find the number of different ways that 570 contestants can win different first, second and third prizes.
184,219,440 ways.
What is contestant?
A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.
There are 570 contestants, and any one of them can win the first prize.
One of the remaining 569 people can receive the second prize.
Third may be assigned to any of the remaining 568.
We can accomplish this in 570*569*568 ways
= 184,219,440 ways.
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At this point, let us extend what you have done in Optimize. Consider the sets of
geometric figures below then answer the questions that follow.
10
1.
2.
3.
4.
5.
1
m
Q
How many points do OO and line / have in common?
How many points do OP and line m have in common?
How many points do OQ and line n have in common?
What kind of angle is formed by the line segments from the center of the
circles and their corresponding lines?
Are the line segments from the center of the circles parallel to their respective
lines? If not, write the correct term.
Answer:
No point,One Point.Reflex Angle Formed .
Last year Raina biked n miles . This year She biked 575 miles . Using n , write an expression for the total number in of miles she Biked
Answer: n+575= total
or n+575=t
Step-by-step explanation:
n is what we start with, plus what she has this year. the total is unknown.
The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 92 feet, find the value of the longest of the four side lengths.
Answer:
The perimeter of the quadrilateral is the sum of the four side lengths. If the perimeter is 92 feet, then we can write the equation $x + (x+2) + (x+4) + (x+6) = 92$, where $x$ is the length of the shortest side. Solving this equation, we find that $x = 20$. This means that the side lengths are 20 feet, 22 feet, 24 feet, and 26 feet, so the longest side is 26 feet.
Avani is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and flips a coin?
The number of possible outcomes when she spins and flips a coin is 8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of sections in the spinner = 4.
The number of possible outcomes in the coin = 2
Now,
The number of possible outcomes when she spins and flips a coin.
= 4 x 2
= 8
i.e
{Red, Green, Blue, Orange} x {H, T}
{Red:H, Red:T, Green:H, Green:T, Blue:H, Blue:T, Orange:H, Orange:T}
______(A)
Thus,
The number of possible outcomes from (A) is 8.
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-5-5(3•5n)=-70
Find N
Alex has $170.42 in his account before making any transactions. Over the course of a week, Alex makes the following transactions:
At the end of the week, how much money is in Alex’s account?
$50.73
$114.13
$119.69
$226.71
Answer:
To find out how much money is in Alex's account at the end of the week, we need to add up all of the transactions that he made over the course of the week.
We start by adding the initial amount that Alex had in his account before making any transactions, which is $170.42.
Then we add the first transaction, which is $50.73. This brings the total to $221.15.
Next, we add the second transaction, which is $114.13. This brings the total to $335.28.
Then we add the third transaction, which is $119.69. This brings the total to $455.97.
Finally, we add the fourth and last transaction, which is $226.71. This brings the total to $682.68.
Therefore, at the end of the week, Alex has $682.68 in his account.
Step-by-step explanation:
Question
a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the lengths of the bases, and use h for the height.
A=
b. Solve the formula for h.
h=
c. Use the new formula to find the height h of the trapezoid.
The height of the trapezoid is
centimeters.
The formula for the area of the trapezoid is A = 1/2(b₁ + b₂)h and the formula for height will be (2A)/(b₁ + b₂).
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
The area of a trapezoid is given as,
A = 1/2(b₁ + b₂)h
The formula for height h will be as,
A = 1/2(b₁ + b₂)h
h = (2A)/(b₁ + b₂)
Hence "The trapezoid's area is calculated using the calculation A = 1/2(b1 + b2)h, and its height is calculated using the formula (2A)/(b1 + b2).".
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find a formula for the exponential function that gives the value of an item initially worth $5000 that loses half its value every 5 years.
The formula for the exponential function is V = 5000 (2)^(−t/4).
What is an exponential function?
A function whose value is a constant raised to the power of an argument is called an exponential function.
Here, we have
The value of an item initially worth $5000 loses half its value every 5 years.
V = V₀eˣⁿ
At t = 0,V = V₀
So, V = 5000eˣⁿ
At t = 4,V = V₀/2 = 2500
Substituting these into our equation, we have
5000e^(4k) = 2500
e^(4k) = 12
4k = −ln2
k = −ln2/4
Finally, we have our equation
V = 5000e^(−tln2/4 )
V = 5000(e^ln2)^(−t/4)
V = 5000 (2)^(−t/4)
Hence, the formula for the exponential function is V = 5000 (2)^(−t/4).
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What are the coordinates of the image of the point (-3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3?
A. (-9, 18)
B. (-3, 6)
C. (-1,2)
D. (0,0)
Answer:
C
Step-by-step explanation:
since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of [tex]\frac{1}{3}[/tex]
(- 3, 6 ) → ([tex]\frac{1}{3}[/tex] (- 3), [tex]\frac{1}{3}[/tex] (6) ) → (- 1, 2 )
What is the value of t that satisfies the equation below? 3(t+4)-2(2t+3)=4
Explain how you got your answer
Answer:
t = 2
Step-by-step explanation:
First, we have to simplify the equation by multiplying 3 and -2 by everything in the corresponding parenthesis:
3(t+4) simplifies = 3t + 12
-2(2t+3) simplifies = -4t - 6
So:
3t + 12 - 4t - 6 = 4
Now we can combine like terms:
-t +6 = 4
Then we subtract 6 on both sides:
-t = -2
Then we divide by -1 in order to get rid of the negative:
t = 2, final answer.
The volume of a cone is 16π in³ and its height is
12 in. Find the radius of the cone.
Answer:
2 inches
Step-by-step explanation:
volume of a cone: 1/3 π r^2 h
h = 12
1/3 π r^2 (12) = 16π
4πr^2 = 16π
r^2 = 16π/4π
r^2 = 4
r = 2
Find The Missing Angles
The value of all the missing angles in the triangles are;
∠1 = 37°
∠6 = 30°
∠4 = 63°
∠3 = 133°
How to find the missing angles of the triangle?We know that the sum of angles in a triangle is equal to 180 degrees. Thus, with this knowledge, we can find the angles 1 and 6.
Therefore;
∠1 = 180 - (70 + 73)
∠1 = 180 - 143
∠1 = 37°
∠6 = 180° - (107° + 43°)
∠6 = 180° - 150°
∠6 = 30°
Now, we know that sum of angles on a straight line is 180 degrees. Thus, we can find angle 4 as follows;
∠4 = 180° - (65° + 42°)
∠4 = 180° - 117°
∠4 = 63°
∠3 = 90 + 43
∠3 = 133°
Thus, the conclusion is that the missing angles are ∠1 = 37°, ∠6 = 30°, ∠4 = 63°, ∠3 = 133°
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12.Todd's teacher asked him to construct a graph with the following specifications.
By studying the graph, it can be concluded that
Todd has done three mistakes
He has y increasing when x is between -5 and 0 instead of decreasing.
He has y decreasing when x is between 0 and 5 instead of increasing.
He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.
What is graph of a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function f(x) is the collection of points of the form (x, f(x))
Original specifications of the graph
y is decreasing when x is between -5 and 0
y is increasing when x is between 0 and 5
The relationship between x and y is non-linear from x = - 5 to x = 0
The relationship between x and y is linear from x = 0 to x = 5
From the graph it can be seen that Todd has done three mistakes
He has y increasing when x is between -5 and 0 instead of decreasing.
He has y decreasing when x is between 0 and 5 instead of increasing.
He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.
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What is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2?
(y2 - y1) / (x2 - x1) is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2.
The slope of the line passing through the points P1 (x1, y1) and P2 (x2, y2) is calculated by: (y2 - y1) / (x2 - x1).
1. Subtract the y-coordinates of the two points: y2 - y1.
2. Subtract the x-coordinates of the two points: x2 - x1.
3. Divide the two results from steps 1 and 2: (y2 - y1) / (x2 - x1).
For example, if the two points are P1 (1, 5) and P2 (3, 8), then the slope is calculated by: (8 - 5) / (3 - 1) = 3 / 2 = 1.5. This means that the line has a slope of 1.5, which means that for every 1 unit increase in x, the y-coordinate increases by 1.5 units. So, for every 2 units increase in x, the y-coordinate increases by 3 units.
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a restaurant menu lists 7 appetizers, 10 entrees, and 4 desserts. how many ways can a diner select a three-course meal?
From the given combination, there are 280 ways to select a three-course meal.
What is the combination?
Combinations are ways of choosing things from a collection when the order of the choices does not matter. The number of selections is denoted by [tex]^{n} C_{r}[/tex] if you have to choose "r" items from "n" things.
Given, 7 appetizers, 10 entrees, and 4 desserts
To select a three-course meal, we will choose 1 item from each course.
i.e. 1 appetizer from 7 appetizers
AND
1 enter from 10 entrees
AND
1 dessert from 4 desserts
So, For appetizers, selections = [tex]^{7} C_{1}[/tex]
For entrees, selections = [tex]^{10} C_{1}[/tex]
For desserts, selections = [tex]^{4} C_{1}[/tex]
Total possibilities = [tex]^{7} C_{1}[/tex] * [tex]^{10} C_{1}[/tex]* [tex]^{4} C_{1}[/tex] = 7*10*4 = 280
Hence, there are 280 ways to select a three-course meal.
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Diego charges $60 for the first hour of consulting and $30 for each additional hour or fraction of an hour.
What are the 2 conditions for a system to be linear?
Homogeneity and additivity are the two conditions for a system to be linear.
A system is called Linear if it has two mathematical properties, homogeneity and additivity. If you can show that system has both properties, then you have proven that the system is linear.
Homogeneity means that a change in the input signal's amplitude results in a corresponding change in the output signal's amplitude.
Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same.
Additivity means signals added at the input produce signals that are added at the output.
The value of a magnitude corresponding to a whole object is equal to the sum of the values of the magnitudes corresponding to its parts for any division of the object into parts.
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Graph and label each figure and its image under a reflection in the given line.
Give the coordinates of the image
S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7), We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).
A graph is what?The link between lines and points is described by a graph, which is a mathematical description of a network.
The link between lines and points is described by a graph, which is a mathematical description of a network.
Plotting a graph based on the provided data is shown in the attachment.
Given, \s (x,y)=(x+7,y-9)
For example, S(-3,6)=S'(x+7,y-9)=S'(-3+7, 6-9)=S' (4,-3)
T(0, 7) = T' (x+7, y-9) = T' (0+7, 7-9) = T' (7,-2)
According to U(1,4)=U'(x+7,y-9)=U'(1+7, 4-9)=U' (8,-5)
Considering that V(-5,2)=V'(x+7,y-9)=V'(-5+7,2-9)=V' (2,-7)
To create the graph, we must plot the points S'(4,-3), T'(7,-2), U'(8,-5), and V'(2,-7).
S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7)
We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).
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help help help help help help help
Answer: 1. 2, 4, 8, 16, 32, 64, and 128,...... I don't know if I should keep going.
2. 5, 11, 17, 23, 29, 35, 41, and 47
Answer: 2.
Step-by-step explanation:
11+3=14
14+3=17
17+3=20
20+3=23
2. 5,11,17,23
select all equations that are true with x=6
Answer:
A, C, and E
Step-by-step explanation:
Express the radical using the imaginary unit,i .
Express your answer in simplified form.
√-30 = ±
Answer:
[tex] + - \sqrt{ - 30}[/tex]
Answer:
[tex]\sqrt{30i}[/tex]
Step-by-step explanation:
khan <3
What is the range of linear function?
A linear function can only have one degree at most but the range of linear function is infinite.
In the given question, we have to explain what is the range of linear function.
A linear function can only have one degree at most. Therefore, it has at least most one x increased by one. The formula for them is f(x) = mx + b.
Nearly invariably, the domains and ranges of linear functions are infinite. When the graph is a horizontal line, there is an exception. This occurs when a function, like f(x) = b, equals a constant. These functions' domains are unlimited, but their range only contains the value b.
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A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?.
The probability that Jeff wins exactly 1 prize is (3/4)³
According to the question,
A fast-food restaurant runs a promotion in which certain food items come with game pieces
Let the event of winning the game piece be A and x be the random variable for winning prize
So, Probability of Winning the game = P(A) = p = 1/4
Probability of not winning = q = 1 - 1/4
=> q = 3/4
Using Binomial distribution,
The Probability that he wins exactly 1 prize = P(x = 1)
=> P(x) = ⁿCₓ pˣ qⁿ⁻ˣ
Here, n = 4 , x = 1
P(1) = ⁴C₁ p¹ q³
=> 4 × (1/4)( 3/4)³
=> (3/4)³ is probability that jeff wins exactly 1 prize
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A pyramid has a base with an area of 25 in² and a
volume of 100 in³. Find the height of the pyramid.
Answer:
12in
Step-by-step explanation:
Area and Volume (Proportion)Base Area and Volume are proportionalised based on their Height.
Eg. Base Area of Cube = Length × Width
Volume of Cube = Length × Width × Height
SolutionGiven from the Question:
Base Area of Pyramid =
[tex]25 \: {in}^{2} [/tex]
Volume of Pyramid =
[tex] \frac{1}{3} (base \: area)(height) = 100 {in}^{2} [/tex]
We already knew the Base Area, so we can substitute it into the Volume of Pyramid Formula to find the height.
[tex] \frac{1}{3} (25)(height) = 100 \\ height = \frac{100(3)}{25} \\ = 12in[/tex]
Therefore the height of the Pyramid is 12in.
0.0
1. Mei is shopping for the items shown in the
table. Write an expression to represent the
total cost of 6 bubbles, 2 beach balls, and
3 sand buckets. Then find the total cost.
(Example 3)
Item bubbles beach ball sand buckets
Cost $1.49
$2.00
$3.50
Bubble cost = $1.49
Beach ball cost = $2.00
Sand bucket cost = $3.50
Bubble = B
Beach Ball = A
Sand bucket = S
total cost = 6B + 2A + 3S
total cost = 6(1.49) + 2(2) + 3(3.5) = 23.44
Hope this helps :)
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- Jeron
Find the volume and surface area of a square pyramid. Volume of a pyramid: v = 1/3(area of base) x (height) surface area of a pyramid: a = 1/2(perimeter of base) x (slant height) + (area of base) a pyramid has a height of 4. 7 in. And a slant height of 5. 2 in. Its base is a square with sides of 3. 5 in. Find the pyramid's volume and surface area. Volume (to the nearest tenth) = in3 surface area (to the nearest tenth) = in2.
The Volume of the Pyramid=19.19in³
Surface Area of the Pyramid=48.65in²
What is meant by volume?Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.
First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers. Calculating the volume of numerous common three-dimensional forms is made simple by arithmetic formulas. The volumes of increasingly complicated shapes can be calculated using integral calculus.
Given that,
Height of the pyramid =4.7
Pyramid's slant height= 5.2
Base of pyramid is a square with side=3.5
Volume of the pyramid=(1/3)(3.5×3.5)×(4.7)
=19.19 in³
The surface area of a pyramid=((1/2)×(4×3.5)×5.2)+(3.5×3.5)
=18.65in²
Therefore, the volume of the pyramid=19.19 in³
And the surface area of the pyramid=18.65in²
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Given h(x)=4x-5 find h(4)
Step-by-step explanation:
16-5= 11
hope it's helpful
Y/y-5+5/5-y= step bye step
The solution of the given equation is, y = -3.
what is solving an equation?
An effective method for solving linear equations can be found in the steps that follow. By deleting parentheses and combining like terms, each side of the equation can be made simpler. The variable term on one side of the equation can be separated using addition or subtraction. To find the variable, use multiplication or division.
Consider, the given equation
[tex]\frac{y}{y}-5 + \frac{5}{5}-y =0[/tex]
Since, If a/a then it is 1.
⇒ 1 - 5 + 1 - y = 0
-3 - y = 0
Add y on both sides,
-3 - y + y = 0 + y
-3 = y
y = -3
Hence, the solution of the given equation is, y = -3.
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Elizabeth is going to roll a fair 666-sided die 600600600 times. Complete the following statement with the best prediction. Elizabeth will roll an even number.
The number of times getting an even number on the top of dice if dice is rolled 600 times is 300.
We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.
Here, favorable outcomes are even number from 6 possible numbers and those are =2,4,6
So, favorable outcomes are={2,4,6)
So, count of favorable outcomes is 3
Total number of outcomes are ={1,2,3,4,5,6}
So, count of total number of outcomes are =6
Therefore, probability of getting an even number on top of dice is =number of favorable outcomes/total number of outcomes
=>P(E) = 3/6
=>P(E)=1/2
Now, dice is rolled 600 times and probability of getting even number is 1/2,so total number of times even number comes on topo of dice is =(1/2)×600=300.
Hence, even number appearance is 300.
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