since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]
Mann Park is the shape of a triangle.
On a map, it has borders that measure 5 inches inches, 7 inches
and 9 inches. If the shortest border of Mann Park is
1000 meters long, how long in meters, is its longest
border?
The longest border of the Mann's park is 228.6 meter.
What is Triangle inequality theorem ?The Triangle Inequality It is a basic principle of geometry that the lengths of any two sides of a triangle must add up to more than the length of the third side. In other words, the longest side of any triangle must be shorter than the total length of the other two sides.
In this case, the shortest side of Mann Park measures 5 inches, and the two longer sides measure 7 inches and 9 inches.
So, the sum of the lengths of the two longer sides is:
' 7 inches + 9 inches = 16 inches.
Since 5 inches is less than 16 inches, we know that the 5-inch side is the shortest side, and the 9-inch side is the longest side.
One inch is approximately equal to 0.0254 meters, so we have:
= 9 inches x 0.0254 meters/inch
= 0.2286 meters
Since the shortest side is 1000 meters long, the longest side is:
= 1000 meters x 0.2286 meters/inch
= 228.6 meters long.
Therefore, the longest border of Mann Park is approximately 228.6 meters long.
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Find |A| if A = 1 1 2 2 2 3 5 6 1 3 5 3 1 1 3 6
Answer:
1 this is the answer because 1 is more than other number
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 18 centimeters. The height of the figure is 12 centimeters. The portion from the vertex to the perpendicular height is 4 centimeters. The portion from a point to a vertical line created by two vertices is 3 centimeters.
Which of the following represents the total area of the figure?
222 cm2
240 cm2
258 cm2
294 cm2
The total area of the figure is 258cm². Thus, option 3 is corect.
Given:
shorter side: 18 centimeters
perpendicular height : 4 centimeters
portion from a point to a vertical line created by two vertices : 3centimeters
height : 12 centimeters
from figure we know that, it is the vertex's height as well as the length of the sides to multiply together and we also have to divide since there is 5 sides
So , after multiplying the vertex height and sides and dividing it by the 5 , we get 258 cm²
Hence , the total area of the figure is 258cm².
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Quick and Simple Algebra 2 question
Write the equation based on 2 points
The equation of line is y = 1.5x + 5.5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We have the reference point as (-2, 2.5) and (-1, 4)
so, slope
= (4- 2.5)/ (-1 + 2)
= 1.5
and, the equation of line is
y- 2.5 = 1.5 (x+ 2)
y- 2.5 = 1.5x + 3
y = 1.5x + 5.5
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Solve number 7 using combinations
Step-by-step explanation:
7.
the probability of picking a defective missile with the first pull is
5/22
the probability of picking a working missile with the first pull is
17/22 = ((22-5)/22)
I have to assume that the picked missiles are not put back into the main pile after the check.
and I have to assume that the sequence of the pulled missiles don't matter.
a.
all are defective.
since there are only 5 defective missiles, there is only one possibility out of all the possibilities to pull 5 out of 22 to get 5 defective missiles.
the possible combinations to pull 5 out of 22 :
C(22, 5) = 22! / ((22 - 5)! × 5!) =
= 22×21×20×19×18×17/(5×4×3×2) =
= 22×21×19×3×17 = 447,678
and we have one desired situation (all 5 are defective).
so, the probability is
1/447678 = 0.000002233748364... = 2.233748364e-006
b.
all 5 are functional.
the total possible cases to pull 5 out of 22 are still
447,678.
the desired cases are all cases to pull 5 out of the 17 (22 - 5) functional missiles.
that is
C(17, 5) = 17! / ((17 - 5)! × 5!) =
= 17×16×15×14×13 / (5×4×3×2) =
= 17×2×14×13 = 6,188
so, the probability to get one of these cases is
6188 / 447678 = 0.013822435...
The probability of picking a defective missile with the first pull is 5/22
The probability of picking a working missile with the first pull is 17/22
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
If we assume that the picked missiles are without replacements and the sequence of the pulled missiles don't matter,
Therefore, the probability that:
a. all are defective is 2.233748364e-006
Since there are only 5 defective missiles, there is only one way to get 5 defective missiles out of 22 possible outcomes.
The possible combinations to pull 5 out of 22 :
C(22, 5) = 22! / ((22 - 5)! × 5!) =
= 22×21×20×19×18×17/(5×4×3×2) =
= 22×21×19×3×17 = 447,678
and we have one desired situation (all 5 are defective).
so, the probability is 1/447678 = 0.000002233748364... = 2.233748364e-006
b. all 5 are functional is 0.013822435
the total possible cases to pull 5 out of 22 are still 447,678.
The ideal scenario is for all incidents to result in the removal of 5 of the 17 (22 - 5) operational missiles.
that is
C(17, 5) = 17! / ((17 - 5)! × 5!) =
= 17×16×15×14×13 / (5×4×3×2) =
= 17×2×14×13 = 6,188
so, the probability to get one of these cases is
6188 / 447678 = 0.013822435
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A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road
Give your answer in seconds
The time it takes the bicycle to travel along the road is 20 seconds.
What is Speed?The rate of change of position of an object in any direction is called as Speed.
The formula for speed is Distance divided by Time.
So Time = distance / speed
we need to know the distance the bicycle travels to use this formula.
If we have this distance, we can divide it by the speed of 5 m/s to find the time.
Let the distance is 100 meters, then the time taken is:
time = distance / speed = 100 / 5 = 20 seconds
Hence, the time it takes the bicycle to travel along the road is 20 seconds.
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The complete question is given below:
A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road of distance 100 meters.
Give your answer in seconds
PLEASE HELP ME AS QUICK AS POSSIBLE !!
Answer:
1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0
Step-by-step explanation:
You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.
SimplificationThe expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.
[tex]\dfrac{1}{a^2+ab}+\dfrac{1}{ab+b^2}=\dfrac{1}{a^2+ab}\cdot\dfrac{b}{b}+\dfrac{1}{ab+b^2}\cdot\dfrac{a}{a}=\dfrac{b+a}{a^2b+ab^2}\\\\=\dfrac{a+b}{ab(a+b)}=\boxed{\dfrac{1}{ab}\quad a\ne0,b\ne0,(a+b)\ne0}[/tex]
The given conditions ensure the denominator(s) will not be zero.
Serenity is making beaded jewelry with no more than 920 beads she currently has in stock. Bracelets use 15 beads
and necklaces use 70 beads.
x= the number of bracelets
y = the number of necklaces
The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.
Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,
15x + 70y ≤ 920
The region below the line is the solution to inequality.
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Write the simplest polynomial function with the given zeros: -2 , 2 , 3
Step-by-step explanation:
Zeros is another term for X intercepts.
We'd right the simplest form as (x-/+a), a being the zero
Just remember when you do that, change the signs. It shows -2, +2, +3. That becomes +2, -2, -3
Following that simple form, we get
[tex](x + 2)(x - 2)(x - 3)[/tex]
If {={ a, b, c, d, e } A={ a, c, e} B={ b, e }. List the members of the following set. (a) A' (b) B' (c) A'uB (d) AuB' (e) A'nB (f) AnB' (g) A'uA (h) B'nB (I) AuB (j) A'uB' (k) [AnB]' (l) A'nB'
Answer:
The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.
Step-by-step explanation:
(a) A' = {b, d}
(b) B' = {a, c, d}
(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)
(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)
(e) A' n B = {} (the intersection of A' and B is an empty set)
(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)
(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)
(h) B' n B = {} (the intersection of B' and B is an empty set)
(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)
(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)
(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)
(l) A' n B' = {} (the intersection of A' and B' is an empty set).
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
A sports trophy is in the shape of a cup
30 cm high. The winners are each given
copies of the cup, 7 cm high. One of the
copies holds 100 ml. What is the capacity of the trophy in liters?
The capacity of the trophy that us 30 cm high is 0.4286 liter
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
7 cm height cup holds 100 ml. Therefore:
7 cm = 100 ml
For a 30 cm height trophy:
30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml
1000 ml = 1 l
428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter
The capacity of the trophy is 0.4286 liter
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(a) Describe the relationship among the lengths of the segments formed by the two secants. You may use words and/or an equation.
(b) Suppose = 3 in., = 2 in. and = 5 in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.
Answer:a
Step-by-step explanation:
Is the pair of events dependent or independent? Explain 14. You pick a number between 1000 and 5000. Then you flip a coin.
Answer:
Step-by-step explanation:
Here is a step-by-step explanation of the independence of the pair of events of choosing a number between 1000 and 5000 and flipping a coin:
Understanding the definition of independent events: Independent events are events that have no influence on each other. The outcome of one event does not affect the outcome of the other.
Event 1: Choose a number between 1000 and 5000: This event involves randomly selecting a number within the specified range.
Event 2: Flip a coin: This event involves flipping a coin and observing whether it lands on heads or tails.
Check for influence: To determine whether the events are independent, we need to check if the outcome of one event affects the outcome of the other. In this case, the outcome of the coin flip has no effect on the number you choose, and your choice of number has no effect on the outcome of the coin flip.
Conclusion: Since the outcome of one event does not affect the outcome of the other, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are considered independent.
So, the pair of events of choosing a number between 1000 and 5000 and flipping a coin are independent events.
In the division example at the right A and B represent
different digits. What is the sum of A and B if the
remainder is zero?
In the division example at the right A and B represent different digits. The sum of A and B if the remainder is zero is 8.
What is Division?
This is one of the four basic mathematical operations and it is the process of splitting a number or an amount into equal parts.
The table shows all possible answers for A÷B with no remainder when digits from 1-9 for A and B are considered.
Since A is not equal to B such as A=6, B=2, divides it with no remainder. Therefore the sum of A and B is 8, so the cell (6,2) contains 8.
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15. "Twice a number, increased by 13, is -21.“
Answer:
Step-by-step explanation:
(X=the number)
2x+13=-21
(-21)-13=34
34x2=68
Problem 1. Compute the complex norm |z|= √zz for the following complex numbers z:
1. z = −i
2. z = (2 + i)2
3. z = (3 −4i)3
4. z = (3 + 4i)3
Recall that the complex norm (or modulus) of a complex number z = a + bi is defined as the nonnegative square root of the product of the complex number and its conjugate, i.e., |z| = √(z × z*), where z* is the complex conjugate of z.
Using this definition, we can calculate the complex norm of each of the given complex numbers as follows:
[tex]z = -i\\z* = i (conjugate of -i)\\|z| = √(z z*) = √(-i i) = √1 = 1Therefore, |z| = 1.[/tex][tex]z = (2 + i)^2\\z* = (2 - i)^2 (conjugate of (2 + i)^2)\\|z| = √(z z*) = √((2 + i)^2 (2 - i)^2) = √((2^2 + 2i + i^2) (2^2 - 2i + i^2))= √((4 + 4i - 1) (4 - 4i - 1)) = √(9 * 9) = 9Therefore, |z| = 9.[/tex][tex]z = (3 - 4i)^3\\z* = (3 + 4i)^3 (conjugate of (3 - 4i)^3)\\|z| = √(z z*) = √((3 - 4i)^3 (3 + 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex][tex]z = (3 + 4i)^3\\z* = (3 - 4i)^3 (conjugate of (3 + 4i)^3)\\|z| = √(z z*) = √((3 + 4i)^3 (3 - 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex]What is complex number?A complex number is a number that can be expressed in the form [tex]a + bi[/tex], where a and b are real numbers, and i is the imaginary unit defined by [tex]i^{2} = -1[/tex]. The real part of the complex number is a, and the imaginary part is bi.
Complex numbers can be added, subtracted, multiplied, and divided in a manner similar to real numbers. They can also be graphed on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part.
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A cellular phone company uses the formula $16+ $0.04m to calculate each subscriber's monthly
bill, where m is the number of minutes used. If Angelo uses 142 minutes on his phone this month,
how much will his bill be?
PLS HELP ME DUE TODAY!!!!
Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by
1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
Answer:
h(x) = 0.5x + 8
Step-by-step explanation:
We are being asked to write an equation where h(x) represents the soil depth in inches and x describes the number of bags. To do this, we need to find b (our y-intercept, ie the value of h(x) or y when x=0) and m (our slope).
"The depth of the soil is currently 8 inches": this means before any bags are added (ie when x=0), the soil depth starts at 8. This makes 8 our y-intercept (b in h(x)=mx+b) as we have to add it on to however much the bagged soil adds in order to get the total depth.
"For each bag of soil he adds, the depth will increase by 1/2 of an inch": this means that the soil depth from added bags is equal to the amount of bags times 0.5, which makes 0.5 our slope (m in h(x)=mx+b).
Therefore our answer is:
h(x) = 0.5x + 8
What is the length of GI
Check the picture below.
so the triangles are similar by AA.
[tex]\cfrac{GI}{10}~~ = ~~\cfrac{15}{12}\implies \cfrac{GI}{10}~~ = ~~\cfrac{5}{4}\implies 4GI=50\implies GI=\cfrac{50}{4}\implies GI=12.5[/tex]
PLEASE HELP QUICKLY
Answer: 10.7 or 10.8
Step-by-step explanation:
so, first [tex]a^{2} +b^{2} =c^{2}[/tex]
while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]
so, it will be written as,
[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]
[tex]14.0625+100=c^2[/tex]
[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:
[tex]10.7=c[/tex]
That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...
while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.
which will equal to...
[tex]4^2+10^2=c^2[/tex]
[tex]16+100=c^2[/tex]
[tex]116=c^2[/tex] then square root both sides to have an answer of:
[tex]10.77=c[/tex]
[tex]10.8[/tex] ≈ [tex]c[/tex]
hope you've understanded.!
12. "The sum of 9 and the product of a number and -7 is -19
Answer:
Step-by-step explanation:
We can use algebra to solve for the unknown number. Let's call the number "x".
The equation can be written as:
9 + x * (-7) = -19
Expanding the product on the left side:
9 + -7x = -19
Subtracting 9 from both sides:
-7x = -28
Dividing both sides by -7:
x = 4
So the number x is 4.
Solve for x
2,4, and 6 i need help with
Answer: 2: 56 degrees
4: 56 degrees
(Number 6 is not in the image)
Step-by-step explanation:
So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56
And for #4, we know the angle is 180 so all we have to do is 180-124=56
Hual takes out a $3200 student loan at 6.4% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and
borrows another $12,400 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and
payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.6%. Find the total
amount of interest that will accrue until payments begin.
(a) Find the total amount of interest that will accrue for loan 1 (community college).
The total amount of interest that will accrue for loan 1 (community college) is $_____ Round your answer to two decimal
places, if necessary.
Part 2 of 3
A ALEKS-Erika Ramirez - Test 2-Chapter 7
(b) Find the total amount of interest that will accrue for loan 2 (state university).
The total amount of interest that will accrue for loan 2 (state university) is $____
Answer:
a) $4096 b) $1884,8 ■■ im not 100% sure
Step-by-step explanation:
a) 3200×0.064×2=$4096 in intrest
b) 12,400×0.076×2=$1884,8 in intrest
5. Abbey and Blanca are playing games at the arcade in the mall. Abbey has $20 and is playing a
game that costs 50 cents per game. Blanca arrived at the arcade with $22 and is playing a game that
costs 75 cents per game.
(a) Create two linear equations below that give the amount that each girl has left as a function of the
number of games they have played.
Let the number of games played = x.
A=
B =
(b) After how many games will the two girls have the same amount of money left?
(c) How much money do they have at this point?
Answer:
A = 0.50x+20
B= 0.75x+22
4 games
$19
Step-by-step explanation:
For abbey, the 20 dollars she starts with is the initial value. the 50 cents per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be A = 0.50x + 20. For Bianca, the 22 dollars she starts with is her initial value. the 75 centers per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be B = 0.75x + 22.
We can find out when they will have the same amount of money left by making two small tables -> one for abbey and one for Bianca.
Abbey: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)
21.502019.501918.50Bianca: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)
21.2520.519.751918.25For both girls after four games, they have the same amount of money- $19.
2-81
When graphing the function f(x)= x2-11x+18
window for determining the domain and range of the function?
O Xmin: -10, Xmax: 10
Ymin: –10, Ymax: 10
O Xmin: -5, Xmax: 5
Ymin: –5, Ymax: 5
Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10
O Xmin: -10, Xmax: 0
Ymin –10 Ymax: 0
on your graphing calculator, what is the most appropriate viewing
The most appropriate viewing range for the quadratic function is given as follows:
Xmin 0, Xmax 10.YMin - 15, Ymax, 15.How to obtain the viewing range?The quadratic function for this problem is defined as follows:
f(x) = x² - 11x + 18.
The function can be factored as follows:
f(x) = (x - 2)(x - 9).
Hence the roots are:
x - 2 = 0 -> x = 2.x - 9 = 0 -> x = 9.Meaning that the viewing range should include x = 2 and x = 9.
The coefficients of the function are:
a = 1, b = -11, c = 18.
Hence the x-coordinate of the vertex is of:
x = -b/2a
x = 11/2
x = 5.5.
Hence the minimum value of the function is the y-coordinate of the vertex, given as follows:
y = 5.5² - 11(5.5) + 18
y = -12.25.
Meaning that Ymin should be less than -12.25.
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Need help with this Question pls
Step-by-step explanation:
a. £5,37
b.£2,07
c.£15,70
If x = logb2 and y = log b5, express log b100 in terms of x and y.
logb100=____?
Using logarithm expressing log b100 in terms of x and y is logb100 = 2y + x
What is the logarithm of a number?The logarithm of a number x to base a written as logₐy is such that when a is raised to the power of x,it equals y.
How to express logb100 in terms of x and y?Since
x = logb2 and y = log b5,We desire to express logb100 in terms of x and y.
So, we proceed as follows.
We have logb100, re-writing this, we have
logb100 = logb(25 × 2)
Now, applying the addition law of logarithm which states that
logab = loga + logb.
So, we have that
logb100 = logb(25 × 2)
logb100 = logb25 + logb2
= logb5² + logb2
Now applying the power rule of logarithm which states that logaⁿ = nloga
So,
logb100 = logb5² + logb2
= 2logb5 + logb2
= 2y + x
So, logb100 = 2y + x
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Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements.
If there are no possible solutions, submit an empty answer.
Answer: 2 hours babysitting
Step-by-step explanation:
18 x 9 = 162
180-162= 18
meaning he'd have to work 2 hours babysitting to get to meet his requirement.
hours used = 11
hours left= 3
Please verify my answer. I am not sure if it is correct.
now, we're making the assumption we're simply doing an identity proof, so
[tex]sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}[/tex]
Number 1 solve use counting principle
The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.
What are factorials?Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.
Given that, three men and three women line up at a checkout counter in a store.
a) Number of ways = 6!
= 6×5×4×3×2×1
= 720 ways
b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on
There are 3 number of ways for woman standing in the odd position and for men standing in the even position.
So, number of ways = 3!×3!
= 3×2×1×3×2×1
= 36 ways
c) There are 3 men and 3 women.
Probability first is a woman is 3/6
Probability second is a man is 3/5
Probability third is a woman is 2/4
Probability fourth is a man is 2/3
Probability fifth is a woman is 1/2
Probability sixth is a man is 1/1
Multiply all these probabilities together and you get:
3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05
Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.
Learn more about factorials here:
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