of water.
Measuring of VolumeTo find the number of 1/2 cups that will fill a gallon, we simply need to know how many cups are in one gallon.
[tex]1cup = 0.0625 gallon[/tex]
This implies that
[tex]\frac{1}{2} cup = 0.03125 gallon[/tex]
Let's equate this and find how many cups are in one gallon.
[tex]\frac{1}{2} cup = 0.03125 gallon\\x cup = 1 gallon\\[/tex]
cross multiply both sides and make x the subject of formula
[tex]x = \frac{0.5}{0.03125}\\x = 16 cups[/tex]
The number of 1/2 cups that will fill 1 gallon will be 16 cups.
Learn more on measuring volume here;
https://brainly.com/question/777464
#SPJ1
Simplify: 12a+7x-3a-2x
Answer:
9a+5x
Step-by-step explanation:
9a+5x
all you need to do here is to collect like terms.
so first ignoring the X's, 12a minus 3a is 9a.
then 7x-2x=5x
then you put these together to give you 9a+5x
Answer:
9a+5x
Step-by-step explanation:
you just have to collect like terms and then you will be able to find your answer!
PLEASE HELP!
Set up the system of equations for this scenario. Let "b" represent hours babysitting
and "w" represent hours walking dogs.
Answer:
I not to sure but I think it is b+w=h(hours)
Step-by-step explanation:
construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer. a) what is the lower limit on the interval? give your answer to three decimal places. 2.077 incorrect: your answer is incorrect. b) what is the upper limit on the interval? give your answer to three decimal places. 2.203 incorrect: your answer is incorrect.
The 99% confidence interval for the population proportion p is 0.833< p < 0.863.
Given that,
x = 3059
n = 3604
Point estimate = sample proportion = x / n =3059/3604=0.848
[tex]1 - \hat p[/tex] = [tex]1-0.848 =0.152[/tex]
At 99% confidence level the z is ,
[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01
[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005
[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576 ( Using z table )
Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]
= [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]
=0.015
A 99% confidence interval for population proportion p is ,
[tex]\hat p - E < p < \hat p + E[/tex]
0.848-0.015< p <0.848+ 0.015
0.833< p < 0.863
Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.
Learn more about domain from the link
https://brainly.com/question/2264373
#SPJ4
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7.50, and tickets for children cost $3.50. How many of each type of ticket were purchased?
There are 23 tickets which are purchased for children and 9 tickets are purchased for adults which cost total $148.
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
To know more about the similar questions like this; click here:
https://brainly.com/question/28861509
#SPJ2
PLEASE HELP!!!!!!!!!!!
Answer:
domain -2<x<2
range -2<y<2
not a function
the hypotenuse of a right triangle is 10 inches. the length of the two legs are given by two consecutive even integers. find the length of the two legs. the lengths of the two legs are and inches. license points possible: 1
Answer:
6 and 8
Step-by-step explanation:
x = one integer
x+2 = other integer
Pythagorean Theorem:
x^2 + ( x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x -48 = 0 Use factoring ( or Quadratic Formula)
(x+8)(x-6) = 0 shows x = 6 the other integer is 8
10) 18p³ - 6p² +3p-1
Answer:
Evaluate
18p
3
−6p
2
+3p−1
Rewrite the expression
18p
3
+3p−6p
2
−1
Factor out 3p from the expression
3p(6p
2
+1)−6p
2
−1
Factor out −1 from the expression
3p(6p
2
+1)−(6p
2
+1)
Solution
(3p−1)(6p
2
+1)
The equation of line c is y=–
7x+10. Line d is perpendicular to line c and passes through (7,4). What is the equation of line d?
Use distributive property to multiply the 3 in the expression 3(x−5)=12
Answer:
x = 9
Step-by-step explanation:
3(x - 5) = 12 ← distribute the parenthesis on the left by 3
3x - 15 = 12 ( add 15 to both sides )
3x = 27 ( divide both sides by 3 )
x = 9
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following. Find f(x) + h(x)
The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.
Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.
Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.
To learn more about this, tap on the link below:
https://brainly.com/question/28105566
#SPJ9
how many groups of 10 milliliters are in 1 liter explains
There are 100 groups of 10 milliliters in 1 liter
How to determine the number of groups?From the question, the given parameters are
Volume 1 = 10 milliliters
Volume 2 = 1 liter
The number of groups of the first group in the second is calculated as
Groups = Volume 2/Volume 1
Substitute the known values in the above equation
So, we have the following equation
Groups = 1 liter/10 milliliters
Evaluate the quotient
Groups = 100
Hence, the number of groups is 100
Read more about metric units at
https://brainly.com/question/28234927
#SPJ1
Which is the equation of the perpendicular bisector of a line segment whose midpoint
is (1, -2) and whose slope is - 1/3
asap
Answer: y = 3x - 5
Step-by-step explanation:
3 is the reciprocal of -1/3 and by plugging in (1,-2) in to y=3x+b you get -2 = 3(1) + b which makes b = -5