Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]
Let h be the height of the box
V = Volume of the box = [tex]620\ \text{cm}^3[/tex]
[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]
Now surface area of the box with an open top is given
[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]
Differentiating with respect to x we get
[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]
Equating with zero
[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]
Double derivative of the function
[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]
So, x at 10.74 is the minimum value of the function.
[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]
The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]
The minimum cost of the box is 69.21 dollars.
Find the 3 ×3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Translate by ( −6, 3), and then scale the x-coordinate by 0.3 and the y-coordinate by 1.3.
Answer:
「0.8 0 -2
0 1.2 3
0 0 1 」
Step-by-step explanation:
The [tex]3\times 3[/tex] matrix will be "[tex]\left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]".
According to the question,
The [tex]3\times 3[/tex] with homogenous coordinates is:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
Translation from (0, 0) to (a, b) will be:
[tex]T = \left[\begin{array}{ccc}1&0&a\\0&1&b\\0&0&1\end{array}\right][/tex]
Here,
a = -6b = 4Translation by (-5,4)
[tex]T = \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]
Now,
Let's find the scaling matrix 5.Scale the x-coordinated by "0.3" and y-coordinates by "1.3".i.e.,
[tex]S = \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right][/tex]
then,
The [tex]3\times 3[/tex] matrix will be:
→ [tex]A = ST[/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right] \ \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&-0.3\times 6\\0&1.3&1.3\times 3\\0&0&1\times 1\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]
Thus the above answer is correct.
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Volume of 120 grams divided by 480cm3
Answer:
= 0.25 g/cm3
Step-by-step explanation:
this is called density the grams per volume.
density = mass
volume
= 120g
480cm3
= 0.25 g/cm3
While scuba diving, Alex counted the number of sea turtles and jellyfish he saw. After a few minutes, he counted 4 sea turtles and 12 jellyfish. This ratio remained constant during the remainder of his dive.
Answer:Alex found 3 jellyfish for very sea turtle.
Step-by-step explanation:
Answer:
3 jelly fish
Step-by-step explanation:
in 7 hours, the temperature on the slopes of a mountain ski resort fell from 9° f to 2° f. what was the average change per hour.
Answer:
1 deggre per hour
Step-by-step explanation:
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). Find the probability that the demand will exceed 170 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)
Answer:
0.1827
Step-by-step explanation:
Given mean of exponential distribution = 100
==> 1/χ = 100 ==> χ = 1/100 ==> χ = 0.01
PDF of χ , f(x) = χe^(-χx), x ≥ 0
===> f(x) = 0.01e^(-0.01x), x ≥ 0
Now we find the probability that the demand will exceed 170 cfs during the early afternoon on a randomly selected day
P(X>170) = ∞∫170 f(x)dx
P(X>170) = ∞∫170 0.01 e^(0.01x) dx
P(X>170) = [e^(-0.01x) / -0.01]^∞ base 170
P(X>170) = -1 [e^-∞ - e^-0.01*170]
P(X>170) = e^-1.7
P(X>170) = 0.1827
The probability that the demand will exceed 170 cfs during the early afternoon on a randomly selected day is 0.1827
A corporation is having a shareholders meeting to vote on a new issue. Not all shareholders are able to attend. In fact, most usually do not. The ownership of the corporation is represented by 2,351,00 shares of stock owned by 111,273 shareholders. Must all of the shareholders own more than one share of stock? If 3,411 shareholders attend the meeting, what percent of the shareholders attended the meeting? Round to the nearest percent. If the shareholders who do not attend own a combined 1.8 million shares of the corporation and the shareholders are voting on a particular issue, these shareholders can vote by proxy - an absentee ballot. If 100,000 of the shareholders vote by proxy, what percent of the shareholders did not vote at all?? Round to the nearest percent.
Answer:
a) The percentage of the shareholders who attended the meeting is 3%.
b) The percentage of the shareholders who did not vote at all is 7%.
Step-by-step explanation:
a) Data and Calculations:
Outstanding shares = 2,351,000
Number of shareholders = 111,273
Number of shareholders who attended the meeting = 3,411
The percentage of the shareholders who attended the meeting = 3,411/111,273 * 100
= 3.065
= 3%
Absent shareholders = 107,862 (111,273 - 3,411) and own 1.8 million shares
Proxy voters = 100,000
Non-voting shareholders 7,862
Therefore, the percentage of shareholders who did not vote at all
= 7,862/111,273*100
= 7.0655
= 7%
Are these two triangles congruent? Use tracing paper to justify your answer
Answer:
no
Step-by-step explanation:
Answer:
Where's the pic shorty
Step-by-step explanation:
????????
write 13.28 as a fraction in the lowest term
Answer:
13 wholes and 7/25
Step-by-step explanation:
write 28 over 100 and just simplify but don't forget 13
Solve the system of equations: x + y + z = 5; x - y + 3z = 9; and z = 6.
PLS PLS HELP ME
what is 4(x-1)^2+2=10
Answer:
Answer below
Step-by-step explanation:
4(x−1)
2
=10−2
4(x−1)
2
=8
(x−1)
2
=
4
8
(x−1)
2
=2
x −1=±√
2
x−1=√
2
x-1=-\sqrt{2}x−1=−√
2
x=√
2
+1
x=−√
2
+1
x=√
2
+1,−√
2
+1
Anybody know how to solve for Y
Answer: y = 108
Step-by-step explanation:
Joe has 6 marbles. Joe and Kay have 11 marbles. Kay and Sara have 7 marbles. How many marbles does Sara have?
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Joe = 6
J + K = 11
Kay = 5
K + S = 7
Sara = 2
fred can complete a work in 6 days and Paul can complete a work in 3 days. if fred and Paul work together, how many days can the work be completed?
Answer:
I think its 3 or 2 days bc if paul can get two works done by the time fred can get one done then the days should be divided.
Step-by-step explanation:
What are there fractions equivalent to 6/24
Answer: Remember how to find equivalent fractions? Here are some:
1/4, 2/8, 3/12, 4/16, 5/20, 25/100, 90/360, 1800/7200
To find all of these, there's a simple method- multiply the denominator and the numerator by the same number. As long as you make sure to use the same number for both the top AND the bottom, you'll always have an equivalent fraction. For example,
1 1800 1800
--- x -------------- = ---------
4 1800 7200
This works because, as you may have noticed, any muliplier you use is in the form of n over n, which, of course, is equivalent to one whole or 100%. Make sense?
The three fractions equivalent to 6/24 are 3/12, 1/4, and 2/8.
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers.
The given fraction is 6/24.
Simplify the fraction:
6/24
= 3/12
= 1/4
Divide and multiply the above fraction by 2:
2/8
Hence, the three fractions equivalent to 6/24 are 3/12, 1/4, and 2/8.
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Answer this please thanks
Answer:
The answer is yes, since the graph is an equal line throughout.
Step-by-step explanation:
the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is 3480,find the number of terms and the common difference of this arithmetic sequence
Answer:
40 termsStep-by-step explanation:
Sum of n terms formula:
Sn = 1/2n(a1 + an)Solving for n
3480 = 1/2n(9 + 165)3480 = 87nn = 3480/87n = 40Answer:
Required Answer:-first term =a=9Last term =l=165 Sn=3480As we know that in a AP
[tex]{:}\longrightarrow[/tex][tex]\sf S_n={\dfrac {1}{2}}(a+l)n[/tex]
Substitute the values[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {1}{2}} (9+165)n[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {1}{2}}(174)n[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {174}{2}}n [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3480=87n [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf n={\dfrac {3480}{87}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf n=40[/tex]
[tex]\therefore[/tex]Number of terms=40.
1) Which statement below is equivalent to - 15 - 12? Ex choice. a) - 15 + 12=-3 b) -15 +-12=-27 c) 15 - 12=3 d) 15--12=-27 ANSWER: EXPLAIN:
What is the equation of the line in slope - intercept form ?Enter your answer in the boxes PLEASE HELP!
Answer: y= 3/5x+
Steps shown in image:
Queue really good summer time happy feeling good memories music
Answer:
u want recommendations?
Step-by-step explanation:
Answer:
Watermelon Sugar
Can you solve this please
Answer:
( 5 × 9 ) + (5 × 4 )
Step-by-step explanation:
What is R ^-3 x R ^5
Answer:
that's good and I'm good
need a little help with this problem
Answer:
Step-by-step explanation:
Rate (slope) of miles per gallon of gas: m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
(0, 0)
(2, 50)
[tex]m_{carA}[/tex] = 25 mi/gal.
(0, 0)
(3, 60)
[tex]m_{carB}[/tex] = 20 mi/gal.
Car B use less gasoline.
PLZZZZZZZZZZZZZZZZZZZZZZ HELP!!!
QUESTION: 5y+(-5)=10
STUDENT WORK: IMAGE DOWN BELOW
1. Explanation of Errors Made
2. Correct Solution (show all work)
Answer:
Step-by-step explanation:
5y + (- 5) = 10
The first mistake made in the image was when they subtracted from an already negative number. You add 5 to both (-5) and 10, which would be 5y = 15, due to the fact that 5 is being multiplied by y, you divide both sides by 5, making 3 the correct answer.
1. 5y + (-5) = 10
2. 5y +5 +5
3. 5y = 15
4. 5y/5 15/5
5. y = 3
what function best models the data and what wil be the chicken breast after 50 miutes
Answer:
Students use linear, quadratic, and exponential functions to model data from tables and choose the regression
most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a
regression model and then interpret the function in context. They then make predictions based on their model
and use an appropriate level of precision for reporting results and solutions.
Lesson 7 focuses on data sets that cannot be modeled accurately, and students are asked
to articulate why. Students use skills learned in Lesson 14 of Module 2 (where they used
calculators to write linear regressions) and apply similar techniques for data sets that are
better suited to modeling with quadratic or exponential regressions. Students use that
same technique to find linear regressions and use their graphing calculators to examine
the correlation coefficient and to find quadratic and exponential regressions. They
compare correlation coefficients to determine which model is best for the data.
Ultimately, students choose the regression model (linear, quadratic, or exponential) most
appropriate to a given data set and then write, verify, and interpret these models in
context. Students need a graphing calculator to complete this lesson. Graphing calculator
instructions are provided, but steps may vary slightly depending on the model of the
graphing calculator.
Refer to the following full modeling cycle during this lesson (Found on page 61 of the CCLS
and page 72 of the CCSSM).
Scaffolding:
Students are more
engaged when working
with relevant and real data
that interests them.
Websites that provide
data sets are a good
resource for classroom
investigations.
This lesson might need to
be divided into two days if
students need more time
to master the technology.
Step-by-step explanation:
What value of a makes the following equation true?
a−8a=210
Answer:
a=-30
Step-by-step explanation:
#2 which table describes a function ??
Answer:
H.
Step-by-step explanation:
A function can only have one y-output per x-input (However, it is ok for one y-output to have multiple x-inputs). The only table that doesn't contain two y-outputs for one x-input is H.
Can a triangle be drawn with side lengths 8.4 inches, 9.2 inches, and 17 inches?
Answer:
yes
Step-by-step explanation:
based on the triangle inequality theorem, add the two smallest numbers together (8.4,9.2) to get 17.6 which is bigger than 17
Cuales son los gráficos que nos permiten analizar el movimiento rectilíneo
Step-by-step explanation:
Un modo de describir y estudiar los movimientos es mediante gráficas que representan distancia-tiempo (distancia en función del tiempo), velocidad-tiempo (velocidad en función del tiempo) y aceleración-tiempo (aceleración en función del tiempo).
Estimate 511 x 637 by first rounding each number so that it only has 1 nonzero digit.
Answer:
Step-by-step explanation:
511 * 637 = 500 * 600
= 300000
511. Here ten's place is 1 and its <= 5. So, it is 500
637. Here ten's place is 3 and its <= 5. So, it is 600
Answer:
300,000
Step-by-step explanation:
Rounding so that a number only has 1 nonzero digit means that you should round to the nearest hundred. Remember when rounding look to the digit to the right of where you are rounding to, if that is 4 or less round down and if it is 5 or greater round up. So to round 511 look at the tens place, since it is less than 4 it rounds to 500. To round 637 look at the tens place, since it is also less than 4 round down to 600. Then to multiply 500 x 600 just multiply the first digits, 5 x 6=30, then add the zeros. In total there were 4 zeros in the estimated equation so the final answer would be 300 plus four zeros.
So 500 x 600=300,000
For the function h(x)=4x-6 find the following: a. f(0) b. f(3) c. f(1/4)
Answer:
a.) -6
b.) 6
c.) -5
Step-by-step explanation:
Plug in each value for x
f(0) = 4(0) - 6 = -6
f(3) = 4(3) - 6 = 6
f(1/4) = 4(1/4) - 6 = -5
Answer:
a f)0)=4(0) - 6= -6
b f(3)=4(3) - 6=6
c f(1/4)=4(1/4)_6= -5