A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1728 mailboxes this week. If each mailbox
has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the
value 3.14 for x, and round up your answer to the next square meter.
?
Answers
Answer:
2145 m^2
Step-by-step explanation:
The area of one mailbox = the area of a rectangular box - the top of the box plus half the area of a cylinder.
SA = SA(box) - SA(top) + ½SA(cylinder)
1. Surface area of box
The formula for the surface area of a rectangular box is
SA = 2(lw + lh + wh)
Data:
l = 0.55 m
w = 0.3 m
h = 0.4 m
Calculations:
2(Top + Bottom = 2lw = 2 × 0.55 × 0.3 = 0.33 m²
2(Left + Right) = 2wh = 2 × 0.55 × 0.4 = 0.44 m²
2(Front + Back) = 2lh = 2 × 0.3 × 0.4 = 0.24 m²
Total area = 1.01 m²
2. Surface area of cylinder
The formula for the surface area of a cylinder is
SA = A(top) + A (base) + A(side) = 2A(base) + A(side)
Data:
d = 0.3 m
h = 0.55 m
Calculations:
r = ½d = ½ × 0.3 = 0.15 m
3. Excluded area
1 top = ½ × 0.33 m² = 0.165 m²
½ cylinder = ½ × 0.6594 m² = 0.3297 m²
Total excluded = 0.4947 m²
4. Surface area of 1 mailbox
SA = (1.01 + 0.6594 - 0.4927) m² = 1.1767 m²
5. Total area of 1823 mailboxes
Answer:
We can start by calculating the total surface area of each mailbox, which includes the surface area of the box and the surface area of the half-cylinder top.
The dimensions of the mailbox are given in the figure, with height h = 40 cm, length l = 60 cm, and width w = 30 cm. The radius of the half-cylinder top is also given as r = 15 cm.
The surface area of the box can be calculated as follows:
Front and back faces: 2lw = 2(60 cm)(40 cm) = 4800 cm^2
Top and bottom faces: 2wh = 2(30 cm)(40 cm) = 2400 cm^2
Side faces: 2lh = 2(60 cm)(40 cm) = 4800 cm^2
Total surface area of the box = 4800 cm^2 + 2400 cm^2 + 4800 cm^2 = 12000 cm^2
The surface area of the half-cylinder top can be calculated as:
Curved surface area: πrh = 3.14(15 cm)(40 cm) = 1884 cm^2
Circular top and bottom faces: 2πr^2 = 2(3.14)(15 cm)^2 = 1413 cm^2
Total surface area of the half-cylinder top = 1884 cm^2 + 1413 cm^2 = 3297 cm^2
Therefore, the total surface area of each mailbox is:
Total surface area = surface area of box + surface area of half-cylinder top
= 12000 cm^2 + 3297 cm^2
= 15297 cm^2
To find the total surface area of 1728 mailboxes, we can multiply the surface area of one mailbox by the number of mailboxes:
Total surface area of 1728 mailboxes = 1728 mailboxes x 15297 cm^2 per mailbox
= 26,431,616 cm^2
Converting this to square meters, we get:
Total surface area of 1728 mailboxes = 264,316.16 cm^2 = 26.43 m^2 (rounded up)
Therefore, approximately 27 square meters of aluminum will be needed to make these mailboxes.
I Hope This Helps!
Related Questions
Mr. McDowell's class read the first $52$ pages of a book during the first week of school, $46$ pages during the second week, $51$ pages during the third week, $42$ pages during the fourth week, $30$ pages during the fifth week, and $44$ pages during the sixth week. There are $75$ pages left to read. How many pages does the book have in all?
Answers
Answer:
340 pages total
Step-by-step explanation:
52+46+51+42+30+44+75=340
hope this helped!
Answer:
340 pages total
Step-by-step explanation:
Just add all the numbers together :)
What is the value of the digit in the ones place?
2,615
A. 50
B. 5
OC. 2,000
OD. 100
Answers
The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2. What is the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2?
(Scroll Down for Answer!)
Answers
the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2 is V = 253.5 * (400/390) * (20/10) = 263.0 in^3
V = 253.5 * (T/390) * (20/P)
V = 253.5 * (400/390) * (20/10)
V = 263.0 in^3
The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. Knowing this, we can calculate the volume for any given temperature and pressure by using the formula V = 253.5 * (T/390) * (20/P). In this problem, the device was calibrated to give V=253.5 in^3 when T=390 degrees and P= 20 lb/in^2. To find the volume on this device when the temperature is 400 degrees and the pressure is 10 lb/in^2, we plug these values into the formula, which gives us V = 253.5 * (400/390) * (20/10) = 263.0 in^3.
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PLZ HELP OFFERING BRAINLIEST
Find the difference. 2/5 (d-10) -2/3 (d+6)
Answers
\(\dfrac 25 (d-10) - \dfrac 23(d+6)\\\\\\=\dfrac{6}{15} (d-10) - \dfrac{10}{15} (d+6)\\\\\\=\dfrac{6(d-10) -10(d+6)}{15}\\\\\\=\dfrac{6d -60-10d-60}{15}\\\\\\=\dfrac{-4d-120}{15}\\\\\\=-\dfrac{4d}{15} - 8\)
What is the midpoint of AC on the grid below?
Answers
Answer: Coordinates of the point E of the middle AC (-1 ; 1 )
Step-by-step explanation:
The middle of AC can be calculated by the formula :\(\sf \displaystyle M=\left (\frac{x_1+x_2}{2} \ ; \ \frac{y_1+y_2}{2} \right ) =(x_m \ ; \ y _m )\) In our case :A(2 ; 4) ; C(-4 ; -2) Then :\(\sf \displaystyle M=\left (\frac{2+(-4)}{2} \ ; \ \frac{4-2}{2} \right ) =(-1 \ ; \ 1 )\) Coordinates of the point E of the middle AC (-1 ; 1 )
20 POINTS for that someone can give me just the anwers
Answers
Answer:
Solutions for x are 2, 1/3
Everything in the second image is correct except you forgot to put 2 for c in the quadratic formula.
Answer:
:)
Step-by-step explanation:
Tom buys 5 shirts for $10 total. He also buys shorts for
$4.50 each. What inequality represents the situation?
He only has $50 to spend/
A. 5x + 10 < 50
B. 4.50x + 5 < 10
c. 10+ 4.5x ≤ 50
d. 5x +4.5x < 50
Answers
Answer:
c
Step-by-step explanation:
we know he spends 10$ on shirts but not how much he spends on shorts. Since we know he has $50 to spend, we can buy shorts up to the $50 limit including $50. The only inequality that includes $50 is c
C, 10+ 4.5x ≤ 50
Happy to help, have a great day! :)
find the slope of the lined graph
Answers
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
As you probably know, there is still a difference in wages for men vs. women in this country. Besides straight-up
discrimination and bias (which has been lessening over the decades), people point to many other factors that continue
to keep the average amount earned by a full-time, year-round female employee lower than males, on average (like
women taking more time off for maternity than men do for paternity, career selection, etc.).
Every ten years as part of the census, data is collected that gives the median income of "full-time year-round workers."
In 2010 the median income of FTYR workers was $42,800 for men, compared to $34,700 for women. In 1960, if you
adjust the wages to 2009 dollars, wages were $38,907 for men and $23,606 for women.
Based on this data, when might we predict women's wages might catch up to men's? Show all work you did to get
your answer. AND NO LINKS TO FILES OR ANYTHING LIKE THAT.
Answers
9514 1404 393
Answer:
year 2066
Step-by-step explanation:
In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.
Then we can write equations for men's and women's wages as follows:
Using the 2-point form of the equation for a line, we have ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Men's wages
y = (42800 -38907)/(2010-1960)(x -1960) +38907
y = 77.86(x -1960) +38907
y = 77.86x -113,698.6 . . . . . where x is the year
Women's wages
y = (34700 -23606)/(2010 -1960)(x -1960) +23606
y = 221.88x -411,278
These values are equal when ...
77.86x -113,698.6 = 221.88x -411,278
297,580.2 = 144.02x . . . . . . . add 411278 -77.86x
2066.2 = x . . . . . . . divide by the coefficient of x
Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.
_____
Alternate solution
In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.
The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.
_____
Additional comment
The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.
Pedro and Rebecca were trying to solve the equation: 0.1x^2-0.7x+1.2=0. Pedro said, “I can multiply the entire equation by 10 and then factor. Then I can solve using the zero product property.” Rebecca said, “I'll solve using the quadratic formula with a=0.1, b=-0.7, c=1.2.” Whose solution strategy would work?
Answers
Answer:both
Step-by-step explanation: I take it on khan and I get it right!
Both methods will work, but Rebecca's one is harder than Pedro's method.
Whose solution strategy would work?
Pedro wants to multiply the whole equation by 10, so he can work with whole numbers which is easier, while Rebecca prefers to just use Bhaskara's formula with the given coefficients.
With that in mind, neither method has a problem, so both will work fine. The only problem that could come is that for Rebbeca, when she wants to evaluate the square root in the Bhaskara's formula, she will get:
\(\sqrt{(-0,7)^2 - 4*0.1*1.2 } = \sqrt{0.01}\)
And that is kinda impossible to compute by hand, but if she has a calculator, everything is fine.
Then we conclude that both methods will work.
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find the missing angle measure
Answers
Answer:
<1 = 77
<2 = 103
<3 = 77
Step-by-step explanation:
<1 = 77 (180-103) by Linear Pair Postulate
<2 = 103 by Vertical Angles Theorem
<3 = 77 by Vertical Angles Theorem
Given f (x) = x2 + 3x + 4, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?
Answers
The function is given as,
\(f(x)=x^2+3x+4\)It is asked to determine the value of the expression,
\(\frac{f(2+h)-f(2)}{h}\)Substitute x = 2+h in the function,
\(\begin{gathered} f(2+h)=(2+h)^2+3(2+h)+4 \\ f(2+h)=2^2+h^2+2(2)(h)+3(2)+3(h)+4 \\ f(2+h)=4+h^2+4h+6+3h+4 \\ f(2+h)=h^2+7h+14 \end{gathered}\)Substitute x = 2 in the function,
\(\begin{gathered} f(2)=(2)^2+3(2)+4 \\ f(2)=4+6+4 \\ f(2)=14 \end{gathered}\)Substitute these values in the required expression,
\(\begin{gathered} \frac{f(2+h)-f(2)}{h} \\ =\frac{(h^2+7h+14)-14}{h} \\ =\frac{h^2+7h+0}{h} \\ =\frac{h(h+7)}{h} \\ =h+7 \\ =7+h \end{gathered}\)Thus, the value of the expression is equal to
\(7+h\)Therefore, 1st option is the correct choice.
What is 56 divided by 89?
Answers
Answer:
0 or 0.62921348314 (if done by the calculator)
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 89 on the left side and the dividend 56 on the right side like this:
8 9 ⟌ 5 6
Step 2:
The divisor (89) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:
0
8 9 ⟌ 5 6
Step 3:
Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer below the dividend.
0
8 9 ⟌ 5 6
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (5 - 0 = 5) and write the answer below.
0
8 9 ⟌ 5 6
- 0
5
Step 5:
Move down the 2nd digit of the dividend (6) like this:
0
8 9 ⟌ 5 6
- 0
5 6
Step 6:
The divisor (89) goes into the bottom number (56), 0 time(s). Therefore, put 0 on top:
0 0
8 9 ⟌ 5 6
- 0
5 6
Step 7:
Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer at the bottom:
0 0
8 9 ⟌ 5 6
- 0
5 6
0
Step 8:
Subtract the result in the previous step from the number written above it. (56 - 0 = 56) and write the answer at the bottom.
0 0
8 9 ⟌ 5 6
- 0
5 6
- 0
5 6
On a number line, 7.05 would be located Choose all answers that make a true statement.
7.05
A. between 8 and 9
B. to the right of 7.02
C. to the left of 7.08
D. between 8.0 and 8.1
Answers
On a number line, 7.05 would be located
B. to the right of 7.02C. to the left of 7.08How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Number = 7.05
The analysis of its position s as follows:
A. between 8 and 9: False. 7.05 is to the left of 8 and is not between 8 and 9.B. to the right of 7.02: True. 7.05 is greater than 7.02, so it is to the right of 7.02 on the number line.C. to the left of 7.08: True. 7.05 is less than 7.08, so it is to the left of 7.08 on the number line.D. between 8.0 and 8.1: False. 7.05 is not between 8.0 and 8.1.So, the true statements are B and C.
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Due in a MINUTE!!! Need help!
Answers
Answer:
GH = 15
Step-by-step explanation:
In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:
\(9x - 3 = \frac{1}{2} (19 + 5x + 1)\)
\(18x - 6 = 5x + 20\)
\(13x = 26\)
\(x = 2\)
\(9(2) - 3 = 18 - 3 = 15\)
A right triangle has a hypotenuse with a length of 130 cm. One leg has a length of 100 cm. What is the length of the other leg of the triangle? A. 130 B. 6900 C. 65 D. 130
Answers
Answer:
B. √6900
Step-by-step explanation:
The square length of hypotenuse is equal to sum of square length of two legs let x represent the other leg
130^2 = 100^2 + x^2
16900 = 10000 + x^2 subtract 10000 from both sides
6900 = x^2 find the root for both sides
x = √6900
The average number of chocolate chips in one ounce is 63 with a standard deviation of 1.8. Find the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips .
Answers
The probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips is 0.6644.
How to find the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chipsUsing the z-score formula to standardize the values and find the probability using a standard normal distribution table:
z1 = (62 - 63) / 1.8 = -0.56
z2 = (66 - 63) / 1.8 = 1.67
Using the standard normal distribution table, we find that the area to the left of z1 is 0.2881 and the area to the left of z2 is 0.9525.
Therefore, the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips is:
P(62 < x < 66) = P(z1 < z < z2) = P(z < z2) - P(z < z1)
= 0.9525 - 0.2881
= 0.6644
Therefore, the probability is approximately 0.6644.
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What is the value of y?
Answers
Answer:
Step-by-step explanation:
Remark
The value of the y can be found by using the Geometric Mean. To use the said mean, you must compare parts of one triangle to parts of the second triangle. In this case, the small triangle containing boy 4 and y, must be compared to the triangle use y and 12
Formula
This translates to
4 / y = y/12
Explanation. The two triangles y and 4 and y and 12 are similar. The short side on the small right triangle on the left is 4. The second longest side on the same triangle is y.
In the triangle containing y and 12 The short side is y and the second side length is 12. You have to read this a couple of times to get the meaning of the two ratios.
Solution
4/y = y / 12 Cross multiply
y^2 = 4 * 12
y^2 = 48 Take the square root of both sides.
√y^2 = √48
y = √2 * 2 * 2 * 2 * 3
y = 2 * 2 * √3
Answer
y = 4√3
Answer:
y = 4√3 y = 4√3
Step-by-step explanation:
i hope it's help
I need help please this is confusing
Answers
Step-by-step explanation:
slope formula when it's perpendicular : m1 × m = -1
Now Differentiate the quadratic function given.
d/dx ( x^2 - x + 1 ) at an x value of -1 from the point "(-1 , 3 )"
= 2x - 1 .... plug in the x value
= 2 × -1 - 1 = -3.
Use this equation...
y - y1 = m(x - x1)
m = slope = derivative at x = -1
y1 = value found by subbing -1 into the original function
x1 = the x value often given.
y - 3 = 1/3 (x + 1)
= 1/3x + 1/3 + 3
y = 1/3x + 10/3.
not sure about this one - it probably intersects at the x & y intercepts of the equation of the normal line.
y = 0 + 10/3 = 10/3
1/3x = 0 - 10/3
x = -10/3 / 1/3 = -10
so the point .... (-10 , 10/3)
A vase is shaped like a triangular prism. The volume of the vase is 540 cm. The area of the base is 120 cm. What is the height of the vase?
Answers
\(\textit{volume of a prism}\\\\\ V=Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ V=540\\ B=120 \end{cases}\implies 540=120h\implies \cfrac{540}{120}=h\implies \cfrac{9}{2}=h\)
Answer:
1.5cm height giving ace
Simplify 0.4(−4.5). (5 points)
Answers
Answer:
-1.8, multiply them, then add the negative sign
Step-by-step explanation:
Answer:
its -1.8
Step-by-step explanation:
i got it right on my exam :)
-Hope this helps!
You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started
Answers
Starting position = Treasure location + distance sailed to the left
Since we know going in the left direction typically is a means of subtraction, we can use inverse operations to solve this. We can set up an addition problem to solve this:
Starting position = 0.085 + 0.055
Starting position = 0.03 units
Therefore, the ship started at 0.03 units.
Please I need help
The area of the shaded region is
Answers
The area of the shaded region in the standard normal distribution can be found to be 0.3510.
How to find the area in the standard normal distribution curve ?To find the area of the shaded region between -2.25 and -0.35 in a standard normal distribution, you would use a Z-table or a calculator with a built-in Z-table function.
Area between -2.25 and -0.35 = Area to the left of -0.35 - Area to the left of -2.25
Area to the left of -0.35 = 0.3632
Area to the left of -2.25 = 0.0122
find the difference between these two areas:
Area between -2.25 and -0.35 = 0.3632 - 0.0122 = 0.3510
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NO LINKS!! Please help me with this statement Part 2mm
Answers
Answer:
y = 2x² + 8x - 5--------------------------------------
Vertex form of a quadratic function:
y = a(x - h)² + k, where (h, k) is vertex and a - constantGiven (h, k) = (-2, -13) and a point (0, - 5).
Substitute all into equation and solve for a:
-5 = a(0 - (-2))² - 13-5 = 4a - 134a = 13 - 54a = 8a = 2The parabola is:
y = 2(x + 2)² - 13Convert it to the standard form:
y = 2(x + 2)² - 13y = 2(x² + 4x + 4) - 13y = 2x² + 8x + 8 - 13y = 2x² + 8x - 5Answer:
\(f(x)=2x^2+8x-5\)
Step-by-step explanation:
\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)
Given:
Vertex = (-2, -13)Point = (0, -5)Substitute the given vertex and point into the Vertex formula and solve for a:
\(\implies -5=a(0-(-2))^2+(-13)\)
\(\implies -5=a(0+2)^2-13\)
\(\implies -5=4a-13\)
\(\implies 4a=8\)
\(\implies a=2\)
Substitute the given vertex and found value of a into the Vertex formula:
\(y=2(x+2)^2-13\)
The standard form of a quadratic function is f(x) = ax² + bx + c
Expand the function in vertex form to standard form:
\(\implies y=2(x^2+4x+4)-13\)
\(\implies y=2x^2+8x+8-13\)
\(\implies y=2x^2+8x-5\)
The mean of first five natural numbers is
Answers
Answer:
Step-by-step explanation:
Mean of first five natural numbers = sum of first 5 natural numbers ÷ 5
= (1 + 2 + 3 + 4 + 5)÷ 5
= 15 ÷ 5
= 3
The equation of a parabola is (x−3)2=16(y+7) . What are the coordinates of the vertex and focus of the parabola? What is the equation of the directrix?
Answers
The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.
The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.
Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).
The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).
To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.
In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.
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Josh's bill for lunch at a restaurant was $49.59. He left an 18% tip. What was the amount
of the tip?
Round your answer to the nearest cent: $
Answers
So 8.93
Hope this helps :D
2+2 giving brainlest!
Answers
Answer:
2+2=876.
Step-by-step explanation:
Find value of X. write answer in simplest form
Answers
Answer:
The answer is X
Step-by-step explanation:
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.