The dimensions of the box if it is to use the minimum possible amount of metal are,
⇒ 2.714 m, 2.714 m, 1.358 m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A container with an open top is to have 10 m³ capacity.
Now,
Let the dimensions are x, y and z.
Since, Volume of box = 10 m³
Hence, We get;
⇒ xyz = 10
⇒ z = 10/xy
Since, A container is open in top.
Hence, The surface area = 2xz + 2yz + xy
Substitute z = 10/xy;
⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy
= 20/y + 20/x + xy
For minimum metal;
⇒ d (S.A)/ dx = 0
⇒ - 20/x² + y = 0
⇒ y = 20/x² ..(i)
And, d (S.A) / dy = 0
⇒ - 20/y² + x = 0
⇒ x = 20/y² ..(ii)
Divide equation (i) and ((ii);
⇒ x = y
Hence, We get;
⇒ xyz = 10
⇒ x³ = 10
⇒ x = 2.714
And, y = 2.714
So, The value of z is,
⇒ z = 10/xy
⇒ z = 10 / 2.714×2.714
⇒ z = 1.358 m
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The amount of vitamin C found in one cup of six
varieties of orange juice is shown below. What is the
median amount of vitamin C in the different varieties?
104 mg, 85 mg, 83 mg, 100 mg, 89 mg
Answer:
Question:The amount of vitamin C found in one cup of six varieties of orange juice is shown below. What is the median amount of vitamin C in the different varieties?104 mg, 85 mg, 83 mg, 100 mg, 89 mgSolution:First thing first, we've to arrange the data in an ascending order=> 83mg ,85mg ,89mg ,100 mg ,104 mg
Now ,Since the no. of observation is odd(here,5), we'd apply this formula[tex] = > (\frac{n + 1}{2})[/tex]
Where ,n= No. of observations, Hence, the median of the above data[tex] = > ( \frac{5 + 1}{2}) \\ = > \frac{6}{2} \\ = > 3[/tex]
is the third observation ↦89mg[tex] \\ \\ [/tex]
Hope it helps
-------☆ﾟ.･｡ﾟᵴɒƙυᴚᴀ_ƨȶäᴎ❀
The median amount of vitamin C in the different varieties is 89mg.
what is median?The median is the value that's exactly in the middle of a dataset when it is ordered.
Given:
104, 85, 83, 100, 89
On arranging the given data:
83, 85, 89, 100, 104
as, the data is in odd number.
So,
median = (n+1)/2
=(5+1)/2
=3
The third element is 89.
Hence, the median amount of vitamin C in the different varieties is 89mg.
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A firm desires to control inventory levels so as to minimize the sum of holding and order costs. It costs the firm $50 to place an order. The firm estimates its annual carrying charge is 20%. Weekly demand is 100 units, and there are 50 weeks in the work year. The item costs $10 per unit. The lead-time for the product is 3 weeks. Assume that there are 5 working days per week. What quantity of items should the firm order each time so as to minimize total inventory costs, i.e., what is the EOQ?
A. 100
B. 224
C. 500
D. 1000
E. none of the above
Answer:
C. 500
Step-by-step explanation:
Given that
The ordering cost per order is $50
The carrying cost percentage is 20%
The weekly demand is 100 units and there are 50 weeks in the work year
The cost per unit is $10
We need to find out the economic order quantity i.e. EOQ
So we applied the above formula
= √(2 × weekly demand × no of weeks × ordering cost) ÷ √(carrying cost × cost per unit)
= √(2 × 100 × 50 × $50) ÷ √(20% × $10)
= √(500,000 ÷ 2)
= 500 units
hence, the option c is correct
What does this statement mean? The probability of drawing a brown sock from a drawer of
socks is 0.
Answer:
there are no brown socks
Step-by-step explanation:
there is zero possibility of pulling a brown sock from the drawer fro this to be possible there would have to be no brown socks
A line has a slope of 3/8 and passes through the point (15.2,-7)
The equation of the line in point-slope form is???
ANSWERS↓↓
Considering the definition of a line, the correct answer is option A: the equation of the line in point-slope form is y + 7= 3/8(x- 15.2)
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.The point-slope form of an equation of a line is written as y-y₁=m(x-x₁)
where:
m is the slope.(x₁, y₁) are the coordinates of the point.Equation of a line in this caseIn this case, you know:
A line has a slope of 3/8.The line passes through the point (15.2,-7).The point-slope form of the line is written as:
y- (-7)= 3/8(x- 15.2)
y + 7= 3/8(x- 15.2)
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Two cards are drawn at random from a well shuffled pack of cards. What is the probability that
i)both are spades or both are diamonds?
ii)both are queens or both are red coloured?
iii)both are diamonds or neither is a king?
Answer:
Step-by-step explanation:
1 in a tenth of a million. I did the math with all the cards and how many are kinds diamonds or red or queens yk.
Which of the following functions describes the graph of g(x)? (5 points)
Rational function with one piece decreasing from the left asymptotic to the line y equals 2 and going through a hole at the point negative 2 comma eight-fifths and going down through the point 2 comma 0 asymptotic to the line x equals 3 and another piece decreasing from the left asymptotic to the line x equals 3 and going through the point 5 comma 3 going up to the right asymptotic to the line y equals 2
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus 5 x plus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus 5 x plus 6 end quantity
The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that,
The function g(x).
The graph of a function never touches the x = 1 line
At x = -1 there will be a vertical asymptote.
At x = -2 there will be a horizontal asymptote.
The equation of the function g(x) will be:
g(x) = (2x + 4)/(x + 1)
The equation of rational function is g(x) = (2x + 4)/(x + 1)
Therefore, g(x) = (2x + 4)/(x + 1) is correct.
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What's the inches equivalent of 63.5 millimeters? A. 2.5, B. 24, C. 3.2. D 31
Answer: A
Step-by-step explanation: 2.5 inches = 63.5 millimeters
Please answer the following answer, AND NO LINKS OR YOU WILL GET REPORTED
Answer:
Step-by-step explanation:
A. 39ft2
you draw a line at top of shape. that small rectangle area is 3ft2. the bigger rectangle area is 36ft2. 36+3= 39ft2
Answer:
[tex]\text{This is a fairly simple problem:}\text{Answer= }3*1+36=39ft^2[/tex]
A
calculate the area of a circle with a diameter of 0, 8m
Answer:
50.24=4squared times pie
Step-by-step explanation:
Answer:
The area of a circle with a diameter of 0.8 meters is approximately 0.50 [tex]m^2[/tex].
Step-by-step explanation:
Since the diameter of the circle is 0.8 meters, that means the radius of the circle would be 0.4 meters. The area of a circle can be found by the formula [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]0.4^2*\pi[/tex] = [tex]0.16 * \pi[/tex] ≈ 0.50 [tex]m^2[/tex].
help me please with the question
Answer:
pretty sure its 499 or 498 but im horible at math so dont quote me on that
tep-by-step explanation:
if 6p = 120 what is p
Answer:
p = 20
Step-by-step explanation:
120 divided by 6 would = 20
Answer: p = 20
Step-by-step explanation:
120/6=20
6x20=120
Please help thank you
Answer:
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Step-by-step explanation:
Help ASAP!!! Pleaseeeeee
Answer:
y = 2 x 2 + 2 x + 4 should be the function.
Step-by-step explanation:
The last one can be anything, it said to predict so basically guess. From what I read from the graph, the y ( number of fruit flies ) doubles.
4 + 4 = 8
8 + 8 = 16
16 + 16 = 32
32 + 32 = 64
I'm sure your able to catch on.
I put a photo of the graph for your sketch, if you need help labeling then you can ask me :)
50 POINT ANSWER (screenshot attached)
Step-by-step explanation:
x + 6y = 8 ........... ( ×2 ) ....... ( 1 )
2x + 4y = -8 ......... ( × 1 ) ....... ( 2 )
2x + 12y = 16
- - -
2x + 4y = -8
+12y - ( +4y ) = 16 - 8
12y - 4y = 8
8y = 8
divide both sides by the coefficient of y ( 8 )
8y / 8 = 8 / 8
y = 1
substitute for x in equation ( 1 )
x + 6y = 8
x + 6 ( 1 ) = 8
x + 6 = 8
x = 8 - 6
x = 2
x = 2 , y = 1
Hey guys can you help me with this math problem I'm stuck
The transformation of function y = |x| is g(x) = f(x + 4) + 2. The equation of transformed graph is y = |x + 4| - 2
What is a function?
An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is y = |x|.
The vertex is (0,0). The vertex of the transformed function is (-4,-2)
It means the graph is shifted 4 units left sides and 2 unit downward direction.
The graph of f(x) is horizontally shifted by a units on left side then the equation function becomes f(x + a).
The graph of f(x) is horizontally shifted by a units on right side then the equation function becomes f(x - a).
The graph of f(x) is vertically shifted by a units upward then the equation function becomes f(x)+a.
The graph of f(x) is vertically shifted by a unit downward then the equation function becomes f(x)-a.
The equation of the transformed equation is g(x) = f(x + 4) - 2
g(x) = |x + 4| -2
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The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard
deviation of 5 points.
About what percent of students have scored less than 45 points?
0.15
2.5
15.5
34
Answer:
0.135%
Step-by-step explanation:
Given :
Mean, m = 60
Standard deviation, σ = 5
x = 45
The Zscore = (x - m) / σ
Z = (45 - 60) / 5 = - 15 / 5 = - 3
P(Z < - 3) = 0.0013499
0.0013499 * 100%
= 0.13499%
Only about 0.135% scored below 45
Compute the MIRR statistic for project I if the appropriate cost of capital is 11 percent.
Cash flow -12,000, 5830, 4680, 2,500
The MIRR statistic for the project I given the cost of capital and the reinvestment rate, is 7. 43 %.
How to find the MIRR statistic ?A monetary indicator of an investment's allure is the modified internal rate of return or MIRR. Ranking equivalent alternative investments is done in capital budgeting.
You can use a spreadsheet to find the MIRR by first ordering the cash flows as shown in the attached image. Then use the = MIRR function.
The cost of capital is the finance charge which is 11 %. The reivestment rate will be the same as the finance charge if not given so it will be 11 % as well.
The MIRR is therefore 7 .43 %.
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two angles add up to 180 if and only if they are supplementary
Answer:
True
Step-by-step explanation:
You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."
Supplementary anglesTwo supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.
Find the value of x .
Answer:
x = 45°
Step-by-step explanation:
x° + 45° + 90° = 180°
x° + 135° = 180°
x° = 180° – 135°
x° = 45°
i hope this helped
1. What property could you use to show that these two triangles are congruent? QRP XWY
The property that could be used to determine that the triangles are congruent is the SSA congruent theorem
How to determine the congruent propertyFrom the question, we have the following parameters that can be used in our computation:
Triangles = QRP and XWY
On the triangles, we can see that:
Two corresponding sides on both triangles are marked with I and IIThe triangles have a pair of corresponding anglesThis means that we make use of the SSA congruent theorem
The SSA congruent theorem implies that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.
In this case, we have
Congruent sides: RQ and HG & PR and HF
Congruent angles: Angles Q and G
Hence, the additional information on the congruency of the triangles is the SSA theorem
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What is the area of the circle with a radius of 21 in . and a circumference of 131.88 in ?
There are a total of 32 books and calculators on a table. The ratio of the number of books to the
number of calculators is 5: 3. How many calculators are on the table?
A. 3
B. 12
C. 20
D. 24
Answer:
B. 12
Step-by-step explanation:
Your ratio of 5:3 means that the ratio includes 8 objects (5+3). If you multiply the whole ratio by 4, then you have 32 objects on your table. Multiplying your ratio by 4 gives you 5*4 : 3*4 which is 20:12. and since 20 is your amount of books and 12 is your amount of calculators, you have 12 calculators on your table.
A cell tower is located 3 miles east and 6 miles north of the center of a small town. The cell tower has a coverage radius of 4 miles.
Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.
A house is located 7 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?
The house is located 6.87 miles to the east of the cell tower.
What is Pythagoras theorem?“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given:
Let the center of the town represent the origin (0,0).
Also 1 unit = 1 mile.
Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)
The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:
(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.
Then, (x - 3)² + (y - 6)² = 4²
(x - 3)² + (y - 6)² = 16
b) The house is 7 miles north. It can be represented by y = 5 line.
To find the distance east of the house we have to substitute y = 5 and solve for x,
(x - 3)² + (y - 6)² = 16
(x - 3)² + (5 - 6)² = 16
(x - 3)² + 1 = 16
(x - 3)² = 15
(x - 3) = ±3.87
x= 3 ±3.87
x= 6.87 or 0.87.
Hence, the house is located 6.87 miles to the east.
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ANSWER ASAP PLS <3
20 points !
Which expression matches the graph?
Answer: the answer is b?
hope this helps
If c = d, then a + c = d + a true or false
Answer:
True
Step-by-step explanation:
First, you need to subtract a then that would make a 0
Answer: true
Step-by-step explanation: c and d are the same, so a+c and a+d will be the same
What is the volume of the rectangular prism shown below?
A. 476 in³
B. 4,760 in³
C. 1,700 in³
D. 340 in³
Answer:
B. 4760 in³
Step-by-step explanation:
V= l×w×h
=34×10×14
=4760 in³
N is an integer -1 < n < 4 list the possible values of n
Answer:
0 1 2 3
Step-by-step explanation:
Since n is an integer
We have n = { 0 1 2 3 }
help me with this question please
Answer:
[tex] \sf \: d) \: 82[/tex]
Step-by-step explanation:
Given information,
→ d = 10
→ u = 7
→ e = 3.2
The expression is,
→ d(e + 5)
Let's evaluate the expression,
→ d(e + 5)
→ 10(3.2 + 5)
→ 10 × 8.2
→ 82
Hence, option (d) is correct.
Answer:
Option D) 82
Step-by-step explanation:
Given ,
d = 10
u = 7
e = 3.2
To Find : [tex]d(e+5)[/tex]
Applying the values in the equations we get
[tex]10(3.2+5)\\[/tex] Applying Distributive property
[tex]32+50 = 82[/tex]
Hence , Option D) is the answer
The dollar value v (t) of a certain car model that is t years old is given by the following exponential function. v (t) = 26,000 (0.84)¹ Find the value of the car after 7 years and after 12 years. Round your answers to the nearest dollar as necessary. Value after 7 years: Value after 12 years: $0
I think it's 84 I'm not good with math though I multipled 7 and 12
1/950/18/4
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
40°
(6b+ 2)°
OLIC
One possible equation is (6b+2)+40 = 90
That equation solves to b = 8
======================================================
Explanation:
The angles (6b+2) and 40 degrees combine to form a right angle, aka 90 degree angle. This is because the upper angle is 90 degrees, so the remaining portion is 180-90 = 90.
So (6b+2)+40 = 90 is one possible equation.
Let's solve for b.
(6b+2)+40 = 90
6b+42 = 90
6b = 90-42
6b = 48
b = 48/6
b = 8
---------------
A slight alternative.
The angles (6b+2), 40, and the 90 degree angle form a straight line.
The three angles add to 180
(6b+2)+(40)+(90) = 180 is another possible equation
6b+132 = 180
6b = 180-132
6b = 48
b = 48/6
b = 8