well im guessing it the average highway speed 60 mph so it is $7
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
Read more about volumes at:
https://brainly.com/question/17056191
PLEASE HELP!
Your class hopes to collect at least 325 of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.
Part 1: Write an equation that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
Part 2: How many cans are needed to meet or surpass the goal?
Answer:
Part 1. 325 - (135 + 89) = c
Part 2. ≤ 101
Step-by-step explanation:
Brainliest Please!find the lcm of 3, 6 and 8
Answer:
24
Step-by-step explanation:
3x8=24
6x4=24
8x3=24
Find the perimeter. Simplify your answer.
Answer:
3z+13
Step-by-step explanation:
Perimeter is found by adding all the sides
z+2+z+2+z+9
3 z variables 2+2+9=13
Simplified equals
3z+13
Hope this helps!
Please mark this answer as brainiest :)
I need this answer!!
[tex] \rm \frac{2}{36} = \frac{3}{x} [/tex]
[tex] \rm\frac{1}{18} = \frac{3}{x} [/tex]
[tex] \rm x = 3 \times 18[/tex]
[tex] \rm x = \bold{54(d.)}[/tex]
:) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
:)!!!!!!!!!!!!!!!!!!!
:)
<3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3 <3
A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
Answer:
60% if this is an edge question
Kate had 50 thousands-blocks in her package of base-ten blocks. How many ten thousands-blocks does that equal?
5
50
500
5000
Step-by-step explanation:
50000÷10
=5000
MARK ME BRAINLIESTPlease help me! Bots keeps answering my questions and I really need an answer
Answer:
D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft
Find the distance between the points
a. 4
b. 5
c. 6
d. 7
Answer:
b. 5
Step-by-step explanation:
Please help me! Im making the first correct answer brainliest!
Answer:
You didn't ask a question.
Step-by-step explanation:
On Tuesday, a restaurant serves iced tea to 24 of its 160 customers. What percent of the customers order iced tea
Answer:
15%
Step-by-step explanation:
24/160 = 0.15
0.15*100 = 15
Teacher Kaye is saving ₱2,000 every month by depositing it in a bank that gives an interest of 1% compounded quarterly. How much will she save in 5 years?
Answer:
1,23,098
Step-by-step explanation:
............
The quotient of a number x and 4 is at most 5.
Answer:
x ÷ 4 ≤ 5
Step-by-step explanation:
Given f(x) = 8x + 1 and g(x) = f(x - 2), which equation represents g?
O A. g(x) = 6x + 1
O B. g(x) = 6x - 1
O C. g(x) = 8x + 15
O D. g(x) = 8x - 15
Answer:Given f(x) = 8x + 1 and g(x) = f(x − 2), which equation represents g substitute x-2 for x in f(x). we have. g(x)=8(x-2)+1. =8x-16+1. =8x-15.
Step-by-step explanation:
Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
Which statements are true based on the diagram? Select three options.
Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y
Answer:
B,D,E
Step-by-step explanation:
Help! Please! Help! Please!
Step-by-step explanation:
a midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments (that create the midsegment triangle). A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side (due to similar triangles and their constant scaling factors, when one side of the similar triangle is half of the sys of the original triangle, then all its sides are half of their original counterparts).
the 3 sides of the main triangle are
2x + 5
3x - 1
5x
the perimeter of the main triangle is the sum of these :
2x + 5 + 3x - 1 + 5x = 10x + 4
since the sides of the midsegment triangle are all exactly half the length of the sides of the main triangle, also the perimeter of the midsegment triangle is half of the perimeter of the original triangle :
(10x + 4) / 2 = 5x + 2
- 3< t <2
t is an integer.
Write down all the possible values of t.
Answer:
-2, -1, 0, 1
Step-by-step explanation:
-2
-1
0
1
All the possible values of t in the inequality - 3 < t < 2 is,
t = - 2, - 1, 0, 1
Used the concept of inequality that states,
A relation by which we can compare two or more mathematical expressions is called an inequality.
Given that;
The inequality is,
- 3 < t < 2
Here the given inequality means all the values of t are lies between - 3 and 2.
That is,
t = - 2, - 1, 0, 1
Therefore, the value of t are t = - 2, - 1, 0, 1
To learn more about inequality visit:
https://brainly.com/question/25944814
#SPJ3
If you multplied 5x10, would you get the same answer as 5x5x5? Explain your reasoning. DO NOT G O O G L E THE ANSWER!!!!!!
No because for 5x10, you just add 10 5 times for 50. For 5x5x5, you multiply 5x5 and get 25 then multiply it again with the other 5 and get 125.
Answer:
No
Step-by-step explanation:
No, because 5 × 5 × 5 = 25 × 5 and that does not equal 10×5.
Is that the right answer
34.98+12.24=?
answers please
Answer:
Hello!
After reading your question I have calculated the correct answer to be:
47.22
Step-by-step explanation:
The way I solved this equation was I first split the equation into two parts.
I took the two whole numbers, being "34" and "12", and made their own equation:
"34+12=?"
And then I took the two partial numbers "0.98" and "0.24" and made their own equation:
"0.98+0.24=?"
I then solved both equations:
"34+12= 46"
"0.98+0.24= 1.22"
And added those two solutions together to come up with the final solution:
"46+1.22= 47.22"
Hope this helped!
Answer:
47.22 is the answer
Step-by-step explanation:
hope it helps you
HELPPPPP!!As soon as possible
Answer:
answer is D :
√24 = 4.89
which is the nearest to 5 and possible answer
Enter the value of x that makes the equation 3x + 4 + 2x + 2 = -24
answer? and how would I answer this.
Answer:
x = -6
Step-by-step explanation:
Combine like terms.
5x + 6 = -24
Subtract 6 from both sides.
5x = -30
Divide by 5 on both sides.
x = -6
Follow Me:-
[tex]3x + 4 + 2x + 2 = - 24 \\ \\ = > 5x + 6 = - 24 \\ \\ = > 5x = - 24 - 6 \\ \\ = > 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{5} \\ \\ = > x = - 6[/tex]
Hope This HelpsThe average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?.
For 30 minutes you do a combination of walking and jogging. At the end of your workout your pedometer displays a total of 2.5 miles. You know that you walk .05 miles per minute and jog .1 miles per minute. For how much time were you walking
Find HGI, FGH and FGI I’ll mark the brainiest
Answer:
∠FGH = ∠HGI = 29°
∠FGI = 58°
Step-by-step explanation:
GH is marked as an angle bisector, so we have ...
∠FGH = ∠HGI
2x -9 = 3x -28
19 = x . . . . . . . . . . . . add 28-2x to both sides
Of course, the angle FGH is the sum of its parts. Then the angle measures are ...
(2x -9)° = (2·19 -9)° = 29°
∠FGH = ∠HGI = 29°
∠FGI = 58°
the percentages of people at different ages in the life span are more similar, creating what is called the
Answer:
it is called rectangularization
Step-by-step explanation:
what is greater: 19/5, 27/5, 10/3, 14/5
Answer:
I think the greater fraction is 27/5
Answer:
27/5Step-by-step explanation:
what is greater: 19/5, 27/5, 10/3, 14/5
fractions are divisions, we divide to see the greater
19/5= 3.8
27/5= 5.4
10/3= 3.33
14/5= 2.8
1.8 0.087 − 0.947 + 2.2 0.044
Answer:
2
Step-by-step explanation:
im smart
There was a sample of 350 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 7.3% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
Answer:
y = 350*0.927^tStep-by-step explanation:
Initial amount = 350 mgDecay = 7.3% per year or 0.073Time = t yearsFinal mass = yThe equation:
y = 350*(1 - 0.073)^t = 350*0.927^t