A bale of hay in the shape of a rectangular prism has a length of 4 feet, a width of 2 feet, and a height of 2 feet. A cylindrical bale of hay has a diameter of 5 feet and a height of 6 feet. How many rectangular bales contain the same amount of hay as one cylindrical bale? Round your answer to the nearest tenth.
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Related Questions
1/3 equivalent first 2 fractions
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1/3 is equivalent to 2/6
Here is why:
1 x 2 = 2
3 x 2 = 6
You can do this by cross multiplying 1/3 and 2/6
That's how you get 2/6 as an equivalent fraction.
1/3 is also equivalent to 3/9
Here is why:
3 x 1 = 3
3 x 3 =9
You can also do this by cross multiplying 1/3 and 3/9
That's how you get 3/9 as an equivalent fraction.
There are also many other fractions that are equal to 1/3, but these are the first two.
Hope this helps you.
Have a great day!
Assume you have a poker chip set containing blue, red, and white chips, all of the same size. you place 15 blue chips, 10 red chips, and 25 white chips in a bag. as you are about to randomly draw a chip from the bag, you bet your friend you will pick a red chip from the bag because you feel that red is your lucky color.
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A rancher wants to fence in a rectangular area of 14900 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?
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.. L = 2x +3*A/x
The derivative of this with respect to x is
.. L' = 2 -3A/x²
L will be minimized when this is zero.
.. 0 = 2 -3A/x²
.. x² = 3A/2
.. x = √(3A/2)
For this value of x, the total length of fence is
.. L = 2√(3A/2) -3A/√(3A/2)
.. L = 4√(3A/2) = 2√(6A)
For this problem, A = 14,900 ft², so
.. L = 2√(6*14,900 ft²) ≈ 597.997 ft
The smallest length of fence required to fence the rectangular area is 598 ft.
the slope of the line passing through (-9,-6) and (-15,y) is 2/3. what is the value of y
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Sir, please show your work
Please completely factor the following expression. e. 3x^2+5xy-2y^2
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Simplifying:
3x^2 + 5xy + - 2y^2
Reorder Terms:
5xy +3x^2 + - 2y^2
Factor a Trinomial.
(3x + - 1y)(x + 2y)
Final Result:
(3x + - 1y)(x + 2y)
Hope this helps!!!
The expression 52x – 169 is equivalent to 13
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Based on each applicant’s median credit score, to which client is Rachel likely to offer the best interest rates? a. Leslie b. Pat c. Sam d. Alex
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Just got this question in a practice test on Edge. The answer is definitely Alex, or D.
Please help with the question. For some reason, I find it confusing and I need some assisstance. Thank you!
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C=4x5+2.
C=20+2
C=22
You need 22 chairs.
Answer: i think it is 22
Step-by-step explanation:
Solve log2 ( x - 1 ) + log2 ( x + 1 ) = 3
check answers are in domain
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What is the solution of the system?
Use the elimination method.
4x+2y=18
2x+3y=15
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{2x+3y=15 -divide both sides by -2
-2x-y=-9
2x+3y=15
-sum the equations vertically to
eliminate at least one variable
2y=6 divide both sides of the equation
by 2
y=3
-substitute the given value of y into the simplest equation
2x+3*3=15
-solve for x
x=3
-the solution of the system is the ordered pair (x,y)
(x,y)= (3,3)
Check √
-check if the given ordered pair is a solution of the system of equations
{4*3+2*3=18
{2*3+3*3=15
simplify the inequalities
{18=18
{15=15
-since all of the equalities are true the ordered pair is the solution of the system
Answer:
-divide both sides by -2
-2x-y=-9
2x+3y=15
-sum the equations vertically to
eliminate at least one variable
2y=6 divide both sides of the equation
by 2
y=3
-substitute the given value of y into the simplest equation
2x+3*3=15
-solve for x
x=3
-the solution of the system is the ordered pair (x,y)
(x,y)= (3,3)
Check √
-check if the given ordered pair is a solution of the system of equations
{4*3+2*3=18
{2*3+3*3=15
simplify the inequalities
{18=18
{15=15
-since all of the equalities are true the ordered pair is the solution of the system
Step-by-step explanation:
The length of a rectangle is 7 m less than triple the width. if w represents the width, write an expression for the length, l. question 13 options:
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Read the statement, and identify the expressions that are equivalent. the product of a number minus 17 and 5
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Answer:
The expressions equivalent to 'the product of a number minus 17 and 5' are (n - 17) x 5 and 5(n - 17), where n is the unknown number. These cannot be simplified further without additional information.
Step-by-step explanation:
The statement 'the product of a number minus 17 and 5' can be translated into an algebraic expression. This expression would look like (n - 17) × 5 or 5(n - 17), where n represents the unknown number. Both expressions are equivalent and represent the same mathematical operation.
When simplifying algebraic expressions, it is important to eliminate terms wherever possible to get a more straightforward expression. However, in this case, since we don't have a specific value for n, we cannot simplify the expression further without additional information.
Always remember to check your answer to ensure that the expression makes sense and is reasonable within the context of the problem.
A pond is freshly stocked with 6 brown trout and 18 lake trout. The first fisherman in the area catches and releases a trout. He catches another trout a while later. What is the probability that the fisherman caught brown trout each time?
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24÷6= 4 so probability of 1 out of 4. times 2 because he caught 2 fish. so then that would be 1 out of 8. :)
Kieran is making a birthday card with construction paper. He wants to cut a circle out of a square piece of construction paper. The circle will have a radius of 6 inches. In square inches, what is the area of the smallest piece of construction paper Kieran could use?
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For this the length of the square paper should be equal to the diameter of the circle.
If so the the area of the square piece of paper needed;
area = length * length
length of the square = diameter of the circle
diameter = 2 radii
= 2 * 6 inches
= 12 inches
Therefore length of square = 12 inches
area of the square = 12 inches * 12 inches
= 144 sq.inches
hello, Can someone please help me with this math problem? thanks!
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Find a linear differential operator that annihilates the given function. (use d for the differential operator.) e−x + 8xex − x2ex
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Explanation:
Let
[tex]f(x) = e^{-x} + 8xe^x - x^2 e^x[/tex].
[tex]d^n (f(x))[/tex] = nth derivative of f
Note that
[tex](d + 1) (e^{-x}) = d (e^{-x}) + e^{-x} = -e^{-x} + e^{-x} = 0 \\ \boxed{\Rightarrow (d + 1)e^{-x} = 0} [/tex]
So, (d + 1) annihilates [tex]e^{-x}[/tex].
Note that
[tex](d + 1) (8x e^x - x^2 e^x) = d(8x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ = (8e^x + 8x e^x - 2x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ \boxed{(d + 1) (8x e^x - x^2 e^x) = 8e^x + 14x e^x - x^2 e^x}[/tex]
Let [tex]g(x) = 8e^x + 14x e^x - x^2 e^x[/tex]
For any real number [tex]\alpha[/tex] and positive integer n,
[tex](d - \alpha)^n (c_1 e^{\alpha x} + c_2 xe^{\alpha x} + c_3 x^2 e^{\alpha x} + ... + c_n x^{n - 1} e^{\alpha x}) = 0 [/tex] (1)
So, for g(x), [tex]\alpha = 1, n = 3[/tex]. Thus, using equation (1),
[tex](d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex] (2)
Since, [tex]8e^x + 14x e^x - x^2 e^x = (d + 1) (8x e^x - x^2 e^x)[/tex] ,
[tex](d - 1)^3 ((d + 1) (8x e^x - x^2 e^x)) = (d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex]
Moreover, since [tex](d + 1) (e^{-x}) = 0[/tex]
[tex](d - 1)^3(d + 1) (e^{-x}) = (d - 1)^3 (0) [/tex]
[tex]\\ \boxed{(d - 1)^3(d + 1) (e^{-x}) = 0 }[/tex] (3)
Hence based on equations (2) and (3),
[tex](d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) \\ = (d - 1)^3(d + 1)(e^{-x}) + (d - 1)^3(d + 1)(8xe^x - x^2e^x) \\ = 0 + 0 \\ \boxed{(d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) = 0}[/tex]
Therefore, the linear operator [tex](d - 1)^3(d + 1)[/tex] annihilates [tex]e^{-x} + 8xe^x - x^2e^x[/tex].
To find the differential operator that annihilates the given function e^(-x) + 8xe^x - x^2e^x, we individually find differential operators for each term. The operators d^2, d^3, and d^4 annihilate e^(-x), 8xe^x, and x^2e^x respectively. The least common multiple of these operators is d^4, which is the common operator that annihilates the entire function.
Explanation:To find a linear differential operator that annihilates the function e−x + 8xex − x2ex, we must apply an operator that, when used on these functions, yields zero. For simplicity, we can use d to represent the differential operator d/dx. We annihilate each term independently and find a differential operator common to all terms.
Starting with the first term e−x, we note that d(e−x) = −e−x. Applying d again gives us d(d(e−x)) which is e−x. Thus, applying d2 annihilates e−x.
Annihilating 8xex and x2exNext, consider the second term 8xex. Applying the operator d3 to 8(xex) would be: d3(8xex) = d3(8(ex + xex))= d3(8ex) + d3(8xex) which results in zero.
For the third term x2ex, applying d4 annihilates the term, following the pattern: d4(x2ex) = d(d(d(d(x2ex)))) = 0.
The common differential operator that annihilates all three terms is the least common multiple of the individual operators for each term, in this case, d4.
Nacir is buying school supplies. He purchases 8 notebooks for $12.48. How much does Nacir pay for 1 notebook?
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write a whole number as a fraction the number 5
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5/1, as 5 divided by 1 = 5
Hope this helps
Hope this helped!
Evaluate. 134 × -7
A)-2,158
B)-828
C)-938
D)938
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Because you are multiplying a positive and a negative your answer should be negative
What is the a-value of the function, then determine if the graph opening up or down f(x)=−5(x+7)2+6?
Question 4 options:
a = -5, opens down
a = -5, opens up
a = 7, opens up
a = 7, opens down
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the equation of the vertical parabola in the vertex form is
y=a(x-h)²+k
where
(h,k) is the vertex of the parabola
if a> 0 then
the parabola opens upwards
if a< 0
then the parabola open downwards
in this problem we have
f(x)=−5(x+7)²+6
a=-5
so
a< 0 -------> the parabola open downwards
the vertex is the point (-7,6) is a maximum
the answer is the option
a = -5, opens down
see the attached figure
a = -5, opens down
Explanation:
The general form of the quadratic equation is:
f(x) = a(x-h)² + k where (h,k) is the vertex of the parabola.
The value of the "a" determines whether the parabola is open upwards or downwards:
1- if the value of "a" is positive, this means that parabola opens upwards
2- if the value of "a" is negative, this means that the parabola opens downwards
Now, for the given:
f(x) = -5(x+7)² + 6
By comparison, we can note that:
a = -5
The value of "a" is negative which means that the parabola opens down.
The attached image shows the graph of the given function
Hope this helps :)
The circumference of a circle is 31.4 inches. What is the circle's diameter? C=31.4 in Use 3.14 for .
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C = 2πr
31.4 = (2)(3.14)(r)
31.4 = 6.28r
5 = r
So our radius is 5 in.
We can multiply it by 2 to get the diameter.
5*2 = 10
So the diameter is 10 inches
this can be calc for a form
If the rules for the lottery game powerball required participants to choose 5 unique numbers (ranging from 1 to 59) in any order along with one "powerball" (ranging from 1 to 35), what is the probability of winning the jackpot under these game rules?
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5,006,386 x 35 = 175,223,510
probability 1: 175,223,510
To calculate the probability of winning the Powerball, you need to identify all possible combinations for drawing 5 unique numbers from a set of 59, then multiply that with the separate 35 options for the 'powerball'. Your chance of winning equals one (the exact match to your ticket) divided by the total possible combinations.
Explanation:The probability of winning the Powerball jackpot can be determined using the concept of combination in probability theory. Probabilities are calculated by taking the total number of successful outcomes or combinations and dividing it by the total number of possible outcomes or combinations.
In the case of Powerball, there are 5 unique numbers to be drawn from a pool of 59 (ignoring order), and 1 'powerball' from a pool of 35. For the 5 unique numbers, there are C(59,5) combinations where C(n,r) = n! / [r!(n-r)!], n being the total number of options available and r being the number of options chosen at a time.
For the 'powerball', since it is a separate pool of 35 numbers and only 1 is chosen, the number of combinations is simply 35. As such, you multiply the two outcomes for total possible combinations: C(59,5)*35.
For the probability of winning, you want to know combinations that match exactly your selection, of which there is only one. Therefore the probability is 1 / [C(59,5)*35], resulting in extremely low chances of winning.
Learn more about Powerball Probability here:
https://brainly.com/question/33176496
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how much water do you add  to make 12% sugar syrup using 5g sugar?
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so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.
now 100% - 12% is 88%, so the 88% leftover will just be water.
if 12% is 5g, how much is 88%?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5&12\\ x&88 \end{array}\implies \cfrac{5}{x}=\cfrac{12}{88}\implies \cfrac{5}{x}=\cfrac{3}{22}\implies 110=3x \\\\\\ \cfrac{110}{3}=x\implies 36\frac{2}{3}=x[/tex]
Answer:
[tex]36\dfrac{2}{3}[/tex] g of water.
Step-by-step explanation:
You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then
5 g - 12%,
x+5 g - 100%.
Mathematically, you can write a proportion:
[tex]\dfrac{5}{x+5}=\dfrac{12}{100}\Rightarrow 500=12(x+5),\ 500=12x+60,\ 12x=440, \\ \\x=\dfrac{440}{12}=\dfrac{110}{3}=36\dfrac{2}{3}.[/tex]
what is the correct answer to this question?
a
b
c
d
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.. from 275/6.58 = $41.79
.. to 275/6.25 = $44.00
which is a change of $2.21.
if f(x) varies directly with x2, and f(x) = 96 when x = 4, find the value of f(6).
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96=k(4)
k=24
f(x)=kx
f(6)=24(6)
f(6)=144
which of the following expressions is equivalent to the expression below ?
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a taxi ride costs $3 plus $2.50 per mile. write and graph an equation in two variables that represents the total cost of a taxi ride.
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the 2 variables in the equation are as follows;
y = total cost of taxi ride
x = number of miles travelled per taxi ride
we need to write the equation in slope- intercept form
y = mx + c
m = gradient /slope
mx = cost per mile travelled x number of miles travelled
c= intercept. a fixed cost for every taxi ride
m = $2.50 per mile
c = $3
the graph equation is as follows;
y = 2.50x + 3
The graph below shows the solution set to which system of inequalities?
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using a graph tool
I proceed to verify each case to get the answer
see the attached figure
case A)
y> 2x-4 y>=-x y<=3
case B)
y> 2x-4 y>=-x y<3
case C)
y< 2x-4 y>=-x y<=3
the answer is the option A)
y> 2x-4 y>=-x y<=3
Kate ran 6 miles. How far did she run in kilometers?
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Final answer:
Kate ran approximately 9.66 kilometers after converting her distance run in miles to kilometers using the conversion factor of 1 mile equaling 1.60934 kilometers.
Explanation:
Kate ran 6 miles and we need to convert that distance into kilometers. To do this, we use the conversion factor that 1 mile is approximately equivalent to 1.60934 kilometers. By multiplying 6 miles by this conversion factor, we get:
6 miles × 1.60934 km/mile = 9.65604 kilometers
So, from the above calculation Kate ran roughly 9.66 kilometers, considering we usually round the result to two decimal places when dealing with distances unless high precision is required.
Lydia drove 302 miles in 10 hours. on average, how fast did she drive in miles per hour? express your answer in simplest form.
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Answer:
30.2 mph
Step-by-step explanation:
Hello, I think I can help you with this
the speed average is the is the quotient of the distance traveled and the time used to do it, mathematical speaking
[tex]Average\ speed =\frac{distance}{time}\\[/tex]
Step 1
Put the values into the equation
Let
Distance:302 miles
Time:10 hours
[tex]Average\ speed =\frac{distance}{time}\\\\Average\ speed =\frac{302\ miles}{10\ hours}\\Average\ speed =30.2 \frac{miles}{hour} \\[/tex]
Average speed=30.2 mph
Have a great day.