The Probability that a total of exactly n tosses will be required is (1/2)^(n-1)
To find the probability that a total of exactly n tosses will be required, we need to consider the different sequences of tosses that would result in exactly n tosses.
For a total of exactly n tosses, there are two possibilities: the head appears on the (n-1)th toss and the tail appears on the nth toss, or the head appears on the nth toss.
Let's calculate the probabilities for each case:
The head appears on the (n-1)th toss and the tail appears on the nth toss:
The probability of getting a head on any toss is 1/2, and the probability of getting a tail on any toss is 1/2.
Therefore, the probability of this case is (1/2)^(n-1) * (1/2) = 1/2^n.
The head appears on the nth toss:
The probability of getting a head on the nth toss is (1/2)^n.
To find the overall probability for a total of exactly n tosses, we sum the probabilities of the two cases:
P(n) = (1/2)^(n-1) * (1/2) + (1/2)^n
= (1/2)^n + (1/2)^n
= 2 * (1/2)^n
= (1/2)^(n-1)
Therefore, the probability that a total of exactly n tosses will be required is (1/2)^(n-1)
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The probability that a total of exactly n tosses will be required is (1/2)^n, and the total probability of the event is 1/2.
Let's consider the case where a total of exactly n tosses are required. This means that the first n-1 tosses must all result in tails, and the nth toss must be a head, followed by a sequence of one or more tails. The probability of this sequence of tosses occurring is:
P(n) = (1/2)^(n-1) * (1/2) * (1/2)^(n-1) = (1/2)^n
So the probability of requiring exactly n tosses is (1/2)^n.
Now we need to sum this probability over all possible values of n to get the total probability of the event. We can express this as an infinite series:
P = Σ (1/2)^n, n=2 to infinity
To evaluate this series, we can use the formula for the sum of an infinite geometric series:
S = a/(1-r)
where a is the first term and r is the common ratio. In this case, a = (1/2)^2 = 1/4 and r = 1/2, so we have:
P = Σ (1/2)^n, n=2 to infinity = 1/4/(1-1/2) = 1/2
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15 athletes are assigned to one of three teams. Each team will have five athletes. The teams are different, so it matters who gets assigned to which team. How many ways are there to assign the athletes to the teams
Answer:
There is only one way to assign the athletes to the team by giving 5 athletes to each team
How many minutes are equal to 2 hours 20 minutes? how many minutes are equal to 2 hours 20 minutes? 100 120 220 240 none of these
Answer:
None of the answers
Step-by-step explanation:
There are 60 minutes in one hour so to find the number of minutes in two hrs we multiply 2 by 60: 2*60 = 120 minutes
We then add the extra 20 minutes: 120+20 = 140 minutes
None of the answers include 140 minutes.
A random sample of n = 4 scores is obtained from a normal population with m = 30 and s = 8. what is the probability that the sample mean will be smaller than m = 22?
the probability that the sample mean will be smaller than m = 22 is 0.02275.
For the given question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Here sample size, n = 4
mean, μ = 30
standard deviation, σ = 8
The probability that the sample mean will be smaller than m = 22 is
z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]
⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]
⇒ z = [tex]-\frac{8}{4}[/tex]
⇒ z = -2
Refer the Z table for p value,
Thus for P(z < -2) is 0.02275.
Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.
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Find the polar coordinates in radians from the given rectangular coordinates (-11, -3).
the polar coordinates are:
(√130, 285.3°)
How to find the polar coordinates?For rectangular coordinates (x, y), the polar coordinates are:
[tex]R = \sqrt{x^2 + y^2}[/tex]
For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:
θ = arctan(y/x) + 270°
In this case, we have:
x = -11
y = -3
Then:
[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]
Then the polar coordinates are:
(√130, 285.3°)
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what is the coefficient of (3y^2 + 9)5
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
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You want to retire on the equivalent of $50,000 per year in today's money. inflation is expected to be 3%. you will retire in 30 years. you will earn 10% annually on your investments from not till retirement and you will earn 8% during retirement (which is expected to last 20 years). how much do you need to save per month in order to fund this retirement?
$662.18 needs to be saved per month.
$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.
i.e. $218,454 is required in retirement years (for 20 years)
Calculating the PV of these payments at 7% is calculated as below.
FV = 0
1/y = 7%
n=20; PMT = 218454; calculate PV = $2,314,305
Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.
FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT = $662.18
So $662.18 needs to be saved per month.
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HELP!!!!!!QUICK!!!!!!!
Select the correct answer from the drop-down menu.
Compare the steps for constructing a perpendicular line to line ABthrough point C using a reflective device and using paper.
.C
A
When using paper to construct the perpendicular line, the paper is folded so that
line ABwill lie exactly on top of each other.
When using a reflective device to construct a line perpendicular to line AB, set one end of the device to coincide with
then swing the other end of the device so the reflection of line ABcoincides with
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and the two sides of
and
The C is perpendicular to AB
When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.
When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB
The question is incomplete hence the complete question is shown here
Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line through point using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line coincides with.
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Answer:
I toke the test, I think the first one is A and B coincide
Step-by-step explanation:
Tom has x bags of apples. he buys 8 times more and sells 12. write the amount he has left as an algebraic expression:
Answer:
Step-by-step explanation:
x times 8 +12
8x+x=9x-12
Answer = 9x-12
10 points to you if you help me
and brainlyist
Answer:
Step-by-step explanation:
For the frequency distribution, count the numbers that satisfy each category.
79 to 83: 4 (81, 82, 83, 81)
84 to 88: 3 (87, 88, 86)
89 to 93: 7 (92, 93, 93, 93, 90, 90, 91)
94 to 98: 1 (97)
For the historagram, raise the bars at the bottom of the histogram to the numbers above (4, 3, 7, 1; in this order)
HELP! what is this? what’s the answer?!
D. not continuous at X=0
if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0
1)Convert the following binary numbwers into decimal number(only a,b,c,f,i)
#1
(11)_2(1×2⁰+1×2¹)_10(1(1)+1(2))_10(1+2)_10(3)_10#b
(110)_2(0+1×2¹+1×2²)_10(2+4)_10(6)_10#c
(111)_2(1×2⁰+1×2¹+1×2²)_10(1+2+4)_10(7)_10#f
(10011)_2(1×2⁰+1×2¹+0+0+1×2⁴)_10(1+2+16)_10(19)_10#i
(10110101)_2(1×2⁰+0+1×2²+0+1×2⁴+1×2⁵+0+1×2⁷)_10(1+4+16+32+128)_10(181)_10Answer:
a) 3₁₀
b) 6₁₀
c) 7₁₀
f) 19₁₀
i) 181₁₀
Step-by-step explanation:
Binary to Decimal Conversion (Positional Notation Method)
Multiply each digit by the base (2) raised to the power dependent upon the position of that digit in the binary number. Sum all the values obtained for each digit.Express the number as a decimal number by placing subscript 10 after it.For a binary number with 'n' digits:
The right-most digit is multiplied by 2⁰The left-most digit is multiplied by [tex]\sf 2^{n-1}[/tex]For example, to convert the binary number 111001₂ into a decimal:
[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]
Multiply each digit by the base (2) raised to the power as indicated above and sum them:
[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]
[tex]= 32+16+8+0+0+1[/tex]
[tex]= 57[/tex]
Finally, express as a decimal number ⇒ 111001₂ = 57₁₀
Question (a)
[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]
Therefore, 11₂ = 3₁₀
Question (b)
[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]
Therefore, 110₂ = 6₁₀
Question (c)
[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]
Therefore, 111₂ = 7₁₀
Question (f)
[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]
Therefore, 10011₂ = 19₁₀
Question (i)
[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]
Therefore, 10110101₂ = 181₁₀
A river flows at 2m/s . Juan's boat can travel twice as fast down the river as it can go up the river. how fast the boat go in still water?
Using proportions, it is found that the boat can go 6 m/s in still water.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
Down the river, the speed is v + 2.Up the river, the speed is v - 2.He goes twice as fast down the river, hence:
v + 2 = 2(v - 2).
v + 2 = 2v - 4
2v - v = 2 + 4
v = 6.
The boat can go 6 m/s in still water.
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An integrated transcriptomic and epigenomic analysis identifies CD44 gene as a potential biomarker for weight loss within an energy-restricted program
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE
What is an integrated transcriptomic and epigenomic analysis?Because of the interindividual variability in response to weight-loss treatments, new predictive biomarkers are needed to improve the efficacy of weight-loss programs. The goal of this work is to find new genes that distinguish individual responses to a weight-loss dietary regimen by combining mRNA expression and DNA methylation arrays.Different expression and DNA methylation profiles were found in LR versus HR. The integrative analysis of the array data found four genes that were differentially methylated and expressed between groups: CD44, ITPR1, MTSS1, and FBXW5. In LR, CD44 expression was higher and DNA methylation levels were lower than in HR.Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.
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Complete question:
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE
I need help solving this problem
Answer:
Please see the picture below.
Step-by-step explanation:
A local salesman receives a base salary of $975 monthly. He also receives a commission of 6% on all sales over $1200. How much would he have to sell in a month if he needed to have a monthly income of $2500
He has to sell in a month $26616.67.
Given that a local salesman receives a base salary of $975 monthly and he also receives a commission of 6% on all sales over $1200.
A numerical assertion wherein two articulations are delivered equivalent to each other is known as an algebraic condition.
Let the Sales amount be s.
We have:
Sales over 1,200 is written as
s-1200
6% is also 0.06 as a decimal,
so according to question, we have
0.06(s - 1200) + 975=2500
Now, we will apply the distributive property a(b+c)=ab+ac, we get
0.06s-0.06×1200+975=2500
Further, we want to simplify the left-hand side, we get
0.06s-72+975=2500
0.06s+903=2500
Furthermore, we will subtract 903 from both sides, we get
0.06s+903-903=2500-903
0.06s=1597
Now, we will divide both sides with 0.06, we get
0.06s/0.06=1597/0.06
s=26616.67
Hence, he have to sell in a month if he needed to have a monthly income of $2500 is $26616.67.
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Tas
The three points marked on the graph are
the vertices (corners) of a parallelogram.
10
9
y
8
7
6
5
4
3
2
1
A
1 2
C
2
B
3 4 5 6 7 8 9
10
What are the coordinates of the fourth
vertex?
Answer: (8,10)
Step-by-step explanation:
To go from A to C, we go right 2 units and up 6 units.
So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.
Therefore, the answer is (8, 10).
1) (x-y)(y-2)(x+2) / 2x^2+4yz+6 =
2) 4(x+y)(x-y)(y-x) / t+d+m =
3) ( √25+√9 / 2 ) + √21675 =
4) (9x^2+3x+27)(3+6y)(4+6y) / 1+2a+38+4c+2000z =
5) (x^2+6x+5) / (x+2)(x+6) =
^^^Simplify
6) (xy/m) + (xm/y) - (m/x) = 63 x=
Isolate
Could anyone help me with these?
See below for the solution to each expression
How to solve the expressions?Expression 1
The expression is given as:
(x-y)(y-z)(x+z)/(2x^2+4yz+6)
Expand the numerator
(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)
Further, expand the numerator
(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Evaluate the like terms
(x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Expression 2
The expression is given as:
4(x+y)(x-y)(y-x)
Apply the difference of two squares
4(x^2 - y^2)(y - x)
Expand the expressions in the brackets
4(x^2y - x^3 - y^3 + xy^2)
Open the bracket
4x^2y - 4x^3 - 4y^3 + 4xy^2
Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2
Expression 3
The expression is given as:
(√25+√9/2) + √21675
Take the square roots of 25, 9 and 21675
(5 +3/2) + 5√867
Evaluate the sum
13/2 + 5√867
Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867
Expression 4
The expression is given as:
(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z
Factor out 3 and 2 from the numerator
3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z
This gives
18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
The expression cannot be further simplified.
Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
Expression 5
The expression is given as:
(x^2+6x+5)/(x+2)(x+6)
Factorize the numerator
(x + 1)(x + 5)/(x + 2)(x + 6)
Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)
Expression 6
6) (xy/m) + (xm/y) - (m/x) = 63
Factor out x
x(y/m + m/y) - m/x = 63
Evaluate the sum
x(y^2 + m^2)/y - m/x = 63
Multiply through by xy
x^2(y^2 + m^2) - my = 63xy
Add my to both sides
x^2(y^2 + m^2) = 63xy + my
The above implies that the variable x cannot be isolated from the equation
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what is 23,578 times 39,344
Answer:927652832
Step-by-step explanation:
using long multiplication step by step multiply.
The expression 40x²-65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the
interior angles of the pentagon are equal, which expression represents the measure of two angles?
Answer:
[tex]16x^2-26x+20[/tex]
Step-by-step explanation:
Since it represents the sum of interior angles, the angle is essentially: [tex]angle + angle + angle + angle + angle[/tex], and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division): [tex]\frac{40x^2-65x+50}{5} = \frac{40x^2}{5} - \frac{65x}{5} + \frac{50}{5}[/tex] this simplifies to: [tex]8x^2-13x+10[/tex]. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2): [tex]2(8x^2-13x+10) = 16x^2-26x+20[/tex] which is the solution
Jake started biking to the coffee shop traveling 8 mph, after some time the bike got a flat so Jake walked the rest of the way, traveling 4 mph. If the total trip to the coffee shop took 9 hours and it was 60 miles away, how long did Jake travel at each speed
Jake travel to the coffee shop by bike with speed of [tex]8mph[/tex] is [tex]56mile[/tex] and when bike got a flat so Jake walked [tex]4mile[/tex]
How to find the speed by biking and walking ?
let [tex]b[/tex] = time spent biking
then [tex]8-b[/tex] =time spent walking
Write distance equation
[tex]dist=speed *time[/tex]
So bike distance [tex]+[/tex] walk distance [tex]=60mile[/tex]
[tex]8b+4(8-b)=60\\8b+32-4b=60\\4b=60-32\\b=28/4\\\\b=7hrs[/tex]
Then [tex]8-7=1 hrs[/tex] spent walking.
For cross check the answer find that actual distance for each
[tex]8(7)=56mi\\4(1)=4mi\\-------\\total distance=60mile[/tex]
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SOMEONE PLEASE HELP!!! Find the area of the sector. Round your answer to the nearest tenth.
Answer:
398.2 cm^2
Step-by-step explanation:
[tex]\frac{270}{360}[/tex] * [tex]169\pi[/tex] ≈398.2 cm^2
pls help me on this one :((
Answer:
The answer is B) b
Step-by-step explanation:
According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.
So d+(a+b)/2=d+b
(a+b)/2=b
a+b=2b
a=b
hope this helps <3
Which of the statements below is true for the following set of numbers?42,10,36,51,70,28
Answer:
statement 1(one)
Step-by-step explanation:
Can you help me,pls
Answer:
x^4 +2 +x^-4
Step-by-step explanation:
The square of a binomial is a form worthy of memorization.
(a +b)² = a² +2ab +b²
ApplicationHere, you have a binomial with a=x² and b=1/x². Using these values in the pattern, we have ...
[tex]\left(x^2+\dfrac{1}{x^2}\right)^2=(x^2)^2+2(x^2)\dfrac{1}{x^2}+\left(\dfrac{1}{x^2}\right)^2\\\\=\boxed{x^4+2+\dfrac{1}{x^4}}[/tex]
One cupcake weighs 3 1/2 ounces how many cupcakes are there in 28 ounce package
Using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.
According to the question,
One cupcake weighs 3 1/2 ounces. In order to find the number of cupcakes are there in 28 ounce package.
1 cupcake = 7/2 ounces
x cupcakes = 28 ounces
28 = 7/2 * x [cross multiplication]
x = (28*2)/7 [Using division]
x = 8
Hence, using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.
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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Answer:
? = 120°
Step-by-step explanation:
the central angle is the same as the arc that subtends it , that is
? = 120°
WILL. GIVE BRAINLIEST IF RIGHT!!
Answer:
The class and exam medians are almost the same.
Step-by-step explanation:
The median of a box-and-whisker plot is the line inside the box.
• As we can see, the medians of class and median are very similar, both around 85. This is why the first option is correct.
•The second option is incorrect because the exam median is not much higher than the class median; the difference is very small.
• The third option is incorrect because exam does not have the lowest median. In fact, exam median is slightly higher than class median.
• The fourth option is incorrect because outliers do not affect the median.
how to simplify cos(6x) + 1
Which expression is equivalent to startfraction 3 x superscript negative 6 baseline y superscript negative 3 baseline over 15 x squared y superscript 10 baseline endfraction? assume x not-equals 0, y not-equals 0.
The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.
Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]
Lets simplify the equation:
[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]
Expression:
An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.
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