The number of ways the first two places can come out is 56.
Permutation and CombinationPermutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given to us,Eight people enter a race, n = 8,
There are no ties, r = 2,
As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.
Permutation[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]
Hence, the number of ways the first two places can come out is 56.
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What would you look for in a word problem that might indicate that you need to use an absolute value inequality?
If (x,y) are the coordinates of a point p in the xy-plane, then x is called the _______ of p and y is the _______ of p.
In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
Explanation:In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.
Together, the x and y coordinates specify the precise location of a point in the xy-plane.
How do you factor the quadratic equation 36^2= 25
Solve for x:p=12-x/1000
Martin bought 30 shares of microsoft at the close price of $24.53. in a few years, martin sells all of his shares at $33.71. how much money did martin make?
Answer:
Money that Martin make is $ 275.9
Step-by-step explanation:
Number of shares Martin Bought = 30
Cost Price of a share = $ 24.53
Total Cost price of all share = 30 × 24.53 = $ 735.9
Selling Price of a share = $ 33.71
Total Selling Price of all shares = 30 × 33.71 = $ 1011.3
Profit money that Martin make = 1011.3 - 735.9 = $ 275.9
Therefore, Money that Martin make is $ 275.9
What two steps are necessary to put this equation into standard form?
x^2-3x+27=8x-3
A. Add 3 to both sides and subtract 8x from both sides.
B. add 3 to both sides and add 8x from both sides.
C. the equation is already in standard form.
D. Subtract 3 from sides and subtract 8x from both sides.
4⋅10 6 4, dot, 10, start superscript, 6, end superscript is how many times as large as 1\cdot10^41⋅10 4 1, dot, 10, start superscript, 4, end superscript?
The given problem is very confusing since it was copy pasted directly from the source so the equations look scrambled and plus it was one words. After my own translation, I believe the given numbers are:
4 ⋅ 10^6
and
1 ⋅ 10^4
The symbol ⋅ means that the two numbers are multiplied while the symbol ^ means an exponent of. Now we are asked to find how much the 1st number is larger than the 2nd number. To solve this, we simply have to divide the bigger number by the smaller number. Since 4 ⋅ 10^6 has bigger exponent than 1 ⋅ 10^4 then it is the bigger number.
Ratio = 4 ⋅ 10^6 / 1 ⋅ 10^4
Ratio = 4 ⋅ 10^2 = 400
Therefore 4 ⋅ 10^6 is 400 times bigger than 1 ⋅ 10^4.
Answer:
400 times
Having knowledge about potencies we will find that the final value will be greater than 400 times.
Recalling the properties of powers we find:
Multiplication of powers with the same base.Division of powers with the same base.Power of potency. Potency of a product.Quotient power.Then we can write the two given powers as:
[tex]4 *10^6\\1 * 10^4[/tex]
We know that we have a multiplication and a power, so solving for each of them, we find:
[tex]Ratio = 4 *10^6 / 1 * 10^4\\Ratio = 4 * 10^2 = 400[/tex]
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Answer for lady stole 100 from owner she bought 70 dollars worth of products and got back 30 how much did the owner lose
Answer: The total loss incurred by the store owner is 100$.
At first look, the answer might seem to be 200$ or 130$, but that's not the correct one. The explanation is below:
The lady stole 100$ from the owner therefore loss incurred is 100$.
The lady went back to the store and:
Step 1 - The lady hands back the 100$ to the store owner. Loss incurred is back to 0$.
Step 2 - The store owner hands over merchandise worth 70$. Loss Incurred is now 70$.
Step 3 - The store owner hands over 30$ worth of change. Loss Incurred is (70 + 30)$ = 100$
Solve each system:
80x+60y=85
100x-40y=20
The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
The four angles of the quadrilateral are °, °, °, and °, respectively.
Answer:
The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Step-by-step explanation:
Given : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
To find : The four angles of the quadrilateral are °, °, °, and °, respectively.
Solution : We have given that The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
Let the angle of the quadrilateral is x
Then all the angles are x , 2x , 5x ,4x
Complete angle formed by circle is 360 °
Sum of all the angle are 360
x + 2x + 5x + 4x = 360 .
12 x = 360 .
On dividing both sids by 12.
x = 30 .
Then
2x = 60
5x = 5 * 30 = 150 .
4x = 4 *30 = 120 .
Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Answer:
for plato users the answers are 45,75,135,105
Step-by-step explanation:
In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. what is the mean of the set?
In the formula that gives the circumference of a circle, which quantity is multiplied by 2Ï€ ?
A. Diameter
B. Radius
C. Area
D. Circumference
The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:
C = 2 π r
We can see that in the formula, what is multiplied by 2 π is the radius (r).
Therefore the answer to this is
B. Radius
A bag contains 7 red marbles, 8 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
The probability of choosing a blue marble from the bag is 1/3.
Explanation:The probability of choosing a blue marble can be calculated by dividing the number of blue marbles by the total number of marbles in the bag. In this case, there are 8 blue marbles out of a total of 7 + 8 + 9 = 24 marbles.
So, the probability of choosing a blue marble is:
P(Blue Marble) = Number of Blue Marbles / Total Number of Marbles = 8 / 24 = 1/3
Final answer:
The probability of choosing a blue marble when one marble is drawn from the bag is 1/3 or approximately 0.333.
Explanation:
To find the probability of choosing a blue marble when one marble is drawn from a bag, we need to determine the number of favorable outcomes (blue marbles) and divide it by the total number of possible outcomes (all the marbles).
In this case, there are 8 blue marbles out of a total of 7 red + 8 blue + 9 green = 24 marbles. So the probability of choosing a blue marble is 8/24, which simplifies to 1/3 or approximately 0.333.
Therefore, the probability of choosing a blue marble when one marble is drawn is 1/3 or approximately 0.333.
Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last month Molly purchased 4 movie tickets and earned $17. Part A: Create an equation that will determine the number of books she purchased. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many books did Molly purchase last month? (1 point)
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.
Answer:
y = sin(4x) + 3
Step-by-step explanation:
y = Asin(Bx + C) + D
A is amplitude = 1
B = 2pi/period = 2pi / (pi/2) = 4
C does not mention.
D: shift up or down = 3
=> y = sin(4x) + 3
A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.
The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.
Let's denote:
- [tex]\( x \)[/tex] as the length of one side of the square (in feet).
- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.
1. Area of the Square [tex](\( A_s \))[/tex]:
The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].
2. Area of the Circle [tex](\( A_c \))[/tex]:
The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:
[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]
Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]
The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].
Substituting the value of [tex]\( r \)[/tex], we get:
[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]
[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]
At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
Answer: The speed of the plane with no wind is 440 miles per hour.
Step-by-step explanation:
Let the maximum speed of the plane be 'x'.
Let the maximum speed of the wind be 'y'.
Since we have given that an airplane travels 2400 miles against the wind in 6 hours.
As we know that
Downstream is given by
[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]
Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.
As we know tha t
Upstream is given by
[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]
We just need to find the speed of the plane with no wind.
Using the elimination method,
[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]
Hence, the speed of the plane with no wind is 440 miles per hour.
Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price. How much does she have left to pay after making the down payment?
A.$80
B.$135.20
C. $1040.00
D. $904.80
Downpayment is the percent amount paid from a sum of money. The amount left after the downpayment is $904.80
Downpayment on a priceDownpayment is the percent amount paid from a sum of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;
Amount left = (100 - 13)% * 1040
Amount left .= 87% of 1040
Amount left = 0.87 * 1040
Amount left = $904.80
Hence the amount left after the downpayment is $904.80
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Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the total amount of the bill. Explain
This question is based on the mental math. Therefore, the total amount of bill is $16.25.
Given:
Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15.
We need to determined the total amount of the bill.
Let start with the price of the dessert and the sales tax $3.85+ $1.15= $5.
Now, added 2.75 to $5 .
We get,
$2.75 + $5 = $ 7.75
Then, add 7.75 + 8.50.
We get,
= $16.25
Therefore, the total amount of bill is $16.25.
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At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current balance?
3/8 of people at a fun fair were children 3/4 of the remaining people were men there were 140 more children than women how many people went to the fun fair
find the GCF 12, 18, 24
A parachutist's speed during a free fall reaches
207
kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 5 seconds of free fall?
If you have 5 distinct positive integers and the median is 17 and the mean is 12, what are the 5 numbers? How do you know for sure? Can you find 5 distinct positive integers with a median of 17 and a mean of 10? What whole-number means will work for 5 distinct positive integers with a median of 17? What medians will work for 5 distinct positive integers with a mean of 12?
Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.
You have ten fewer quarters than dimes and 5 fewer nickles than quarters. The total value of the coins is $4.75. How many quarters, nickles, and dimes do you have?
Four times the complement increased by forty-six is the same as twice the supplement. find the measures of the angle, the complement, and the supplement
Ivanna deposits $600 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?
What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.
what is the distance between the points (3,7) and (15,16) on a coordinate plane?
distance = Sqrt((x2-x1)^2 +(y2-y1)^2)
15-3 =12
16-7=9
12^2 = 144
9^2 = 81
144+81 = 225
square root of 225 = 15
the distance is 15