The correct answer is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.
To determine the volume of the empty space in the box, we need to calculate the volume of the box and the volume of the basketball, and then subtract the volume of the basketball from the volume of the box.
First, let's calculate the volume of the cubic box. Since the edge of the cube is given as 9.5 inches, the volume of the cube [tex]\( V_{box} \)[/tex] is the edge length cubed:
[tex]\[ V_{box} = 9.5^3 \][/tex]
[tex]\[ V_{box} = \left(\frac{95}{10}\right)^3 \][/tex]
[tex]\[ V_{box} = \frac{95^3}{10^3} \][/tex]
[tex]\[ V_{box} = \frac{95^3}{1000} \][/tex]
[tex]\[ V_{box} = \frac{857375}{1000} \][/tex]
[tex]\[ V_{box} = \frac{1919}{4} \][/tex] cubic inches.
Next, we calculate the volume of the basketball. The basketball is a sphere with a diameter of 9.5 inches, so its radius [tex]\( r \)[/tex] is half of that:
[tex]\[ r = \frac{9.5}{2} \][/tex]
[tex]\[ r = \frac{95}{20} \][/tex]
[tex]\[ r = \frac{19}{4} \] inches.[/tex]
The volume of a sphere [tex]\( V_{sphere} \)[/tex] is given by the formula:
[tex]\[ V_{sphere} = \frac{4}{3}\pi r^3 \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19}{4}\right)^3 \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19^3}{4^3}\right) \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{6859}{64}\right) \][/tex]
[tex]\[ V_{sphere} = \frac{481\pi}{128} \] cubic inches.[/tex]
Now, we subtract the volume of the basketball from the volume of the box to find the volume of the empty space [tex]\( V_{empty} \):[/tex]
[tex]\[ V_{empty} = V_{box} - V_{sphere} \][/tex]
[tex]\[ V_{empty} = \frac{1919}{4} - \frac{481\pi}{128} \] cubic inches.[/tex]
To simplify the expression, we can multiply the terms by a common denominator of 128 to combine them:
[tex]\[ V_{empty} = \frac{1919 \times 32}{128} - \frac{481\pi}{128} \][/tex]
[tex]\[ V_{empty} = \frac{61408}{128} - \frac{481\pi}{128} \][/tex]
[tex]\[ V_{empty} = \frac{61408 - 481\pi}{128} \] cubic inches.[/tex]
However, we notice that the denominator of 128 can be simplified by dividing both numerator and denominator by 4, which gives us the final
[tex]\[ V_{empty} = \frac{1919}{16} - \frac{481\pi}{128} \][/tex] cubic inches.
Therefore, the volume of the empty space in the box is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.
What is the scale factor of AABC to AXYZ?
Answer: A. 1/5 because it's the actual right answer.
Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].
What is scale factor?The ratio of corresponding sides are equal, and this ratio is called the scale factor.
We know that
ΔABC and ΔXYZ are similar from the figure
[tex]\frac{XY}{AB}=\frac{YZ}{BC} =\frac{XZ}{AC}[/tex]
Substitute the values
[tex]\frac{9}{45} =\frac{12}{60}=\frac{7}{35} =\frac{1}{5}[/tex]
Therefore, Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].
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What are the solutions of 12 – x2 = 0?
O x=273 and x = -213
O x= 3,
and x = -3/2
x = 4/5 and x = -4/3
x = 6 and x = -6
Answer:
x = ± 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
12 - x² = 0 ( add x² to both sides )
12 = x² or
x² = 12 ( take the square root of both sides )
x = ±[tex]\sqrt{12}[/tex]
= ± [tex]\sqrt{4(3)}[/tex] = ± 2[tex]\sqrt{3}[/tex]
Only a triangle can be the base of a pyramid. True or False
Answer:
True
Step-by-step explanation:
I did it on ap3x and got it right!
Determine if the two expressions are equivalent and explain your reasoning. show all work plzs
11p + 2(p + 3) and 1 + p(13) + 2
Answer:
Not equivalent.
Step-by-step explanation:
Simplifying the first expression:
11p + 2(p + 3) Distribute the + 2 over the parentheses:
= 11p + 2p + 6
= 13p + 6. **
Now, the second:
1 + p(13) + 2
= 13p + 1 + 2
= 13p + 3. **
So they are not equivalent.
Find the equation of the ellipse with the following properties.
The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ a=5\\ b=3 \end{cases}\implies \cfrac{(x-0)^2}{5^2}+\cfrac{(y-0)^2}{3^2}=1\implies \cfrac{x^2}{25}+\cfrac{y^2}{9}=1[/tex]
Help me fill the boxes in !! !! Will mark brainliest
Answer:
Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)
The graph in the attached figure
Step-by-step explanation:
we have
[tex]-3x-y < 12[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line [tex]-3x-y=12[/tex]
[tex]2x+3y\geq 9[/tex] -----> inequality B
The solution of the inequality B is the shaded area above the solid line [tex]2x+3y=9[/tex]
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
A solution to the system of inequalities is any point in the shaded area.
therefore
Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)
Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 27° and side c = 15.
Answer:
Part 1) [tex]C=90\°[/tex]
Part 2) [tex]A=63\°[/tex]
Part 3) [tex]b=6.8\ units[/tex]
Part 4) [tex]a=13.4\ units[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The triangle ABC is a right triangle
so
Angle C is a right angle
therefore
[tex]C=90\°[/tex]
step 2
Fin the measure of angle A
we know that
In the right triangle ABC
∠B+∠A=90° -----> by complementary angles
we have
[tex]B=27\°[/tex]
substitute
[tex]27\°+A=90\°[/tex]
[tex]A=63\°[/tex]
step 3
Find the length side b
we know that
In the right triangle ABC
[tex]sin(B)=b/c[/tex]
[tex]b=(c)sin(B)[/tex]
substitute the given values
[tex]b=(15)sin(27\°)=6.8\ units[/tex]
step 4
Find the length side a
we know that
In the right triangle ABC
[tex]sin(A)=a/c[/tex]
[tex]a=(c)sin(A)[/tex]
substitute the given values
[tex]a=(15)sin(63\°)=13.4\ units[/tex]
Answer:
A = 63 , a = 13.4, b = 6.8
Step-by-step explanation:
f(x) = 3x^4 is even or odd?
Answer:
Step-by-step explanation:
it's even because f(-x)=f(x)
Answer:
even function
Step-by-step explanation:
recall that:
a function is EVEN if and only if f(-x) = f(x) for all x in the domain of f
a function is ODD if and only if f(-x) = -f(x) for all x in the domain of f
we observe that for the function
f(x) = 3x^4
because x has been raised to an even power, that f(x) will always be positive (or zero), regardless of whether x is negative or positive.
i.e
f(x) = f(x) and f(-x) = f(x)
This behavior is described by the definition of an EVEN function (given above)
Hence f(x) is an even function
Help lolll!!!!!!!!!!!!!!!!! Will mark as brainliest
Answer:
Last one.
Step-by-step explanation:
Let's look at the fist one
x+1<-1 and x+1<1
Subtract one on both sides for both inequalities:
x<-2 and x<0
Graph it!
*********************************o x<0
*************o x<-2
________(-2)_________(0)____________
So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.
Let's look at the second one
x+1<=1 and x+1>=1
Subtract one on both sides for both inequalities:
x<=0 and x>=0
Graph it!
@***************** x>=0
*********************@ x<=0
-----------------------(0)-------------------
The only number included by both graphs is 0 so it still has a solution. The solution is 0.
Let's look at the third one:
x+1<1 and x+1>1
Subtract one on both sides for both inequalities:
x<0 and x>0
Graph it!
************************O x<0
O************************* x>0
---------------------------(0)------------------------------
These inequalities have no overlap. They don't even both include zero because of the open circle (the lack of equal sign). This is the compound inequality that has no solution.
A watch company is developing packaging for its new watch. The designer uses hexagons with a base area of 25 in squared and rectangles with a length of 10 in to create a prototype for the new package. What is the volume of the prototype?
How do I set this up?
Answer:
The volume of the prototype is [tex]V=250\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a hexagonal prism is equal to
[tex]V=BH[/tex]
where
B is the area of the hexagonal base
H is the length of the rectangular face
we have
[tex]B=25\ in^{2}[/tex]
[tex]H=10\ in[/tex]
substitute
[tex]V=(25)(10)[/tex]
[tex]V=250\ in^{3}[/tex]
Answer:
Volume of the prototype is 250 in.³
Step-by-step explanation:
Given:
Base area of the watch packaging case = 25 in.²
Length of the rectangle on the side = 10 in.
To find: Volume of the packaging prototype.
Prototype of the packaging of the watch is in shape of prism whose base is a hexagon and sides are in shape of rectangle.
So, Volume of the prism = Base Area × Height
Thus, Volume of the Prototype = 25 × 10
= 250 in.³
Therefore, Volume of the prototype is 250 in.³
assume the probability of having a boy or a girl is the same. what is the probability of have a boy then a girl then another girl
Answer:
[tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
If the probability of having a boy or a girl is the same, then
the probability of having a boy = a probability of having a girl = 1/2.
Let B denote boy and G denote the girl.
The sample space of having three children is:
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.
The probabilities of each of those events is
[tex]Pr(BBB)=Pr(BBG)=Pr(BGB)=Pr(GBB)=\\ \\=Pr(BGG)=Pr(GBG)=Pr(GGB)=Pr(GGG)=\\ \\=\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{8}.[/tex]
???? I’m very confused
which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?
Answer:
See attachment
Step-by-step explanation:
The given function is [tex]f(x)=\frac{5x-2}{x+2}[/tex].
This rational function has a vertical asymptote at where the denominator is zero.
The denominator [tex]x+2=0[/tex] when [tex]x=-2[/tex]
There is vertical asymptote at [tex]x=-2[/tex]
The horizontal asymptote for this rational function is given by the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator.
[tex]y=\frac{5}{1}[/tex]
The horizontal asymptote is [tex]y=5[/tex]
The graph of this rational function is shown in the attachment
Which statements are true about parallelogram LMNO? Check all that apply.
x = 11
please insert the entire of the question
Answer:
1, 4, 5
Step-by-step explanation:
The shapes of the horizontal cross-sections of the cone below are all congruent
except for the vertex.
True or False
Answer: false
Step-by-step explanation:
The statement that the shapes of the horizontal cross-sections of the cone below are all congruent except for the vertex is false
The horizontal cross-sections of a cone contains a circle, while the vertical cross-sections contains a triangle
The triangle and the cone may or may not have the same area.
Hence, the statement is false
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Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water is this per hour? (Round your answer to the nearest whole number.) cubic feet
Answer:
16 cubic feet per hour
Step-by-step explanation:
This is simple conversion from inches to feet.
Step 1: Write the scale of conversion
---> quantity of water in 1 minute = 462 cubic inches
--->1 cubic feet = 1728 cubic inches
--->1 hour = 60 minutes,
Step 2: Calculate feet per hour
Quantity of water in 1 hour = 0.0347 x 462
---> quantity of water in 1 hour = = 16.0314 cubic feet
---> Rounded off to--> 16 cubic feet
Therefore, 462 cubic inches per minute is 16 cubic feet of water per hour
Answer:
16 cubic feet of water
Step-by-step explanation:
Given,
Water leaves the spigot at a rate of 462 cubic inches per minute,
That is, the quantity of water in 1 minute = 462 cubic inches
1 cubic feet = 1728 cubic inches
⇒ 1 cubic inches = [tex]\frac{1}{1728}[/tex] cubic feet,
Thus, the quantity of water in 1 minute = [tex]\frac{462}{1728}[/tex] = [tex]\frac{77}{288}[/tex] cubic feet
Also, 1 hour = 60 minutes,
⇒ 1 minute = [tex]\frac{1}{60}[/tex] hours,
Hence, quantity of water in [tex]\frac{1}{60}[/tex] hour = [tex]\frac{77}{288}[/tex] cubic feet
⇒ quantity of water in 1 hour = [tex]\frac{60\times 77}{288}=\frac{4620}{288}[/tex] = 16.0416666667 cubic feet ≈ 16 cubic feet,
Hence, 16 cubic feet of water is this per hour.
Write the Explicit Rule for the arithmetic sequence:
Qp = Q1 +(n-1)d
8, 5, 2, -1, ...
Answer:
Last choice.
Step-by-step explanation:
8, 5, 2, -1, ...
Make a table
n | 1 2 3 4 5
an | 8 5 2 -1 -4
You really should just think of this as finding the equation of a line.
The slope can be used by using any two points.
How about
(1 , 8) and
(2 , 5)?
------------I really like to find the slope by lining up my points and subtracting vertically and then putting second number on top of first.
That is the same as using the formula directly which is (y2-y1)/(x2-x1)
or (y1-y2)/(x1-x2) which gives you the same thing too.
Subtracting the pairs now:
(1 , 8)
-(2 , 5)
-----------
-1 3
So the slope is 3/-1 or -3/1 or -3.
So you can already rule out choice B.
So we have the equation is y=-3x+b
where y really represents an and x really represents n here.
You can use any point that you know is on the line to find b.
How about (1,8)?
Plug it into y=-3x+b.
y=-3x+b
8=-3(1)+b
8=-3+b
11=b
So the line is y=-3x+11
Want to confirm?
No problem:
At x=1 you have y=-3(1)+11=-3+11=8 which is first number in the list.
At x=2 you have y=-3(2)+11=-6+11=5 which is second number in the list.
At x=3 you have y=-3(3)+11=-9+11=2 which is the third number in the list.
At x=4 you have y=-3(4)+11=-12+11=-1 which is the fourth number in the list.
So we have confirmed our solution of y=-3x+11.
So the answer is an=-3n+11
Which of the following expressions is equal to
-3x^2 - 27 ?
Answer: D. -3x+9i)(x+3i) i hope this helped :)
Answer: D is the correct answer
Step-by-step explanation:
A P E X
To which subsets of the real numbers does 2 radical 2 belong?
(a) Natural
b) Whole
c) Irrational
d) Integers
e) Rational
Answer:
[tex]2\sqrt{2}[/tex] is irrational .
Step-by-step explanation:
The Natural numbers are {1,2,3,4,5,6,7,....}.
Natural numbers are also called counting numbers because they are numbers people use to count with.
Whole numbers are almost the same as natural numbers. They include one extra number which is 0.
So the whole numbers are {0,1,2,3,4,5,6,7,...}.
Irrational numbers are real numbers that aren't rational numbers.
Rational numbers are number that can be written as fractions where the numerator and denominator are integers (bottom integer is not 0).
Terminating decimals, repeating decimals, and integers all can be written this way which makes them rational.
Integers are numbers in the set {...,-4,-3,-2,-1,0,1,2,3,4,...}. So these are your counting numbers, 0, and the opposite of your counting numbers.
You want to figure out which set does [tex]2\sqrt{2}[/tex] belong to.
You cannot simplify this number anymore than it is. So this is definitely not a number you can count to. It is not the opposite of a counting number. It is also not 0. We have ruled out the following sets: Natural, whole, and integers.
So it is between rational and irrational.
[tex]\sqrt{a} \text{ is irrational if } a \text{ is not a perfect square}[/tex].
[tex]\sqrt{a} \text{ is rational if } a \text{ is a perfect square}[/tex].
2 is not a perfect square.
[tex]\sqrt{2} \text{ is irrational}[/tex]
So [tex]2\sqrt{2} \text{ is also irrational}[/tex]
27a⁰c³ for a =⅔, c = -⅓
need answer and if you could explain how to solve problem that would be much appreciated.
Answer:
- 1
Step-by-step explanation:
Using the rules of exponents
[tex]a^{0}[/tex] = 1
[tex](a^n)^{m}[/tex] = [tex]a^{nm}[/tex]
Given
27[tex]a^{0}[/tex][tex](-\frac{1}{3}) ^{3}[/tex]
Note [tex]a^{0}[/tex] = 1 for any value of a, thus
= 27 × 1 × - [tex]\frac{1}{3^{3} }[/tex]
= 27 × 1 × - [tex]\frac{1}{27}[/tex] ← cancel the 27 on numerator/ denominator
= 1 × - 1
= - 1
Solve for x: 2/5 (x − 2) = 4x. (1 point) I don't understand what to do for this problem. Can someone help??
Answer:
-2/9 =x
Step-by-step explanation:
2/5 (x − 2) = 4x
Multiply each side by 5/2
I do this because we want to get rid of the fraction in the denominator. I also know that the right side has a 4 in the numerator so, the 2 in the denominator that we are multiplying by will cancel.
5/2 *2/5 (x − 2) = 4x*5/2
x-2 = 20/2 x
x-2 = 10x
Subtract x from each side
x-2 -x = 10 -x
-2 = 9x
Divide each side by 9
-2/9 =9x/9
-2/9 =x
Answer:
x=-2/9
Step-by-step explanation:
First, divide both sides by 2/5
(2/5)*(x-2)/2/5=4x*5/2
x-2=10x, Subtract x from both sides.
-2=9x, Divide both sides by 9
x=-2/9, If you need you can check your answer by substituting the value of x into the original equation.
What is the exact value of sin 112.5
Answer:
The fourth one: [tex]\frac{\sqrt{2+\sqrt{2} } }{2}[/tex]
Step-by-step explanation:
The exact value of sin 112.5° can be found using the half-angle identity formula. Substituting values for sin 45° and cos 90°, we find that the exact value of sin 112.5° is ± √2/2.
Explanation:We can find the exact value of sin 112.5 using half-angle identity. As we know, 112.5 degrees is equal to 45 degrees/2 + 90 degrees, these values are much simpler to work with. Let's start by understanding the half-angle formula, which is sin(x/2) = ± √[(1 - cos x) / 2] .
The exact value of sin 45 degrees is √2/2 and cos 90 degrees is 0.
Now, let's put these values in our half-angle formula
sin 112.5 = sin(45/2 + 90) = √[(1 - 0) / 2] = ± √[1/2] = ± √2/2
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Solve for x 2 + 2 * x = 10
Answer:
6
Step by step explanation:
2 + 2 * x = 10
2x+2=10
2x+2−2=10−2
Therefore, x = 6
what equation describes the same line as y-5 =-2(x+4)
Answer:
y = - 2x - 3
Step-by-step explanation:
Given
y - 5 = - 2(x + 4) ← in point- slope form
Distribute the right side
y - 5 = - 2x - 8 ( add 5 to both sides )
y = - 2x - 3 ← in slope- intercept form
which logic statement represents this argument? If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise. Assume that p represents it’s a weekend and q represents “I exercise.”
28 points!!
Answer:
p->q.
~p.
[tex]\therefore[/tex] ~q.
Step-by-step explanation:
I'm going to assume you are looking for symbolic representation.
p=it's a weekend
q=I exercise
The arrangement is this:
If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.
If p , q . ~p . So, ~q.
I try to space out my symbols to show you what I was replacing with what. (By the way I'm still not done.)
I replaced "it's a weekend" with p.
I replaced "it's not a weekend" with ~p which means not p.
I replaced "I exercise" with q.
I replaced 'I won't exercise" with ~q which means not q.
If then, statements are symbolized with an arrow, ->. Example, p->q means if p then q.
Back to the argument:
If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.
If p , q . ~p . So, ~q.
This first sentence is an if then statement with hypothesis p and conclusion q so it can be rewritten as p->q.
I'm going to replace so with [tex]\therefore[/tex]. I'm just trying to show what the conclusion of the argument is with this symbol.
This is the argument in symbolic representation:
p->q.
~p.
[tex]\therefore[/tex] ~q.
This is translated into English as "If it's a weekend, I exercise" (p q), "It's not a weekend" (p), and "I won't exercise" (q).
What exactly is a logic statement?A logic statement is a statement that uses logical symbols and operators to represent the relationships between propositions or statements.
It is a formal expression of symbolic logic that can be evaluated as true or false based on the truth values of its constituents.
Logic statements are used to reason about the truth of statements and the validity of arguments in mathematics, philosophy, computer science, and other fields.
"If p then q," "p and q," "p or q," "not p," and "p if and only if q" are all logical statements.
The logic statement that represents this argument is:
(p → q) ∧ ¬p → ¬q
Thus, when translated into English, this reads: "If it's a weekend, I exercise" (p → q), "It's not a weekend" (¬p), therefore "I won't exercise" (¬q).
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Your question seems incomplete, the probable complete question is:
Which logic statement represents this argument? If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise. Assume that p represents “It’s a weekend” and q represents “I exercise.” (p q) p [(p q) p] q [(p q) p] q [(p q) p] q
TUL
The graph of y= -5x + 1 is:
Answer:
negative, with slope of -5 and the y-intercept is at 1.
Step-by-step explanation:
5x^2 - 9 - 7x^2 - x + 1
Answer:
−2x^2−x−8
Step-by-step explanation:
5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8
5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8
6. The digital sum for the year 1989 is 1 + 9 + 8 + 9 or 27. How many years from 1990 to
2800 have a digital sum of 27?
A.
O
B. 1
C. 2
D. 3
Answer:
c. 2
Step-by-step explanation:
if you mix up the numbers you can find that 1998 is 27. then you have to start adding and subtracting numbers. Your digital sum includes a basic three 9's so, you also have 2799.
solve the equation V/7=3
Answer:
21
Step-by-step explanation:
[tex] \frac{v}{7} = 3[/tex]
Multiplying both sides by 7, we get
[tex] \frac{v}{7} \times 7 = 3 \times 7 [/tex]
The two 7s on the left cancel out to give 1, so
[tex]v = 21[/tex]
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In the election for class president, there were two candidates, Joel and Sean. Joel got 60% of the votes, which was 38 votes more than Sean. Find the total number of votes cast.
Answer:
190
Step-by-step explanation:
40/100 x 198= 76
40/100 x 198= 114
114-76= 38
Answer:
190.
Step-by-step explanation:
Let x represent total number of votes.
We have been given that Joel got 60% of the votes, which was 38 votes more than Sean.
60% of total votes: [tex]\frac{60}{100}x=0.60x[/tex]
Since Joel got 60% of total votes, so Sean got 40% of total votes that is [tex]\frac{40}{100}x=0.40x[/tex]
Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:
[tex]0.60x=0.40x+38[/tex]
[tex]0.60x-0.40x=0.40x-0.40x+38[/tex]
[tex]0.20x=38[/tex]
[tex]\frac{0.20x}{.20}=\frac{38}{.20}[/tex]
[tex]x=190[/tex]
Therefore, the total number of votes cast is 190.