3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of
cardboard that is 10 inches by 18 inches. The box will be formed by making cuts as shown in
the diagram and folding up the sides.
a) Write a function that models the volume of the box.
b) What are the dimensions of the box with the maximum volume? Round to the nearest tenth.
el
at
c) What is the maximum volume of the box?
The volume of the box is the amount of space in it.
The dimension of the postcard is:
[tex]\mathbf{Length = 10}[/tex]
[tex]\mathbf{Width = 18}[/tex]
Let x represents the length of the cut.
So, the dimension of the box is:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
(a) The function that represents the volume of the box
This is calculated as:
[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]
So, we have:
[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
(b) The dimension that maximizes the volume
We have:
[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = 7.3,2.1}[/tex]
The value x = 7.3 is greater than the dimension of the box.
So, we have:
[tex]\mathbf{x = 2.1}[/tex]
Recall that:
[tex]\mathbf{Length = 10 -2x}[/tex]
[tex]\mathbf{Width = 18 -2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, we have:
[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]
[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]
[tex]\mathbf{Height = 2.1}[/tex]
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
(c) The maximum volume
This is calculated as the product of the dimension of the box
So, we have:
[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]
[tex]\mathbf{Volume = 168.1}[/tex]
Hence, the maximum volume of the box is 168.1 cubic inches
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When 4 × 102 is divided by 2 × 10–2 the resulting quotient has 10 raised to the power of
Answer:
2038 that's a answer po because hindi kasali ang 10
The exponent is represented as [tex]A=2*10^{4}[/tex] where the resulting quotient has 10 raised to the power of 4.
Given data:
To perform the given division of [tex]A=\frac{4*10^{2}}{2*10^{-2}}[/tex] , we can use the properties of exponents and arithmetic operations.
When dividing numbers with the same base (in this case, 10), we subtract the exponent in the denominator from the exponent in the numerator:
So, the exponent is represented as A.
The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.
Now, the value of [tex]A=\frac{4*10^{2}}{2*10^{-2}}[/tex].
Now, simplify the exponent expression:
[tex]A=\frac{4*10^{2+2}}{2}[/tex]
[tex]A=2*10^{4}[/tex]
Hence, the exponential form is [tex]A=2*10^{4}[/tex].
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-
6 less than the product of a number and 3 is -18.. What is the
number?
Answer:X= -4
Step-by-step explanation:
6 less than the product of a number and 3 is -18.
Make each part of the sentence into numbers:
"the product of a number and 3": becomes X*(3), where X is the "number."
"6 less than": is -6, so we have:
X*(3) - 6
"is -18" means = -18
Put the segments into one equation and solve:
X*(3) - 6 = -18
3X-6=-18
3X = -12
X = -4
====
See if this works: If X=-4, then the product of it and 3 is -12. Six less than -12 is -18. And that is correct. X= -4
Lindsey's new car travels 93 miles on 3 gallons of gasoline. how many gallons are needed to travel 310 miles?
Given the net of dimensions below find the volume of the shape
Answer:
140cm^3
Step-by-step explanation:
4*5*7 = 140
Given f(x) = x â’ 7 and g(x) = x2. Find g(f(4)). G(f(4)) =.
Answer:
g(f(4))=9 is the answer
(30 Points) A catering company has small tables and large tables. Small tables seat 2 people and large tables seat 5 people. You are planning a party for at most 75 guests. Write an inequality that represents this situation. Let s represent the small tables and I represent the large tables.
Answer:
lllllllllllllll
Step-by-step explanation:
its is 15 large tables
Write the solution to the inequality:
y - 4 < -11
Answer:
y < -7
Step-by-step explanation:
add 4 to both sides to get y<-7
Answer:
add 4 to both side
y-4+4>-11+4
y>-7
PLEASE HELP
What is required in order to win a game of pickleball?
Group of answer choices
The winning team must serve.
The winning team must smash the ball.
The winning team must return service.
Answer:
I think A
Step-by-step explanation:
Unlike tennis or badminton, only the serving team can win a point.
Answer:
I believe its c but I barely know how to play that
PLS HELP!! I WILL GIVE BRAINLIEST
refer to attachments for the question
In ∆PQR and ∆MNR
PQ=MNQR=RN<Q=<M=90°Hence by
Side angle side congruency
[tex]\\ \sf\longmapsto ∆PQR\cong ∆MNR[/tex]
Step-by-step explanation:
PQ ≅ MN ⇒ Given
QR ≅ NR ⇒ Given
R is midpoint of PM ⇒ Given
PR ≅ MR ⇒ Definition of midpoint
ΔPQR ≅ ΔMNR ⇒ SSS postulate
please help this is a hard question and i just cant figure it out
Answer:
y=x+6.
Step-by-step explanation:
the slope-interception form is: y=s*x+i, where s - slope, i - interception.
according to the data in the graph i=6, s=1, then finally,
y=x+6.
Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of the
number of hours, x. She wants to be sure her graph shows her pay for 10 and 20 hours of work.
Answer:
see image; 200; 400
Step-by-step explanation:
y=20x
graph
Question
Solve the equation.
q+5/9=1/6
q=
Answer:
q = - [tex]\frac{7}{18}[/tex]
Step-by-step explanation:
q + [tex]\frac{5}{9}[/tex] = [tex]\frac{1}{6}[/tex]
Multiply through by 18 ( the LCM of 9 and 6 ) to clear the fractions
18q + 10 = 3 ( subtract 10 from both sides )
18q = - 7 ( divide both sides by 18 )
q = - [tex]\frac{7}{18}[/tex]
PLEASE HELP 7th GRADE MATH ASAP!
I dont know what the constant of proportionality is, so HELP
Answer:
a. 28.7 miles
b. 40 miles
Step-by-step explanation:
See attachment.
Convert minutes to hours and divide that into 1 1/2 miles to get a speed of 40 miles/hr (mph). Multiply 40 mph by each of the two times (converted to hours) to find the miles travelled for the two times.
a. 28.7 miles
b. 40 miles
Plz Help!!! Fast!!
A statue is made of gold and silver in the ratio of 2:5. If the weight of the silver in the statue is 140 pounds, what is the weight of the gold?
Show all work!
Answer:
if the gold in this ratio is the 2 out of the 2:5 then the answer is 56 but if its the 5 then its 350
Step-by-step explanation:
The weight of gold is 56
Step-by-step explanation:
gold= 2
sliver = 5
weight of gold = x
weight of silver = 140
2/5 = x/140 solve for x
280=5x
x=280/5
x= 56
I don’t really understand this, if you don’t mind please explain.
Answer:
Roman is wrong because 6/31 is bigger than 9/47
Step-by-step explanation:
no.
i want you to BRING OUT THAT AWESOME CALCULATOR RIGHT NOW! I DONT CARE IF ITS ON YOUR COMPUTER or even an ol fashioned one right in your hands
ok now enter 6 and then divide by (division sign), and then 31. and press Enter or equal sign. now notice that we get A SUPER LONG NUMBER like this
0.19354838....
DO THE SAME THING WITH 9 divided by 47!!
0.19148936....
ok notice. take a look at the third number from the decimal point for each result. they are different. for some SILLY REASON, Roman decided to ignore the rest of the numbers.
6/31 is bigger than 9/47!!!!
PLEASE HELP!! Which grabh does NOT represent a function?
Α) Α
B) B
C) С
D) D
Answer:
D
4th option is correct
............
What is the distance between (-8, -1) and (-4, -9)?
Answer:
The distance formula between two points is
D=√([tex]x_{2} \\[/tex] -[tex]x_{1\\}[/tex])^2 + ([tex]y_{2}[/tex]-[tex]y_{1}[/tex])^2
Whereas
d is distance
So in this case
(-8, -1)
(-4, -9)
x2 is -4
x1 is -8
y2 is -9
y1 is -1
Now we plug them in
d= √(-4 + 8)^2 + (-9+1)^2
Now solve
it’s about
8.94427
Write the equation of the graphed line that has a slope of 2 and passes through the point (2,-2)
Answer:
y = 2x - 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2 , then
y = 2x + c ← is the partial equation
To find c substitute (2, - 2 ) into the partial equation
- 2 = 4 + c ⇒ c = - 2 - 4 = - 6
y = 2x - 6 ← equation of line
Subtract the equations.
3x + 4y = 17
(3x +2y = 3)
-
O A. 6x = 20
O B. -6x = 14
c. 2y = 14
O D. 6y = 20
Answer:
C
Step-by-step explanation:
solve pls brainliest
Answer:
1)3 meters/second
2)-16°C
Step-by-step explanation:
Hope it can help you lovelots
True or false: Least squares regression problems always have a unique solution, since they are modelled by the normal equation
Answer: (((trueeee))))
Since the least squares problem always has a unique solution. Therefore, the given statement is true.
The given statement is "Least squares regression problems always have a unique solution since they are modelled by the normal equation".
Do least squares always have a unique solution?The least squares problem always has a solution. The solution is unique if and only if A has linearly independent columns. S equals Span(A) := {Ax : x ∈ Rn}, the column space of A, and x = b.
Therefore, the given statement is true.
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What is the value of x?
(picture attached)
x= 48
P/s: sorry. I cant explain
ok done.thank to me :>
If sin(0) > 0, then in which quadrants could 0 lie? Select all correct answers.
Select all that apply:
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:
I and IV
Step-by-step explanation:
based on the unity circle 0 and 360 is on the same plane..hope it's answerd
IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.
a) What is the difference between Einstein's IQ and the mean?
b) How many standard deviations is that?
c) Convert Einstein's IQ score to a Z-score
d) If we consider "usual IQ scores to be those that convert z-scores between -2 and 2, is Einstein's IQ usual or unusual?
Answer:
A) 60
B) Between 3 and 4
C) [tex] \frac{160 - 60}{16} [/tex]
D) Extremely unusual.
The difference between Einstein's IQ and the mean is 60. There are standard deviations between 3 and 4. Einstein's IQ score to a Z-score is 9.375. If we consider usual IQ scores to be those that convert z-scores between -2 and 2, is extremely unusual.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.
The difference between Einstein's IQ and the mean :
⇒ 160 - 100 = 60
There are standard deviations between 3 and 4.
Einstein's IQ score to a Z-score:
Here,
ц = 160
σ = 16
X = 100
⇒ z-score = (X-ц )/σ
Substitute the values,
⇒ z-score = (160- 10)/16
⇒ z-score = 150/16
⇒ z-score = 9.375
If we consider usual IQ scores to be those that convert z-scores between -2 and 2, is extremely unusual.
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please help me with mathhhh.
Answer:
B
Step-by-step explanation:
You can't multiply only one side of an equation by anything. That would make it unbalanced, and math is all about balancing equations.
Math 8 Question! :)
Four different positive integers have a mean (average) of 100. If the positive difference between the smallest and largest of these integers is as large as possible, determine the average of the other two integers.
Answer:
2.5
Step-by-step explanation:
"Four different positive integers have a mean (average) of 100"
The total of the 4 numbers is then 4* 100 = 400
"the positive difference between the smallest and largest of these integers is as large as possible"
to get the greatest difference the first 3 numbers must be
1, 2 and 3 which totals 6
the 4th number is then 400 - 6 = 394
the four numbers are 1, 2, 3 and 394
The greatest difference is between 1 and 394
"the average of the other two integers"
(2 + 3)/2 = 2.5
The average of the other two integers is 1.5.
What is the average of the two numbers?
An integer is an whole number. An example of an integer is 20.
If the mean of the four integers is 100. It means that the sum of the integers must be 400. If the integers are 0,1,2, 397. The largest number is 397 and the smallest number is 0. The average of the other two integers is (1 + 2 ) / 2 = 1.5
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Weighted Sums and Averages: Quarterback Ratings
Use the following equation to determine quarterback ratings.
25 + 10(%COMP) + 40(%TD) - 50(%INT) + 50(YD)
OR =
12
1. Using the equation above, find the quarterback rating for Dak Prescott, Dallas Cowboys
Quarterback for 2019.
.
.
% comp 65.1
% TD 5
% Int 1.8
YD 8.2
Answer:
22
Step-by-step explanation:
2x+3y=10
-6x-9y=30
elmantation method
Answer:
• First assign any label to the equations:
[tex]{ \tt{2x + 3y = 10 - - - \{eqution \: (a) \}}} \\ { \tt{ - 6x - 9y = 30 - - - \{equation \: (b) \}}} \\ [/tex]
• Multiply equation (a) by 3
[tex] \dashrightarrow \: { \tt{3 \times (2x + 3y = 10)}} \\ \dashrightarrow \: { \tt{6x + 9y = 30}}[/tex]
• Sum up the result with equation (b)
[tex]{ \underline{ + { \tt{ \binom{6x + 9y = 30}{ - 6x - 9y = 30} }}}} \\ { \tt{0x + 0y = 60}}[/tex]
Answers:
No solutions
solve pls brainliest
Answer:2 3/4 for mixed 11/4 for improper
Step-by-step explanation: