Answer:
72 is equal to 2 yards.
Explanation:
There are 36 inches in one yard.
(another way to look at this is there are 3 feet in one yard, each feet is 12 inches. So, 12 multiplied by 3 is equal to 36 inches, or one yard)
Then, since in this question we are finding out in relation to 2 yards, add 36 inches + 36 inches, and that is equal to 72 inches.
72 and 72 are equal :)
A lidless box is constructed by cutting a square with side length x from a rectangular sheet of paper with dimensions a x b. After the cut is removed, the sides are folded up to form the
box.
a) Find the value of x (in terms of a and b) that maximizes the volume of the box.
b) Find the value of x that maximizes the volume of the box when a = 8.5 inches and b= 11 inches.
Answer:
a) [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
b) The volume of the box is maximized when 'x' is approximately 1.585 feet
Step-by-step explanation:
a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;
The length of the side of the square cut from the corners of the rectangular sheet of paper = x
The length of the box formed after cutting the square sides are;
The length of the box, l = a - 2·x
The width of the box, w = b - 2·x
The height of the box, h = x
The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x
The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;
At the extremum, dV/dx = 0
∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0
12·x² - 4·(a + b)·x + a·b = 0
[tex]x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]
b), When a = 8.5 inches and b = 11 inches, we have;
x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914
x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585
We get;
When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15
When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65
Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585
(The value of 'x' in terms of 'a' and 'b' is therefore;
[tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex])
The volume of the box is maximized when, x ≈ 1.585 feet
After a month of successful fundraising,
Elena and her classmates voted on
whether to donate the money they had
raised to hunger relief or to environmental
causes. 50% of the 12 votes were in favor
Of hunger relief. How many votes were
for hunger relief?
Answer:
6
Step-by-step explanation:
50% of 12= 1/2 of 12= 6
Answer:
6 votes were for hunger relief.
Step-by-step explanation:
Total number of votes = 12
Percentage of votes for hunger relief = 50%
So, number of votes for hunger relief would be:-
50% of 12 votes
That equals--> [tex]\frac{50}{100}[/tex] x 12
= 0.5 x 12
= 6 votes
please help me
i’m so stuck
Answer:
2 cm
Step-by-step explanation:
V=πr2h = 20π
-π -π
r2h = 20
h= 5
r2(5) = 20
/5 /5
r2=4
/2 /2
r=2cm
(my work is complicated, but trust me 2 cm is the answer)
I haven’t done this since 7th grade sorry I just don’t remember
A bakery owner wants to keep his bakery open a few more hours every evening. He wants to conduct a survey to determine whether extending the bakery's hours would be what costumers want. Which survey method would likely produce the most representative sample?
Answer:
Ask every tenth customer over the period of a week.
Step-by-step explanation:
Required
Select which of the options is true
(a) Every 5th male customer
This method will not produce a correct representative sample because only the male customers are surveyed. The opinion of the female customers will not be represented in the sample
(b) Every customer after 5:00pm
This method will not produce a correct representative sample because only the customers who come to the bakery before 5:00pm will not be represented. The opinion of these customers will not be represented in the sample
(c) Every 10th customer over the week
This method will produce a correct representative sample because the opinions of the customers are taken, irrespective of the gender or the time the customer walks into the bakery.
Help me with this please.
What is the mean absolute deviation of the data set?
{5, 7, 12, 11, 3, 10}
Answer:
3
Step-by-step explanation: First, you find the mean of the data set. Then you take that mean and find the difference of that and each value, you add those up and find the mean of that number.
Write an algebraic expression for the phrase below.
12 less than twice a number n
A- 12 - n - n B- 6 - 2n C 2n - 12 D- 12n-2
Need help!! please/Thank you
Answer:
[tex]50~in[/tex]
Step-by-step explanation:
[tex]perimter=AB+AM+BM[/tex]
[tex]AM=2EM=2(9in)=18in[/tex]
[tex]BM=25E=2(7in)=14in[/tex]
∠m= [tex]180-[/tex] (∠A+∠B)= 180-(70+40)
∠m= 70⇒ AB= AM⇒AB=18
[tex]perimeter=18+14+18=[/tex]
[tex]50~in[/tex]
--------------------------
hope it helps...
have a great day!!
Answer:
your answer will be 50 in
Step-by-step explanation:
The Cohens found 8 pairs of shorts with the following prices:
$10, $11, $11, $16, $16, $17, $18, $38
Which statements about the prices are true? Select all that apply.
A. The Median is $16
B. The range of the prices is $28.
C. The interquartile range is between $6 and $7
D. If the price that is the farthest from the mean is removed, The median will change.
E.If the price that is farthest from the mean is removed, the mean will become larger.
PLEASE EXPLAIN THIS ALSO, DO NOT PUT ANY LINKS EITHER, LINKS WILL BE REPORTED.
Answer:
A. B. and C.
(and hi again)
PLEASE HELP ASAP!!!
Answer:
4. x=0 x=5
5. x=-4 x=8
The average rate of change over the interval [2,5] is ____.
The average rate of change over the interval [5,7] is ____.
The average rate of change over the interval [2,8] is ____.
Answer:
The average rate of change over the interval [2,5] is 3
The average rate of change over the interval [5,7] is -2
The average rate of change over the interval [2,8] is 0
Step-by-step explanation:
in photo
what is the measure of each angle
lets find the answer
Answer:
(-3,0)
Step-by-step explanation:
1) find the coordinate of x
x = -3
2) find the coordinate of y
the point lies on x axis so y = 0
The coordinates are (-3, 0)
:)
a man cycles a distance of 63km in less than 3hours what is the average speed
Answer:
21 km/h
Step-by-step explanation:
Helppppppppppppppppp
Answer:
I just need points sorry love But the answer is A.
Step-by-step explanation:
A ship takes 18 days to reach its designated part. It starts with food for its crew
of 450 men at the rate of 720gm per day per head. After 11 days of its journey they
rescued 180 passangers from a sinking ship. While rescuing the captain noticed a technical
problem in the ship's engine, and estimated the ship would reach the destination after 9
days. How much food should they now consume per day per head so that it lasts for the
rest of the journey.
plzz plzzz do it
Answer:
nsovurhnvurnvhfbsybvhnfshugb
Step-by-step explanation:
You and three of your friends go parasailing for 128.40 you split the cost
evenly. How much does each person pay?
Answer:
40 each i think maybe 30 if not
2x + 2y = -2
3x - 2y = 12
Answer:
Answer:
(2,-3)
Step-by-step explanation:
2x + 2y = -2
3x - 2y = 12
Add the two equations to eliminate y
2x + 2y = -2
3x - 2y = 12
-----------------------
5x = 10
5x/5 = 10/5
x = 2
Now find y
2x+2y = -2
2(2)+2y = -2
4+2y = -2
Subtract 4 from each side
4-4 +2y = -2-4
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
(2,-3)
A shoe store marks up the recommended price of a pair of shoes by 12.5% when they are first released. A month later, the store decides to put these shoes on sale. They want the new sale price to be equivalent to the original recommended price. By what percent should they decrease the marked–up price to make it equivalent to the original recommended price? Round your answer to the nearest tenth.
Answer:
I know the answer come follow me to see
helpppppppppppp plzzzzz!!!!
Answer: 132.7 square inches
Area of a circle formula: [tex]\pi r^{2}[/tex]
Because we know that a diameter is twice the size of the radius and the diameter is 13 inches, we can divide 13 by 2 to get 6.5
Plug in this value into the formula, to get [tex]\pi (6.5^{2})[/tex]. Simplify the equation to get [tex]\pi (42.25)[/tex]. Multiply to get 132.7.
Answer:
It's A
Step-by-step explanation:
To find area= pie*raduis*radius
To find raduis you'll divide diameter by two
so 13 divided by 2 is 6.5
6.5*6.5*3.14=132.7
Someone please help!!!! I’ll give brainliest!!!
can you make the picture more clear?
-3•x^3. Help! pls and thankyou
Suppose HIJK is a parallelogram. Find the value of x and y.
Answer:
x = 90, y = 12
Step-by-step explanation:
The key to this problem is the fact that opposite sides of a parallelogram are congruent (their lengths are equal).
Set up and solve two equations, one for x and one for y.
x + 80 = 2x - 10
80 = x - 10
90 = x
--------------------------
3y - 4 = y + 20
2y - 4 = 20
2y = 24
y = 12
Below. What is m∠1?
m∠1 =
Answer:
m∠1 = 70°
Step-by-step explanation:
Step 1
Sum of angles on a straight line = 180°
Hence:
180° - 101°
= 79°
Sum of interior angles in a triangle = 180°
Hence
m∠1 = 180° - (79 ° + 31°)
m∠1 = 70°
The graph of a polynomial function may have no x-intercepts.
true or false
true (I don't know if this is the answer but it would be my guess)
A jar contains 9 marbles marked with the numbers 1 through 9. You pick a marble at random. What is the probability of not picking the marble marked with the number 2? Enter your answer as a simplified fraction. The probability of not picking the marble marked with the number 2 is
Answer:
1/9 or unlikely
Step-by-step explanation:
Answer:
8/9
Step-by-step explanation:
Which value of x is a solution of x < -2?
A. -3
B. -2
C. - 1
D. O
Answer:
A
Step-by-step explanation:
-3 is less than -2, so A (-3) is the answer.
Only x = -3 is less than -2.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following inequality -
x < - 2
Given is -
x < - 2
Now, it can be seen that -
- 3 < - 2
Therefore, only x = -3 is less than -2.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work.
Answer:
i wrote "13 8/9 because 16 2/3 x 16 2/3= 50/3 x 50/3 = 250/9 then 250/9 ÷ 2 = 125/9 = 13 8/9"
Step-by-step explanation: if u add in some words or something so you teacher isnt sus hope you pass!!
Four times a number is greater than 48. What are the possible values for the
number?
Answer:
Any number greater than 12 but not including 12
Step-by-step explanation:
hope it helps u
FOLLOW MY ACCOUNT PLS PLS
Answer:
this is a very easy question all you have to know is your times table.
the working is shown below:
12
×4
--------
48
---------
OR
------
12×4= 48