The closest value of x that would produce the box with the minimum surface area would be 117 ft.
The volume of a lidless box with height h and a square base with sides of length x is given by V = x^2 * h.
To have a volume of 117 ft^3, we have:
x^2 * h = 117
The surface area of a lidless box is given by:
A = 2x^2 + 4xh
We want to minimize this surface area while still keeping the volume of the box at 117 ft^3. To do this, we need to find an expression for h in terms of x, and then minimize A in terms of x.
From the volume equation, we can solve for h:
h = 117 / x^2
Substituting this expression into the surface area equation, we get:
A = 2x^2 + 4x * (117 / x^2)
= 2x^2 + 466 / x
Now, we can use calculus to find the minimum of A in terms of x.
The derivative of A with respect to x is:
dA/dx = 4x - 466 / x^2
Setting dA/dx equal to zero, we find the critical points:
4x - 466 / x^2 = 0
4x = 466
x = 116.5
We now need to check if x = 116.5 is a local minimum or maximum.
To do this, we need to examine the second derivative of A with respect to x:
d^2A/dx^2 = -932 / x^3
Since the second derivative is negative, this means that A has a local minimum at x = 116.5.
Hence, the value of x that produces the box with a minimum surface area is approximately 116.5 ft.
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NO LINKS!!
British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 330 grams of a copper-silver alloy that is 10% copper by weight? (Round your answers to one decimal place.)
British sterling silver ____________ g
Copper ___________g
British sterling silver = 321.1 grams
Copper = 8.9 grams
========================================================
Work Shown:
x = amount of British sterling silver (in grams)330-x = amount of pure copper (in grams)The two amounts add to 330 grams total. The x is some number in the interval 0 < x < 330.
7.5% of x = 0.075x = amount of pure copper from the British sterling0.075x+(330-x) = -0.925x+330 = total amount of pure copperWe want to end up with 330 grams of 10% copper, so we want 0.10*330 = 33 grams of pure copper after mixing the two metals.
Set the 33 equal to the expression -0.925x+330 and solve for x.
-----------
-0.925x+330 = 33
-0.925x = 33-330
-0.925x = -297
x = -297/(-0.925)
x = 321.081 approximately
x = 321.1 when rounding to one decimal place
330-x = 330-321.1 = 8.9
-----------
We'll need 321.1 grams of British sterling silver.
We'll also need 8.9 grams of pure copper.
B-1+3/15 pls help me I’m like stuck on this what’s the variable
Answer:
Step-by-step explanation:
b= -3
Help! Giving brainiest corrections due at 12pm today but I dont understand how to do this either
The length of the side BC is 96 units.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given that AD is an altitude of triangle ABC.
Altitude of a triangle is the line of perpendicular drawn from a vertex to the opposite side.
∠ADC = ∠ADB = 90°
Given that, ∠ADC = 4x + 10
4x + 10 = 90
4x = 80
x = 20
Length of BC = BD + DC
= 2x + 3x - 4
= 5x - 4
= (5 × 20) - 4
= 100 - 4
= 96
Hence the length of the side BC is 96.
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Please help, I am trying to get this question answered.
Answer: yes the triangles are similar
Step-by-step explanation: a congruent comparison would have the exact same size and shape, similar triangles have the same shape but can be smaller or larger than the original
The sun of Planet X has a diameter of about 860, 000 mi. The sun's distance from the surface of Planet X is
approximately 147,000,000 mi. Planet X's moon has a diameter of 18.7 mi. For a total solar eclipse to occur,
the moon must pass between the sun and Planet X. The moon must also be close enough to Planet X for the
moon's umbra (shadow) to reach the surface of Planet X. Complete parts (a) and (b) below
The Sun's diameter is 1.075*10² times the Earth's diameter.
Compare the Sun's and Earth's diameter ?Sun's Dimensions.The Sun's diameter is equal to 1.4 x 106 km when we multiply its distance by its observed angular diameter (about 0.5 degrees).
This is around ten times as big as Jupiter, the largest planet, and about 100 times as big as the Earth.
The Sun's diameter is times the Earth's diameter.
We are given the following in the question:
Sun's diameter = 860,000 miles
Earth's diameter = 8000 miles
Comparison of Sun's and Earth's diameter:
sun s diameter / earth diameter
= 860000/8000
8.6 *10(5)/8*10(3)
= 1.075*10(2)
Thus, the Sun's diameter is 1.075*10² times the Earth's diameter.
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please help asap
• it would mean sm and make my day
For the given number line plot the inequality obtained is { -∞ < x < -2 and 5 < x < ∞}.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
To represent inequalities on a number line show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.
An open circle shows it does not include the value.
A closed circle shows it does include the value.
Let the unknown value be x.
The first range is starting form -2 and moving towards -∞.
Since the circle is open it will not include the value.
So the inequality is -∞ < x < -2.
The second range is starting form 5 and moving towards ∞.
Since the circle is open it will not include the value.
So the inequality is 5 < x < ∞.
Therefore, the inequality is { -∞ < x < -2 and 5 < x < ∞}.
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six more than the quotient of a number and 8 is equal to 4
The required solution of the equation is -16.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given :six more than the quotient of a number and 8 is equal to 4
To solve this, we can convert the statement into an algebraic equation, Express it in an equation:
6+(x/8) = 4
subtracted 6 from both sides,
x/8 = -2
multiplied both sides by 8,
x = -16
Therefore, the required solution of the equation is -16.
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1 gallon=4.546 10 litres in gallon is approximately?
If 1 gallon = 4.546 litres, then 10 litres in gallon is approximately 2.2 gallons.
1 gallon = 4.546 litres,
∴ 1 litre = [tex]\frac{1}{4.546}[/tex] = 0.2199 gallon
∴ 10 litres = 10 × 0.2199 = 2.199 gallons ≅ 2.2 gallons
Thus, 10 litres in gallon is approximately equal to 2.2 gallons.
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can someone just try to answer this ?:(
Ima fail
The compound inequality for the graph shown above include the following:
x < -2.
x > 5.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
Since the first point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.
Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.
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find(-3) if f(x)=6x-8
Given:-
[tex] \: [/tex]
[tex] \rm \: f(x) = 6x - 8 \: ... eqⁿ[/tex][tex] \: [/tex]
To find:-
[tex] \: [/tex]
[tex] \rm \: {f ( -3 ) = ?}[/tex][tex] \: [/tex]
Solution:-
[tex] \: [/tex]
[tex] \rm \: f(x) = 6x - 8[/tex][tex] \: [/tex]
now , put the value of x= -3 in given eqⁿ ∼
[tex] \: [/tex]
[tex] \rm \: f( - 3) = 6( - 3) - 8[/tex][tex] \: [/tex]
[tex]\rm \: f( - 3) = - 18 - 8 [/tex][tex] \: [/tex]
[tex] \underline{ \boxed{\rm \orange{f( - 3) = -26}}}[/tex][tex] \: [/tex]
hope it helps! :)
Lori mixes 1/4 cup of cocoa powder with 3 3/4 cups of silk to make hot cocoa.What is the ratio of cocoa powder to one cup of milk
Answer:
Step-by-step explanation:
The ratio of cocoa powder to one cup of milk is 1/4 cup of cocoa powder to 3 3/4 cups of milk or 1/4 : 3 3/4 or 1 : 15.
=
Choose the correct description of the set {4,8,12,16,...}.
A. {x|x is a multiple of a natural number and -4}
B. {x|x is an odd integer}
C. {x|xEN and x is a multiple of 4 greater than 0}
The correct description of the set {4,8,12,16,...} is {x|xEN and x is a multiple of 4 greater than 0}.
What is a set?
The way a person always represents a set is as a collection of items or elements with definite boundaries. A set is indicated by a capital letter. The number of items in a finite set is known as the cardinal number of the set.
We are given a set {4,8,12,16,...}
In the given set, we can see that they are all multiples of 4 but not -4.
Also, 4 is not an odd integer.
Therefore, it is a multiple of 4 greater than 0.
Hence, the correct description of the set {4,8,12,16,...} is {x|xEN and x is a multiple of 4 greater than 0}.
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Which of the following is a solution on x^2-2x=-8
Find the area of the trapezoid by composition of rectangle and triangles.
Responses
A 88 units2
B 72 units2
C 48 units2
D 84 units2
Classify each polynomial by its degree and number of terms.
One term is referred to as a polynomial function (where n = 1), a 2 polynomials (when n = 2), and a 3 polynomials (when n = 3) depending on the value. Example: The polynomial is categorized according to the quantity of terms as: Monomial: One phrase, three times.
How are the polynomials categorized in terms of degree and term count?There are three different forms of polynomials, depending on how many terms they contain. Monomial, binomial, and trinomial are the three. A polynomial can be divided into zero polynomial, straight polynomial, cubic polynomial, and cubic polynomial depending on its degree.
How can you tell what degree a phrase is?
The degrees of a component in the polynomials equation is given as a+b if a and b are the proponents of the many variables in a term. For instance, the polynomial contains the equation x2y5, whose degree is 2+5 and hence equals 7.
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Classify each polynomial by its degree and number of terms.
The equation 1 – 4∕3x = 1∕2(–x + 7) has what type of solution set?
Question 14 options:
A)
One solution
B)
Infinitely many solutions
C)
Two solutions
D)
No solutions
The linear equation:
1 - (4/3)x = (1/2)*(-x + 7)
Has one solution.
Which type of solution set the equation has?So here we have a linear equation:
1 - (4/3)x = (1/2)*(-x + 7)
To solve it, let's isolate the variable x.
1 - (4/3)*x = -(1/2)*x + (1/2)*7
-(4/3)*x + (1/2)*x = 3.5 - 1
-(8/6)*x + (3/6)*x = 2.5
(-5/6)*x = 2.5
x = (-6/5)*2.5
x = 3
So the linear equation has a single solution, thus, the correct option is A.
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How many solutions does the following system of equations have?
There are zero number of solutions the system of equations have.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=5/2x+2 ------(I) and 2y=5x+8 ------(II)
Substitute equation (I) in (II), we get
2(5/2x+2)=5x+8
5x+4=5x+8
5x-5x=8-4
Therefore, there are zero number of solutions the system of equations have.
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"Your question is incomplete, probably the complete question/missing part is:"
How many solutions does the following system of equations have? y=5/2x+2 and 2y=5x+8
A box contains 3.69 g of supplies. How many milligrams more need to be added to bring the total weight up to an even 10,000 mg?
To make an even 10,000 mg of supplies, _____ mg need to be added.
Answer:
To find out how many milligrams more need to be added to bring the total weight of the supplies to 10,000 mg, we can subtract the current weight from 10,000:
10,000 - 3.69 g = 10,000 - 3,690 mg
Answer:
6,310 mg more need to be added to bring the total weight of the supplies to 10,000 mg.
Please help me with this question.
Answer:
The student's GPA is 3.06
This student did not make the dean's list because their GPA is less than 3.20
(I can't see the drop down choices - I am using my own words)
Step-by-step explanation:
The process of computing the overall GPA based on letter grades with quality points and the number of credit hours for each course is as follows:
Multiply the point value of the letter grade by the number of credit hours. The result is the quality points earned.Total the credit hours for the term.Total the quality points for the term.Divide the total quality points by the total credit hours.The result is the G.P.A. for the term.We have the following data
Course Letter Quality Credit Points x Credit Hours
Grade Points Hours
-----------------------------------------------------------------------------------------------
1 A 4 5 4 x 5 = 20
2 C 2 3 2 x 3 = 6
3 B 3 5 3 x 5 = 15
4 A 4 3 4 x 3 = 12
5 D 1 2 1 x 2 = 2
------------------------------------------------------------------------------------------------
Totals 18 55
-----------------------------------------------------------------------------------------------
Overall GPA = 55/18 = 3.06
Since the minimum GPA to make the dean's list is 3.20 and 3.06 is less than 3.20, the student did not make the dean's list
Find 16/21 divided by 4/3 show your reasoning
Answer: 4/7
Step-by-step explanation:
(16/21)/(4/3) = (16/21)*(3/4) = (16*3)/(21*4) = 48/84 = 4/7
is defined as research that collects information using any kind of numeric and measurable scale and often has limited response options
Quantitative research is a form of qualitative research that focuses on gathering and evaluating data that can be measured and quantified. This study style use numerical data and statistical approaches to uncover patterns, correlations, and trends in data.
Data is frequently collected through surveys, questionnaires, or standardised tests, and the findings are generally evaluated using statistical software. Response options in quantitative research are frequently constrained and organised, with participants picking from a pre-determined range of answers.
The goal of quantitative research is to produce data that is trustworthy, valid, and generalizable to a broader population. Based on the data acquired, this form of study is frequently used to test hypotheses.
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translate the sentence into an equation two less than the product of 6 and a number is 3 .
Answer:
Equation = (6*3) - 2
Solution
Let x represent the unknown number
The number is multiplied by 6
= (6 × x )
= 6x
two is subtracted from the product
= 6x - 2
The product is equated to 3
= 6x-2= 3
Hence the equation is 6x-2= 3
Any help with this will greatly appreciated! <3
Exercise 1: Your friends are organizing a trip for the upcoming spring break. They are
undecided between visiting a national park or visiting a city in the USA. The probability your
friends decide to visit a national park is .35. If your friends decide to visit a national park, the
probability you will join them is .75. On the other hand, if your friends decide to visit a city in
the USA, the probability you will join them is .40.
a) What is the probability you will join them? (Hint: the appropriate visualization
tool might be helpful).
b) If you end up joining them, what is the probability your friends have decided to
visit a national park?
A) The probability that you will join them is 0.523;
B) If you end up joining them, the probability your friends have decided to visit a national park is 0.50.
What is probability?Note that probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
In the above case, Note that to determine the probability that you will join them, we need to use the formula for conditional probability, which is:
P(A and B) = P(A|B) * P(B)
In this case, A is the event that you join them, and B is the event of your friends deciding to visit either a national park or a city in the USA.
Given the above, we have:
P(join and national park) = P(join|national park) * P(national park) = 0.75 * 0.35
P(join and city) = P(join|city) * P(city) = 0.40 * 0.65
Thus to obtain the probability that you will join them: we must add the two probabilities: P(join and national park) and P(join and city)
⇒ P(join) = P(join and national park) + P(join and city)
= 0.75 * 0.35 + 0.40 * 0.65
= 0.523
Thus, it is correct to state that the probability or likelihood that you join them is: 0.523
B) If you decide to join them, the probability that your friends have decided to go to a national park is determined using the Bayes Theorem. This theorem is given as:
P(B|A) = P(A|B) * P(B) / P(A)
Where A is the event of you going with them, and B is the event of your friends deciding to go to a national park.
P(national park|join) = P(join|national park) * P(national park) / P(join)
= 0.75 * 0.35 / 0.525
= 0.5019120459
[tex]\approx[/tex] 0.50
Thus, it is correct to state that the probability your friends have decided to visit a national park is 0.57 if you eventually join them.
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In a sample of size 100 how many observations are below the median? How many are between the median and Q1 (first quartile)? How many are in the IQR? The numbers are listed in the order in which the questions are asked.
Group of answer choices
50, 50, 100
50, 25, 50
50, 75, 25
25, 50, 75
In a sample of size 100, the median splits the data into two equal parts of 50 observations each. So, 50 observations are below the median and 50 observations are above the median.
The first quartile (Q1) separates the lowest 25% of the data from the rest, so 50 observations are between the median and Q1.
The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and Q1, and represents the range of the middle 50% of the data. Since the IQR contains both Q1 and the median, it encompasses all observations between Q1 and the median,
or a total of 75 observations.
therefore the answer is 25,50,75
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Place theindicated product in the proper location on the grid.
(2a²b) 4
The simplified exponential notation of the given expression is 9a²b
What is an exponential expression?
An expression in the form of a² is called exponential expression.
The simplified exponential notation of the given expression is 18 * a³ b² / 2ab
The given expression is: 18a³b² / 2ab
We can write the above expression as:
(18/2 ) (a³ / a ) (b² / b )
We know that
aˣ / aⁿ= aˣ⁻ⁿ
a³ / a = a³⁻¹ = a²
b² / b = b²⁻¹= b
So, ( 18/2) ( a³/a) (b²/ b) = 9 a²b
Hence, The simplified exponential notation of the given expression is 9a²b
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Patients coming to a medical clinic have a mean weight of 207.6 pounds, with a standard deviation of 22.6 pounds. The distribution of weights is not assumed to be symmetric.
Between what two weights does Chebyshev's Theorem guarantee that we will find at least 95% of the patients?
Round your answers to the nearest tenth. Enter the pounds in ascending order.
Between 105.9 and 309.3 pounds, Chebyshev's Theorem guarantee that we will find at least 95% of the patients.
k = 4.5.
Weight 4.5 standard deviations below the mean is 207.6 − 4.5 (22.6) = 105.9 pounds.
Weight 4.5 standard deviations above the mean is 207.6 + 4.5 (22.6) = 309.3 pounds.
Therefore, at least 95% of patients weigh between 105.9 and 309.3 pounds.
About Chebyshev theoremIn probability theory, the Chebyshev inequality guarantees that for any sample data or probability distribution, nearly all values are close to the mean. Precisely, that no more 1/k2 of the distribution value exceeds the k standard deviation.
Chebyshev's inequality theorem can be used to find the probability range for an unknown distribution based on its mean and variance.
Chebyshev is named after a Russian mathematician, although the first formulation of the inequality was obtained from his colleague, Irénée-Jules Bienaymé. Chebyshev's inequality theorem was introduced without any proof in 1874, which later, in 1884,
Chebyshev's student, Andrey Markov presented a proof. Therefore, in the context of the analysis, the Chebyshev inequality is also expressed in the Markov inequality.
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You can model the population of a certain city between the years 1970 and 1955 by the radical function P(x)=80000x−1940√3 . Using this model, in what year was the population of that city 290,000?
The year the population of that city was 290,000 is 1988.
What year was the population of that city 290,000?A model function is a mathematical or computational representation of a system or process that is designed to capture its behavior, relationships, and interactions.
The model is p(x) = 80,000 ∛(x - 1940)
Now use p(x) = 290,000and solve for x
290,000 = 80,000 ∛(x - 1940) =
290,000 / 80,000 = ∛(x - 1940)
29/8 = ∛(x - 1940)
x - 1940 = [29/8]³
x - 1940 = 47.63
x = 1940 + 47.63
x = 1987.63
Therefore, the year is 1988
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The graph of f passes through (- 8, 8) and is perpendicular to the line that has an x- intercept of 1 and a y-intercept of - 2
Equation of graph of f is : y = (-1/2)x + 4
What is line?A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.
Given,
The graph of f passes through (- 8, 8)
Line that has
x- intercept a = 1
y-intercept b = - 2.
Intercept equation of the line
x/a + y/b = 1
x/1 + y/-2 = 1
x - y/2 = 1
-y/2 = 1-x
y = 2x - 2
Comparing it with slope intercept equation of the line y = mx + c
slope m = 2
Product of slopes of two perpendicular lines = -1
If m' is the slope of its perpendicular
then m.m' = -1
2.m' = -1
m' = -1/2
Equation of the line
y - y₁ = m'(x - x₁)
Graph of f passes through (-8, 8) and is perpendicular to line y = 2x - 2
y -8 = (-1/2)(x - -8)
y - 8 = (-1/2)(x+8)
y - 8 = (-1/2)x - 4
y = (-1/2)x + 4
Hence, y = (-1/2)x + 4 is the equation graph of f.
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A metallurgist has one alloy containing 35% titanium and another containing 69% titanium. How many pounds of each alloy must he use to make 53 pounds of a third alloy containing 40% titanium?
Answer:
Let x be the amount of alloy 1 used, and y be the amount of alloy 2 used.
We know that:
x + y = 53 (total weight of alloy 3 is 53 pounds)
0.35x + 0.69y = 0.40(53) (40% of the alloy 3 is titanium)
We can use the first equation to solve for one of the variables in terms of the other:
y = 53 - x
Substitute this expression into the second equation:
0.35x + 0.69(53-x) = 0.40(53)
0.35x + 36.97 - 0.69x = 21.2
-0.34x = -15.77
x = 46.44 pounds of alloy 1.
y = 53 - x = 6.56 pounds of alloy 2.
Solve for x: −7 < x − 1 < 8
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
To solve this inequality, you can add 1 to both sides of the inequality to get:
−7 + 1 < x − 1 + 1 < 8 + 1
-6 < x < 9
This inequality is a compound inequality, which is made up of two separate inequalities joined by the word "and".
