The required solution to the given inequality is x < 7/4.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Given that,
To determine the simplified solution of the inequality 1/2x−1/4 < 5/8.
1/2x−1/4<5/8 .
Adding 1/4 on both sides of the equality,
1/2x < 5 / 8 + 1 / 4
Multiply by 2 on both sides of equality,
1 / 2x < 7 / 8
x < 7 / 4
So, the solution of inequality lies x greater than 7/4, as of the given conditions.
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Evaluate the function graphically.
By evaluating the function graphically , f (4) = -4
What is a function ?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
How to represent Function Graphically ?The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).
According to the Given information
f( x ) = y
where x is an input and y is an output
We need to find the value for f(4)
f( 4 ) = y
For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant
f (4) = -4
By evaluating the function graphically , f (4) = -4
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What is the absolute value of 3/2?
what is the value of 32^4?
what is the value of 32 to the fourth power?
what is the value of 42?
The value of all the given expression are as follow:
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
As given in the question,
Simplification of the given expressions are :
a. The absolute value of ( -3 / 2 )is
| - 3 / 2 | = ( 3/2 )
b. The value of the expression 32^4 is:
32^4
= 32 × 32 × 32 × 32
= 1048576
c. The value of the given expression ( 32 ) ^ 1/4 :
( 32 ) ^ 1/4
= ( 2⁵) ^ 1/4
= 2^(5/4)
d. Value of 4^2 is
4^2
= 4 × 4
= 16
Therefore, the value of the given expression is given by :
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
The complete question is:
What is the absolute value of -3/2 ?
what is the value of 32^4?
what is the value of 32 to the one - fourth power?
what is the value of 4^2?
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Ana is a teacher who plays a review game with her class. The game involves writing each student's name on an identical slip of paper and selecting students at random. Here's the makeup of her class: grade 9^\text{th}9 th 9, start superscript, start text, t, h, end text, end superscript 10^\text{th}10 th 10, start superscript, start text, t, h, end text, end superscript 11^\text{th}11 th 11, start superscript, start text, t, h, end text, end superscript number of students 121212 999 777 suppose that ana picks a name, replaces it, and picks a name again. What is the probability that neither of the students selected are 9^\text{th}9 th 9, start superscript, start text, t, h, end text, end superscript graders? round your answer to two decimal places.
Ana is a teacher who plays review games with the class. If Ana picks a name, replaces it, and picks a name again there is a 0.33 percent chance that none of the students is in ninth grade.
Probability is used to find out the number of chances that an event occurs.
Number of students that are not in nine grade
N9 = 9 + 7
N9 = 16
The total number of students are
Total = 12 + 9 + 7
Total = 28
The probability of neither of a student in nine grade
P = P (N9) x P (N9)
P = 16/28 x 16/28
P = 256/784
divide and approximate
P = 0.33
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true or false: a confidence interval is the rejection region of a two-sided test. group of answer choices true false
This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).
Given that,
The statement is a confidence interval is the rejection region of a two-sided test.
We have to say if the statement is true or false.
We know that,
In statistics, a confidence interval describes the probability that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.
Therefore, This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).
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a line is graphed on the coordinate plane write the equation of a line in slope-intercept form. Explain how you found the slope and the y- intercept
The slope (m) of the line that passes through the points (0, 4) and (8, 0) is -1/2 and the y-Intercept is (0, 4).
What is the slop of the line?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
We have,
The line that passes through the points (0, 4) and (8, 0)
Slop (m) = ?
The slope formula is:
m = (y₂-y₁) ÷ (x₂-x₁)
so here,
m = (0 - 4) ÷ (8 - 0)
m = -4 ÷ 8
m = -1/2
Hence, the slope (m) of the line that passes through the points (0, 4) and (8, 0) is -1/2 and the y-Intercept is (0, 4).
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What is the solution to the equation 5 (x minus 6) = 2 (x 3)? x =
the solution to the equation is x=12
The distributive property is defined as
Let us now solve the equation.
5(x - 6) = 2(x + 3)
Using the distributive property, simplify the parentheses on both sides.
5(x - 6) = 2(x + 3)
5x - 30 = 2x + 6
The parenthesis was simplified. However, we have one x term on one side and another x term on the other.
5x - 30 - 2x = 2x + 6 - 2x
3x - 30 = 6
We only have an x term on one side of the equation now.
To begin, reverse the subtraction by adding 30 to either side of the equation.
To keep an equation balanced or true, we do the identical operation on both sides.
3x - 30 + 30 = 6 + 30
3x = 36
We're getting close to an answer. Only one more step.
The x term is multiplied by 3.
We can undo the multiplication operation by dividing both sides by 3.
3x / 3 = 36 / 3
x = 12
So, x is equal to 12.
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Helppp mememmemm plese it is do Tm
Answer: the same line
Step-by-step explanation:
Let us transform the equation:
[tex]\displaystyle\\y=\frac{4}{3} x+1\\\\[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\3y=\frac{4}{3}(3) x+1(3)\\\\3y=4x+3\\\\3y-4x=4x+3-4x\\\\3y-4x=3[/tex]
The equation for line q is 3x + 5y 10, Line r is parallel to line q and passes through the
point (5,-4).
Write the equation for line r in slope-intercept form.
The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.
What is the equation for line r in slope-intercept form?The slope-intercept form is expressed as;
y = mx + b
The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line q : 3x + 5y = 10Point: (5,-4)Equation line r = ?First, determine the slope of the line q using the slope intercept-form.
y = mx + b
3x + 5y = 10
5y = -3x + 10
y = (-3/5)x + 10/5
y = (-3/5)x + 2
Hence;
Slope of line q m = -3/5
Since, line r is parallel to line q, they both have the same slope.
Therefore, slope of line r will be m = -3/5
Now, plug the point (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - (-4) = (-3/5)( x - 5 )
y + 4 = (-3/5)x + 3
y = (-3/5)x + 3 - 4
y = (-3/5)x - 1
Therefore, the equation of line r is y = (-3/5)x - 1.
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Reese's monthly bank statement says she has a balance of $228.32, but Reese's check register says that her balance is $248.32. Which of the following are still outstanding?
I. A $48.16 deposit from Reece's mom
II. A $116.16 deposit from Reece's work
III. $28.16 check to the nail salon
IV. A $126.16 check to the hair salon
I and II
I and III
II and III
Answer:
l and lll
Step-by-step explanation:
228.32 + 48.16 - 28.16 = 248.32
Use completing the square to rewrite the given function in vertex form. Determine whether the vertex is a maximum or minimum value. Select the TWO correct answers.
y = x2 + 10x + 15
A The vertex is a maximum value at point (5, 10)The vertex is a maximum value at point (5, 10)
B The vertex form is y = (x+5)2 − 10.The vertex form is y = ( x + 5 ) 2 − 10.
C The vertex form is y = (x−5)2 + 10.The vertex form is y = ( x − 5 ) 2 + 10.
D The vertex form is y = (x+5)2 + 10The vertex form is y = ( x + 5 ) 2 + 10
E The vertex is a minimum value at point (−5, −10)
The function x^2 +10x +15 in vertex form is (x+5)^2 - 10 and the vertex is a minimum at (-5, -10)
What is the vertex of a curve?The vertex of a parabola is a point at which the parabola makes its sharpest turn. A parabolic function has either a maximum value (if it is of the shape '∩') or a minimum value (if it is of the shape 'U"). The vertex of a parabola is also the point of intersection of the parabola and its axis of symmetry.
y = x^2 + 10x +15
making x^2 + 10x +15 a perfect square expression we square the half of the coefficient of x on both sides which is (5)^2
y + (5)^2 = x^2 + 10x + (5)^2 + 15
y + 25 = x^2 + 10x + (5)^2 + 15
x^2 + 10x + (5)^2 can be written as (x+5)^2 since iti is now a perfect square expression
y + 25 = (x+5)^2 + 15
y = (x+5)^2 + 15 - 25
y = (x+5)^2 -10
Equation of parabola in vertex form is y = a (x - h)2 + k
where k is the minimum or maximum point of vertex and h is the x coordinate of vertex.
comparing both equations, the coordinate of vertex (h, k) is (-5, -10) which is a minimum point.
In conclusion the vertex is a minimum at (-5, -10) and the equation in vertex form is (x+5)^2 -10
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Only 30% of teams beat The Great Escape Challenge. If 15 teams beat the challenge,
how many teams have played The Great Escape Challenge?
conte the problem
Answer: 50 teams
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{30\%}{15\;\;\text{teams}} =\frac{100\%}{x\;\;\text{teams}}[/tex]
A percent divided by 100 becomes a decimal.
[tex]\displaystyle \frac{0.3}{15\;\;\text{teams}} =\frac{1}{x\;\;\text{teams}}[/tex]
Next, we will cross-multiply:
0.3x = 15
Lastly, we will divide.
x = 50
huck finn is interested in the average length of catfish in the mississippi river bordering st. louis. to collect his sample, huck breaks the river into 5 regions and catches 8 catfish from each region. what method did huck use to select his sample?
The method that he chooses to select his sample is Stratified Sampling.
In Stratified, the population is divided into subpopulations and then the same sampling is applied to each region or subpopulation.
The ability to obtain a sample population that most accurately represents the overall population being investigated while ensuring that each subgroup of interest is represented makes stratified random sampling one popular technique employed by researchers. Researchers use stratified sampling to ensure that specific subgroups are represented in the sample. It also helps in the precise evaluation of each group's characteristics. This technique is often used in surveys to better understand disparities between subpopulations.
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Is triangle ABC a dilation of triangle def?
The triangle ABC is a Dilation of triangle DEF.
A dilation is a transformation that produces an image that is the same shape as the original one but in a different size. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. So, the shape of triangles ABC and DEF are the same.
Since they have similar shapes, their angles will be the same. The largest angle measured in triangle DEF = The largest angle measured in triangle ABC.
Dilation can reduce the shape of an object. The dilation can also enlarge a shape proportionally resulting in a giant monster version of itself.
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Consider a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola y=c−x2, with c
The area of a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola [tex]y=c-x^2[/tex] is [tex]4(\frac{c}{3})^\frac{3}{2}[/tex].
A rectangle has a width [tex]2x[/tex] ⇒ w= [tex]2x[/tex]
height of the rectangle is [tex]c-x^2[/tex] ⇒ [tex]y=c-x^2[/tex]
Area=width multiplied by the height
⇒[tex]area=width*height[/tex]
we maximize Area by setting [tex]\frac{dA}{dx} =0[/tex] .
[tex]\frac{d(2c-2x^3)}{dx} =0\\\\2c-6x^2=0\\\\x^2=\frac{1}{3}c\\ \\x=\sqrt{\frac{c}{3} }[/tex]
substituting back the value of x in the formula of the area we get
[tex]area=2\sqrt{\frac{c}{3} } *2\frac{c}{3} \\\\area=4(\frac{c}{3})^\frac{3}{2}[/tex]
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Joe is on a sidewalk 100ft away from the tree ,jim is on a perpendicular sidewalk 70ft from the tree how far away are they from earth other
Answer:
30 ft
Step-by-step explanation:
Answer:
122 ft
Step-by-step explanation:
The 100 ft and the 70 ft are two legs of a right triangle....their distance apart is the hypotenuse of this triangle ....use Pythagorean theorem
d^2 = 100^2 + 70 ^2
d = 122 ft
Write a reflection rule for each triangle and
its image.
a. J(1, 0), K(-5, 2), L(4, -4) and
J'(-9, 0), K'(-3, 2), L'(-12, -4)
The rule of reflection for the triangle △JKL to △J'K'L' is x = -4.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Given that the vertices of △JKL are J(1, 0), K(-5, 2), L(4, -4).
The vertices of △J'K'L' are J'(-9, 0), K'(-3, 2), L'(-12, -4).
The formula of midpoint of (x₁, y₁) and (x₂, y₂) is
((x₁+x₂)/2, (y₁+y₂)/2)
The midpoint of J(1, 0) and J'(-9, 0) is ((1+(-9)/2,(0+0)/2) = (-8/2,0) = (-4,0)
The midpoint of K(-5, 2) and K'(-3, 2) is ((-5+(-3)/2,(2+2)/2) = (-8/2,4/2) = (-4,2)
The midpoint of L(4, -4) and L'(-12, -4) is ((4+(-12)/2,(-4+(-4))/2) = (-8/2,-8/2) = (-4,-4)
Thus the x-coordinate of the midpoint is the same.
Thus the line of reflection is x = -4.
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In which of the options below will the number 10 correctly fill in the blank? Select all that apply. A) 3 : 5 = 6 : ___ B) 2 : ___ = 4 : 16 C) 1 : ___ = 4 : 40 D) 5 : 8 = ___ : 24
Answer: i think c and a
Step-by-step explanation:
Jeff spent $50 on gifts for his tamily. The first 2 items cost a total of $15 and then he bought 2 more for a total of $20. How many additional gifts did Jeff buy if their average cost was $10 each?
The number of additional gifts Jeff can buy with the remaining cost is 1.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given,
Total cost = $15 + $20 = $35
Total spent = $50
Remaining = $50 - $35 = $15
Since one gift cost $10
Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.
Hence "With the money still available, Jeff can purchase 1 more present".
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Help me on this please and thank you
Answer:
The probability for the green one is 6/10
and for the next one, it is 4/10
Step-by-step explanation:
Flo had 3 packages of paper that each had p pieces of paper. After she gives away 6 pieces of paper, she has 23 pieces of paper left. Which equation can be used to determine how many pieces of paper are in each package? * 10 points A. 3p + 6 = 23 B. 23 = 3p – 6 C. 6 – 3p = 23 D. 6p + 23 = 3p
Answer:
D
Step-by-step explanation:
Seven friends shared a two-thirds pound bag of pistachios. If each person had the same amount of nuts, how many pounds did each person eat?.
Each person ate 21/2 pounds of nut
First of all, we have 7 friends who are going to share 2/3 pound bag of pistachios
This will mean that we will have to divide equally the two-thirds-pound bag of pistachios among the seven people that we have so that we get the share that each person will get
There are 7 friends that share a 2/3-pound bag.
The first step will be: 7÷2/3
7÷0.6666
we will get 21/2 or 10.5
This will imply or mean that each of the friends will get an equal share of 21/2 of the a two-thirds pound bag of pistachios
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Simplify:
-x²+2-1+ 6x² - 4x²
Answer: x^2 + 1
Step-by-step explanation:
-x²+2-1+ 6x² - 4x²
We combine the x^2 and the numbers and we have the equation
x^2 + 1
Which numbers are less than –8/3? Select all that apply.
The number which is less than that of -2.67 are -2.8, -2.9, -3.0.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
Which numbers are less than –8/3 = -2.67
So given in the option which is less than -2.67
Numberless -2.7 are
-2.8, -2.9, -3.0.
Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.
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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2
Jesus borrowed $1000 for 1 week at an APR of 350%. How much interest did he have to pay at
the end of the week? (There are 52 weeks in a year)
$52.70
$67.31
$78.42
$86.21
If Jesus borrowed $1,000 for 1 week at an APR of 350%, the interest he has to pay at the end of the week is B. $67.31.
What is the interest?The interest represents the cost of borrowing.
The interest is computed as the principal multiplied by the annual percentage rate (APR) and time (period).
The interest formula used here is the simple interest instead of the compound interest, which charges interest on accumulated interest and the principal every period.
Principal borrowed for 1 week = $1,000
Annual percentage rate (APR) = 350%
Loan period = 1 week
52 weeks = 1 year
Interest = Principal x APR x Time
= $1,000 x 350% x 1/52
= $67.31.
Thus, the interest that the borrower pays for $1,000 for 1 week at 350% APR is not $52.70, $78.42, or $86.21, but $67.31.
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To indirectly measure the distance across a river, Carson stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Carson draws the diagram below to show the lengths and angles that he measured. Find P R PR, the distance across the river. Round your answer to the nearest foot.
Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
ABC refers to a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
So, the triangles PRE and POC appear to be comparable triangles in the diagram.
Utilizing the similarity theorem:
PR/RE = PR+RO/OC
x/135 = (x+140)/230
By cross-multiply:
230x = 135(x+ 140)
230x = 135x + 18,900
230x - 135x = 18,900
95x = 18900
x =18900/95
x = 198.94
Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative.) f(x)
The given function is x² - 7x + 5 and the most general antiderivative of the function is F(x) = x³/3 - 7x²/2 + 5x + c.
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = ∫f(x)dx
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = ∫x² - 7x + 5
F(x) = x³/3 - 7x²/2 + 5x + c
Where c is the constant of the integration (antiderivative).
The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
Therefore, F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.
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The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards. Enter the function f(x) that describes the area, in square yards, as a function of the width, x.
f(x) = _____
f(x) = Area = (length)(width)
width = x
The length is 16 yards greater than 3 times x
length = 3x+16
f(x) = (3x+16)(x) = 3x^2 + 16x
Answer:
f(x) = 3x² + 16xStep-by-step explanation:
We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards
Length of parking lot is 16 + 3x
Width of parking lot is x
We have to write the function f(x) that describes the area, in square yards, as a function of the width, x
Area of rectangle is Length × width
[tex] \sf Area = f(x) [/tex]
put value of length and width here,
[tex] \sf f(x) = (16 + 3x)(x )[/tex]
[tex] \sf f(x) = 3x^2 + 16x [/tex]
Therefore, f(x) = 3x² + 16x
A parabola has a y intercept of 5 and contains the points (2,-3)
and (-1,12). What are the coordinates of the vertex?
Answer:
Here
Step-by-step explanation:
The vertex of the parabola is at (0.5, 8.5).
2x + y = 5
x - 2y = -15
Answer: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `
Step-by-step explanation: Straight lines `2x + y = 5` and `x-2y = 3` intersect at point `A`. Points `B` and `C` are chosen on these two lines such that `AB = AC`. Then the equation of a line `BC` passing through the point `(2.3)` is: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `
I hope this helps :)
A rectangular solid has width w, a length of 7 more than the width, and a height that is equivalent to 15 decreased by 3 times the width. Express the volume in terms of the width, w. Then find the maximum volume to the nearest whole number cubic unit.
The maximum volume of the rectangular solid in cubic units in terms of the width, w is [tex]-3w^{3}-6w^{2}+105w[/tex].
Information from the question is known as follows :
width = w
length = w+7
height = 15-3w
The maximum volume of a rectangular solid can be found by the formula :
Volume = length x width x height
Volume = (w+7) x w x (15-3w)
Volume = [tex](w+7)(15w-3w^{2} )[/tex]
Volume = [tex]15w^{2}-3w^{3} +105w-21w^{2}[/tex]
Volume = [tex]-3w^{3}-6w^{2}+105w[/tex]
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