To make an open box from a 175cm by 100cm piece of cardboard, equal-sized squares will be cut from each of the four corners and then the sides will be folded up. What is the approximate volume of the largest possible box that can be made?Group of answer choices:A) 324,146 cm^3B)162,073cm^3C) 251,707cm^3D)189,640cm^3
Answers
Given that dimensions of the piece of cardboard are:
[tex]\begin{gathered} l=175\text{ }cm \\ w=100\text{ }cm \end{gathered}[/tex]Where "l" is the length and "w" is the width, you can determine that it has the shape of a rectangle.
You know that equal-sized squares will be cut from each of the four corners and then the sides will be folded up. Then, you can make the following drawing:
By definition, the volume of a rectangle is:
[tex]Volume=length\cdot width\cdot height[/tex]In this case, you can set up that:
[tex]\begin{gathered} length=175-2x \\ width=100-2x \\ height=x \end{gathered}[/tex]Therefore, you can write this equation:
[tex]V=(175-2x)(100-2x)(x)[/tex]Expand it:
[tex]V=(175-2x)(100x-2x^2)[/tex][tex]V=(175)(100x)-(175)(2x)-(2x)(100x+(2x)(2x^2)[/tex][tex]V=4x^3-550x^2+17500x[/tex]Now you need to derivate it using the Power Derivative Rule:
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]Then:
[tex]V^{\prime}=(4)(3)x^2-(550)(2)x+17500[/tex][tex]V^{\prime}=12x^2-1100x+17500[/tex]Make the equation equal to zero and sove for "x":
[tex]12x^2-1100x+17500=0[/tex]Use the Quadratic Formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substituting:
[tex]\begin{gathered} a=12 \\ b=-1100 \\ c=17500 \end{gathered}[/tex]You get:
[tex]\begin{gathered} x_1\approx20.49 \\ x_2\approx71.18 \end{gathered}[/tex]Therefore, you can make the following Sign Chart:
Then, you can substitute these:
[tex]\begin{gathered} x=20 \\ x=50 \\ x=72 \end{gathered}[/tex]Into the factorize form of the derivated function:
[tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex][tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex]
Related Questions
A pair of jeans is on sale for $30. If this price represents a 20% discount from the original price, what is the original price to the nearest cent ?
Answers
Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
A company purchased 10,000 pairs of men'sslacks for $18.66 per pair and marked them up $22.93. What was the selling price of each pair of slacks? Use the formulaS=CMThe selling price of each pairs of slacks is ?
Answers
Given:
A company purchased slacks for $18.66 per pair.
Mark up= $22.93
[tex]\begin{gathered} \text{Selling price= cost price +mark up} \\ \text{Selling price=}18.66+22.93 \\ \text{Selling price= \$41.59} \end{gathered}[/tex]Ashley watches a giant that has 16 equally spread seats. Identify w.
Answers
The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]What is the line of reflection for
Answers
SOLUTION:
Step 1:
In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:
Step 2:
The line of reflection for Triangle ABC and its image is:
[tex]\text{y = x --- OPTION D}[/tex]How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
Answers
Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Write in terms of confunction of a complementary angle:tan 26°
Answers
ANSWER
The cofunction of tan 36 degrees is cot 54 degrees
STEP-BY-STEP EXPLANATION
Given information
[tex]\text{tan 26}\degree[/tex]Co function of tan can be written below as
[tex]\begin{gathered} \tan \text{ }(A)\text{ = cot (B)} \\ \text{if, A + B = 90} \end{gathered}[/tex][tex]\begin{gathered} \text{tan 36 = cot (90 - 36)} \\ \tan \text{ 36 = cot 54} \end{gathered}[/tex]Therefore,
tan 36 = 0.7265
cot 54 = 0.7265
Hence, the cofunction of tan 36 is cot 54
A linear equation written in the form y = mx + b is in ?
Answers
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
1: Are the two slopes parallel.
perpendicular or neither?
Answers
The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.
P.S hopes this helps
probleme 1-2 show two Parallel lines and a transversal. Find the values of x
Answers
From the blurry picture shown, we can concur that:
x and 123.25 degree angle are interior corresponding angles.
They add up to 180 degrees, thus we can write the equation:
[tex]123.25\degree+x\degree=180\degree[/tex]We can now easily solve for x:
[tex]\begin{gathered} 123.25\degree+x\degree=180\degree \\ x\degree=180-123.25 \\ x=56.75\degree \end{gathered}[/tex]The solution:
[tex]x=56.75\degree[/tex]Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Answers
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
Answers
The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
im having a hard time understanding this could you please help me
Answers
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
Use the order of operations to demonstrate that the Distributive Property holds by showing that both sides of each equation are equal.
2/5(4/3-1/3)=2/5*4/3-2/5*1/3
LHS= 2/5(4/3-1/3)
=2/5(4-1/3)
=2/5( /3)
= /15
= 2/5
RHS= 2/5*4/3-2/5*1/3
= /15-2/15
= -2/15
= /15
=2/5
Answers
The Distributive Property holds as both sides of the given equality are equal.
Distributive PropertyThe distributive property means that the outer time of the expression multiplies each of the inner terms of the expression. Then, these terms may be combined, if they contain like-terms.
The left-hand side of the expression is given as follows:
2/5(4/3 - 1/3).
Applying the distributive property, it is found that:
2/5 x 4/3 = 8/15.2/5 x 1/3 = 2/15.Subtracting them, it is found that:
2/5(4/3 - 1/3) = 8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Precedence of operationsThe right-hand side of the expression is:
2/5 x 4/3 - 2/5 x 1/3
Multiplication takes precedence over subtraction, hence:
2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15
Same denominator, hence the numerators can be subtracted as follows:
8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Both sides of the expression have the same value, hence the distributive property holds for this problem.
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in CDE, J is the centroid. If DH=72 find DJ
Answers
Answer:
DJ = 24
Explanation:
We are told from the question that J is the centroid of CDE, this means that J is the midpoint of DH, CJ and FE
If J is the centroid of DH, then 2DJ = JH
Also DJ + JH = DH
The equation becomes:
DJ + 2DJ = DH
3DJ= DH
Given
DH = 72
Hence 3DJ = 72
DJ = 72/3
DJ = 24
Hence the measure of DJ is 24
Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
Answers
316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find the savings plan balance after 8 months with an APR of 8% and monthly payments of $300.00.
Let 8% is changed to decimal value by dividing with hundred.
8/100=0.08.
Now we are required to find the growth factor.
growth factor = (1 + (0.08 / 12)) per month = 1.00667
After 9 months, the balance is
($300.00)*(1.00667)8
316.21 is the balance after 6 months.
Hence 316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
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write the equation of the line passing through the given points write your awnser in slope intercept form Y=mx+b (5 1) and (-3 17)
Answers
The given points are (5, 1) and (-3, 17).
First, we have to find the slope using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=5 \\ x_2=-3 \\ y_1=1 \\ y_2=17 \end{gathered}[/tex]Let's use the coordinates above to find the slope.
[tex]m=\frac{17-1}{-3-5}=\frac{16}{-8}\Rightarrow m=-2[/tex]The slope is -2.
Now, we use the point-slope formula to find the equation.
[tex]y-y_1=m(x-x_1)[/tex]Let's use the same coordinates x_1 and y_1, and the slope m = -2.
[tex]y-1=-2(x-5)[/tex]Now, we solve for y to express the equation in slope-intercept form.
[tex]y-1=-2x+10\Rightarrow y=-2x+10+1\Rightarrow y=-2x+11[/tex]Therefore, the slope-intercept form of the equation is[tex]y=-2x+11[/tex]Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answers
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
Can you help me with this problem? I will send a screenshot of the problem and the answer choices.
Answers
Given:
Distance of her beagle = 25/4 meters to the right
Distance of her labrador = 51/20 meters directly to her left.
Let's determine the expression which represents how far apart the two dogs are.
We have the following:
Since the beagle is to the right, the distance is = 25/4 meters
Since the labrador is to the left, the distance is = -51/20 meters.
Now, to find how far apart the two dogs are, let's use the absolute value expression:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})|[/tex]Therefore, the expression which represents how far the two dogs are is:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]ANSWER:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]a washer and dryer cost 1001 combined the washer costs 51 more the than the dryer how much does the dryer cost
Answers
we can write equations from the statements
a washer and dryer cost 1001 combined
[tex]w+d=1001[/tex]where w is the price of the washer and d the price of the dryer
the washer costs 51 more the than the dryer
[tex]w=51+d[/tex]then we can replace the value of w from the second equation to the first equation
[tex]\begin{gathered} (51+d)+d=1001 \\ 51+d+d=1001 \\ 51+2d=1001 \end{gathered}[/tex]and solve for d
[tex]\begin{gathered} 2d=1001-51 \\ 2d=950 \\ d=\frac{950}{2} \\ \\ d=475 \end{gathered}[/tex]the cost of the dryer was $475
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
Answer:
it would be the same since reflection doesn't change the andle
Answer:
A: It would have the same measure as the original angle.
Step-by-step explanation:
Well, reflecting is where you take the original image, which you see now, and flipping it like a mirror image. So, I think the answer would be: A It would have the same measure as the original angle. Because, it is literally the same thing, just in a mirror image. Like, if you look in the mirror, you see yourself, still the same.
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
Answers
A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20
Answers
Solution
- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.
- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.
Statement 1:
- "1 tomato, 1 eggplant, 2 potatoes for $10"
- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).
- We are told that the total cost for this package is $10.
- Thus, the first equation must be:
[tex]a+b+2c=10[/tex]- We can interprete the other packages in a similar manner.
Statement 2:
"2 tomatoes, 1 eggplant, 3 potatoes for $14"
- This implies that the farmer would price the packages as follows:
2 tomatoes: 2(a)
1 eggplant: 1(b)
3 potatoes: 3(c)
- Since the total cost is $14, we can write the second equation as follows:
[tex]2a+b+3c=14[/tex]Statement 3:
"4 tomatoes, 3 eggplants, 5 potatoes for $20"
- This implies that the farmer would price the packages as follows:
4 tomatoes: 4(a)
3 eggplants: 3(b)
5 potatoes: 5(c)
- Since the total cost is $20, we can write the third equation as follows:
[tex]4a+3b+5c=20[/tex]Final Answer
The 3 equations are:
[tex]\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}[/tex]OPTION C
Question 8 of 20If f(x) = 2x²+2 and g(x)=x2-1, find (f- g)(x).O A.3x²+3O B.x2²+1 O C.3x2² +1O D.x² +3
Answers
Solution
Step 1
Write the two functions:
[tex]f\mleft(x\mright)=2x²+2\text{ }and\text{ }g\left(x\right)=x2-1[/tex]Step 2
(f- g)(x) = f(g) - g(x)
[tex]\begin{gathered} \left(f-g\right)\left(x\right)=2x²+2\text{ - \lparen}x^2-1) \\ \\ (f-g)(x)=2x^2+\text{ 2 - x}^2\text{ + 1} \\ \\ (f-g)(x)=x^2+3 \end{gathered}[/tex]Final answer
D. x² +3
The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
Answers
The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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Find the volume of a cylinder and cinema given the following dimensions
Answers
Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
Error Analysis On a math test a student, Sarah, has to identify all the coefficients and constantsof the expression y +n + 2. Sarah says that 6 is a coefficient and 2 is a constant. Identify all thecoefficients and constants of the expression. What error might Sarah have made?The coefficient(s) of the expression is/are
Answers
the coefficients are the numbers that accompany a variable on this case we have 2 variables y and n so the numbers that accompany each one are 1 for y and 6 for n
so there area 2 coefficients 1 and 6
the constant are the numbers without a variable on this case only the 2
If Nintendo had sold 12.2 million games in March and they had thought that they had sold 20.9 million how off was there percent error?
Answers
First let's calculate the absolute error by subtracting both values:
[tex]20.9-12.2=8.7[/tex]So the absolute error is 8.7 millions.
Now, in order to find the percent error, we just need to divide the absolute error by the number of games sold:
[tex]\frac{8.7}{12.2}=0.7131=71.31\text{\%}[/tex]So the percent error is 71.31%.
Making an inference usingig a two-way frequency tableA group of 150 college students who took math fost term were interviewed. They were asked whether they passed their math course and whether they live oncampus. Their responses are summarized in the following tablePassed math Failed mathve on campus2466Live off campus392152(a) What percentage of the students passed moth? []%(b) What percentage of the students live off campus? []%(c) What percentage of the students who live off campus passed math? []%(d) Is there evidence that students who live off campus tend to pass math more often than average?Yes, because the percentage found in part (e) is much greater than the percentage found in part (0)Yes, because the percentage found in part() is much greater than the percentage found in part (b)No, because the percentage found in part(e) is about the same as the percentage found in part (a).No, because the percentage found in part (5) is about the same as the percentage found in part (b).
Answers
1) Considering that there are 150 students
A) Adding 24+39 we got 63 students
150------------100%
63 ----------- x
x=6300/150
x= 42% of the students passed Math.
B) Adding the number of those students who live off-campus 39 +21
150 ----------------100%
60------------------ y
y=6000/150
y=40%
C) 60 students live off-campus 39 succeded. So we can write
60 --------- 100%
39 --------- z
z= 3900/60
z=65% passed math (off-campus)
D) Comparing that 65% of students who live off-campus passed math and that among those who live on campus and that 58% of all students failed
Then we can state:
A)
I need help with my math
Answers
Answer:
Histogram Tells you how many pumpkins had mass below 6 kg
The box plot can be used to determine that the median was 8
Explanation:
A histogram is a chart the plots frequency of a certain quantity.
In our case, the histogram given tell us how many pumpkins fall within a certain mass range. Therefore, to find out how many pumpkins are below 6 kg, we use a histogram.
On the other hand, the box plot summarizes the numerical data. In our case, it can be used to find the median weight of the pumpkins by just reading off the position of the median line.
Write a linear function f with f(0) = 3.75 and f(-6) =3.75
f(x) = ???
Answers
The linear function will be;
⇒ f (x) = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (0) = 3.75
And, f (-6) = 3.75
Now,
Let the linear function is,
f (x) = ax + b
Since, The values is given as;
f (0) = 3.75
And, f (-6) = 3.75
So, We can substitute the given values in the linear function, we get;
f (x) = ax + b
Substitute x = 0 we get;
f (0) = a × 0 + b
f (0) = b
3.75 = b
b = 3.75
And, We can substitute x = -6 and f(0) = 3.75 we get;
f (-6) = a × -6 + b
3.75 = -6a + 3.75
- 6a = 0
a = 0
So, Substitute a = 0 and b = 3.75 in linear function we get;
f (x) = ax + b
f (x) = a × 0 + 3.75
f (x) = 3.75
Therefore,
The linear function will be;
⇒ f (x) = 3.75
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